1,1,60,0,5.131263," ","integrate((b*x)**p*(c*x)**m,x)","\begin{cases} \frac{b^{p} c^{m} x x^{m} x^{p}}{m + p + 1} & \text{for}\: m \neq - p - 1 \\\begin{cases} \frac{b^{p} c^{- p} \log{\left(x \right)}}{c} & \text{for}\: \left|{x}\right| < 1 \\- \frac{b^{p} c^{- p} {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)}}{c} + \frac{b^{p} c^{- p} {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)}}{c} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*c**m*x*x**m*x**p/(m + p + 1), Ne(m, -p - 1)), (Piecewise((b**p*c**(-p)*log(x)/c, Abs(x) < 1), (-b**p*c**(-p)*meijerg(((), (1, 1)), ((0, 0), ()), x)/c + b**p*c**(-p)*meijerg(((1, 1), ()), ((), (0, 0)), x)/c, True)), True))","A",0
2,1,15,0,0.303880," ","integrate(x**3*(b*x**2)**(1/2),x)","\frac{\sqrt{b} x^{4} \sqrt{x^{2}}}{5}"," ",0,"sqrt(b)*x**4*sqrt(x**2)/5","A",0
3,1,15,0,0.241930," ","integrate(x**2*(b*x**2)**(1/2),x)","\frac{\sqrt{b} x^{3} \sqrt{x^{2}}}{4}"," ",0,"sqrt(b)*x**3*sqrt(x**2)/4","A",0
4,1,15,0,0.194499," ","integrate(x*(b*x**2)**(1/2),x)","\frac{\sqrt{b} x^{2} \sqrt{x^{2}}}{3}"," ",0,"sqrt(b)*x**2*sqrt(x**2)/3","A",0
5,1,14,0,0.165529," ","integrate((b*x**2)**(1/2),x)","\frac{\sqrt{b} x \sqrt{x^{2}}}{2}"," ",0,"sqrt(b)*x*sqrt(x**2)/2","A",0
6,1,10,0,0.169703," ","integrate((b*x**2)**(1/2)/x,x)","\sqrt{b} \sqrt{x^{2}}"," ",0,"sqrt(b)*sqrt(x**2)","A",0
7,0,0,0,0.000000," ","integrate((b*x**2)**(1/2)/x**2,x)","\int \frac{\sqrt{b x^{2}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(b*x**2)/x**2, x)","F",0
8,1,15,0,0.393593," ","integrate((b*x**2)**(1/2)/x**3,x)","- \frac{\sqrt{b} \sqrt{x^{2}}}{x^{2}}"," ",0,"-sqrt(b)*sqrt(x**2)/x**2","A",0
9,1,17,0,0.468383," ","integrate((b*x**2)**(1/2)/x**4,x)","- \frac{\sqrt{b} \sqrt{x^{2}}}{2 x^{3}}"," ",0,"-sqrt(b)*sqrt(x**2)/(2*x**3)","A",0
10,1,17,0,0.600317," ","integrate((b*x**2)**(1/2)/x**5,x)","- \frac{\sqrt{b} \sqrt{x^{2}}}{3 x^{4}}"," ",0,"-sqrt(b)*sqrt(x**2)/(3*x**4)","A",0
11,1,3,0,0.067219," ","integrate(x**2*(x**2)**(1/2),x)","\frac{x^{4}}{4}"," ",0,"x**4/4","A",0
12,1,15,0,0.685834," ","integrate(x**2*(b*x**2)**(3/2),x)","\frac{b^{\frac{3}{2}} x^{3} \left(x^{2}\right)^{\frac{3}{2}}}{6}"," ",0,"b**(3/2)*x**3*(x**2)**(3/2)/6","A",0
13,1,15,0,0.512193," ","integrate(x*(b*x**2)**(3/2),x)","\frac{b^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}}{5}"," ",0,"b**(3/2)*x**2*(x**2)**(3/2)/5","A",0
14,1,14,0,0.376121," ","integrate((b*x**2)**(3/2),x)","\frac{b^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}}{4}"," ",0,"b**(3/2)*x*(x**2)**(3/2)/4","A",0
15,1,12,0,0.395135," ","integrate((b*x**2)**(3/2)/x,x)","\frac{b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{3}"," ",0,"b**(3/2)*(x**2)**(3/2)/3","A",0
16,1,14,0,0.416702," ","integrate((b*x**2)**(3/2)/x**2,x)","\frac{b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{2 x}"," ",0,"b**(3/2)*(x**2)**(3/2)/(2*x)","A",0
17,1,14,0,0.546410," ","integrate((b*x**2)**(3/2)/x**3,x)","\frac{b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{x^{2}}"," ",0,"b**(3/2)*(x**2)**(3/2)/x**2","A",0
18,0,0,0,0.000000," ","integrate((b*x**2)**(3/2)/x**4,x)","\int \frac{\left(b x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((b*x**2)**(3/2)/x**4, x)","F",0
19,1,15,0,0.851153," ","integrate((b*x**2)**(3/2)/x**5,x)","- \frac{b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{x^{4}}"," ",0,"-b**(3/2)*(x**2)**(3/2)/x**4","A",0
20,1,17,0,1.022983," ","integrate((b*x**2)**(3/2)/x**6,x)","- \frac{b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{2 x^{5}}"," ",0,"-b**(3/2)*(x**2)**(3/2)/(2*x**5)","A",0
21,1,17,0,1.292516," ","integrate((b*x**2)**(3/2)/x**7,x)","- \frac{b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{3 x^{6}}"," ",0,"-b**(3/2)*(x**2)**(3/2)/(3*x**6)","A",0
22,1,3,0,0.069571," ","integrate((x**2)**(5/2),x)","\frac{x^{6}}{6}"," ",0,"x**6/6","A",0
23,1,15,0,1.299183," ","integrate(x*(b*x**2)**(5/2),x)","\frac{b^{\frac{5}{2}} x^{2} \left(x^{2}\right)^{\frac{5}{2}}}{7}"," ",0,"b**(5/2)*x**2*(x**2)**(5/2)/7","A",0
24,1,14,0,1.004708," ","integrate((b*x**2)**(5/2),x)","\frac{b^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}}{6}"," ",0,"b**(5/2)*x*(x**2)**(5/2)/6","A",0
25,1,12,0,1.017277," ","integrate((b*x**2)**(5/2)/x,x)","\frac{b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{5}"," ",0,"b**(5/2)*(x**2)**(5/2)/5","A",0
26,1,14,0,1.063298," ","integrate((b*x**2)**(5/2)/x**2,x)","\frac{b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{4 x}"," ",0,"b**(5/2)*(x**2)**(5/2)/(4*x)","A",0
27,1,15,0,1.219842," ","integrate((b*x**2)**(5/2)/x**3,x)","\frac{b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{3 x^{2}}"," ",0,"b**(5/2)*(x**2)**(5/2)/(3*x**2)","A",0
28,1,15,0,1.231454," ","integrate((b*x**2)**(5/2)/x**4,x)","\frac{b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{2 x^{3}}"," ",0,"b**(5/2)*(x**2)**(5/2)/(2*x**3)","A",0
29,1,14,0,1.239193," ","integrate((b*x**2)**(5/2)/x**5,x)","\frac{b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{x^{4}}"," ",0,"b**(5/2)*(x**2)**(5/2)/x**4","A",0
30,0,0,0,0.000000," ","integrate((b*x**2)**(5/2)/x**6,x)","\int \frac{\left(b x^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx"," ",0,"Integral((b*x**2)**(5/2)/x**6, x)","F",0
31,1,15,0,1.866416," ","integrate((b*x**2)**(5/2)/x**7,x)","- \frac{b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{x^{6}}"," ",0,"-b**(5/2)*(x**2)**(5/2)/x**6","A",0
32,1,17,0,2.238695," ","integrate((b*x**2)**(5/2)/x**8,x)","- \frac{b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{2 x^{7}}"," ",0,"-b**(5/2)*(x**2)**(5/2)/(2*x**7)","A",0
33,1,17,0,2.671355," ","integrate((b*x**2)**(5/2)/x**9,x)","- \frac{b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{3 x^{8}}"," ",0,"-b**(5/2)*(x**2)**(5/2)/(3*x**8)","A",0
34,1,3,0,0.069932," ","integrate((x**2)**(7/2),x)","\frac{x^{8}}{8}"," ",0,"x**8/8","A",0
35,1,15,0,0.487909," ","integrate(x**3/(b*x**2)**(1/2),x)","\frac{x^{4}}{3 \sqrt{b} \sqrt{x^{2}}}"," ",0,"x**4/(3*sqrt(b)*sqrt(x**2))","A",0
36,1,14,0,0.399083," ","integrate(x/(b*x**2)**(1/2),x)","\frac{x^{2}}{\sqrt{b} \sqrt{x^{2}}}"," ",0,"x**2/(sqrt(b)*sqrt(x**2))","A",0
37,1,14,0,0.458661," ","integrate(1/x/(b*x**2)**(1/2),x)","- \frac{1}{\sqrt{b} \sqrt{x^{2}}}"," ",0,"-1/(sqrt(b)*sqrt(x**2))","A",0
38,1,19,0,0.623928," ","integrate(1/x**3/(b*x**2)**(1/2),x)","- \frac{1}{3 \sqrt{b} x^{2} \sqrt{x^{2}}}"," ",0,"-1/(3*sqrt(b)*x**2*sqrt(x**2))","A",0
39,1,15,0,0.449518," ","integrate(x**2/(b*x**2)**(1/2),x)","\frac{x^{3}}{2 \sqrt{b} \sqrt{x^{2}}}"," ",0,"x**3/(2*sqrt(b)*sqrt(x**2))","A",0
40,0,0,0,0.000000," ","integrate(1/(b*x**2)**(1/2),x)","\int \frac{1}{\sqrt{b x^{2}}}\, dx"," ",0,"Integral(1/sqrt(b*x**2), x)","F",0
41,1,17,0,0.501580," ","integrate(1/x**2/(b*x**2)**(1/2),x)","- \frac{1}{2 \sqrt{b} x \sqrt{x^{2}}}"," ",0,"-1/(2*sqrt(b)*x*sqrt(x**2))","A",0
42,1,15,0,0.707710," ","integrate(x**5/(b*x**2)**(3/2),x)","\frac{x^{6}}{3 b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"x**6/(3*b**(3/2)*(x**2)**(3/2))","A",0
43,1,14,0,0.513406," ","integrate(x**3/(b*x**2)**(3/2),x)","\frac{x^{4}}{b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"x**4/(b**(3/2)*(x**2)**(3/2))","A",0
44,1,15,0,0.518928," ","integrate(x/(b*x**2)**(3/2),x)","- \frac{x^{2}}{b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-x**2/(b**(3/2)*(x**2)**(3/2))","A",0
45,1,15,0,0.591676," ","integrate(1/x/(b*x**2)**(3/2),x)","- \frac{1}{3 b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/(3*b**(3/2)*(x**2)**(3/2))","A",0
46,1,19,0,0.863454," ","integrate(1/x**3/(b*x**2)**(3/2),x)","- \frac{1}{5 b^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/(5*b**(3/2)*x**2*(x**2)**(3/2))","A",0
47,1,15,0,0.850737," ","integrate(x**6/(b*x**2)**(3/2),x)","\frac{x^{7}}{4 b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"x**7/(4*b**(3/2)*(x**2)**(3/2))","A",0
48,1,15,0,0.583942," ","integrate(x**4/(b*x**2)**(3/2),x)","\frac{x^{5}}{2 b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"x**5/(2*b**(3/2)*(x**2)**(3/2))","A",0
49,0,0,0,0.000000," ","integrate(x**2/(b*x**2)**(3/2),x)","\int \frac{x^{2}}{\left(b x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/(b*x**2)**(3/2), x)","F",0
50,1,15,0,0.502977," ","integrate(1/(b*x**2)**(3/2),x)","- \frac{x}{2 b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-x/(2*b**(3/2)*(x**2)**(3/2))","A",0
51,1,17,0,0.732383," ","integrate(1/x**2/(b*x**2)**(3/2),x)","- \frac{1}{4 b^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/(4*b**(3/2)*x*(x**2)**(3/2))","A",0
52,1,15,0,1.202392," ","integrate(x**7/(b*x**2)**(5/2),x)","\frac{x^{8}}{3 b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"x**8/(3*b**(5/2)*(x**2)**(5/2))","A",0
53,1,14,0,0.825156," ","integrate(x**5/(b*x**2)**(5/2),x)","\frac{x^{6}}{b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"x**6/(b**(5/2)*(x**2)**(5/2))","A",0
54,1,15,0,0.857805," ","integrate(x**3/(b*x**2)**(5/2),x)","- \frac{x^{4}}{b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-x**4/(b**(5/2)*(x**2)**(5/2))","A",0
55,1,17,0,0.849377," ","integrate(x/(b*x**2)**(5/2),x)","- \frac{x^{2}}{3 b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-x**2/(3*b**(5/2)*(x**2)**(5/2))","A",0
56,1,15,0,1.031023," ","integrate(1/x/(b*x**2)**(5/2),x)","- \frac{1}{5 b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-1/(5*b**(5/2)*(x**2)**(5/2))","A",0
57,1,15,0,1.020120," ","integrate(x**6/(b*x**2)**(5/2),x)","\frac{x^{7}}{2 b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"x**7/(2*b**(5/2)*(x**2)**(5/2))","A",0
58,0,0,0,0.000000," ","integrate(x**4/(b*x**2)**(5/2),x)","\int \frac{x^{4}}{\left(b x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4/(b*x**2)**(5/2), x)","F",0
59,1,17,0,0.851233," ","integrate(x**2/(b*x**2)**(5/2),x)","- \frac{x^{3}}{2 b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-x**3/(2*b**(5/2)*(x**2)**(5/2))","A",0
60,1,15,0,0.843157," ","integrate(1/(b*x**2)**(5/2),x)","- \frac{x}{4 b^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-x/(4*b**(5/2)*(x**2)**(5/2))","A",0
61,1,17,0,1.252546," ","integrate(1/x**2/(b*x**2)**(5/2),x)","- \frac{1}{6 b^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-1/(6*b**(5/2)*x*(x**2)**(5/2))","A",0
62,0,0,0,0.000000," ","integrate((c*x)**m*(b*x**2)**(3/2),x)","\begin{cases} \frac{b^{\frac{3}{2}} c^{m} x x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m + 4} & \text{for}\: m \neq -4 \\\frac{\int \frac{\left(b x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx}{c^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**(3/2)*c**m*x*x**m*(x**2)**(3/2)/(m + 4), Ne(m, -4)), (Integral((b*x**2)**(3/2)/x**4, x)/c**4, True))","F",0
63,0,0,0,0.000000," ","integrate((c*x)**m*(b*x**2)**(1/2),x)","\begin{cases} \frac{\sqrt{b} c^{m} x x^{m} \sqrt{x^{2}}}{m + 2} & \text{for}\: m \neq -2 \\\frac{\int \frac{\sqrt{b x^{2}}}{x^{2}}\, dx}{c^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(b)*c**m*x*x**m*sqrt(x**2)/(m + 2), Ne(m, -2)), (Integral(sqrt(b*x**2)/x**2, x)/c**2, True))","F",0
64,0,0,0,0.000000," ","integrate((c*x)**m/(b*x**2)**(1/2),x)","\begin{cases} \frac{c^{m} x x^{m}}{\sqrt{b} m \sqrt{x^{2}}} & \text{for}\: m \neq 0 \\\int \frac{1}{\sqrt{b x^{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**m*x*x**m/(sqrt(b)*m*sqrt(x**2)), Ne(m, 0)), (Integral(1/sqrt(b*x**2), x), True))","F",0
65,0,0,0,0.000000," ","integrate((c*x)**m/(b*x**2)**(3/2),x)","\begin{cases} \frac{c^{m} x x^{m}}{b^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}} - 2 b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{for}\: m \neq 2 \\c^{2} \int \frac{x^{2}}{\left(b x^{2}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**m*x*x**m/(b**(3/2)*m*(x**2)**(3/2) - 2*b**(3/2)*(x**2)**(3/2)), Ne(m, 2)), (c**2*Integral(x**2/(b*x**2)**(3/2), x), True))","F",0
66,0,0,0,0.000000," ","integrate(x**m*(b*x**2)**p,x)","\begin{cases} \frac{b^{p} x x^{m} \left(x^{2}\right)^{p}}{m + 2 p + 1} & \text{for}\: m \neq - 2 p - 1 \\\int x^{- 2 p - 1} \left(b x^{2}\right)^{p}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x*x**m*(x**2)**p/(m + 2*p + 1), Ne(m, -2*p - 1)), (Integral(x**(-2*p - 1)*(b*x**2)**p, x), True))","F",0
67,0,0,0,0.000000," ","integrate((c*x)**m*(b*x**2)**p,x)","\begin{cases} \frac{b^{p} c^{m} x x^{m} \left(x^{2}\right)^{p}}{m + 2 p + 1} & \text{for}\: m \neq - 2 p - 1 \\\int \left(b x^{2}\right)^{p} \left(c x\right)^{- 2 p - 1}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*c**m*x*x**m*(x**2)**p/(m + 2*p + 1), Ne(m, -2*p - 1)), (Integral((b*x**2)**p*(c*x)**(-2*p - 1), x), True))","F",0
68,0,0,0,0.000000," ","integrate(x**(-1-2*p)*(x**2)**p,x)","\int x^{- 2 p - 1} \left(x^{2}\right)^{p}\, dx"," ",0,"Integral(x**(-2*p - 1)*(x**2)**p, x)","F",0
69,1,24,0,0.424248," ","integrate(x**3*(b*x**2)**p,x)","\begin{cases} \frac{b^{p} x^{4} \left(x^{2}\right)^{p}}{2 p + 4} & \text{for}\: p \neq -2 \\\frac{\log{\left(x \right)}}{b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x**4*(x**2)**p/(2*p + 4), Ne(p, -2)), (log(x)/b**2, True))","A",0
70,0,0,0,0.000000," ","integrate(x**2*(b*x**2)**p,x)","\begin{cases} \frac{b^{p} x^{3} \left(x^{2}\right)^{p}}{2 p + 3} & \text{for}\: p \neq - \frac{3}{2} \\\int \frac{x^{2}}{\left(b x^{2}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x**3*(x**2)**p/(2*p + 3), Ne(p, -3/2)), (Integral(x**2/(b*x**2)**(3/2), x), True))","F",0
71,1,22,0,0.235842," ","integrate(x*(b*x**2)**p,x)","\begin{cases} \frac{b^{p} x^{2} \left(x^{2}\right)^{p}}{2 p + 2} & \text{for}\: p \neq -1 \\\frac{\log{\left(x \right)}}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x**2*(x**2)**p/(2*p + 2), Ne(p, -1)), (log(x)/b, True))","A",0
72,0,0,0,0.000000," ","integrate((b*x**2)**p,x)","\begin{cases} \frac{b^{p} x \left(x^{2}\right)^{p}}{2 p + 1} & \text{for}\: p \neq - \frac{1}{2} \\\int \frac{1}{\sqrt{b x^{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x*(x**2)**p/(2*p + 1), Ne(p, -1/2)), (Integral(1/sqrt(b*x**2), x), True))","F",0
73,1,14,0,0.199684," ","integrate((b*x**2)**p/x,x)","\begin{cases} \frac{b^{p} \left(x^{2}\right)^{p}}{2 p} & \text{for}\: p \neq 0 \\\log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*(x**2)**p/(2*p), Ne(p, 0)), (log(x), True))","A",0
74,0,0,0,0.000000," ","integrate((b*x**2)**p/x**2,x)","\begin{cases} \frac{b^{p} \left(x^{2}\right)^{p}}{2 p x - x} & \text{for}\: p \neq \frac{1}{2} \\\int \frac{\sqrt{b x^{2}}}{x^{2}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*(x**2)**p/(2*p*x - x), Ne(p, 1/2)), (Integral(sqrt(b*x**2)/x**2, x), True))","F",0
75,1,24,0,0.479312," ","integrate((b*x**2)**p/x**3,x)","\begin{cases} \frac{b^{p} \left(x^{2}\right)^{p}}{2 p x^{2} - 2 x^{2}} & \text{for}\: p \neq 1 \\b \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*(x**2)**p/(2*p*x**2 - 2*x**2), Ne(p, 1)), (b*log(x), True))","A",0
76,0,0,0,0.000000," ","integrate((b*x**2)**p/x**4,x)","\begin{cases} \frac{b^{p} \left(x^{2}\right)^{p}}{2 p x^{3} - 3 x^{3}} & \text{for}\: p \neq \frac{3}{2} \\\int \frac{\left(b x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*(x**2)**p/(2*p*x**3 - 3*x**3), Ne(p, 3/2)), (Integral((b*x**2)**(3/2)/x**4, x), True))","F",0
77,1,15,0,0.168628," ","integrate((b*x**3)**(1/2),x)","\frac{2 \sqrt{b} x \sqrt{x^{3}}}{5}"," ",0,"2*sqrt(b)*x*sqrt(x**3)/5","A",0
78,1,14,0,0.164367," ","integrate((b*x**2)**(1/2),x)","\frac{\sqrt{b} x \sqrt{x^{2}}}{2}"," ",0,"sqrt(b)*x*sqrt(x**2)/2","A",0
79,1,10,0,0.060517," ","integrate((b*x)**(1/2),x)","\frac{2 \left(b x\right)^{\frac{3}{2}}}{3 b}"," ",0,"2*(b*x)**(3/2)/(3*b)","A",0
80,1,14,0,0.166911," ","integrate((b/x)**(1/2),x)","2 \sqrt{b} x \sqrt{\frac{1}{x}}"," ",0,"2*sqrt(b)*x*sqrt(1/x)","A",0
81,0,0,0,0.000000," ","integrate((b/x**2)**(1/2),x)","\int \sqrt{\frac{b}{x^{2}}}\, dx"," ",0,"Integral(sqrt(b/x**2), x)","F",0
82,1,17,0,0.299042," ","integrate((b/x**3)**(1/2),x)","- 2 \sqrt{b} x \sqrt{\frac{1}{x^{3}}}"," ",0,"-2*sqrt(b)*x*sqrt(x**(-3))","A",0
83,1,15,0,0.385717," ","integrate((b*x**3)**(3/2),x)","\frac{2 b^{\frac{3}{2}} x \left(x^{3}\right)^{\frac{3}{2}}}{11}"," ",0,"2*b**(3/2)*x*(x**3)**(3/2)/11","A",0
84,1,14,0,0.393415," ","integrate((b*x**2)**(3/2),x)","\frac{b^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}}{4}"," ",0,"b**(3/2)*x*(x**2)**(3/2)/4","A",0
85,1,10,0,0.062586," ","integrate((b*x)**(3/2),x)","\frac{2 \left(b x\right)^{\frac{5}{2}}}{5 b}"," ",0,"2*(b*x)**(5/2)/(5*b)","A",0
86,1,15,0,0.419658," ","integrate((b/x)**(3/2),x)","- 2 b^{\frac{3}{2}} x \left(\frac{1}{x}\right)^{\frac{3}{2}}"," ",0,"-2*b**(3/2)*x*(1/x)**(3/2)","A",0
87,1,17,0,0.531152," ","integrate((b/x**2)**(3/2),x)","- \frac{b^{\frac{3}{2}} x \left(\frac{1}{x^{2}}\right)^{\frac{3}{2}}}{2}"," ",0,"-b**(3/2)*x*(x**(-2))**(3/2)/2","A",0
88,1,19,0,0.539312," ","integrate((b/x**3)**(3/2),x)","- \frac{2 b^{\frac{3}{2}} x \left(\frac{1}{x^{3}}\right)^{\frac{3}{2}}}{7}"," ",0,"-2*b**(3/2)*x*(x**(-3))**(3/2)/7","A",0
89,1,15,0,0.401947," ","integrate(1/(b*x**3)**(1/2),x)","- \frac{2 x}{\sqrt{b} \sqrt{x^{3}}}"," ",0,"-2*x/(sqrt(b)*sqrt(x**3))","A",0
90,0,0,0,0.000000," ","integrate(1/(b*x**2)**(1/2),x)","\int \frac{1}{\sqrt{b x^{2}}}\, dx"," ",0,"Integral(1/sqrt(b*x**2), x)","F",0
91,1,8,0,0.061942," ","integrate(1/(b*x)**(1/2),x)","\frac{2 \sqrt{b x}}{b}"," ",0,"2*sqrt(b*x)/b","A",0
92,1,15,0,0.392748," ","integrate(1/(b/x)**(1/2),x)","\frac{2 x}{3 \sqrt{b} \sqrt{\frac{1}{x}}}"," ",0,"2*x/(3*sqrt(b)*sqrt(1/x))","A",0
93,1,15,0,0.394486," ","integrate(1/(b/x**2)**(1/2),x)","\frac{x}{2 \sqrt{b} \sqrt{\frac{1}{x^{2}}}}"," ",0,"x/(2*sqrt(b)*sqrt(x**(-2)))","A",0
94,1,17,0,0.407375," ","integrate(1/(b/x**3)**(1/2),x)","\frac{2 x}{5 \sqrt{b} \sqrt{\frac{1}{x^{3}}}}"," ",0,"2*x/(5*sqrt(b)*sqrt(x**(-3)))","A",0
95,1,17,0,0.512050," ","integrate(1/(b*x**3)**(3/2),x)","- \frac{2 x}{7 b^{\frac{3}{2}} \left(x^{3}\right)^{\frac{3}{2}}}"," ",0,"-2*x/(7*b**(3/2)*(x**3)**(3/2))","A",0
96,1,15,0,0.507382," ","integrate(1/(b*x**2)**(3/2),x)","- \frac{x}{2 b^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-x/(2*b**(3/2)*(x**2)**(3/2))","A",0
97,1,10,0,0.060936," ","integrate(1/(b*x)**(3/2),x)","- \frac{2}{b \sqrt{b x}}"," ",0,"-2/(b*sqrt(b*x))","A",0
98,1,15,0,0.502661," ","integrate(1/(b/x)**(3/2),x)","\frac{2 x}{5 b^{\frac{3}{2}} \left(\frac{1}{x}\right)^{\frac{3}{2}}}"," ",0,"2*x/(5*b**(3/2)*(1/x)**(3/2))","A",0
99,1,15,0,0.505382," ","integrate(1/(b/x**2)**(3/2),x)","\frac{x}{4 b^{\frac{3}{2}} \left(\frac{1}{x^{2}}\right)^{\frac{3}{2}}}"," ",0,"x/(4*b**(3/2)*(x**(-2))**(3/2))","A",0
100,1,17,0,0.510149," ","integrate(1/(b/x**3)**(3/2),x)","\frac{2 x}{11 b^{\frac{3}{2}} \left(\frac{1}{x^{3}}\right)^{\frac{3}{2}}}"," ",0,"2*x/(11*b**(3/2)*(x**(-3))**(3/2))","A",0
101,0,0,0,0.000000," ","integrate((b*x**n)**(1/3),x)","\begin{cases} \frac{3 \sqrt[3]{b} x \sqrt[3]{x^{n}}}{n + 3} & \text{for}\: n \neq -3 \\\int \sqrt[3]{\frac{b}{x^{3}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*b**(1/3)*x*(x**n)**(1/3)/(n + 3), Ne(n, -3)), (Integral((b/x**3)**(1/3), x), True))","F",0
102,1,14,0,0.190918," ","integrate((b*x**3)**(1/3),x)","\frac{\sqrt[3]{b} x \sqrt[3]{x^{3}}}{2}"," ",0,"b**(1/3)*x*(x**3)**(1/3)/2","A",0
103,1,15,0,0.195974," ","integrate((b*x**2)**(1/3),x)","\frac{3 \sqrt[3]{b} x \sqrt[3]{x^{2}}}{5}"," ",0,"3*b**(1/3)*x*(x**2)**(1/3)/5","A",0
104,1,10,0,0.064029," ","integrate((b*x)**(1/3),x)","\frac{3 \left(b x\right)^{\frac{4}{3}}}{4 b}"," ",0,"3*(b*x)**(4/3)/(4*b)","A",0
105,1,15,0,0.190805," ","integrate((b/x)**(1/3),x)","\frac{3 \sqrt[3]{b} x \sqrt[3]{\frac{1}{x}}}{2}"," ",0,"3*b**(1/3)*x*(1/x)**(1/3)/2","A",0
106,1,15,0,0.322145," ","integrate((b/x**2)**(1/3),x)","3 \sqrt[3]{b} x \sqrt[3]{\frac{1}{x^{2}}}"," ",0,"3*b**(1/3)*x*(x**(-2))**(1/3)","A",0
107,0,0,0,0.000000," ","integrate((b/x**3)**(1/3),x)","\int \sqrt[3]{\frac{b}{x^{3}}}\, dx"," ",0,"Integral((b/x**3)**(1/3), x)","F",0
108,1,17,0,0.325292," ","integrate((b/x**4)**(1/3),x)","- 3 \sqrt[3]{b} x \sqrt[3]{\frac{1}{x^{4}}}"," ",0,"-3*b**(1/3)*x*(x**(-4))**(1/3)","A",0
109,0,0,0,0.000000," ","integrate((b*x**n)**(2/3),x)","\begin{cases} \frac{3 b^{\frac{2}{3}} x \left(x^{n}\right)^{\frac{2}{3}}}{2 n + 3} & \text{for}\: n \neq - \frac{3}{2} \\\int \left(\frac{b}{x^{\frac{3}{2}}}\right)^{\frac{2}{3}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*b**(2/3)*x*(x**n)**(2/3)/(2*n + 3), Ne(n, -3/2)), (Integral((b/x**(3/2))**(2/3), x), True))","F",0
110,1,15,0,0.298791," ","integrate((b*x**2)**(2/3),x)","\frac{3 b^{\frac{2}{3}} x \left(x^{2}\right)^{\frac{2}{3}}}{7}"," ",0,"3*b**(2/3)*x*(x**2)**(2/3)/7","A",0
111,1,10,0,0.061712," ","integrate((b*x)**(2/3),x)","\frac{3 \left(b x\right)^{\frac{5}{3}}}{5 b}"," ",0,"3*(b*x)**(5/3)/(5*b)","A",0
112,1,14,0,0.328134," ","integrate((b/x)**(2/3),x)","3 b^{\frac{2}{3}} x \left(\frac{1}{x}\right)^{\frac{2}{3}}"," ",0,"3*b**(2/3)*x*(1/x)**(2/3)","A",0
113,1,17,0,0.479958," ","integrate((b/x**2)**(2/3),x)","- 3 b^{\frac{2}{3}} x \left(\frac{1}{x^{2}}\right)^{\frac{2}{3}}"," ",0,"-3*b**(2/3)*x*(x**(-2))**(2/3)","A",0
114,1,15,0,0.505417," ","integrate((b/x**3)**(2/3),x)","- b^{\frac{2}{3}} x \left(\frac{1}{x^{3}}\right)^{\frac{2}{3}}"," ",0,"-b**(2/3)*x*(x**(-3))**(2/3)","A",0
115,1,19,0,0.442932," ","integrate((b/x**4)**(2/3),x)","- \frac{3 b^{\frac{2}{3}} x \left(\frac{1}{x^{4}}\right)^{\frac{2}{3}}}{5}"," ",0,"-3*b**(2/3)*x*(x**(-4))**(2/3)/5","A",0
116,-1,0,0,0.000000," ","integrate(1/(b*x**n)**(1/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,1,15,0,0.592241," ","integrate(1/(b*x**4)**(1/3),x)","- \frac{3 x}{\sqrt[3]{b} \sqrt[3]{x^{4}}}"," ",0,"-3*x/(b**(1/3)*(x**4)**(1/3))","A",0
118,0,0,0,0.000000," ","integrate(1/(b*x**3)**(1/3),x)","\int \frac{1}{\sqrt[3]{b x^{3}}}\, dx"," ",0,"Integral((b*x**3)**(-1/3), x)","F",0
119,1,14,0,0.829974," ","integrate(1/(b*x**2)**(1/3),x)","\frac{3 x}{\sqrt[3]{b} \sqrt[3]{x^{2}}}"," ",0,"3*x/(b**(1/3)*(x**2)**(1/3))","A",0
120,1,10,0,0.070696," ","integrate(1/(b*x)**(1/3),x)","\frac{3 \left(b x\right)^{\frac{2}{3}}}{2 b}"," ",0,"3*(b*x)**(2/3)/(2*b)","A",0
121,1,15,0,0.429096," ","integrate(1/(b/x)**(1/3),x)","\frac{3 x}{4 \sqrt[3]{b} \sqrt[3]{\frac{1}{x}}}"," ",0,"3*x/(4*b**(1/3)*(1/x)**(1/3))","A",0
122,1,17,0,0.435686," ","integrate(1/(b/x**2)**(1/3),x)","\frac{3 x}{5 \sqrt[3]{b} \sqrt[3]{\frac{1}{x^{2}}}}"," ",0,"3*x/(5*b**(1/3)*(x**(-2))**(1/3))","A",0
123,1,15,0,0.447868," ","integrate(1/(b/x**3)**(1/3),x)","\frac{x}{2 \sqrt[3]{b} \sqrt[3]{\frac{1}{x^{3}}}}"," ",0,"x/(2*b**(1/3)*(x**(-3))**(1/3))","A",0
124,-1,0,0,0.000000," ","integrate(1/(b*x**n)**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,1,14,0,0.543034," ","integrate(1/(b*x**3)**(2/3),x)","- \frac{x}{b^{\frac{2}{3}} \left(x^{3}\right)^{\frac{2}{3}}}"," ",0,"-x/(b**(2/3)*(x**3)**(2/3))","A",0
126,1,15,0,0.728107," ","integrate(1/(b*x**2)**(2/3),x)","- \frac{3 x}{b^{\frac{2}{3}} \left(x^{2}\right)^{\frac{2}{3}}}"," ",0,"-3*x/(b**(2/3)*(x**2)**(2/3))","A",0
127,1,8,0,0.104085," ","integrate(1/(b*x)**(2/3),x)","\frac{3 \sqrt[3]{b x}}{b}"," ",0,"3*(b*x)**(1/3)/b","A",0
128,1,15,0,0.958799," ","integrate(1/(b/x)**(2/3),x)","\frac{3 x}{5 b^{\frac{2}{3}} \left(\frac{1}{x}\right)^{\frac{2}{3}}}"," ",0,"3*x/(5*b**(2/3)*(1/x)**(2/3))","A",0
129,1,17,0,0.678813," ","integrate(1/(b/x**2)**(2/3),x)","\frac{3 x}{7 b^{\frac{2}{3}} \left(\frac{1}{x^{2}}\right)^{\frac{2}{3}}}"," ",0,"3*x/(7*b**(2/3)*(x**(-2))**(2/3))","A",0
130,1,15,0,0.725348," ","integrate(1/(b/x**3)**(2/3),x)","\frac{x}{3 b^{\frac{2}{3}} \left(\frac{1}{x^{3}}\right)^{\frac{2}{3}}}"," ",0,"x/(3*b**(2/3)*(x**(-3))**(2/3))","A",0
131,0,0,0,0.000000," ","integrate(x**2*(b*x**n)**(1/2),x)","\begin{cases} \frac{2 \sqrt{b} x^{3} \sqrt{x^{n}}}{n + 6} & \text{for}\: n \neq -6 \\\int x^{2} \sqrt{\frac{b}{x^{6}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b)*x**3*sqrt(x**n)/(n + 6), Ne(n, -6)), (Integral(x**2*sqrt(b/x**6), x), True))","F",0
132,0,0,0,0.000000," ","integrate(x*(b*x**n)**(1/2),x)","\begin{cases} \frac{2 \sqrt{b} x^{2} \sqrt{x^{n}}}{n + 4} & \text{for}\: n \neq -4 \\\int x \sqrt{\frac{b}{x^{4}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b)*x**2*sqrt(x**n)/(n + 4), Ne(n, -4)), (Integral(x*sqrt(b/x**4), x), True))","F",0
133,0,0,0,0.000000," ","integrate((b*x**n)**(1/2),x)","\begin{cases} \frac{2 \sqrt{b} x \sqrt{x^{n}}}{n + 2} & \text{for}\: n \neq -2 \\\int \sqrt{\frac{b}{x^{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b)*x*sqrt(x**n)/(n + 2), Ne(n, -2)), (Integral(sqrt(b/x**2), x), True))","F",0
134,1,22,0,0.377841," ","integrate((b*x**n)**(1/2)/x,x)","\begin{cases} \frac{2 \sqrt{b} \sqrt{x^{n}}}{n} & \text{for}\: n \neq 0 \\\sqrt{b} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b)*sqrt(x**n)/n, Ne(n, 0)), (sqrt(b)*log(x), True))","A",0
135,0,0,0,0.000000," ","integrate((b*x**n)**(1/2)/x**2,x)","\begin{cases} \frac{2 \sqrt{b} \sqrt{x^{n}}}{n x - 2 x} & \text{for}\: n \neq 2 \\\int \frac{\sqrt{b x^{2}}}{x^{2}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b)*sqrt(x**n)/(n*x - 2*x), Ne(n, 2)), (Integral(sqrt(b*x**2)/x**2, x), True))","F",0
136,0,0,0,0.000000," ","integrate((b*x**n)**(1/2)/x**3,x)","\begin{cases} \frac{2 \sqrt{b} \sqrt{x^{n}}}{n x^{2} - 4 x^{2}} & \text{for}\: n \neq 4 \\\int \frac{\sqrt{b x^{4}}}{x^{3}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b)*sqrt(x**n)/(n*x**2 - 4*x**2), Ne(n, 4)), (Integral(sqrt(b*x**4)/x**3, x), True))","F",0
137,0,0,0,0.000000," ","integrate(x*(b*x**n)**(3/2),x)","\begin{cases} \frac{2 b^{\frac{3}{2}} x^{2} \left(x^{n}\right)^{\frac{3}{2}}}{3 n + 4} & \text{for}\: n \neq - \frac{4}{3} \\\int x \left(\frac{b}{x^{\frac{4}{3}}}\right)^{\frac{3}{2}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(3/2)*x**2*(x**n)**(3/2)/(3*n + 4), Ne(n, -4/3)), (Integral(x*(b/x**(4/3))**(3/2), x), True))","F",0
138,0,0,0,0.000000," ","integrate((b*x**n)**(3/2),x)","\begin{cases} \frac{2 b^{\frac{3}{2}} x \left(x^{n}\right)^{\frac{3}{2}}}{3 n + 2} & \text{for}\: n \neq - \frac{2}{3} \\\int \left(\frac{b}{x^{\frac{2}{3}}}\right)^{\frac{3}{2}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(3/2)*x*(x**n)**(3/2)/(3*n + 2), Ne(n, -2/3)), (Integral((b/x**(2/3))**(3/2), x), True))","F",0
139,1,24,0,6.693695," ","integrate((b*x**n)**(3/2)/x,x)","\begin{cases} \frac{2 b^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}}{3 n} & \text{for}\: n \neq 0 \\b^{\frac{3}{2}} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(3/2)*(x**n)**(3/2)/(3*n), Ne(n, 0)), (b**(3/2)*log(x), True))","A",0
140,0,0,0,0.000000," ","integrate((b*x**n)**(3/2)/x**2,x)","\begin{cases} \frac{2 b^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}}{3 n x - 2 x} & \text{for}\: n \neq \frac{2}{3} \\\int \frac{\left(b x^{\frac{2}{3}}\right)^{\frac{3}{2}}}{x^{2}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(3/2)*(x**n)**(3/2)/(3*n*x - 2*x), Ne(n, 2/3)), (Integral((b*x**(2/3))**(3/2)/x**2, x), True))","F",0
141,0,0,0,0.000000," ","integrate((b*x**n)**(3/2)/x**3,x)","\begin{cases} \frac{2 b^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}}{3 n x^{2} - 4 x^{2}} & \text{for}\: n \neq \frac{4}{3} \\\int \frac{\left(b x^{\frac{4}{3}}\right)^{\frac{3}{2}}}{x^{3}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(3/2)*(x**n)**(3/2)/(3*n*x**2 - 4*x**2), Ne(n, 4/3)), (Integral((b*x**(4/3))**(3/2)/x**3, x), True))","F",0
142,0,0,0,0.000000," ","integrate((b*x**n)**(3/2)/x**4,x)","\begin{cases} \frac{2 b^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}}{3 n x^{3} - 6 x^{3}} & \text{for}\: n \neq 2 \\\int \frac{\left(b x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(3/2)*(x**n)**(3/2)/(3*n*x**3 - 6*x**3), Ne(n, 2)), (Integral((b*x**2)**(3/2)/x**4, x), True))","F",0
143,0,0,0,0.000000," ","integrate(x**2/(b*x**n)**(1/2),x)","\begin{cases} - \frac{2 x^{3}}{\sqrt{b} n \sqrt{x^{n}} - 6 \sqrt{b} \sqrt{x^{n}}} & \text{for}\: n \neq 6 \\\int \frac{x^{2}}{\sqrt{b x^{6}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*x**3/(sqrt(b)*n*sqrt(x**n) - 6*sqrt(b)*sqrt(x**n)), Ne(n, 6)), (Integral(x**2/sqrt(b*x**6), x), True))","F",0
144,0,0,0,0.000000," ","integrate(x/(b*x**n)**(1/2),x)","\begin{cases} - \frac{2 x^{2}}{\sqrt{b} n \sqrt{x^{n}} - 4 \sqrt{b} \sqrt{x^{n}}} & \text{for}\: n \neq 4 \\\int \frac{x}{\sqrt{b x^{4}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*x**2/(sqrt(b)*n*sqrt(x**n) - 4*sqrt(b)*sqrt(x**n)), Ne(n, 4)), (Integral(x/sqrt(b*x**4), x), True))","F",0
145,0,0,0,0.000000," ","integrate(1/(b*x**n)**(1/2),x)","\begin{cases} - \frac{2 x}{\sqrt{b} n \sqrt{x^{n}} - 2 \sqrt{b} \sqrt{x^{n}}} & \text{for}\: n \neq 2 \\\int \frac{1}{\sqrt{b x^{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*x/(sqrt(b)*n*sqrt(x**n) - 2*sqrt(b)*sqrt(x**n)), Ne(n, 2)), (Integral(1/sqrt(b*x**2), x), True))","F",0
146,1,24,0,2.042629," ","integrate(1/x/(b*x**n)**(1/2),x)","\begin{cases} - \frac{2}{\sqrt{b} n \sqrt{x^{n}}} & \text{for}\: n \neq 0 \\\frac{\log{\left(x \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(sqrt(b)*n*sqrt(x**n)), Ne(n, 0)), (log(x)/sqrt(b), True))","A",0
147,0,0,0,0.000000," ","integrate(1/x**2/(b*x**n)**(1/2),x)","\begin{cases} - \frac{2}{\sqrt{b} n x \sqrt{x^{n}} + 2 \sqrt{b} x \sqrt{x^{n}}} & \text{for}\: n \neq -2 \\\int \frac{1}{x^{2} \sqrt{\frac{b}{x^{2}}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(sqrt(b)*n*x*sqrt(x**n) + 2*sqrt(b)*x*sqrt(x**n)), Ne(n, -2)), (Integral(1/(x**2*sqrt(b/x**2)), x), True))","F",0
148,0,0,0,0.000000," ","integrate(1/x**3/(b*x**n)**(1/2),x)","\begin{cases} - \frac{2}{\sqrt{b} n x^{2} \sqrt{x^{n}} + 4 \sqrt{b} x^{2} \sqrt{x^{n}}} & \text{for}\: n \neq -4 \\\int \frac{1}{x^{3} \sqrt{\frac{b}{x^{4}}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(sqrt(b)*n*x**2*sqrt(x**n) + 4*sqrt(b)*x**2*sqrt(x**n)), Ne(n, -4)), (Integral(1/(x**3*sqrt(b/x**4)), x), True))","F",0
149,0,0,0,0.000000," ","integrate(x**2/(b*x**n)**(3/2),x)","\begin{cases} - \frac{2 x^{3}}{3 b^{\frac{3}{2}} n \left(x^{n}\right)^{\frac{3}{2}} - 6 b^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: n \neq 2 \\\int \frac{x^{2}}{\left(b x^{2}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*x**3/(3*b**(3/2)*n*(x**n)**(3/2) - 6*b**(3/2)*(x**n)**(3/2)), Ne(n, 2)), (Integral(x**2/(b*x**2)**(3/2), x), True))","F",0
150,0,0,0,0.000000," ","integrate(x/(b*x**n)**(3/2),x)","\begin{cases} - \frac{2 x^{2}}{3 b^{\frac{3}{2}} n \left(x^{n}\right)^{\frac{3}{2}} - 4 b^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: n \neq \frac{4}{3} \\\int \frac{x}{\left(b x^{\frac{4}{3}}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*x**2/(3*b**(3/2)*n*(x**n)**(3/2) - 4*b**(3/2)*(x**n)**(3/2)), Ne(n, 4/3)), (Integral(x/(b*x**(4/3))**(3/2), x), True))","F",0
151,0,0,0,0.000000," ","integrate(1/(b*x**n)**(3/2),x)","\begin{cases} - \frac{2 x}{3 b^{\frac{3}{2}} n \left(x^{n}\right)^{\frac{3}{2}} - 2 b^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: n \neq \frac{2}{3} \\\int \frac{1}{\left(b x^{\frac{2}{3}}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*x/(3*b**(3/2)*n*(x**n)**(3/2) - 2*b**(3/2)*(x**n)**(3/2)), Ne(n, 2/3)), (Integral((b*x**(2/3))**(-3/2), x), True))","F",0
152,1,26,0,3.306288," ","integrate(1/x/(b*x**n)**(3/2),x)","\begin{cases} - \frac{2}{3 b^{\frac{3}{2}} n \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: n \neq 0 \\\frac{\log{\left(x \right)}}{b^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(3*b**(3/2)*n*(x**n)**(3/2)), Ne(n, 0)), (log(x)/b**(3/2), True))","A",0
153,0,0,0,0.000000," ","integrate(1/x**2/(b*x**n)**(3/2),x)","\begin{cases} - \frac{2}{3 b^{\frac{3}{2}} n x \left(x^{n}\right)^{\frac{3}{2}} + 2 b^{\frac{3}{2}} x \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: n \neq - \frac{2}{3} \\\int \frac{1}{x^{2} \left(\frac{b}{x^{\frac{2}{3}}}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(3*b**(3/2)*n*x*(x**n)**(3/2) + 2*b**(3/2)*x*(x**n)**(3/2)), Ne(n, -2/3)), (Integral(1/(x**2*(b/x**(2/3))**(3/2)), x), True))","F",0
154,0,0,0,0.000000," ","integrate(1/x**3/(b*x**n)**(3/2),x)","\begin{cases} - \frac{2}{3 b^{\frac{3}{2}} n x^{2} \left(x^{n}\right)^{\frac{3}{2}} + 4 b^{\frac{3}{2}} x^{2} \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: n \neq - \frac{4}{3} \\\int \frac{1}{x^{3} \left(\frac{b}{x^{\frac{4}{3}}}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(3*b**(3/2)*n*x**2*(x**n)**(3/2) + 4*b**(3/2)*x**2*(x**n)**(3/2)), Ne(n, -4/3)), (Integral(1/(x**3*(b/x**(4/3))**(3/2)), x), True))","F",0
155,0,0,0,0.000000," ","integrate(1/x**4/(b*x**n)**(3/2),x)","\begin{cases} - \frac{2}{3 b^{\frac{3}{2}} n x^{3} \left(x^{n}\right)^{\frac{3}{2}} + 6 b^{\frac{3}{2}} x^{3} \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: n \neq -2 \\\int \frac{1}{x^{4} \left(\frac{b}{x^{2}}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(3*b**(3/2)*n*x**3*(x**n)**(3/2) + 6*b**(3/2)*x**3*(x**n)**(3/2)), Ne(n, -2)), (Integral(1/(x**4*(b/x**2)**(3/2)), x), True))","F",0
156,0,0,0,0.000000," ","integrate(x**m/(a*x**n)**(3/2),x)","\begin{cases} \frac{2 x x^{m}}{2 a^{\frac{3}{2}} m \left(x^{n}\right)^{\frac{3}{2}} - 3 a^{\frac{3}{2}} n \left(x^{n}\right)^{\frac{3}{2}} + 2 a^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: m \neq \frac{3 n}{2} - 1 \\\int \frac{x^{\frac{3 n}{2} - 1}}{\left(a x^{n}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x*x**m/(2*a**(3/2)*m*(x**n)**(3/2) - 3*a**(3/2)*n*(x**n)**(3/2) + 2*a**(3/2)*(x**n)**(3/2)), Ne(m, 3*n/2 - 1)), (Integral(x**(3*n/2 - 1)/(a*x**n)**(3/2), x), True))","F",0
157,0,0,0,0.000000," ","integrate((c*x)**m/(a*x**n)**(3/2),x)","\begin{cases} \frac{2 c^{m} x x^{m}}{2 a^{\frac{3}{2}} m \left(x^{n}\right)^{\frac{3}{2}} - 3 a^{\frac{3}{2}} n \left(x^{n}\right)^{\frac{3}{2}} + 2 a^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: m \neq \frac{3 n}{2} - 1 \\\int \frac{\left(c x\right)^{\frac{3 n}{2} - 1}}{\left(a x^{n}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c**m*x*x**m/(2*a**(3/2)*m*(x**n)**(3/2) - 3*a**(3/2)*n*(x**n)**(3/2) + 2*a**(3/2)*(x**n)**(3/2)), Ne(m, 3*n/2 - 1)), (Integral((c*x)**(3*n/2 - 1)/(a*x**n)**(3/2), x), True))","F",0
158,-1,0,0,0.000000," ","integrate(x**m*(b*x**n)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,0,0,0,0.000000," ","integrate(x**m*(b*x**n)**(1/2),x)","\begin{cases} \frac{2 \sqrt{b} x x^{m} \sqrt{x^{n}}}{2 m + n + 2} & \text{for}\: m \neq - \frac{n}{2} - 1 \\\int x^{- \frac{n}{2} - 1} \sqrt{b x^{n}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b)*x*x**m*sqrt(x**n)/(2*m + n + 2), Ne(m, -n/2 - 1)), (Integral(x**(-n/2 - 1)*sqrt(b*x**n), x), True))","F",0
160,0,0,0,0.000000," ","integrate(x**m/(b*x**n)**(1/2),x)","\begin{cases} \frac{2 x x^{m}}{2 \sqrt{b} m \sqrt{x^{n}} - \sqrt{b} n \sqrt{x^{n}} + 2 \sqrt{b} \sqrt{x^{n}}} & \text{for}\: m \neq \frac{n}{2} - 1 \\\int \frac{x^{\frac{n}{2} - 1}}{\sqrt{b x^{n}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x*x**m/(2*sqrt(b)*m*sqrt(x**n) - sqrt(b)*n*sqrt(x**n) + 2*sqrt(b)*sqrt(x**n)), Ne(m, n/2 - 1)), (Integral(x**(n/2 - 1)/sqrt(b*x**n), x), True))","F",0
161,0,0,0,0.000000," ","integrate(x**m/(b*x**n)**(3/2),x)","\begin{cases} \frac{2 x x^{m}}{2 b^{\frac{3}{2}} m \left(x^{n}\right)^{\frac{3}{2}} - 3 b^{\frac{3}{2}} n \left(x^{n}\right)^{\frac{3}{2}} + 2 b^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: m \neq \frac{3 n}{2} - 1 \\\int \frac{x^{\frac{3 n}{2} - 1}}{\left(b x^{n}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x*x**m/(2*b**(3/2)*m*(x**n)**(3/2) - 3*b**(3/2)*n*(x**n)**(3/2) + 2*b**(3/2)*(x**n)**(3/2)), Ne(m, 3*n/2 - 1)), (Integral(x**(3*n/2 - 1)/(b*x**n)**(3/2), x), True))","F",0
162,-1,0,0,0.000000," ","integrate((c*x)**m*(b*x**n)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate((c*x)**m*(b*x**n)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,0,0,0,0.000000," ","integrate((c*x)**m*(b*x**n)**(1/2),x)","\begin{cases} \frac{2 \sqrt{b} c^{m} x x^{m} \sqrt{x^{n}}}{2 m + n + 2} & \text{for}\: m \neq - \frac{n}{2} - 1 \\\int \sqrt{b x^{n}} \left(c x\right)^{- \frac{n}{2} - 1}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b)*c**m*x*x**m*sqrt(x**n)/(2*m + n + 2), Ne(m, -n/2 - 1)), (Integral(sqrt(b*x**n)*(c*x)**(-n/2 - 1), x), True))","F",0
165,0,0,0,0.000000," ","integrate((c*x)**m/(b*x**n)**(1/2),x)","\begin{cases} \frac{2 c^{m} x x^{m}}{2 \sqrt{b} m \sqrt{x^{n}} - \sqrt{b} n \sqrt{x^{n}} + 2 \sqrt{b} \sqrt{x^{n}}} & \text{for}\: m \neq \frac{n}{2} - 1 \\\int \frac{\left(c x\right)^{\frac{n}{2} - 1}}{\sqrt{b x^{n}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c**m*x*x**m/(2*sqrt(b)*m*sqrt(x**n) - sqrt(b)*n*sqrt(x**n) + 2*sqrt(b)*sqrt(x**n)), Ne(m, n/2 - 1)), (Integral((c*x)**(n/2 - 1)/sqrt(b*x**n), x), True))","F",0
166,0,0,0,0.000000," ","integrate((c*x)**m/(b*x**n)**(3/2),x)","\begin{cases} \frac{2 c^{m} x x^{m}}{2 b^{\frac{3}{2}} m \left(x^{n}\right)^{\frac{3}{2}} - 3 b^{\frac{3}{2}} n \left(x^{n}\right)^{\frac{3}{2}} + 2 b^{\frac{3}{2}} \left(x^{n}\right)^{\frac{3}{2}}} & \text{for}\: m \neq \frac{3 n}{2} - 1 \\\int \frac{\left(c x\right)^{\frac{3 n}{2} - 1}}{\left(b x^{n}\right)^{\frac{3}{2}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c**m*x*x**m/(2*b**(3/2)*m*(x**n)**(3/2) - 3*b**(3/2)*n*(x**n)**(3/2) + 2*b**(3/2)*(x**n)**(3/2)), Ne(m, 3*n/2 - 1)), (Integral((c*x)**(3*n/2 - 1)/(b*x**n)**(3/2), x), True))","F",0
167,-1,0,0,0.000000," ","integrate((c*x)**m/(b*x**n)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate(x**(-1-3/2*n)*(b*x**n)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,0,0,0,0.000000," ","integrate(x**(-1-1/2*n)*(b*x**n)**(1/2),x)","\int x^{- \frac{n}{2} - 1} \sqrt{b x^{n}}\, dx"," ",0,"Integral(x**(-n/2 - 1)*sqrt(b*x**n), x)","F",0
170,0,0,0,0.000000," ","integrate(x**(-1+1/2*n)/(b*x**n)**(1/2),x)","\int \frac{x^{\frac{n}{2} - 1}}{\sqrt{b x^{n}}}\, dx"," ",0,"Integral(x**(n/2 - 1)/sqrt(b*x**n), x)","F",0
171,0,0,0,0.000000," ","integrate(x**(-1+3/2*n)/(b*x**n)**(3/2),x)","\int \frac{x^{\frac{3 n}{2} - 1}}{\left(b x^{n}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(3*n/2 - 1)/(b*x**n)**(3/2), x)","F",0
172,0,0,0,0.000000," ","integrate(x**m*(b*x**n)**p,x)","\begin{cases} \frac{b^{p} x x^{m} \left(x^{n}\right)^{p}}{m + n p + 1} & \text{for}\: m \neq - n p - 1 \\\int x^{- n p - 1} \left(b x^{n}\right)^{p}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x*x**m*(x**n)**p/(m + n*p + 1), Ne(m, -n*p - 1)), (Integral(x**(-n*p - 1)*(b*x**n)**p, x), True))","F",0
173,0,0,0,0.000000," ","integrate((c*x)**m*(b*x**n)**p,x)","\begin{cases} \frac{b^{p} c^{m} x x^{m} \left(x^{n}\right)^{p}}{m + n p + 1} & \text{for}\: m \neq - n p - 1 \\\int \left(b x^{n}\right)^{p} \left(c x\right)^{- n p - 1}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*c**m*x*x**m*(x**n)**p/(m + n*p + 1), Ne(m, -n*p - 1)), (Integral((b*x**n)**p*(c*x)**(-n*p - 1), x), True))","F",0
174,0,0,0,0.000000," ","integrate(x**2*(b*x**n)**p,x)","\begin{cases} \frac{b^{p} x^{3} \left(x^{n}\right)^{p}}{n p + 3} & \text{for}\: n \neq - \frac{3}{p} \\\int x^{2} \left(b x^{- \frac{3}{p}}\right)^{p}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x**3*(x**n)**p/(n*p + 3), Ne(n, -3/p)), (Integral(x**2*(b*x**(-3/p))**p, x), True))","F",0
175,0,0,0,0.000000," ","integrate(x*(b*x**n)**p,x)","\begin{cases} \frac{b^{p} x^{2} \left(x^{n}\right)^{p}}{n p + 2} & \text{for}\: n \neq - \frac{2}{p} \\\int x \left(b x^{- \frac{2}{p}}\right)^{p}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x**2*(x**n)**p/(n*p + 2), Ne(n, -2/p)), (Integral(x*(b*x**(-2/p))**p, x), True))","F",0
176,0,0,0,0.000000," ","integrate((b*x**n)**p,x)","\begin{cases} \frac{b^{p} x \left(x^{n}\right)^{p}}{n p + 1} & \text{for}\: n \neq - \frac{1}{p} \\\int \left(b x^{- \frac{1}{p}}\right)^{p}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x*(x**n)**p/(n*p + 1), Ne(n, -1/p)), (Integral((b*x**(-1/p))**p, x), True))","F",0
177,1,22,0,0.316478," ","integrate((b*x**n)**p/x,x)","\begin{cases} \log{\left(x \right)} & \text{for}\: p = 0 \wedge \left(n = 0 \vee p = 0\right) \\b^{p} \log{\left(x \right)} & \text{for}\: n = 0 \\\frac{b^{p} \left(x^{n}\right)^{p}}{n p} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x), Eq(p, 0) & (Eq(n, 0) | Eq(p, 0))), (b**p*log(x), Eq(n, 0)), (b**p*(x**n)**p/(n*p), True))","A",0
178,0,0,0,0.000000," ","integrate((b*x**n)**p/x**2,x)","\begin{cases} \frac{b^{p} \left(x^{n}\right)^{p}}{n p x - x} & \text{for}\: n \neq \frac{1}{p} \\\int \frac{\left(b x^{\frac{1}{p}}\right)^{p}}{x^{2}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*(x**n)**p/(n*p*x - x), Ne(n, 1/p)), (Integral((b*x**(1/p))**p/x**2, x), True))","F",0
179,0,0,0,0.000000," ","integrate((b*x**n)**p/x**3,x)","\begin{cases} \frac{b^{p} \left(x^{n}\right)^{p}}{n p x^{2} - 2 x^{2}} & \text{for}\: n \neq \frac{2}{p} \\\int \frac{\left(b x^{\frac{2}{p}}\right)^{p}}{x^{3}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*(x**n)**p/(n*p*x**2 - 2*x**2), Ne(n, 2/p)), (Integral((b*x**(2/p))**p/x**3, x), True))","F",0
180,0,0,0,0.000000," ","integrate(x**m/((a*x**n)**(1/n)),x)","\begin{cases} - \frac{x}{0^{n} \tilde{\infty}^{n} \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} - \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}}} & \text{for}\: a = 0^{n} \wedge m = 0 \\\int \left(a x^{n}\right)^{- \frac{1}{n}}\, dx & \text{for}\: m = 0 \\\frac{x x^{m}}{- 0^{n} \tilde{\infty}^{n} \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} + m \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} + \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}}} & \text{for}\: a = 0^{n} \\\frac{a^{- \frac{1}{n}} x x^{m} \left(x^{n}\right)^{- \frac{1}{n}}}{m} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x/(0**n*zoo**n*(0**n)**(1/n)*(x**n)**(1/n) - (0**n)**(1/n)*(x**n)**(1/n)), Eq(m, 0) & Eq(a, 0**n)), (Integral((a*x**n)**(-1/n), x), Eq(m, 0)), (x*x**m/(-0**n*zoo**n*(0**n)**(1/n)*(x**n)**(1/n) + m*(0**n)**(1/n)*(x**n)**(1/n) + (0**n)**(1/n)*(x**n)**(1/n)), Eq(a, 0**n)), (a**(-1/n)*x*x**m*(x**n)**(-1/n)/m, True))","F",0
181,0,0,0,0.000000," ","integrate((c*x)**m/((a*x**n)**(1/n)),x)","\begin{cases} - \frac{x}{0^{n} \tilde{\infty}^{n} \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} - \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}}} & \text{for}\: a = 0^{n} \wedge m = 0 \\\int \left(a x^{n}\right)^{- \frac{1}{n}}\, dx & \text{for}\: m = 0 \\\frac{c^{m} x x^{m}}{- 0^{n} \tilde{\infty}^{n} \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} + m \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} + \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}}} & \text{for}\: a = 0^{n} \\\frac{a^{- \frac{1}{n}} c^{m} x x^{m} \left(x^{n}\right)^{- \frac{1}{n}}}{m} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x/(0**n*zoo**n*(0**n)**(1/n)*(x**n)**(1/n) - (0**n)**(1/n)*(x**n)**(1/n)), Eq(m, 0) & Eq(a, 0**n)), (Integral((a*x**n)**(-1/n), x), Eq(m, 0)), (c**m*x*x**m/(-0**n*zoo**n*(0**n)**(1/n)*(x**n)**(1/n) + m*(0**n)**(1/n)*(x**n)**(1/n) + (0**n)**(1/n)*(x**n)**(1/n)), Eq(a, 0**n)), (a**(-1/n)*c**m*x*x**m*(x**n)**(-1/n)/m, True))","F",0
182,1,58,0,3.563762," ","integrate(x**2/((a*x**n)**(1/n)),x)","\begin{cases} \frac{a^{- \frac{1}{n}} x^{3} \left(x^{n}\right)^{- \frac{1}{n}}}{2} & \text{for}\: a \neq 0^{n} \\- \frac{x^{3}}{0^{n} \tilde{\infty}^{n} \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} - 3 \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(-1/n)*x**3*(x**n)**(-1/n)/2, Ne(a, 0**n)), (-x**3/(0**n*zoo**n*(0**n)**(1/n)*(x**n)**(1/n) - 3*(0**n)**(1/n)*(x**n)**(1/n)), True))","A",0
183,1,56,0,2.014974," ","integrate(x/((a*x**n)**(1/n)),x)","\begin{cases} a^{- \frac{1}{n}} x^{2} \left(x^{n}\right)^{- \frac{1}{n}} & \text{for}\: a \neq 0^{n} \\- \frac{x^{2}}{0^{n} \tilde{\infty}^{n} \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} - 2 \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(-1/n)*x**2*(x**n)**(-1/n), Ne(a, 0**n)), (-x**2/(0**n*zoo**n*(0**n)**(1/n)*(x**n)**(1/n) - 2*(0**n)**(1/n)*(x**n)**(1/n)), True))","A",0
184,0,0,0,0.000000," ","integrate(1/((a*x**n)**(1/n)),x)","\int \left(a x^{n}\right)^{- \frac{1}{n}}\, dx"," ",0,"Integral((a*x**n)**(-1/n), x)","F",0
185,1,32,0,1.308893," ","integrate(1/x/((a*x**n)**(1/n)),x)","\begin{cases} - a^{- \frac{1}{n}} \left(x^{n}\right)^{- \frac{1}{n}} & \text{for}\: a \neq 0^{n} \\- \left(0^{n}\right)^{- \frac{1}{n}} \left(x^{n}\right)^{- \frac{1}{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**(-1/n)*(x**n)**(-1/n), Ne(a, 0**n)), (-(0**n)**(-1/n)*(x**n)**(-1/n), True))","A",0
186,1,60,0,2.032600," ","integrate(1/x**2/((a*x**n)**(1/n)),x)","\begin{cases} - \frac{a^{- \frac{1}{n}} \left(x^{n}\right)^{- \frac{1}{n}}}{2 x} & \text{for}\: a \neq 0^{n} \\- \frac{1}{0^{n} \tilde{\infty}^{n} x \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} + x \left(0^{n}\right)^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**(-1/n)*(x**n)**(-1/n)/(2*x), Ne(a, 0**n)), (-1/(0**n*zoo**n*x*(0**n)**(1/n)*(x**n)**(1/n) + x*(0**n)**(1/n)*(x**n)**(1/n)), True))","A",0
187,0,0,0,0.000000," ","integrate(x**m/((a*x**n)**((1+m)/n)),x)","\int x^{m} \left(a x^{n}\right)^{- \frac{m + 1}{n}}\, dx"," ",0,"Integral(x**m*(a*x**n)**(-(m + 1)/n), x)","F",0
188,0,0,0,0.000000," ","integrate(x**(-n*p-1)*(a*x**n)**p,x)","\int x^{- n p - 1} \left(a x^{n}\right)^{p}\, dx"," ",0,"Integral(x**(-n*p - 1)*(a*x**n)**p, x)","F",0
189,0,0,0,0.000000," ","integrate(x**m*(a*(b*x**n)**p)**q,x)","\int x^{m} \left(a \left(b x^{n}\right)^{p}\right)^{q}\, dx"," ",0,"Integral(x**m*(a*(b*x**n)**p)**q, x)","F",0
190,0,0,0,0.000000," ","integrate(x**2*(a*(b*x**n)**p)**q,x)","\int x^{2} \left(a \left(b x^{n}\right)^{p}\right)^{q}\, dx"," ",0,"Integral(x**2*(a*(b*x**n)**p)**q, x)","F",0
191,0,0,0,0.000000," ","integrate(x*(a*(b*x**n)**p)**q,x)","\int x \left(a \left(b x^{n}\right)^{p}\right)^{q}\, dx"," ",0,"Integral(x*(a*(b*x**n)**p)**q, x)","F",0
192,0,0,0,0.000000," ","integrate((a*(b*x**n)**p)**q,x)","\int \left(a \left(b x^{n}\right)^{p}\right)^{q}\, dx"," ",0,"Integral((a*(b*x**n)**p)**q, x)","F",0
193,1,41,0,0.721640," ","integrate((a*(b*x**n)**p)**q/x,x)","\begin{cases} \log{\left(x \right)} & \text{for}\: n = 0 \wedge p = 0 \wedge q = 0 \\a^{q} \log{\left(x \right)} & \text{for}\: p = 0 \\\left(a b^{p}\right)^{q} \log{\left(x \right)} & \text{for}\: n = 0 \\\log{\left(x \right)} & \text{for}\: q = 0 \\\frac{a^{q} \left(b^{p}\right)^{q} \left(\left(x^{n}\right)^{p}\right)^{q}}{n p q} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x), Eq(n, 0) & Eq(p, 0) & Eq(q, 0)), (a**q*log(x), Eq(p, 0)), ((a*b**p)**q*log(x), Eq(n, 0)), (log(x), Eq(q, 0)), (a**q*(b**p)**q*((x**n)**p)**q/(n*p*q), True))","A",0
194,0,0,0,0.000000," ","integrate((a*(b*x**n)**p)**q/x**2,x)","\int \frac{\left(a \left(b x^{n}\right)^{p}\right)^{q}}{x^{2}}\, dx"," ",0,"Integral((a*(b*x**n)**p)**q/x**2, x)","F",0
195,0,0,0,0.000000," ","integrate((a*(b*x**n)**p)**q/x**3,x)","\int \frac{\left(a \left(b x^{n}\right)^{p}\right)^{q}}{x^{3}}\, dx"," ",0,"Integral((a*(b*x**n)**p)**q/x**3, x)","F",0
196,1,248,0,20.009985," ","integrate(x**2/((a*(b*x**m)**n)**(1/m/n)),x)","\begin{cases} - \frac{x^{3}}{0^{m n} \tilde{\infty}^{m n} \left(0^{m n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{\frac{1}{m n}} - 3 \left(0^{m n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{\frac{1}{m n}}} & \text{for}\: a = 0^{m n} \wedge b = \left(0^{m n}\right)^{\frac{1}{n}} \\\frac{a^{- \frac{1}{m n}} x^{3} \left(\left(x^{m}\right)^{n}\right)^{- \frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{- \frac{1}{m n}}}{2} & \text{for}\: b = \left(0^{m n}\right)^{\frac{1}{n}} \\- \frac{x^{3}}{0^{m n} \tilde{\infty}^{m n} \left(0^{m n}\right)^{\frac{1}{m n}} \left(b^{n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}} - 3 \left(0^{m n}\right)^{\frac{1}{m n}} \left(b^{n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}}} & \text{for}\: a = 0^{m n} \\\frac{a^{- \frac{1}{m n}} x^{3} \left(b^{n}\right)^{- \frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{- \frac{1}{m n}}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**3/(0**(m*n)*zoo**(m*n)*(0**(m*n))**(1/(m*n))*((x**m)**n)**(1/(m*n))*(((0**(m*n))**(1/n))**n)**(1/(m*n)) - 3*(0**(m*n))**(1/(m*n))*((x**m)**n)**(1/(m*n))*(((0**(m*n))**(1/n))**n)**(1/(m*n))), Eq(a, 0**(m*n)) & Eq(b, (0**(m*n))**(1/n))), (a**(-1/(m*n))*x**3*((x**m)**n)**(-1/(m*n))*(((0**(m*n))**(1/n))**n)**(-1/(m*n))/2, Eq(b, (0**(m*n))**(1/n))), (-x**3/(0**(m*n)*zoo**(m*n)*(0**(m*n))**(1/(m*n))*(b**n)**(1/(m*n))*((x**m)**n)**(1/(m*n)) - 3*(0**(m*n))**(1/(m*n))*(b**n)**(1/(m*n))*((x**m)**n)**(1/(m*n))), Eq(a, 0**(m*n))), (a**(-1/(m*n))*x**3*(b**n)**(-1/(m*n))*((x**m)**n)**(-1/(m*n))/2, True))","A",0
197,1,245,0,10.351703," ","integrate(x/((a*(b*x**m)**n)**(1/m/n)),x)","\begin{cases} - \frac{x^{2}}{0^{m n} \tilde{\infty}^{m n} \left(0^{m n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{\frac{1}{m n}} - 2 \left(0^{m n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{\frac{1}{m n}}} & \text{for}\: a = 0^{m n} \wedge b = \left(0^{m n}\right)^{\frac{1}{n}} \\a^{- \frac{1}{m n}} x^{2} \left(\left(x^{m}\right)^{n}\right)^{- \frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{- \frac{1}{m n}} & \text{for}\: b = \left(0^{m n}\right)^{\frac{1}{n}} \\- \frac{x^{2}}{0^{m n} \tilde{\infty}^{m n} \left(0^{m n}\right)^{\frac{1}{m n}} \left(b^{n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}} - 2 \left(0^{m n}\right)^{\frac{1}{m n}} \left(b^{n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}}} & \text{for}\: a = 0^{m n} \\a^{- \frac{1}{m n}} x^{2} \left(b^{n}\right)^{- \frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{- \frac{1}{m n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**2/(0**(m*n)*zoo**(m*n)*(0**(m*n))**(1/(m*n))*((x**m)**n)**(1/(m*n))*(((0**(m*n))**(1/n))**n)**(1/(m*n)) - 2*(0**(m*n))**(1/(m*n))*((x**m)**n)**(1/(m*n))*(((0**(m*n))**(1/n))**n)**(1/(m*n))), Eq(a, 0**(m*n)) & Eq(b, (0**(m*n))**(1/n))), (a**(-1/(m*n))*x**2*((x**m)**n)**(-1/(m*n))*(((0**(m*n))**(1/n))**n)**(-1/(m*n)), Eq(b, (0**(m*n))**(1/n))), (-x**2/(0**(m*n)*zoo**(m*n)*(0**(m*n))**(1/(m*n))*(b**n)**(1/(m*n))*((x**m)**n)**(1/(m*n)) - 2*(0**(m*n))**(1/(m*n))*(b**n)**(1/(m*n))*((x**m)**n)**(1/(m*n))), Eq(a, 0**(m*n))), (a**(-1/(m*n))*x**2*(b**n)**(-1/(m*n))*((x**m)**n)**(-1/(m*n)), True))","A",0
198,0,0,0,0.000000," ","integrate(1/((a*(b*x**m)**n)**(1/m/n)),x)","\int \left(a \left(b x^{m}\right)^{n}\right)^{- \frac{1}{m n}}\, dx"," ",0,"Integral((a*(b*x**m)**n)**(-1/(m*n)), x)","F",0
199,1,153,0,5.882958," ","integrate(1/x/((a*(b*x**m)**n)**(1/m/n)),x)","\begin{cases} - \left(0^{m n}\right)^{- \frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{- \frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{- \frac{1}{m n}} & \text{for}\: a = 0^{m n} \wedge b = \left(0^{m n}\right)^{\frac{1}{n}} \\- a^{- \frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{- \frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{- \frac{1}{m n}} & \text{for}\: b = \left(0^{m n}\right)^{\frac{1}{n}} \\- \left(0^{m n}\right)^{- \frac{1}{m n}} \left(b^{n}\right)^{- \frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{- \frac{1}{m n}} & \text{for}\: a = 0^{m n} \\- a^{- \frac{1}{m n}} \left(b^{n}\right)^{- \frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{- \frac{1}{m n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(0**(m*n))**(-1/(m*n))*((x**m)**n)**(-1/(m*n))*(((0**(m*n))**(1/n))**n)**(-1/(m*n)), Eq(a, 0**(m*n)) & Eq(b, (0**(m*n))**(1/n))), (-a**(-1/(m*n))*((x**m)**n)**(-1/(m*n))*(((0**(m*n))**(1/n))**n)**(-1/(m*n)), Eq(b, (0**(m*n))**(1/n))), (-(0**(m*n))**(-1/(m*n))*(b**n)**(-1/(m*n))*((x**m)**n)**(-1/(m*n)), Eq(a, 0**(m*n))), (-a**(-1/(m*n))*(b**n)**(-1/(m*n))*((x**m)**n)**(-1/(m*n)), True))","A",0
200,1,252,0,11.057190," ","integrate(1/x**2/((a*(b*x**m)**n)**(1/m/n)),x)","\begin{cases} - \frac{1}{0^{m n} \tilde{\infty}^{m n} x \left(0^{m n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{\frac{1}{m n}} + x \left(0^{m n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{\frac{1}{m n}}} & \text{for}\: a = 0^{m n} \wedge b = \left(0^{m n}\right)^{\frac{1}{n}} \\- \frac{a^{- \frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{- \frac{1}{m n}} \left(\left(\left(0^{m n}\right)^{\frac{1}{n}}\right)^{n}\right)^{- \frac{1}{m n}}}{2 x} & \text{for}\: b = \left(0^{m n}\right)^{\frac{1}{n}} \\- \frac{1}{0^{m n} \tilde{\infty}^{m n} x \left(0^{m n}\right)^{\frac{1}{m n}} \left(b^{n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}} + x \left(0^{m n}\right)^{\frac{1}{m n}} \left(b^{n}\right)^{\frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{\frac{1}{m n}}} & \text{for}\: a = 0^{m n} \\- \frac{a^{- \frac{1}{m n}} \left(b^{n}\right)^{- \frac{1}{m n}} \left(\left(x^{m}\right)^{n}\right)^{- \frac{1}{m n}}}{2 x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(0**(m*n)*zoo**(m*n)*x*(0**(m*n))**(1/(m*n))*((x**m)**n)**(1/(m*n))*(((0**(m*n))**(1/n))**n)**(1/(m*n)) + x*(0**(m*n))**(1/(m*n))*((x**m)**n)**(1/(m*n))*(((0**(m*n))**(1/n))**n)**(1/(m*n))), Eq(a, 0**(m*n)) & Eq(b, (0**(m*n))**(1/n))), (-a**(-1/(m*n))*((x**m)**n)**(-1/(m*n))*(((0**(m*n))**(1/n))**n)**(-1/(m*n))/(2*x), Eq(b, (0**(m*n))**(1/n))), (-1/(0**(m*n)*zoo**(m*n)*x*(0**(m*n))**(1/(m*n))*(b**n)**(1/(m*n))*((x**m)**n)**(1/(m*n)) + x*(0**(m*n))**(1/(m*n))*(b**n)**(1/(m*n))*((x**m)**n)**(1/(m*n))), Eq(a, 0**(m*n))), (-a**(-1/(m*n))*(b**n)**(-1/(m*n))*((x**m)**n)**(-1/(m*n))/(2*x), True))","A",0
201,0,0,0,0.000000," ","integrate(x**(-n*p*q+2)*(a*(b*x**n)**p)**q,x)","\int x^{- n p q + 2} \left(a \left(b x^{n}\right)^{p}\right)^{q}\, dx"," ",0,"Integral(x**(-n*p*q + 2)*(a*(b*x**n)**p)**q, x)","F",0
202,0,0,0,0.000000," ","integrate(x**(-n*p*q+1)*(a*(b*x**n)**p)**q,x)","\int x^{- n p q + 1} \left(a \left(b x^{n}\right)^{p}\right)^{q}\, dx"," ",0,"Integral(x**(-n*p*q + 1)*(a*(b*x**n)**p)**q, x)","F",0
203,1,22,0,2.632737," ","integrate((a*(b*x**n)**p)**q/(x**(n*p*q)),x)","a^{q} x x^{- n p q} \left(b^{p}\right)^{q} \left(\left(x^{n}\right)^{p}\right)^{q}"," ",0,"a**q*x*x**(-n*p*q)*(b**p)**q*((x**n)**p)**q","A",0
204,0,0,0,0.000000," ","integrate(x**(-n*p*q-1)*(a*(b*x**n)**p)**q,x)","\int x^{- n p q - 1} \left(a \left(b x^{n}\right)^{p}\right)^{q}\, dx"," ",0,"Integral(x**(-n*p*q - 1)*(a*(b*x**n)**p)**q, x)","F",0
205,1,24,0,93.319354," ","integrate(x**(-n*p*q-2)*(a*(b*x**n)**p)**q,x)","- \frac{a^{q} x^{- n p q} \left(b^{p}\right)^{q} \left(\left(x^{n}\right)^{p}\right)^{q}}{x}"," ",0,"-a**q*x**(-n*p*q)*(b**p)**q*((x**n)**p)**q/x","A",0
206,1,12,0,0.071897," ","integrate(x**3*(b*x**3+a),x)","\frac{a x^{4}}{4} + \frac{b x^{7}}{7}"," ",0,"a*x**4/4 + b*x**7/7","A",0
207,1,12,0,0.064330," ","integrate(x**2*(b*x**3+a),x)","\frac{a x^{3}}{3} + \frac{b x^{6}}{6}"," ",0,"a*x**3/3 + b*x**6/6","A",0
208,1,12,0,0.077718," ","integrate(x*(b*x**3+a),x)","\frac{a x^{2}}{2} + \frac{b x^{5}}{5}"," ",0,"a*x**2/2 + b*x**5/5","A",0
209,1,8,0,0.089453," ","integrate(b*x**3+a,x)","a x + \frac{b x^{4}}{4}"," ",0,"a*x + b*x**4/4","A",0
210,1,10,0,0.139107," ","integrate((b*x**3+a)/x,x)","a \log{\left(x \right)} + \frac{b x^{3}}{3}"," ",0,"a*log(x) + b*x**3/3","A",0
211,1,8,0,0.091600," ","integrate((b*x**3+a)/x**2,x)","- \frac{a}{x} + \frac{b x^{2}}{2}"," ",0,"-a/x + b*x**2/2","A",0
212,1,8,0,0.096327," ","integrate((b*x**3+a)/x**3,x)","- \frac{a}{2 x^{2}} + b x"," ",0,"-a/(2*x**2) + b*x","A",0
213,1,10,0,0.139048," ","integrate((b*x**3+a)/x**4,x)","- \frac{a}{3 x^{3}} + b \log{\left(x \right)}"," ",0,"-a/(3*x**3) + b*log(x)","A",0
214,1,14,0,0.155783," ","integrate((b*x**3+a)/x**5,x)","\frac{- a - 4 b x^{3}}{4 x^{4}}"," ",0,"(-a - 4*b*x**3)/(4*x**4)","A",0
215,1,15,0,0.173014," ","integrate((b*x**3+a)/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
216,1,14,0,0.155747," ","integrate((b*x**3+a)/x**7,x)","\frac{- a - 2 b x^{3}}{6 x^{6}}"," ",0,"(-a - 2*b*x**3)/(6*x**6)","A",0
217,1,15,0,0.158546," ","integrate((b*x**3+a)/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
218,1,24,0,0.074121," ","integrate(x**4*(b*x**3+a)**2,x)","\frac{a^{2} x^{5}}{5} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{11}}{11}"," ",0,"a**2*x**5/5 + a*b*x**8/4 + b**2*x**11/11","A",0
219,1,26,0,0.079013," ","integrate(x**3*(b*x**3+a)**2,x)","\frac{a^{2} x^{4}}{4} + \frac{2 a b x^{7}}{7} + \frac{b^{2} x^{10}}{10}"," ",0,"a**2*x**4/4 + 2*a*b*x**7/7 + b**2*x**10/10","A",0
220,1,24,0,0.078278," ","integrate(x**2*(b*x**3+a)**2,x)","\frac{a^{2} x^{3}}{3} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{9}}{9}"," ",0,"a**2*x**3/3 + a*b*x**6/3 + b**2*x**9/9","B",0
221,1,26,0,0.086455," ","integrate(x*(b*x**3+a)**2,x)","\frac{a^{2} x^{2}}{2} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{8}}{8}"," ",0,"a**2*x**2/2 + 2*a*b*x**5/5 + b**2*x**8/8","A",0
222,1,20,0,0.084847," ","integrate((b*x**3+a)**2,x)","a^{2} x + \frac{a b x^{4}}{2} + \frac{b^{2} x^{7}}{7}"," ",0,"a**2*x + a*b*x**4/2 + b**2*x**7/7","A",0
223,1,24,0,0.118629," ","integrate((b*x**3+a)**2/x,x)","a^{2} \log{\left(x \right)} + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{6}}{6}"," ",0,"a**2*log(x) + 2*a*b*x**3/3 + b**2*x**6/6","A",0
224,1,19,0,0.115243," ","integrate((b*x**3+a)**2/x**2,x)","- \frac{a^{2}}{x} + a b x^{2} + \frac{b^{2} x^{5}}{5}"," ",0,"-a**2/x + a*b*x**2 + b**2*x**5/5","A",0
225,1,22,0,0.110197," ","integrate((b*x**3+a)**2/x**3,x)","- \frac{a^{2}}{2 x^{2}} + 2 a b x + \frac{b^{2} x^{4}}{4}"," ",0,"-a**2/(2*x**2) + 2*a*b*x + b**2*x**4/4","A",0
226,1,24,0,0.214908," ","integrate((b*x**3+a)**2/x**4,x)","- \frac{a^{2}}{3 x^{3}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{3}}{3}"," ",0,"-a**2/(3*x**3) + 2*a*b*log(x) + b**2*x**3/3","A",0
227,1,26,0,0.179132," ","integrate((b*x**3+a)**2/x**5,x)","\frac{b^{2} x^{2}}{2} + \frac{- a^{2} - 8 a b x^{3}}{4 x^{4}}"," ",0,"b**2*x**2/2 + (-a**2 - 8*a*b*x**3)/(4*x**4)","A",0
228,1,22,0,0.178987," ","integrate((b*x**3+a)**2/x**6,x)","b^{2} x + \frac{- a^{2} - 5 a b x^{3}}{5 x^{5}}"," ",0,"b**2*x + (-a**2 - 5*a*b*x**3)/(5*x**5)","A",0
229,1,24,0,0.250435," ","integrate((b*x**3+a)**2/x**7,x)","b^{2} \log{\left(x \right)} + \frac{- a^{2} - 4 a b x^{3}}{6 x^{6}}"," ",0,"b**2*log(x) + (-a**2 - 4*a*b*x**3)/(6*x**6)","A",0
230,1,27,0,0.223328," ","integrate((b*x**3+a)**2/x**8,x)","\frac{- 2 a^{2} - 7 a b x^{3} - 14 b^{2} x^{6}}{14 x^{7}}"," ",0,"(-2*a**2 - 7*a*b*x**3 - 14*b**2*x**6)/(14*x**7)","A",0
231,1,27,0,0.232971," ","integrate((b*x**3+a)**2/x**9,x)","\frac{- 5 a^{2} - 16 a b x^{3} - 20 b^{2} x^{6}}{40 x^{8}}"," ",0,"(-5*a**2 - 16*a*b*x**3 - 20*b**2*x**6)/(40*x**8)","A",0
232,1,26,0,0.267578," ","integrate((b*x**3+a)**2/x**10,x)","\frac{- a^{2} - 3 a b x^{3} - 3 b^{2} x^{6}}{9 x^{9}}"," ",0,"(-a**2 - 3*a*b*x**3 - 3*b**2*x**6)/(9*x**9)","A",0
233,1,27,0,0.276356," ","integrate((b*x**3+a)**2/x**11,x)","\frac{- 14 a^{2} - 40 a b x^{3} - 35 b^{2} x^{6}}{140 x^{10}}"," ",0,"(-14*a**2 - 40*a*b*x**3 - 35*b**2*x**6)/(140*x**10)","A",0
234,1,27,0,0.274229," ","integrate((b*x**3+a)**2/x**12,x)","\frac{- 20 a^{2} - 55 a b x^{3} - 44 b^{2} x^{6}}{220 x^{11}}"," ",0,"(-20*a**2 - 55*a*b*x**3 - 44*b**2*x**6)/(220*x**11)","A",0
235,1,27,0,0.282396," ","integrate((b*x**3+a)**2/x**13,x)","\frac{- 3 a^{2} - 8 a b x^{3} - 6 b^{2} x^{6}}{36 x^{12}}"," ",0,"(-3*a**2 - 8*a*b*x**3 - 6*b**2*x**6)/(36*x**12)","A",0
236,1,36,0,0.073304," ","integrate(x**14*(b*x**3+a)**3,x)","\frac{a^{3} x^{15}}{15} + \frac{a^{2} b x^{18}}{6} + \frac{a b^{2} x^{21}}{7} + \frac{b^{3} x^{24}}{24}"," ",0,"a**3*x**15/15 + a**2*b*x**18/6 + a*b**2*x**21/7 + b**3*x**24/24","A",0
237,1,36,0,0.074406," ","integrate(x**11*(b*x**3+a)**3,x)","\frac{a^{3} x^{12}}{12} + \frac{a^{2} b x^{15}}{5} + \frac{a b^{2} x^{18}}{6} + \frac{b^{3} x^{21}}{21}"," ",0,"a**3*x**12/12 + a**2*b*x**15/5 + a*b**2*x**18/6 + b**3*x**21/21","A",0
238,1,36,0,0.079623," ","integrate(x**8*(b*x**3+a)**3,x)","\frac{a^{3} x^{9}}{9} + \frac{a^{2} b x^{12}}{4} + \frac{a b^{2} x^{15}}{5} + \frac{b^{3} x^{18}}{18}"," ",0,"a**3*x**9/9 + a**2*b*x**12/4 + a*b**2*x**15/5 + b**3*x**18/18","A",0
239,1,36,0,0.085418," ","integrate(x**5*(b*x**3+a)**3,x)","\frac{a^{3} x^{6}}{6} + \frac{a^{2} b x^{9}}{3} + \frac{a b^{2} x^{12}}{4} + \frac{b^{3} x^{15}}{15}"," ",0,"a**3*x**6/6 + a**2*b*x**9/3 + a*b**2*x**12/4 + b**3*x**15/15","A",0
240,1,36,0,0.077130," ","integrate(x**2*(b*x**3+a)**3,x)","\frac{a^{3} x^{3}}{3} + \frac{a^{2} b x^{6}}{2} + \frac{a b^{2} x^{9}}{3} + \frac{b^{3} x^{12}}{12}"," ",0,"a**3*x**3/3 + a**2*b*x**6/2 + a*b**2*x**9/3 + b**3*x**12/12","B",0
241,1,32,0,0.132540," ","integrate((b*x**3+a)**3/x,x)","a^{3} \log{\left(x \right)} + a^{2} b x^{3} + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{9}}{9}"," ",0,"a**3*log(x) + a**2*b*x**3 + a*b**2*x**6/2 + b**3*x**9/9","A",0
242,1,34,0,0.170773," ","integrate((b*x**3+a)**3/x**4,x)","- \frac{a^{3}}{3 x^{3}} + 3 a^{2} b \log{\left(x \right)} + a b^{2} x^{3} + \frac{b^{3} x^{6}}{6}"," ",0,"-a**3/(3*x**3) + 3*a**2*b*log(x) + a*b**2*x**3 + b**3*x**6/6","A",0
243,1,37,0,0.247934," ","integrate((b*x**3+a)**3/x**7,x)","3 a b^{2} \log{\left(x \right)} + \frac{b^{3} x^{3}}{3} + \frac{- a^{3} - 6 a^{2} b x^{3}}{6 x^{6}}"," ",0,"3*a*b**2*log(x) + b**3*x**3/3 + (-a**3 - 6*a**2*b*x**3)/(6*x**6)","A",0
244,1,37,0,0.323580," ","integrate((b*x**3+a)**3/x**10,x)","b^{3} \log{\left(x \right)} + \frac{- 2 a^{3} - 9 a^{2} b x^{3} - 18 a b^{2} x^{6}}{18 x^{9}}"," ",0,"b**3*log(x) + (-2*a**3 - 9*a**2*b*x**3 - 18*a*b**2*x**6)/(18*x**9)","A",0
245,1,37,0,0.380354," ","integrate((b*x**3+a)**3/x**13,x)","\frac{- a^{3} - 4 a^{2} b x^{3} - 6 a b^{2} x^{6} - 4 b^{3} x^{9}}{12 x^{12}}"," ",0,"(-a**3 - 4*a**2*b*x**3 - 6*a*b**2*x**6 - 4*b**3*x**9)/(12*x**12)","B",0
246,1,39,0,0.505350," ","integrate((b*x**3+a)**3/x**16,x)","\frac{- 4 a^{3} - 15 a^{2} b x^{3} - 20 a b^{2} x^{6} - 10 b^{3} x^{9}}{60 x^{15}}"," ",0,"(-4*a**3 - 15*a**2*b*x**3 - 20*a*b**2*x**6 - 10*b**3*x**9)/(60*x**15)","A",0
247,1,39,0,0.570682," ","integrate((b*x**3+a)**3/x**19,x)","\frac{- 10 a^{3} - 36 a^{2} b x^{3} - 45 a b^{2} x^{6} - 20 b^{3} x^{9}}{180 x^{18}}"," ",0,"(-10*a**3 - 36*a**2*b*x**3 - 45*a*b**2*x**6 - 20*b**3*x**9)/(180*x**18)","A",0
248,1,39,0,0.486642," ","integrate((b*x**3+a)**3/x**22,x)","\frac{- 20 a^{3} - 70 a^{2} b x^{3} - 84 a b^{2} x^{6} - 35 b^{3} x^{9}}{420 x^{21}}"," ",0,"(-20*a**3 - 70*a**2*b*x**3 - 84*a*b**2*x**6 - 35*b**3*x**9)/(420*x**21)","A",0
249,1,39,0,0.130072," ","integrate(x**4*(b*x**3+a)**3,x)","\frac{a^{3} x^{5}}{5} + \frac{3 a^{2} b x^{8}}{8} + \frac{3 a b^{2} x^{11}}{11} + \frac{b^{3} x^{14}}{14}"," ",0,"a**3*x**5/5 + 3*a**2*b*x**8/8 + 3*a*b**2*x**11/11 + b**3*x**14/14","A",0
250,1,39,0,0.082649," ","integrate(x**3*(b*x**3+a)**3,x)","\frac{a^{3} x^{4}}{4} + \frac{3 a^{2} b x^{7}}{7} + \frac{3 a b^{2} x^{10}}{10} + \frac{b^{3} x^{13}}{13}"," ",0,"a**3*x**4/4 + 3*a**2*b*x**7/7 + 3*a*b**2*x**10/10 + b**3*x**13/13","A",0
251,1,39,0,0.071658," ","integrate(x*(b*x**3+a)**3,x)","\frac{a^{3} x^{2}}{2} + \frac{3 a^{2} b x^{5}}{5} + \frac{3 a b^{2} x^{8}}{8} + \frac{b^{3} x^{11}}{11}"," ",0,"a**3*x**2/2 + 3*a**2*b*x**5/5 + 3*a*b**2*x**8/8 + b**3*x**11/11","A",0
252,1,36,0,0.075504," ","integrate((b*x**3+a)**3,x)","a^{3} x + \frac{3 a^{2} b x^{4}}{4} + \frac{3 a b^{2} x^{7}}{7} + \frac{b^{3} x^{10}}{10}"," ",0,"a**3*x + 3*a**2*b*x**4/4 + 3*a*b**2*x**7/7 + b**3*x**10/10","A",0
253,1,36,0,0.124506," ","integrate((b*x**3+a)**3/x**2,x)","- \frac{a^{3}}{x} + \frac{3 a^{2} b x^{2}}{2} + \frac{3 a b^{2} x^{5}}{5} + \frac{b^{3} x^{8}}{8}"," ",0,"-a**3/x + 3*a**2*b*x**2/2 + 3*a*b**2*x**5/5 + b**3*x**8/8","A",0
254,1,36,0,0.148405," ","integrate((b*x**3+a)**3/x**3,x)","- \frac{a^{3}}{2 x^{2}} + 3 a^{2} b x + \frac{3 a b^{2} x^{4}}{4} + \frac{b^{3} x^{7}}{7}"," ",0,"-a**3/(2*x**2) + 3*a**2*b*x + 3*a*b**2*x**4/4 + b**3*x**7/7","A",0
255,1,39,0,0.194201," ","integrate((b*x**3+a)**3/x**5,x)","\frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} x^{5}}{5} + \frac{- a^{3} - 12 a^{2} b x^{3}}{4 x^{4}}"," ",0,"3*a*b**2*x**2/2 + b**3*x**5/5 + (-a**3 - 12*a**2*b*x**3)/(4*x**4)","A",0
256,1,37,0,0.201549," ","integrate((b*x**3+a)**3/x**6,x)","3 a b^{2} x + \frac{b^{3} x^{4}}{4} + \frac{- 2 a^{3} - 15 a^{2} b x^{3}}{10 x^{5}}"," ",0,"3*a*b**2*x + b**3*x**4/4 + (-2*a**3 - 15*a**2*b*x**3)/(10*x**5)","A",0
257,1,39,0,0.276484," ","integrate((b*x**3+a)**3/x**8,x)","\frac{b^{3} x^{2}}{2} + \frac{- 4 a^{3} - 21 a^{2} b x^{3} - 84 a b^{2} x^{6}}{28 x^{7}}"," ",0,"b**3*x**2/2 + (-4*a**3 - 21*a**2*b*x**3 - 84*a*b**2*x**6)/(28*x**7)","A",0
258,1,65,0,0.094783," ","integrate(x**17*(b*x**3+a)**5,x)","\frac{a^{5} x^{18}}{18} + \frac{5 a^{4} b x^{21}}{21} + \frac{5 a^{3} b^{2} x^{24}}{12} + \frac{10 a^{2} b^{3} x^{27}}{27} + \frac{a b^{4} x^{30}}{6} + \frac{b^{5} x^{33}}{33}"," ",0,"a**5*x**18/18 + 5*a**4*b*x**21/21 + 5*a**3*b**2*x**24/12 + 10*a**2*b**3*x**27/27 + a*b**4*x**30/6 + b**5*x**33/33","A",0
259,1,66,0,0.095350," ","integrate(x**14*(b*x**3+a)**5,x)","\frac{a^{5} x^{15}}{15} + \frac{5 a^{4} b x^{18}}{18} + \frac{10 a^{3} b^{2} x^{21}}{21} + \frac{5 a^{2} b^{3} x^{24}}{12} + \frac{5 a b^{4} x^{27}}{27} + \frac{b^{5} x^{30}}{30}"," ",0,"a**5*x**15/15 + 5*a**4*b*x**18/18 + 10*a**3*b**2*x**21/21 + 5*a**2*b**3*x**24/12 + 5*a*b**4*x**27/27 + b**5*x**30/30","A",0
260,1,65,0,0.082653," ","integrate(x**11*(b*x**3+a)**5,x)","\frac{a^{5} x^{12}}{12} + \frac{a^{4} b x^{15}}{3} + \frac{5 a^{3} b^{2} x^{18}}{9} + \frac{10 a^{2} b^{3} x^{21}}{21} + \frac{5 a b^{4} x^{24}}{24} + \frac{b^{5} x^{27}}{27}"," ",0,"a**5*x**12/12 + a**4*b*x**15/3 + 5*a**3*b**2*x**18/9 + 10*a**2*b**3*x**21/21 + 5*a*b**4*x**24/24 + b**5*x**27/27","A",0
261,1,66,0,0.083263," ","integrate(x**8*(b*x**3+a)**5,x)","\frac{a^{5} x^{9}}{9} + \frac{5 a^{4} b x^{12}}{12} + \frac{2 a^{3} b^{2} x^{15}}{3} + \frac{5 a^{2} b^{3} x^{18}}{9} + \frac{5 a b^{4} x^{21}}{21} + \frac{b^{5} x^{24}}{24}"," ",0,"a**5*x**9/9 + 5*a**4*b*x**12/12 + 2*a**3*b**2*x**15/3 + 5*a**2*b**3*x**18/9 + 5*a*b**4*x**21/21 + b**5*x**24/24","A",0
262,1,66,0,0.093302," ","integrate(x**5*(b*x**3+a)**5,x)","\frac{a^{5} x^{6}}{6} + \frac{5 a^{4} b x^{9}}{9} + \frac{5 a^{3} b^{2} x^{12}}{6} + \frac{2 a^{2} b^{3} x^{15}}{3} + \frac{5 a b^{4} x^{18}}{18} + \frac{b^{5} x^{21}}{21}"," ",0,"a**5*x**6/6 + 5*a**4*b*x**9/9 + 5*a**3*b**2*x**12/6 + 2*a**2*b**3*x**15/3 + 5*a*b**4*x**18/18 + b**5*x**21/21","B",0
263,1,65,0,0.091970," ","integrate(x**2*(b*x**3+a)**5,x)","\frac{a^{5} x^{3}}{3} + \frac{5 a^{4} b x^{6}}{6} + \frac{10 a^{3} b^{2} x^{9}}{9} + \frac{5 a^{2} b^{3} x^{12}}{6} + \frac{a b^{4} x^{15}}{3} + \frac{b^{5} x^{18}}{18}"," ",0,"a**5*x**3/3 + 5*a**4*b*x**6/6 + 10*a**3*b**2*x**9/9 + 5*a**2*b**3*x**12/6 + a*b**4*x**15/3 + b**5*x**18/18","B",0
264,1,65,0,0.162948," ","integrate((b*x**3+a)**5/x,x)","a^{5} \log{\left(x \right)} + \frac{5 a^{4} b x^{3}}{3} + \frac{5 a^{3} b^{2} x^{6}}{3} + \frac{10 a^{2} b^{3} x^{9}}{9} + \frac{5 a b^{4} x^{12}}{12} + \frac{b^{5} x^{15}}{15}"," ",0,"a**5*log(x) + 5*a**4*b*x**3/3 + 5*a**3*b**2*x**6/3 + 10*a**2*b**3*x**9/9 + 5*a*b**4*x**12/12 + b**5*x**15/15","A",0
265,1,65,0,0.217490," ","integrate((b*x**3+a)**5/x**4,x)","- \frac{a^{5}}{3 x^{3}} + 5 a^{4} b \log{\left(x \right)} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{6}}{3} + \frac{5 a b^{4} x^{9}}{9} + \frac{b^{5} x^{12}}{12}"," ",0,"-a**5/(3*x**3) + 5*a**4*b*log(x) + 10*a**3*b**2*x**3/3 + 5*a**2*b**3*x**6/3 + 5*a*b**4*x**9/9 + b**5*x**12/12","A",0
266,1,65,0,0.331542," ","integrate((b*x**3+a)**5/x**7,x)","10 a^{3} b^{2} \log{\left(x \right)} + \frac{10 a^{2} b^{3} x^{3}}{3} + \frac{5 a b^{4} x^{6}}{6} + \frac{b^{5} x^{9}}{9} + \frac{- a^{5} - 10 a^{4} b x^{3}}{6 x^{6}}"," ",0,"10*a**3*b**2*log(x) + 10*a**2*b**3*x**3/3 + 5*a*b**4*x**6/6 + b**5*x**9/9 + (-a**5 - 10*a**4*b*x**3)/(6*x**6)","A",0
267,1,65,0,0.407113," ","integrate((b*x**3+a)**5/x**10,x)","10 a^{2} b^{3} \log{\left(x \right)} + \frac{5 a b^{4} x^{3}}{3} + \frac{b^{5} x^{6}}{6} + \frac{- 2 a^{5} - 15 a^{4} b x^{3} - 60 a^{3} b^{2} x^{6}}{18 x^{9}}"," ",0,"10*a**2*b**3*log(x) + 5*a*b**4*x**3/3 + b**5*x**6/6 + (-2*a**5 - 15*a**4*b*x**3 - 60*a**3*b**2*x**6)/(18*x**9)","A",0
268,1,63,0,0.566393," ","integrate((b*x**3+a)**5/x**13,x)","5 a b^{4} \log{\left(x \right)} + \frac{b^{5} x^{3}}{3} + \frac{- 3 a^{5} - 20 a^{4} b x^{3} - 60 a^{3} b^{2} x^{6} - 120 a^{2} b^{3} x^{9}}{36 x^{12}}"," ",0,"5*a*b**4*log(x) + b**5*x**3/3 + (-3*a**5 - 20*a**4*b*x**3 - 60*a**3*b**2*x**6 - 120*a**2*b**3*x**9)/(36*x**12)","A",0
269,1,61,0,0.677113," ","integrate((b*x**3+a)**5/x**16,x)","b^{5} \log{\left(x \right)} + \frac{- 12 a^{5} - 75 a^{4} b x^{3} - 200 a^{3} b^{2} x^{6} - 300 a^{2} b^{3} x^{9} - 300 a b^{4} x^{12}}{180 x^{15}}"," ",0,"b**5*log(x) + (-12*a**5 - 75*a**4*b*x**3 - 200*a**3*b**2*x**6 - 300*a**2*b**3*x**9 - 300*a*b**4*x**12)/(180*x**15)","A",0
270,1,61,0,0.761116," ","integrate((b*x**3+a)**5/x**19,x)","\frac{- a^{5} - 6 a^{4} b x^{3} - 15 a^{3} b^{2} x^{6} - 20 a^{2} b^{3} x^{9} - 15 a b^{4} x^{12} - 6 b^{5} x^{15}}{18 x^{18}}"," ",0,"(-a**5 - 6*a**4*b*x**3 - 15*a**3*b**2*x**6 - 20*a**2*b**3*x**9 - 15*a*b**4*x**12 - 6*b**5*x**15)/(18*x**18)","B",0
271,1,63,0,0.733472," ","integrate((b*x**3+a)**5/x**22,x)","\frac{- 6 a^{5} - 35 a^{4} b x^{3} - 84 a^{3} b^{2} x^{6} - 105 a^{2} b^{3} x^{9} - 70 a b^{4} x^{12} - 21 b^{5} x^{15}}{126 x^{21}}"," ",0,"(-6*a**5 - 35*a**4*b*x**3 - 84*a**3*b**2*x**6 - 105*a**2*b**3*x**9 - 70*a*b**4*x**12 - 21*b**5*x**15)/(126*x**21)","A",0
272,1,63,0,0.880280," ","integrate((b*x**3+a)**5/x**25,x)","\frac{- 21 a^{5} - 120 a^{4} b x^{3} - 280 a^{3} b^{2} x^{6} - 336 a^{2} b^{3} x^{9} - 210 a b^{4} x^{12} - 56 b^{5} x^{15}}{504 x^{24}}"," ",0,"(-21*a**5 - 120*a**4*b*x**3 - 280*a**3*b**2*x**6 - 336*a**2*b**3*x**9 - 210*a*b**4*x**12 - 56*b**5*x**15)/(504*x**24)","A",0
273,1,63,0,0.786574," ","integrate((b*x**3+a)**5/x**28,x)","\frac{- 56 a^{5} - 315 a^{4} b x^{3} - 720 a^{3} b^{2} x^{6} - 840 a^{2} b^{3} x^{9} - 504 a b^{4} x^{12} - 126 b^{5} x^{15}}{1512 x^{27}}"," ",0,"(-56*a**5 - 315*a**4*b*x**3 - 720*a**3*b**2*x**6 - 840*a**2*b**3*x**9 - 504*a*b**4*x**12 - 126*b**5*x**15)/(1512*x**27)","A",0
274,1,63,0,0.995506," ","integrate((b*x**3+a)**5/x**31,x)","\frac{- 126 a^{5} - 700 a^{4} b x^{3} - 1575 a^{3} b^{2} x^{6} - 1800 a^{2} b^{3} x^{9} - 1050 a b^{4} x^{12} - 252 b^{5} x^{15}}{3780 x^{30}}"," ",0,"(-126*a**5 - 700*a**4*b*x**3 - 1575*a**3*b**2*x**6 - 1800*a**2*b**3*x**9 - 1050*a*b**4*x**12 - 252*b**5*x**15)/(3780*x**30)","A",0
275,1,66,0,0.097198," ","integrate(x**4*(b*x**3+a)**5,x)","\frac{a^{5} x^{5}}{5} + \frac{5 a^{4} b x^{8}}{8} + \frac{10 a^{3} b^{2} x^{11}}{11} + \frac{5 a^{2} b^{3} x^{14}}{7} + \frac{5 a b^{4} x^{17}}{17} + \frac{b^{5} x^{20}}{20}"," ",0,"a**5*x**5/5 + 5*a**4*b*x**8/8 + 10*a**3*b**2*x**11/11 + 5*a**2*b**3*x**14/7 + 5*a*b**4*x**17/17 + b**5*x**20/20","A",0
276,1,63,0,0.090677," ","integrate(x**3*(b*x**3+a)**5,x)","\frac{a^{5} x^{4}}{4} + \frac{5 a^{4} b x^{7}}{7} + a^{3} b^{2} x^{10} + \frac{10 a^{2} b^{3} x^{13}}{13} + \frac{5 a b^{4} x^{16}}{16} + \frac{b^{5} x^{19}}{19}"," ",0,"a**5*x**4/4 + 5*a**4*b*x**7/7 + a**3*b**2*x**10 + 10*a**2*b**3*x**13/13 + 5*a*b**4*x**16/16 + b**5*x**19/19","A",0
277,1,63,0,0.086376," ","integrate(x*(b*x**3+a)**5,x)","\frac{a^{5} x^{2}}{2} + a^{4} b x^{5} + \frac{5 a^{3} b^{2} x^{8}}{4} + \frac{10 a^{2} b^{3} x^{11}}{11} + \frac{5 a b^{4} x^{14}}{14} + \frac{b^{5} x^{17}}{17}"," ",0,"a**5*x**2/2 + a**4*b*x**5 + 5*a**3*b**2*x**8/4 + 10*a**2*b**3*x**11/11 + 5*a*b**4*x**14/14 + b**5*x**17/17","A",0
278,1,60,0,0.106467," ","integrate((b*x**3+a)**5,x)","a^{5} x + \frac{5 a^{4} b x^{4}}{4} + \frac{10 a^{3} b^{2} x^{7}}{7} + a^{2} b^{3} x^{10} + \frac{5 a b^{4} x^{13}}{13} + \frac{b^{5} x^{16}}{16}"," ",0,"a**5*x + 5*a**4*b*x**4/4 + 10*a**3*b**2*x**7/7 + a**2*b**3*x**10 + 5*a*b**4*x**13/13 + b**5*x**16/16","A",0
279,1,61,0,0.146290," ","integrate((b*x**3+a)**5/x**2,x)","- \frac{a^{5}}{x} + \frac{5 a^{4} b x^{2}}{2} + 2 a^{3} b^{2} x^{5} + \frac{5 a^{2} b^{3} x^{8}}{4} + \frac{5 a b^{4} x^{11}}{11} + \frac{b^{5} x^{14}}{14}"," ",0,"-a**5/x + 5*a**4*b*x**2/2 + 2*a**3*b**2*x**5 + 5*a**2*b**3*x**8/4 + 5*a*b**4*x**11/11 + b**5*x**14/14","A",0
280,1,61,0,0.161790," ","integrate((b*x**3+a)**5/x**3,x)","- \frac{a^{5}}{2 x^{2}} + 5 a^{4} b x + \frac{5 a^{3} b^{2} x^{4}}{2} + \frac{10 a^{2} b^{3} x^{7}}{7} + \frac{a b^{4} x^{10}}{2} + \frac{b^{5} x^{13}}{13}"," ",0,"-a**5/(2*x**2) + 5*a**4*b*x + 5*a**3*b**2*x**4/2 + 10*a**2*b**3*x**7/7 + a*b**4*x**10/2 + b**5*x**13/13","A",0
281,1,63,0,0.212640," ","integrate((b*x**3+a)**5/x**5,x)","5 a^{3} b^{2} x^{2} + 2 a^{2} b^{3} x^{5} + \frac{5 a b^{4} x^{8}}{8} + \frac{b^{5} x^{11}}{11} + \frac{- a^{5} - 20 a^{4} b x^{3}}{4 x^{4}}"," ",0,"5*a**3*b**2*x**2 + 2*a**2*b**3*x**5 + 5*a*b**4*x**8/8 + b**5*x**11/11 + (-a**5 - 20*a**4*b*x**3)/(4*x**4)","A",0
282,1,65,0,0.256396," ","integrate((b*x**3+a)**5/x**6,x)","10 a^{3} b^{2} x + \frac{5 a^{2} b^{3} x^{4}}{2} + \frac{5 a b^{4} x^{7}}{7} + \frac{b^{5} x^{10}}{10} + \frac{- 2 a^{5} - 25 a^{4} b x^{3}}{10 x^{5}}"," ",0,"10*a**3*b**2*x + 5*a**2*b**3*x**4/2 + 5*a*b**4*x**7/7 + b**5*x**10/10 + (-2*a**5 - 25*a**4*b*x**3)/(10*x**5)","A",0
283,1,61,0,0.283825," ","integrate((b*x**3+a)**5/x**8,x)","5 a^{2} b^{3} x^{2} + a b^{4} x^{5} + \frac{b^{5} x^{8}}{8} + \frac{- 4 a^{5} - 35 a^{4} b x^{3} - 280 a^{3} b^{2} x^{6}}{28 x^{7}}"," ",0,"5*a**2*b**3*x**2 + a*b**4*x**5 + b**5*x**8/8 + (-4*a**5 - 35*a**4*b*x**3 - 280*a**3*b**2*x**6)/(28*x**7)","A",0
284,1,61,0,0.294147," ","integrate((b*x**3+a)**5/x**9,x)","10 a^{2} b^{3} x + \frac{5 a b^{4} x^{4}}{4} + \frac{b^{5} x^{7}}{7} + \frac{- a^{5} - 8 a^{4} b x^{3} - 40 a^{3} b^{2} x^{6}}{8 x^{8}}"," ",0,"10*a**2*b**3*x + 5*a*b**4*x**4/4 + b**5*x**7/7 + (-a**5 - 8*a**4*b*x**3 - 40*a**3*b**2*x**6)/(8*x**8)","A",0
285,1,105,0,0.109109," ","integrate(x**20*(b*x**3+a)**8,x)","\frac{a^{8} x^{21}}{21} + \frac{a^{7} b x^{24}}{3} + \frac{28 a^{6} b^{2} x^{27}}{27} + \frac{28 a^{5} b^{3} x^{30}}{15} + \frac{70 a^{4} b^{4} x^{33}}{33} + \frac{14 a^{3} b^{5} x^{36}}{9} + \frac{28 a^{2} b^{6} x^{39}}{39} + \frac{4 a b^{7} x^{42}}{21} + \frac{b^{8} x^{45}}{45}"," ",0,"a**8*x**21/21 + a**7*b*x**24/3 + 28*a**6*b**2*x**27/27 + 28*a**5*b**3*x**30/15 + 70*a**4*b**4*x**33/33 + 14*a**3*b**5*x**36/9 + 28*a**2*b**6*x**39/39 + 4*a*b**7*x**42/21 + b**8*x**45/45","A",0
286,1,107,0,0.114249," ","integrate(x**17*(b*x**3+a)**8,x)","\frac{a^{8} x^{18}}{18} + \frac{8 a^{7} b x^{21}}{21} + \frac{7 a^{6} b^{2} x^{24}}{6} + \frac{56 a^{5} b^{3} x^{27}}{27} + \frac{7 a^{4} b^{4} x^{30}}{3} + \frac{56 a^{3} b^{5} x^{33}}{33} + \frac{7 a^{2} b^{6} x^{36}}{9} + \frac{8 a b^{7} x^{39}}{39} + \frac{b^{8} x^{42}}{42}"," ",0,"a**8*x**18/18 + 8*a**7*b*x**21/21 + 7*a**6*b**2*x**24/6 + 56*a**5*b**3*x**27/27 + 7*a**4*b**4*x**30/3 + 56*a**3*b**5*x**33/33 + 7*a**2*b**6*x**36/9 + 8*a*b**7*x**39/39 + b**8*x**42/42","A",0
287,1,107,0,0.107355," ","integrate(x**14*(b*x**3+a)**8,x)","\frac{a^{8} x^{15}}{15} + \frac{4 a^{7} b x^{18}}{9} + \frac{4 a^{6} b^{2} x^{21}}{3} + \frac{7 a^{5} b^{3} x^{24}}{3} + \frac{70 a^{4} b^{4} x^{27}}{27} + \frac{28 a^{3} b^{5} x^{30}}{15} + \frac{28 a^{2} b^{6} x^{33}}{33} + \frac{2 a b^{7} x^{36}}{9} + \frac{b^{8} x^{39}}{39}"," ",0,"a**8*x**15/15 + 4*a**7*b*x**18/9 + 4*a**6*b**2*x**21/3 + 7*a**5*b**3*x**24/3 + 70*a**4*b**4*x**27/27 + 28*a**3*b**5*x**30/15 + 28*a**2*b**6*x**33/33 + 2*a*b**7*x**36/9 + b**8*x**39/39","A",0
288,1,107,0,0.158741," ","integrate(x**11*(b*x**3+a)**8,x)","\frac{a^{8} x^{12}}{12} + \frac{8 a^{7} b x^{15}}{15} + \frac{14 a^{6} b^{2} x^{18}}{9} + \frac{8 a^{5} b^{3} x^{21}}{3} + \frac{35 a^{4} b^{4} x^{24}}{12} + \frac{56 a^{3} b^{5} x^{27}}{27} + \frac{14 a^{2} b^{6} x^{30}}{15} + \frac{8 a b^{7} x^{33}}{33} + \frac{b^{8} x^{36}}{36}"," ",0,"a**8*x**12/12 + 8*a**7*b*x**15/15 + 14*a**6*b**2*x**18/9 + 8*a**5*b**3*x**21/3 + 35*a**4*b**4*x**24/12 + 56*a**3*b**5*x**27/27 + 14*a**2*b**6*x**30/15 + 8*a*b**7*x**33/33 + b**8*x**36/36","A",0
289,1,107,0,0.105972," ","integrate(x**8*(b*x**3+a)**8,x)","\frac{a^{8} x^{9}}{9} + \frac{2 a^{7} b x^{12}}{3} + \frac{28 a^{6} b^{2} x^{15}}{15} + \frac{28 a^{5} b^{3} x^{18}}{9} + \frac{10 a^{4} b^{4} x^{21}}{3} + \frac{7 a^{3} b^{5} x^{24}}{3} + \frac{28 a^{2} b^{6} x^{27}}{27} + \frac{4 a b^{7} x^{30}}{15} + \frac{b^{8} x^{33}}{33}"," ",0,"a**8*x**9/9 + 2*a**7*b*x**12/3 + 28*a**6*b**2*x**15/15 + 28*a**5*b**3*x**18/9 + 10*a**4*b**4*x**21/3 + 7*a**3*b**5*x**24/3 + 28*a**2*b**6*x**27/27 + 4*a*b**7*x**30/15 + b**8*x**33/33","B",0
290,1,107,0,0.109276," ","integrate(x**5*(b*x**3+a)**8,x)","\frac{a^{8} x^{6}}{6} + \frac{8 a^{7} b x^{9}}{9} + \frac{7 a^{6} b^{2} x^{12}}{3} + \frac{56 a^{5} b^{3} x^{15}}{15} + \frac{35 a^{4} b^{4} x^{18}}{9} + \frac{8 a^{3} b^{5} x^{21}}{3} + \frac{7 a^{2} b^{6} x^{24}}{6} + \frac{8 a b^{7} x^{27}}{27} + \frac{b^{8} x^{30}}{30}"," ",0,"a**8*x**6/6 + 8*a**7*b*x**9/9 + 7*a**6*b**2*x**12/3 + 56*a**5*b**3*x**15/15 + 35*a**4*b**4*x**18/9 + 8*a**3*b**5*x**21/3 + 7*a**2*b**6*x**24/6 + 8*a*b**7*x**27/27 + b**8*x**30/30","B",0
291,1,105,0,0.094437," ","integrate(x**2*(b*x**3+a)**8,x)","\frac{a^{8} x^{3}}{3} + \frac{4 a^{7} b x^{6}}{3} + \frac{28 a^{6} b^{2} x^{9}}{9} + \frac{14 a^{5} b^{3} x^{12}}{3} + \frac{14 a^{4} b^{4} x^{15}}{3} + \frac{28 a^{3} b^{5} x^{18}}{9} + \frac{4 a^{2} b^{6} x^{21}}{3} + \frac{a b^{7} x^{24}}{3} + \frac{b^{8} x^{27}}{27}"," ",0,"a**8*x**3/3 + 4*a**7*b*x**6/3 + 28*a**6*b**2*x**9/9 + 14*a**5*b**3*x**12/3 + 14*a**4*b**4*x**15/3 + 28*a**3*b**5*x**18/9 + 4*a**2*b**6*x**21/3 + a*b**7*x**24/3 + b**8*x**27/27","B",0
292,1,105,0,0.202107," ","integrate((b*x**3+a)**8/x,x)","a^{8} \log{\left(x \right)} + \frac{8 a^{7} b x^{3}}{3} + \frac{14 a^{6} b^{2} x^{6}}{3} + \frac{56 a^{5} b^{3} x^{9}}{9} + \frac{35 a^{4} b^{4} x^{12}}{6} + \frac{56 a^{3} b^{5} x^{15}}{15} + \frac{14 a^{2} b^{6} x^{18}}{9} + \frac{8 a b^{7} x^{21}}{21} + \frac{b^{8} x^{24}}{24}"," ",0,"a**8*log(x) + 8*a**7*b*x**3/3 + 14*a**6*b**2*x**6/3 + 56*a**5*b**3*x**9/9 + 35*a**4*b**4*x**12/6 + 56*a**3*b**5*x**15/15 + 14*a**2*b**6*x**18/9 + 8*a*b**7*x**21/21 + b**8*x**24/24","A",0
293,1,105,0,0.299658," ","integrate((b*x**3+a)**8/x**4,x)","- \frac{a^{8}}{3 x^{3}} + 8 a^{7} b \log{\left(x \right)} + \frac{28 a^{6} b^{2} x^{3}}{3} + \frac{28 a^{5} b^{3} x^{6}}{3} + \frac{70 a^{4} b^{4} x^{9}}{9} + \frac{14 a^{3} b^{5} x^{12}}{3} + \frac{28 a^{2} b^{6} x^{15}}{15} + \frac{4 a b^{7} x^{18}}{9} + \frac{b^{8} x^{21}}{21}"," ",0,"-a**8/(3*x**3) + 8*a**7*b*log(x) + 28*a**6*b**2*x**3/3 + 28*a**5*b**3*x**6/3 + 70*a**4*b**4*x**9/9 + 14*a**3*b**5*x**12/3 + 28*a**2*b**6*x**15/15 + 4*a*b**7*x**18/9 + b**8*x**21/21","A",0
294,1,105,0,0.373211," ","integrate((b*x**3+a)**8/x**7,x)","28 a^{6} b^{2} \log{\left(x \right)} + \frac{56 a^{5} b^{3} x^{3}}{3} + \frac{35 a^{4} b^{4} x^{6}}{3} + \frac{56 a^{3} b^{5} x^{9}}{9} + \frac{7 a^{2} b^{6} x^{12}}{3} + \frac{8 a b^{7} x^{15}}{15} + \frac{b^{8} x^{18}}{18} + \frac{- a^{8} - 16 a^{7} b x^{3}}{6 x^{6}}"," ",0,"28*a**6*b**2*log(x) + 56*a**5*b**3*x**3/3 + 35*a**4*b**4*x**6/3 + 56*a**3*b**5*x**9/9 + 7*a**2*b**6*x**12/3 + 8*a*b**7*x**15/15 + b**8*x**18/18 + (-a**8 - 16*a**7*b*x**3)/(6*x**6)","A",0
295,1,104,0,0.474648," ","integrate((b*x**3+a)**8/x**10,x)","56 a^{5} b^{3} \log{\left(x \right)} + \frac{70 a^{4} b^{4} x^{3}}{3} + \frac{28 a^{3} b^{5} x^{6}}{3} + \frac{28 a^{2} b^{6} x^{9}}{9} + \frac{2 a b^{7} x^{12}}{3} + \frac{b^{8} x^{15}}{15} + \frac{- a^{8} - 12 a^{7} b x^{3} - 84 a^{6} b^{2} x^{6}}{9 x^{9}}"," ",0,"56*a**5*b**3*log(x) + 70*a**4*b**4*x**3/3 + 28*a**3*b**5*x**6/3 + 28*a**2*b**6*x**9/9 + 2*a*b**7*x**12/3 + b**8*x**15/15 + (-a**8 - 12*a**7*b*x**3 - 84*a**6*b**2*x**6)/(9*x**9)","A",0
296,1,104,0,0.542227," ","integrate((b*x**3+a)**8/x**13,x)","70 a^{4} b^{4} \log{\left(x \right)} + \frac{56 a^{3} b^{5} x^{3}}{3} + \frac{14 a^{2} b^{6} x^{6}}{3} + \frac{8 a b^{7} x^{9}}{9} + \frac{b^{8} x^{12}}{12} + \frac{- 3 a^{8} - 32 a^{7} b x^{3} - 168 a^{6} b^{2} x^{6} - 672 a^{5} b^{3} x^{9}}{36 x^{12}}"," ",0,"70*a**4*b**4*log(x) + 56*a**3*b**5*x**3/3 + 14*a**2*b**6*x**6/3 + 8*a*b**7*x**9/9 + b**8*x**12/12 + (-3*a**8 - 32*a**7*b*x**3 - 168*a**6*b**2*x**6 - 672*a**5*b**3*x**9)/(36*x**12)","A",0
297,1,102,0,0.808460," ","integrate((b*x**3+a)**8/x**16,x)","56 a^{3} b^{5} \log{\left(x \right)} + \frac{28 a^{2} b^{6} x^{3}}{3} + \frac{4 a b^{7} x^{6}}{3} + \frac{b^{8} x^{9}}{9} + \frac{- 3 a^{8} - 30 a^{7} b x^{3} - 140 a^{6} b^{2} x^{6} - 420 a^{5} b^{3} x^{9} - 1050 a^{4} b^{4} x^{12}}{45 x^{15}}"," ",0,"56*a**3*b**5*log(x) + 28*a**2*b**6*x**3/3 + 4*a*b**7*x**6/3 + b**8*x**9/9 + (-3*a**8 - 30*a**7*b*x**3 - 140*a**6*b**2*x**6 - 420*a**5*b**3*x**9 - 1050*a**4*b**4*x**12)/(45*x**15)","A",0
298,1,100,0,0.825268," ","integrate((b*x**3+a)**8/x**19,x)","28 a^{2} b^{6} \log{\left(x \right)} + \frac{8 a b^{7} x^{3}}{3} + \frac{b^{8} x^{6}}{6} + \frac{- 5 a^{8} - 48 a^{7} b x^{3} - 210 a^{6} b^{2} x^{6} - 560 a^{5} b^{3} x^{9} - 1050 a^{4} b^{4} x^{12} - 1680 a^{3} b^{5} x^{15}}{90 x^{18}}"," ",0,"28*a**2*b**6*log(x) + 8*a*b**7*x**3/3 + b**8*x**6/6 + (-5*a**8 - 48*a**7*b*x**3 - 210*a**6*b**2*x**6 - 560*a**5*b**3*x**9 - 1050*a**4*b**4*x**12 - 1680*a**3*b**5*x**15)/(90*x**18)","A",0
299,1,99,0,1.178691," ","integrate((b*x**3+a)**8/x**22,x)","8 a b^{7} \log{\left(x \right)} + \frac{b^{8} x^{3}}{3} + \frac{- 15 a^{8} - 140 a^{7} b x^{3} - 588 a^{6} b^{2} x^{6} - 1470 a^{5} b^{3} x^{9} - 2450 a^{4} b^{4} x^{12} - 2940 a^{3} b^{5} x^{15} - 2940 a^{2} b^{6} x^{18}}{315 x^{21}}"," ",0,"8*a*b**7*log(x) + b**8*x**3/3 + (-15*a**8 - 140*a**7*b*x**3 - 588*a**6*b**2*x**6 - 1470*a**5*b**3*x**9 - 2450*a**4*b**4*x**12 - 2940*a**3*b**5*x**15 - 2940*a**2*b**6*x**18)/(315*x**21)","A",0
300,1,97,0,1.204532," ","integrate((b*x**3+a)**8/x**25,x)","b^{8} \log{\left(x \right)} + \frac{- 105 a^{8} - 960 a^{7} b x^{3} - 3920 a^{6} b^{2} x^{6} - 9408 a^{5} b^{3} x^{9} - 14700 a^{4} b^{4} x^{12} - 15680 a^{3} b^{5} x^{15} - 11760 a^{2} b^{6} x^{18} - 6720 a b^{7} x^{21}}{2520 x^{24}}"," ",0,"b**8*log(x) + (-105*a**8 - 960*a**7*b*x**3 - 3920*a**6*b**2*x**6 - 9408*a**5*b**3*x**9 - 14700*a**4*b**4*x**12 - 15680*a**3*b**5*x**15 - 11760*a**2*b**6*x**18 - 6720*a*b**7*x**21)/(2520*x**24)","A",0
301,1,97,0,2.455262," ","integrate((b*x**3+a)**8/x**28,x)","\frac{- a^{8} - 9 a^{7} b x^{3} - 36 a^{6} b^{2} x^{6} - 84 a^{5} b^{3} x^{9} - 126 a^{4} b^{4} x^{12} - 126 a^{3} b^{5} x^{15} - 84 a^{2} b^{6} x^{18} - 36 a b^{7} x^{21} - 9 b^{8} x^{24}}{27 x^{27}}"," ",0,"(-a**8 - 9*a**7*b*x**3 - 36*a**6*b**2*x**6 - 84*a**5*b**3*x**9 - 126*a**4*b**4*x**12 - 126*a**3*b**5*x**15 - 84*a**2*b**6*x**18 - 36*a*b**7*x**21 - 9*b**8*x**24)/(27*x**27)","B",0
302,1,99,0,1.364915," ","integrate((b*x**3+a)**8/x**31,x)","\frac{- 9 a^{8} - 80 a^{7} b x^{3} - 315 a^{6} b^{2} x^{6} - 720 a^{5} b^{3} x^{9} - 1050 a^{4} b^{4} x^{12} - 1008 a^{3} b^{5} x^{15} - 630 a^{2} b^{6} x^{18} - 240 a b^{7} x^{21} - 45 b^{8} x^{24}}{270 x^{30}}"," ",0,"(-9*a**8 - 80*a**7*b*x**3 - 315*a**6*b**2*x**6 - 720*a**5*b**3*x**9 - 1050*a**4*b**4*x**12 - 1008*a**3*b**5*x**15 - 630*a**2*b**6*x**18 - 240*a*b**7*x**21 - 45*b**8*x**24)/(270*x**30)","B",0
303,1,99,0,1.552722," ","integrate((b*x**3+a)**8/x**34,x)","\frac{- 45 a^{8} - 396 a^{7} b x^{3} - 1540 a^{6} b^{2} x^{6} - 3465 a^{5} b^{3} x^{9} - 4950 a^{4} b^{4} x^{12} - 4620 a^{3} b^{5} x^{15} - 2772 a^{2} b^{6} x^{18} - 990 a b^{7} x^{21} - 165 b^{8} x^{24}}{1485 x^{33}}"," ",0,"(-45*a**8 - 396*a**7*b*x**3 - 1540*a**6*b**2*x**6 - 3465*a**5*b**3*x**9 - 4950*a**4*b**4*x**12 - 4620*a**3*b**5*x**15 - 2772*a**2*b**6*x**18 - 990*a*b**7*x**21 - 165*b**8*x**24)/(1485*x**33)","A",0
304,1,99,0,1.492081," ","integrate((b*x**3+a)**8/x**37,x)","\frac{- 165 a^{8} - 1440 a^{7} b x^{3} - 5544 a^{6} b^{2} x^{6} - 12320 a^{5} b^{3} x^{9} - 17325 a^{4} b^{4} x^{12} - 15840 a^{3} b^{5} x^{15} - 9240 a^{2} b^{6} x^{18} - 3168 a b^{7} x^{21} - 495 b^{8} x^{24}}{5940 x^{36}}"," ",0,"(-165*a**8 - 1440*a**7*b*x**3 - 5544*a**6*b**2*x**6 - 12320*a**5*b**3*x**9 - 17325*a**4*b**4*x**12 - 15840*a**3*b**5*x**15 - 9240*a**2*b**6*x**18 - 3168*a*b**7*x**21 - 495*b**8*x**24)/(5940*x**36)","A",0
305,1,99,0,2.958760," ","integrate((b*x**3+a)**8/x**40,x)","\frac{- 495 a^{8} - 4290 a^{7} b x^{3} - 16380 a^{6} b^{2} x^{6} - 36036 a^{5} b^{3} x^{9} - 50050 a^{4} b^{4} x^{12} - 45045 a^{3} b^{5} x^{15} - 25740 a^{2} b^{6} x^{18} - 8580 a b^{7} x^{21} - 1287 b^{8} x^{24}}{19305 x^{39}}"," ",0,"(-495*a**8 - 4290*a**7*b*x**3 - 16380*a**6*b**2*x**6 - 36036*a**5*b**3*x**9 - 50050*a**4*b**4*x**12 - 45045*a**3*b**5*x**15 - 25740*a**2*b**6*x**18 - 8580*a*b**7*x**21 - 1287*b**8*x**24)/(19305*x**39)","A",0
306,1,99,0,3.016026," ","integrate((b*x**3+a)**8/x**43,x)","\frac{- 1287 a^{8} - 11088 a^{7} b x^{3} - 42042 a^{6} b^{2} x^{6} - 91728 a^{5} b^{3} x^{9} - 126126 a^{4} b^{4} x^{12} - 112112 a^{3} b^{5} x^{15} - 63063 a^{2} b^{6} x^{18} - 20592 a b^{7} x^{21} - 3003 b^{8} x^{24}}{54054 x^{42}}"," ",0,"(-1287*a**8 - 11088*a**7*b*x**3 - 42042*a**6*b**2*x**6 - 91728*a**5*b**3*x**9 - 126126*a**4*b**4*x**12 - 112112*a**3*b**5*x**15 - 63063*a**2*b**6*x**18 - 20592*a*b**7*x**21 - 3003*b**8*x**24)/(54054*x**42)","A",0
307,1,99,0,1.917272," ","integrate((b*x**3+a)**8/x**46,x)","\frac{- 3003 a^{8} - 25740 a^{7} b x^{3} - 97020 a^{6} b^{2} x^{6} - 210210 a^{5} b^{3} x^{9} - 286650 a^{4} b^{4} x^{12} - 252252 a^{3} b^{5} x^{15} - 140140 a^{2} b^{6} x^{18} - 45045 a b^{7} x^{21} - 6435 b^{8} x^{24}}{135135 x^{45}}"," ",0,"(-3003*a**8 - 25740*a**7*b*x**3 - 97020*a**6*b**2*x**6 - 210210*a**5*b**3*x**9 - 286650*a**4*b**4*x**12 - 252252*a**3*b**5*x**15 - 140140*a**2*b**6*x**18 - 45045*a*b**7*x**21 - 6435*b**8*x**24)/(135135*x**45)","A",0
308,1,102,0,0.105270," ","integrate(x**4*(b*x**3+a)**8,x)","\frac{a^{8} x^{5}}{5} + a^{7} b x^{8} + \frac{28 a^{6} b^{2} x^{11}}{11} + 4 a^{5} b^{3} x^{14} + \frac{70 a^{4} b^{4} x^{17}}{17} + \frac{14 a^{3} b^{5} x^{20}}{5} + \frac{28 a^{2} b^{6} x^{23}}{23} + \frac{4 a b^{7} x^{26}}{13} + \frac{b^{8} x^{29}}{29}"," ",0,"a**8*x**5/5 + a**7*b*x**8 + 28*a**6*b**2*x**11/11 + 4*a**5*b**3*x**14 + 70*a**4*b**4*x**17/17 + 14*a**3*b**5*x**20/5 + 28*a**2*b**6*x**23/23 + 4*a*b**7*x**26/13 + b**8*x**29/29","A",0
309,1,107,0,0.101394," ","integrate(x**3*(b*x**3+a)**8,x)","\frac{a^{8} x^{4}}{4} + \frac{8 a^{7} b x^{7}}{7} + \frac{14 a^{6} b^{2} x^{10}}{5} + \frac{56 a^{5} b^{3} x^{13}}{13} + \frac{35 a^{4} b^{4} x^{16}}{8} + \frac{56 a^{3} b^{5} x^{19}}{19} + \frac{14 a^{2} b^{6} x^{22}}{11} + \frac{8 a b^{7} x^{25}}{25} + \frac{b^{8} x^{28}}{28}"," ",0,"a**8*x**4/4 + 8*a**7*b*x**7/7 + 14*a**6*b**2*x**10/5 + 56*a**5*b**3*x**13/13 + 35*a**4*b**4*x**16/8 + 56*a**3*b**5*x**19/19 + 14*a**2*b**6*x**22/11 + 8*a*b**7*x**25/25 + b**8*x**28/28","A",0
310,1,105,0,0.093270," ","integrate(x*(b*x**3+a)**8,x)","\frac{a^{8} x^{2}}{2} + \frac{8 a^{7} b x^{5}}{5} + \frac{7 a^{6} b^{2} x^{8}}{2} + \frac{56 a^{5} b^{3} x^{11}}{11} + 5 a^{4} b^{4} x^{14} + \frac{56 a^{3} b^{5} x^{17}}{17} + \frac{7 a^{2} b^{6} x^{20}}{5} + \frac{8 a b^{7} x^{23}}{23} + \frac{b^{8} x^{26}}{26}"," ",0,"a**8*x**2/2 + 8*a**7*b*x**5/5 + 7*a**6*b**2*x**8/2 + 56*a**5*b**3*x**11/11 + 5*a**4*b**4*x**14 + 56*a**3*b**5*x**17/17 + 7*a**2*b**6*x**20/5 + 8*a*b**7*x**23/23 + b**8*x**26/26","A",0
311,1,100,0,0.092278," ","integrate((b*x**3+a)**8,x)","a^{8} x + 2 a^{7} b x^{4} + 4 a^{6} b^{2} x^{7} + \frac{28 a^{5} b^{3} x^{10}}{5} + \frac{70 a^{4} b^{4} x^{13}}{13} + \frac{7 a^{3} b^{5} x^{16}}{2} + \frac{28 a^{2} b^{6} x^{19}}{19} + \frac{4 a b^{7} x^{22}}{11} + \frac{b^{8} x^{25}}{25}"," ",0,"a**8*x + 2*a**7*b*x**4 + 4*a**6*b**2*x**7 + 28*a**5*b**3*x**10/5 + 70*a**4*b**4*x**13/13 + 7*a**3*b**5*x**16/2 + 28*a**2*b**6*x**19/19 + 4*a*b**7*x**22/11 + b**8*x**25/25","A",0
312,1,99,0,0.206523," ","integrate((b*x**3+a)**8/x**2,x)","- \frac{a^{8}}{x} + 4 a^{7} b x^{2} + \frac{28 a^{6} b^{2} x^{5}}{5} + 7 a^{5} b^{3} x^{8} + \frac{70 a^{4} b^{4} x^{11}}{11} + 4 a^{3} b^{5} x^{14} + \frac{28 a^{2} b^{6} x^{17}}{17} + \frac{2 a b^{7} x^{20}}{5} + \frac{b^{8} x^{23}}{23}"," ",0,"-a**8/x + 4*a**7*b*x**2 + 28*a**6*b**2*x**5/5 + 7*a**5*b**3*x**8 + 70*a**4*b**4*x**11/11 + 4*a**3*b**5*x**14 + 28*a**2*b**6*x**17/17 + 2*a*b**7*x**20/5 + b**8*x**23/23","A",0
313,1,99,0,0.205986," ","integrate((b*x**3+a)**8/x**3,x)","- \frac{a^{8}}{2 x^{2}} + 8 a^{7} b x + 7 a^{6} b^{2} x^{4} + 8 a^{5} b^{3} x^{7} + 7 a^{4} b^{4} x^{10} + \frac{56 a^{3} b^{5} x^{13}}{13} + \frac{7 a^{2} b^{6} x^{16}}{4} + \frac{8 a b^{7} x^{19}}{19} + \frac{b^{8} x^{22}}{22}"," ",0,"-a**8/(2*x**2) + 8*a**7*b*x + 7*a**6*b**2*x**4 + 8*a**5*b**3*x**7 + 7*a**4*b**4*x**10 + 56*a**3*b**5*x**13/13 + 7*a**2*b**6*x**16/4 + 8*a*b**7*x**19/19 + b**8*x**22/22","A",0
314,1,104,0,0.295307," ","integrate((b*x**3+a)**8/x**5,x)","14 a^{6} b^{2} x^{2} + \frac{56 a^{5} b^{3} x^{5}}{5} + \frac{35 a^{4} b^{4} x^{8}}{4} + \frac{56 a^{3} b^{5} x^{11}}{11} + 2 a^{2} b^{6} x^{14} + \frac{8 a b^{7} x^{17}}{17} + \frac{b^{8} x^{20}}{20} + \frac{- a^{8} - 32 a^{7} b x^{3}}{4 x^{4}}"," ",0,"14*a**6*b**2*x**2 + 56*a**5*b**3*x**5/5 + 35*a**4*b**4*x**8/4 + 56*a**3*b**5*x**11/11 + 2*a**2*b**6*x**14 + 8*a*b**7*x**17/17 + b**8*x**20/20 + (-a**8 - 32*a**7*b*x**3)/(4*x**4)","A",0
315,1,99,0,0.279418," ","integrate((b*x**3+a)**8/x**6,x)","28 a^{6} b^{2} x + 14 a^{5} b^{3} x^{4} + 10 a^{4} b^{4} x^{7} + \frac{28 a^{3} b^{5} x^{10}}{5} + \frac{28 a^{2} b^{6} x^{13}}{13} + \frac{a b^{7} x^{16}}{2} + \frac{b^{8} x^{19}}{19} + \frac{- a^{8} - 20 a^{7} b x^{3}}{5 x^{5}}"," ",0,"28*a**6*b**2*x + 14*a**5*b**3*x**4 + 10*a**4*b**4*x**7 + 28*a**3*b**5*x**10/5 + 28*a**2*b**6*x**13/13 + a*b**7*x**16/2 + b**8*x**19/19 + (-a**8 - 20*a**7*b*x**3)/(5*x**5)","A",0
316,1,100,0,0.335151," ","integrate((b*x**3+a)**8/x**8,x)","28 a^{5} b^{3} x^{2} + 14 a^{4} b^{4} x^{5} + 7 a^{3} b^{5} x^{8} + \frac{28 a^{2} b^{6} x^{11}}{11} + \frac{4 a b^{7} x^{14}}{7} + \frac{b^{8} x^{17}}{17} + \frac{- a^{8} - 14 a^{7} b x^{3} - 196 a^{6} b^{2} x^{6}}{7 x^{7}}"," ",0,"28*a**5*b**3*x**2 + 14*a**4*b**4*x**5 + 7*a**3*b**5*x**8 + 28*a**2*b**6*x**11/11 + 4*a*b**7*x**14/7 + b**8*x**17/17 + (-a**8 - 14*a**7*b*x**3 - 196*a**6*b**2*x**6)/(7*x**7)","A",0
317,1,102,0,0.362901," ","integrate((b*x**3+a)**8/x**9,x)","56 a^{5} b^{3} x + \frac{35 a^{4} b^{4} x^{4}}{2} + 8 a^{3} b^{5} x^{7} + \frac{14 a^{2} b^{6} x^{10}}{5} + \frac{8 a b^{7} x^{13}}{13} + \frac{b^{8} x^{16}}{16} + \frac{- 5 a^{8} - 64 a^{7} b x^{3} - 560 a^{6} b^{2} x^{6}}{40 x^{8}}"," ",0,"56*a**5*b**3*x + 35*a**4*b**4*x**4/2 + 8*a**3*b**5*x**7 + 14*a**2*b**6*x**10/5 + 8*a*b**7*x**13/13 + b**8*x**16/16 + (-5*a**8 - 64*a**7*b*x**3 - 560*a**6*b**2*x**6)/(40*x**8)","A",0
318,1,32,0,0.374822," ","integrate(x**8/(b*x**3+a),x)","\frac{a^{2} \log{\left(a + b x^{3} \right)}}{3 b^{3}} - \frac{a x^{3}}{3 b^{2}} + \frac{x^{6}}{6 b}"," ",0,"a**2*log(a + b*x**3)/(3*b**3) - a*x**3/(3*b**2) + x**6/(6*b)","A",0
319,1,20,0,0.197284," ","integrate(x**5/(b*x**3+a),x)","- \frac{a \log{\left(a + b x^{3} \right)}}{3 b^{2}} + \frac{x^{3}}{3 b}"," ",0,"-a*log(a + b*x**3)/(3*b**2) + x**3/(3*b)","A",0
320,1,10,0,0.166993," ","integrate(x**2/(b*x**3+a),x)","\frac{\log{\left(a + b x^{3} \right)}}{3 b}"," ",0,"log(a + b*x**3)/(3*b)","A",0
321,1,15,0,0.291385," ","integrate(1/x/(b*x**3+a),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
322,1,31,0,0.694704," ","integrate(1/x**4/(b*x**3+a),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
323,1,32,0,0.206280," ","integrate(x**4/(b*x**3+a),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
324,1,22,0,0.232633," ","integrate(x**3/(b*x**3+a),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
325,1,24,0,0.153507," ","integrate(x/(b*x**3+a),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
326,1,20,0,0.166732," ","integrate(1/(b*x**3+a),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
327,1,29,0,0.204382," ","integrate(1/x**2/(b*x**3+a),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
328,1,32,0,0.318540," ","integrate(1/x**3/(b*x**3+a),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
329,1,42,0,0.374496," ","integrate(x**8/(b*x**3+a)**2,x)","- \frac{a^{2}}{3 a b^{3} + 3 b^{4} x^{3}} - \frac{2 a \log{\left(a + b x^{3} \right)}}{3 b^{3}} + \frac{x^{3}}{3 b^{2}}"," ",0,"-a**2/(3*a*b**3 + 3*b**4*x**3) - 2*a*log(a + b*x**3)/(3*b**3) + x**3/(3*b**2)","A",0
330,1,29,0,0.325369," ","integrate(x**5/(b*x**3+a)**2,x)","\frac{a}{3 a b^{2} + 3 b^{3} x^{3}} + \frac{\log{\left(a + b x^{3} \right)}}{3 b^{2}}"," ",0,"a/(3*a*b**2 + 3*b**3*x**3) + log(a + b*x**3)/(3*b**2)","A",0
331,1,15,0,0.247574," ","integrate(x**2/(b*x**3+a)**2,x)","- \frac{1}{3 a b + 3 b^{2} x^{3}}"," ",0,"-1/(3*a*b + 3*b**2*x**3)","A",0
332,1,34,0,0.431892," ","integrate(1/x/(b*x**3+a)**2,x)","\frac{1}{3 a^{2} + 3 a b x^{3}} + \frac{\log{\left(x \right)}}{a^{2}} - \frac{\log{\left(\frac{a}{b} + x^{3} \right)}}{3 a^{2}}"," ",0,"1/(3*a**2 + 3*a*b*x**3) + log(x)/a**2 - log(a/b + x**3)/(3*a**2)","A",0
333,1,54,0,0.562672," ","integrate(1/x**4/(b*x**3+a)**2,x)","\frac{- a - 2 b x^{3}}{3 a^{3} x^{3} + 3 a^{2} b x^{6}} - \frac{2 b \log{\left(x \right)}}{a^{3}} + \frac{2 b \log{\left(\frac{a}{b} + x^{3} \right)}}{3 a^{3}}"," ",0,"(-a - 2*b*x**3)/(3*a**3*x**3 + 3*a**2*b*x**6) - 2*b*log(x)/a**3 + 2*b*log(a/b + x**3)/(3*a**3)","A",0
334,1,44,0,0.283022," ","integrate(x**4/(b*x**3+a)**2,x)","- \frac{x^{2}}{3 a b + 3 b^{2} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a b^{5} + 8, \left( t \mapsto t \log{\left(\frac{81 t^{2} a b^{3}}{4} + x \right)} \right)\right)}"," ",0,"-x**2/(3*a*b + 3*b**2*x**3) + RootSum(729*_t**3*a*b**5 + 8, Lambda(_t, _t*log(81*_t**2*a*b**3/4 + x)))","A",0
335,1,39,0,0.283744," ","integrate(x**3/(b*x**3+a)**2,x)","- \frac{x}{3 a b + 3 b^{2} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{2} b^{4} - 1, \left( t \mapsto t \log{\left(9 t a b + x \right)} \right)\right)}"," ",0,"-x/(3*a*b + 3*b**2*x**3) + RootSum(729*_t**3*a**2*b**4 - 1, Lambda(_t, _t*log(9*_t*a*b + x)))","A",0
336,1,44,0,0.286907," ","integrate(x/(b*x**3+a)**2,x)","\frac{x^{2}}{3 a^{2} + 3 a b x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{4} b^{2} + 1, \left( t \mapsto t \log{\left(81 t^{2} a^{3} b + x \right)} \right)\right)}"," ",0,"x**2/(3*a**2 + 3*a*b*x**3) + RootSum(729*_t**3*a**4*b**2 + 1, Lambda(_t, _t*log(81*_t**2*a**3*b + x)))","A",0
337,1,39,0,0.308683," ","integrate(1/(b*x**3+a)**2,x)","\frac{x}{3 a^{2} + 3 a b x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{5} b - 8, \left( t \mapsto t \log{\left(\frac{9 t a^{2}}{2} + x \right)} \right)\right)}"," ",0,"x/(3*a**2 + 3*a*b*x**3) + RootSum(729*_t**3*a**5*b - 8, Lambda(_t, _t*log(9*_t*a**2/2 + x)))","A",0
338,1,56,0,0.380486," ","integrate(1/x**2/(b*x**3+a)**2,x)","\frac{- 3 a - 4 b x^{3}}{3 a^{3} x + 3 a^{2} b x^{4}} + \operatorname{RootSum} {\left(729 t^{3} a^{7} - 64 b, \left( t \mapsto t \log{\left(\frac{81 t^{2} a^{5}}{16 b} + x \right)} \right)\right)}"," ",0,"(-3*a - 4*b*x**3)/(3*a**3*x + 3*a**2*b*x**4) + RootSum(729*_t**3*a**7 - 64*b, Lambda(_t, _t*log(81*_t**2*a**5/(16*b) + x)))","A",0
339,1,58,0,0.456934," ","integrate(1/x**3/(b*x**3+a)**2,x)","\frac{- 3 a - 5 b x^{3}}{6 a^{3} x^{2} + 6 a^{2} b x^{5}} + \operatorname{RootSum} {\left(729 t^{3} a^{8} + 125 b^{2}, \left( t \mapsto t \log{\left(- \frac{9 t a^{3}}{5 b} + x \right)} \right)\right)}"," ",0,"(-3*a - 5*b*x**3)/(6*a**3*x**2 + 6*a**2*b*x**5) + RootSum(729*_t**3*a**8 + 125*b**2, Lambda(_t, _t*log(-9*_t*a**3/(5*b) + x)))","A",0
340,1,65,0,0.525050," ","integrate(x**11/(b*x**3+a)**3,x)","- \frac{a \log{\left(a + b x^{3} \right)}}{b^{4}} + \frac{- 5 a^{3} - 6 a^{2} b x^{3}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} + \frac{x^{3}}{3 b^{3}}"," ",0,"-a*log(a + b*x**3)/b**4 + (-5*a**3 - 6*a**2*b*x**3)/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) + x**3/(3*b**3)","A",0
341,1,53,0,0.456663," ","integrate(x**8/(b*x**3+a)**3,x)","\frac{3 a^{2} + 4 a b x^{3}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} + \frac{\log{\left(a + b x^{3} \right)}}{3 b^{3}}"," ",0,"(3*a**2 + 4*a*b*x**3)/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) + log(a + b*x**3)/(3*b**3)","A",0
342,1,36,0,0.386163," ","integrate(x**5/(b*x**3+a)**3,x)","\frac{- a - 2 b x^{3}}{6 a^{2} b^{2} + 12 a b^{3} x^{3} + 6 b^{4} x^{6}}"," ",0,"(-a - 2*b*x**3)/(6*a**2*b**2 + 12*a*b**3*x**3 + 6*b**4*x**6)","B",0
343,1,27,0,0.319684," ","integrate(x**2/(b*x**3+a)**3,x)","- \frac{1}{6 a^{2} b + 12 a b^{2} x^{3} + 6 b^{3} x^{6}}"," ",0,"-1/(6*a**2*b + 12*a*b**2*x**3 + 6*b**3*x**6)","A",0
344,1,56,0,0.539685," ","integrate(1/x/(b*x**3+a)**3,x)","\frac{3 a + 2 b x^{3}}{6 a^{4} + 12 a^{3} b x^{3} + 6 a^{2} b^{2} x^{6}} + \frac{\log{\left(x \right)}}{a^{3}} - \frac{\log{\left(\frac{a}{b} + x^{3} \right)}}{3 a^{3}}"," ",0,"(3*a + 2*b*x**3)/(6*a**4 + 12*a**3*b*x**3 + 6*a**2*b**2*x**6) + log(x)/a**3 - log(a/b + x**3)/(3*a**3)","A",0
345,1,76,0,0.679304," ","integrate(1/x**4/(b*x**3+a)**3,x)","\frac{- 2 a^{2} - 9 a b x^{3} - 6 b^{2} x^{6}}{6 a^{5} x^{3} + 12 a^{4} b x^{6} + 6 a^{3} b^{2} x^{9}} - \frac{3 b \log{\left(x \right)}}{a^{4}} + \frac{b \log{\left(\frac{a}{b} + x^{3} \right)}}{a^{4}}"," ",0,"(-2*a**2 - 9*a*b*x**3 - 6*b**2*x**6)/(6*a**5*x**3 + 12*a**4*b*x**6 + 6*a**3*b**2*x**9) - 3*b*log(x)/a**4 + b*log(a/b + x**3)/a**4","A",0
346,1,70,0,0.513457," ","integrate(x**7/(b*x**3+a)**3,x)","\frac{- 5 a x^{2} - 8 b x^{5}}{18 a^{2} b^{2} + 36 a b^{3} x^{3} + 18 b^{4} x^{6}} + \operatorname{RootSum} {\left(19683 t^{3} a b^{8} + 125, \left( t \mapsto t \log{\left(\frac{729 t^{2} a b^{5}}{25} + x \right)} \right)\right)}"," ",0,"(-5*a*x**2 - 8*b*x**5)/(18*a**2*b**2 + 36*a*b**3*x**3 + 18*b**4*x**6) + RootSum(19683*_t**3*a*b**8 + 125, Lambda(_t, _t*log(729*_t**2*a*b**5/25 + x)))","A",0
347,1,68,0,0.474328," ","integrate(x**6/(b*x**3+a)**3,x)","\frac{- 4 a x - 7 b x^{4}}{18 a^{2} b^{2} + 36 a b^{3} x^{3} + 18 b^{4} x^{6}} + \operatorname{RootSum} {\left(19683 t^{3} a^{2} b^{7} - 8, \left( t \mapsto t \log{\left(\frac{27 t a b^{2}}{2} + x \right)} \right)\right)}"," ",0,"(-4*a*x - 7*b*x**4)/(18*a**2*b**2 + 36*a*b**3*x**3 + 18*b**4*x**6) + RootSum(19683*_t**3*a**2*b**7 - 8, Lambda(_t, _t*log(27*_t*a*b**2/2 + x)))","A",0
348,1,70,0,0.468044," ","integrate(x**4/(b*x**3+a)**3,x)","\frac{- a x^{2} + 2 b x^{5}}{18 a^{3} b + 36 a^{2} b^{2} x^{3} + 18 a b^{3} x^{6}} + \operatorname{RootSum} {\left(19683 t^{3} a^{4} b^{5} + 1, \left( t \mapsto t \log{\left(729 t^{2} a^{3} b^{3} + x \right)} \right)\right)}"," ",0,"(-a*x**2 + 2*b*x**5)/(18*a**3*b + 36*a**2*b**2*x**3 + 18*a*b**3*x**6) + RootSum(19683*_t**3*a**4*b**5 + 1, Lambda(_t, _t*log(729*_t**2*a**3*b**3 + x)))","A",0
349,1,65,0,0.454310," ","integrate(x**3/(b*x**3+a)**3,x)","\frac{- 2 a x + b x^{4}}{18 a^{3} b + 36 a^{2} b^{2} x^{3} + 18 a b^{3} x^{6}} + \operatorname{RootSum} {\left(19683 t^{3} a^{5} b^{4} - 1, \left( t \mapsto t \log{\left(27 t a^{2} b + x \right)} \right)\right)}"," ",0,"(-2*a*x + b*x**4)/(18*a**3*b + 36*a**2*b**2*x**3 + 18*a*b**3*x**6) + RootSum(19683*_t**3*a**5*b**4 - 1, Lambda(_t, _t*log(27*_t*a**2*b + x)))","A",0
350,1,70,0,0.398625," ","integrate(x/(b*x**3+a)**3,x)","\frac{7 a x^{2} + 4 b x^{5}}{18 a^{4} + 36 a^{3} b x^{3} + 18 a^{2} b^{2} x^{6}} + \operatorname{RootSum} {\left(19683 t^{3} a^{7} b^{2} + 8, \left( t \mapsto t \log{\left(\frac{729 t^{2} a^{5} b}{4} + x \right)} \right)\right)}"," ",0,"(7*a*x**2 + 4*b*x**5)/(18*a**4 + 36*a**3*b*x**3 + 18*a**2*b**2*x**6) + RootSum(19683*_t**3*a**7*b**2 + 8, Lambda(_t, _t*log(729*_t**2*a**5*b/4 + x)))","A",0
351,1,63,0,0.452324," ","integrate(1/(b*x**3+a)**3,x)","\frac{8 a x + 5 b x^{4}}{18 a^{4} + 36 a^{3} b x^{3} + 18 a^{2} b^{2} x^{6}} + \operatorname{RootSum} {\left(19683 t^{3} a^{8} b - 125, \left( t \mapsto t \log{\left(\frac{27 t a^{3}}{5} + x \right)} \right)\right)}"," ",0,"(8*a*x + 5*b*x**4)/(18*a**4 + 36*a**3*b*x**3 + 18*a**2*b**2*x**6) + RootSum(19683*_t**3*a**8*b - 125, Lambda(_t, _t*log(27*_t*a**3/5 + x)))","A",0
352,1,34,0,0.229635," ","integrate(x**8/(-b*x**3+a),x)","- \frac{a^{2} \log{\left(- a + b x^{3} \right)}}{3 b^{3}} - \frac{a x^{3}}{3 b^{2}} - \frac{x^{6}}{6 b}"," ",0,"-a**2*log(-a + b*x**3)/(3*b**3) - a*x**3/(3*b**2) - x**6/(6*b)","A",0
353,1,22,0,0.216497," ","integrate(x**5/(-b*x**3+a),x)","- \frac{a \log{\left(- a + b x^{3} \right)}}{3 b^{2}} - \frac{x^{3}}{3 b}"," ",0,"-a*log(-a + b*x**3)/(3*b**2) - x**3/(3*b)","A",0
354,1,12,0,0.161897," ","integrate(x**2/(-b*x**3+a),x)","- \frac{\log{\left(- a + b x^{3} \right)}}{3 b}"," ",0,"-log(-a + b*x**3)/(3*b)","A",0
355,1,15,0,0.274975," ","integrate(1/x/(-b*x**3+a),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
356,1,31,0,0.425018," ","integrate(1/x**4/(-b*x**3+a),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
357,1,34,0,0.196039," ","integrate(x**4/(-b*x**3+a),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
358,1,24,0,0.241833," ","integrate(x**3/(-b*x**3+a),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
359,1,26,0,0.173426," ","integrate(x/(-b*x**3+a),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
360,1,22,0,0.254526," ","integrate(1/(-b*x**3+a),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
361,1,31,0,0.251813," ","integrate(1/x**2/(-b*x**3+a),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
362,1,34,0,0.589117," ","integrate(1/x**3/(-b*x**3+a),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
363,1,32,0,0.318715," ","integrate(1/(b*x**3+a+1),x)","\operatorname{RootSum} {\left(t^{3} \left(27 a^{2} b + 54 a b + 27 b\right) - 1, \left( t \mapsto t \log{\left(3 t a + 3 t + x \right)} \right)\right)}"," ",0,"RootSum(_t**3*(27*a**2*b + 54*a*b + 27*b) - 1, Lambda(_t, _t*log(3*_t*a + 3*_t + x)))","A",0
364,1,34,0,0.418043," ","integrate(1/(-b*x**3+a+1),x)","- \operatorname{RootSum} {\left(t^{3} \left(27 a^{2} b + 54 a b + 27 b\right) - 1, \left( t \mapsto t \log{\left(- 3 t a - 3 t + x \right)} \right)\right)}"," ",0,"-RootSum(_t**3*(27*a**2*b + 54*a*b + 27*b) - 1, Lambda(_t, _t*log(-3*_t*a - 3*_t + x)))","A",0
365,1,32,0,0.367577," ","integrate(1/(b*x**3+a-1),x)","\operatorname{RootSum} {\left(t^{3} \left(27 a^{2} b - 54 a b + 27 b\right) - 1, \left( t \mapsto t \log{\left(3 t a - 3 t + x \right)} \right)\right)}"," ",0,"RootSum(_t**3*(27*a**2*b - 54*a*b + 27*b) - 1, Lambda(_t, _t*log(3*_t*a - 3*_t + x)))","A",0
366,1,34,0,0.283963," ","integrate(1/(-b*x**3+a-1),x)","- \operatorname{RootSum} {\left(t^{3} \left(27 a^{2} b - 54 a b + 27 b\right) - 1, \left( t \mapsto t \log{\left(- 3 t a + 3 t + x \right)} \right)\right)}"," ",0,"-RootSum(_t**3*(27*a**2*b - 54*a*b + 27*b) - 1, Lambda(_t, _t*log(-3*_t*a + 3*_t + x)))","A",0
367,1,42,0,1.223123," ","integrate(x**(1/2)/(x**3+1),x)","- \frac{2 \operatorname{atan}{\left(\sqrt{x} \right)}}{3} + \frac{2 \operatorname{atan}{\left(2 \sqrt{x} - \sqrt{3} \right)}}{3} + \frac{2 \operatorname{atan}{\left(2 \sqrt{x} + \sqrt{3} \right)}}{3}"," ",0,"-2*atan(sqrt(x))/3 + 2*atan(2*sqrt(x) - sqrt(3))/3 + 2*atan(2*sqrt(x) + sqrt(3))/3","B",0
368,1,114,0,4.984789," ","integrate(x**11*(b*x**3+a)**(1/2),x)","\begin{cases} - \frac{32 a^{4} \sqrt{a + b x^{3}}}{945 b^{4}} + \frac{16 a^{3} x^{3} \sqrt{a + b x^{3}}}{945 b^{3}} - \frac{4 a^{2} x^{6} \sqrt{a + b x^{3}}}{315 b^{2}} + \frac{2 a x^{9} \sqrt{a + b x^{3}}}{189 b} + \frac{2 x^{12} \sqrt{a + b x^{3}}}{27} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*a**4*sqrt(a + b*x**3)/(945*b**4) + 16*a**3*x**3*sqrt(a + b*x**3)/(945*b**3) - 4*a**2*x**6*sqrt(a + b*x**3)/(315*b**2) + 2*a*x**9*sqrt(a + b*x**3)/(189*b) + 2*x**12*sqrt(a + b*x**3)/27, Ne(b, 0)), (sqrt(a)*x**12/12, True))","A",0
369,1,90,0,2.389882," ","integrate(x**8*(b*x**3+a)**(1/2),x)","\begin{cases} \frac{16 a^{3} \sqrt{a + b x^{3}}}{315 b^{3}} - \frac{8 a^{2} x^{3} \sqrt{a + b x^{3}}}{315 b^{2}} + \frac{2 a x^{6} \sqrt{a + b x^{3}}}{105 b} + \frac{2 x^{9} \sqrt{a + b x^{3}}}{21} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{9}}{9} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**3*sqrt(a + b*x**3)/(315*b**3) - 8*a**2*x**3*sqrt(a + b*x**3)/(315*b**2) + 2*a*x**6*sqrt(a + b*x**3)/(105*b) + 2*x**9*sqrt(a + b*x**3)/21, Ne(b, 0)), (sqrt(a)*x**9/9, True))","A",0
370,1,66,0,0.826974," ","integrate(x**5*(b*x**3+a)**(1/2),x)","\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True))","A",0
371,1,42,0,0.221589," ","integrate(x**2*(b*x**3+a)**(1/2),x)","\begin{cases} \frac{2 a \sqrt{a + b x^{3}}}{9 b} + \frac{2 x^{3} \sqrt{a + b x^{3}}}{9} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*sqrt(a + b*x**3)/(9*b) + 2*x**3*sqrt(a + b*x**3)/9, Ne(b, 0)), (sqrt(a)*x**3/3, True))","A",0
372,1,76,0,2.074571," ","integrate((b*x**3+a)**(1/2)/x,x)","- \frac{2 \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{2 a}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 \sqrt{b} x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}}"," ",0,"-2*sqrt(a)*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + 2*a/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*sqrt(b)*x**(3/2)/(3*sqrt(a/(b*x**3) + 1))","B",0
373,1,49,0,2.842302," ","integrate((b*x**3+a)**(1/2)/x**4,x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 \sqrt{a}}"," ",0,"-sqrt(b)*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) - b*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*sqrt(a))","A",0
374,1,100,0,6.010274," ","integrate((b*x**3+a)**(1/2)/x**7,x)","- \frac{a}{6 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{\sqrt{b}}{4 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{\frac{3}{2}}}{12 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{12 a^{\frac{3}{2}}}"," ",0,"-a/(6*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) - sqrt(b)/(4*x**(9/2)*sqrt(a/(b*x**3) + 1)) - b**(3/2)/(12*a*x**(3/2)*sqrt(a/(b*x**3) + 1)) + b**2*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(12*a**(3/2))","A",0
375,1,129,0,7.145424," ","integrate((b*x**3+a)**(1/2)/x**10,x)","- \frac{a}{9 \sqrt{b} x^{\frac{21}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{5 \sqrt{b}}{36 x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{b^{\frac{3}{2}}}{72 a x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{b^{\frac{5}{2}}}{24 a^{2} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{24 a^{\frac{5}{2}}}"," ",0,"-a/(9*sqrt(b)*x**(21/2)*sqrt(a/(b*x**3) + 1)) - 5*sqrt(b)/(36*x**(15/2)*sqrt(a/(b*x**3) + 1)) + b**(3/2)/(72*a*x**(9/2)*sqrt(a/(b*x**3) + 1)) + b**(5/2)/(24*a**2*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b**3*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(24*a**(5/2))","A",0
376,1,39,0,1.074186," ","integrate(x**6*(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"sqrt(a)*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3))","A",0
377,1,39,0,0.937507," ","integrate(x**3*(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"sqrt(a)*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3))","A",0
378,1,37,0,0.871475," ","integrate((b*x**3+a)**(1/2),x)","\frac{\sqrt{a} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"sqrt(a)*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3))","A",0
379,1,42,0,1.539883," ","integrate((b*x**3+a)**(1/2)/x**3,x)","\frac{\sqrt{a} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"sqrt(a)*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3))","A",0
380,1,46,0,1.185788," ","integrate((b*x**3+a)**(1/2)/x**6,x)","\frac{\sqrt{a} \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"sqrt(a)*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3))","A",0
381,1,46,0,1.390474," ","integrate((b*x**3+a)**(1/2)/x**9,x)","\frac{\sqrt{a} \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, - \frac{1}{2} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{8} \Gamma\left(- \frac{5}{3}\right)}"," ",0,"sqrt(a)*gamma(-8/3)*hyper((-8/3, -1/2), (-5/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**8*gamma(-5/3))","A",0
382,1,39,0,2.375176," ","integrate(x**7*(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)}"," ",0,"sqrt(a)*x**8*gamma(8/3)*hyper((-1/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(11/3))","A",0
383,1,39,0,1.236678," ","integrate(x**4*(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)}"," ",0,"sqrt(a)*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3))","A",0
384,1,39,0,1.236411," ","integrate(x*(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"sqrt(a)*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3))","A",0
385,1,41,0,1.699744," ","integrate((b*x**3+a)**(1/2)/x**2,x)","\frac{\sqrt{a} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)}"," ",0,"sqrt(a)*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3))","A",0
386,1,46,0,3.424386," ","integrate((b*x**3+a)**(1/2)/x**5,x)","\frac{\sqrt{a} \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"sqrt(a)*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3))","A",0
387,1,136,0,9.732552," ","integrate(x**11*(b*x**3+a)**(3/2),x)","\begin{cases} - \frac{32 a^{5} \sqrt{a + b x^{3}}}{3465 b^{4}} + \frac{16 a^{4} x^{3} \sqrt{a + b x^{3}}}{3465 b^{3}} - \frac{4 a^{3} x^{6} \sqrt{a + b x^{3}}}{1155 b^{2}} + \frac{2 a^{2} x^{9} \sqrt{a + b x^{3}}}{693 b} + \frac{8 a x^{12} \sqrt{a + b x^{3}}}{99} + \frac{2 b x^{15} \sqrt{a + b x^{3}}}{33} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{2}} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*a**5*sqrt(a + b*x**3)/(3465*b**4) + 16*a**4*x**3*sqrt(a + b*x**3)/(3465*b**3) - 4*a**3*x**6*sqrt(a + b*x**3)/(1155*b**2) + 2*a**2*x**9*sqrt(a + b*x**3)/(693*b) + 8*a*x**12*sqrt(a + b*x**3)/99 + 2*b*x**15*sqrt(a + b*x**3)/33, Ne(b, 0)), (a**(3/2)*x**12/12, True))","A",0
388,1,112,0,4.806810," ","integrate(x**8*(b*x**3+a)**(3/2),x)","\begin{cases} \frac{16 a^{4} \sqrt{a + b x^{3}}}{945 b^{3}} - \frac{8 a^{3} x^{3} \sqrt{a + b x^{3}}}{945 b^{2}} + \frac{2 a^{2} x^{6} \sqrt{a + b x^{3}}}{315 b} + \frac{20 a x^{9} \sqrt{a + b x^{3}}}{189} + \frac{2 b x^{12} \sqrt{a + b x^{3}}}{27} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{2}} x^{9}}{9} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**4*sqrt(a + b*x**3)/(945*b**3) - 8*a**3*x**3*sqrt(a + b*x**3)/(945*b**2) + 2*a**2*x**6*sqrt(a + b*x**3)/(315*b) + 20*a*x**9*sqrt(a + b*x**3)/189 + 2*b*x**12*sqrt(a + b*x**3)/27, Ne(b, 0)), (a**(3/2)*x**9/9, True))","A",0
389,1,88,0,4.020570," ","integrate(x**5*(b*x**3+a)**(3/2),x)","\begin{cases} - \frac{4 a^{3} \sqrt{a + b x^{3}}}{105 b^{2}} + \frac{2 a^{2} x^{3} \sqrt{a + b x^{3}}}{105 b} + \frac{16 a x^{6} \sqrt{a + b x^{3}}}{105} + \frac{2 b x^{9} \sqrt{a + b x^{3}}}{21} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{2}} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**3*sqrt(a + b*x**3)/(105*b**2) + 2*a**2*x**3*sqrt(a + b*x**3)/(105*b) + 16*a*x**6*sqrt(a + b*x**3)/105 + 2*b*x**9*sqrt(a + b*x**3)/21, Ne(b, 0)), (a**(3/2)*x**6/6, True))","A",0
390,1,65,0,1.970721," ","integrate(x**2*(b*x**3+a)**(3/2),x)","\begin{cases} \frac{2 a^{2} \sqrt{a + b x^{3}}}{15 b} + \frac{4 a x^{3} \sqrt{a + b x^{3}}}{15} + \frac{2 b x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{2}} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*sqrt(a + b*x**3)/(15*b) + 4*a*x**3*sqrt(a + b*x**3)/15 + 2*b*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (a**(3/2)*x**3/3, True))","A",0
391,1,83,0,6.240238," ","integrate((b*x**3+a)**(3/2)/x,x)","\frac{8 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{3}}{a}}}{9} + \frac{a^{\frac{3}{2}} \log{\left(\frac{b x^{3}}{a} \right)}}{3} - \frac{2 a^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{b x^{3}}{a}} + 1 \right)}}{3} + \frac{2 \sqrt{a} b x^{3} \sqrt{1 + \frac{b x^{3}}{a}}}{9}"," ",0,"8*a**(3/2)*sqrt(1 + b*x**3/a)/9 + a**(3/2)*log(b*x**3/a)/3 - 2*a**(3/2)*log(sqrt(1 + b*x**3/a) + 1)/3 + 2*sqrt(a)*b*x**3*sqrt(1 + b*x**3/a)/9","A",0
392,1,100,0,5.248567," ","integrate((b*x**3+a)**(3/2)/x**4,x)","- \sqrt{a} b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)} - \frac{a^{2}}{3 \sqrt{b} x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{a \sqrt{b}}{3 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 b^{\frac{3}{2}} x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}}"," ",0,"-sqrt(a)*b*asinh(sqrt(a)/(sqrt(b)*x**(3/2))) - a**2/(3*sqrt(b)*x**(9/2)*sqrt(a/(b*x**3) + 1)) + a*sqrt(b)/(3*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*b**(3/2)*x**(3/2)/(3*sqrt(a/(b*x**3) + 1))","B",0
393,1,78,0,7.535110," ","integrate((b*x**3+a)**(3/2)/x**7,x)","- \frac{a \sqrt{b} \sqrt{\frac{a}{b x^{3}} + 1}}{6 x^{\frac{9}{2}}} - \frac{5 b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}}{12 x^{\frac{3}{2}}} - \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{4 \sqrt{a}}"," ",0,"-a*sqrt(b)*sqrt(a/(b*x**3) + 1)/(6*x**(9/2)) - 5*b**(3/2)*sqrt(a/(b*x**3) + 1)/(12*x**(3/2)) - b**2*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(4*sqrt(a))","A",0
394,1,39,0,1.841763," ","integrate(x**6*(b*x**3+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"a**(3/2)*x**7*gamma(7/3)*hyper((-3/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3))","A",0
395,1,39,0,2.565408," ","integrate(x**3*(b*x**3+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"a**(3/2)*x**4*gamma(4/3)*hyper((-3/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3))","A",0
396,1,37,0,1.328027," ","integrate((b*x**3+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"a**(3/2)*x*gamma(1/3)*hyper((-3/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3))","A",0
397,1,42,0,1.282671," ","integrate((b*x**3+a)**(3/2)/x**3,x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{2}{3} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"a**(3/2)*gamma(-2/3)*hyper((-3/2, -2/3), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3))","A",0
398,1,46,0,1.566714," ","integrate((b*x**3+a)**(3/2)/x**6,x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{3}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"a**(3/2)*gamma(-5/3)*hyper((-5/3, -3/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3))","A",0
399,1,39,0,3.753882," ","integrate(x**7*(b*x**3+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)}"," ",0,"a**(3/2)*x**8*gamma(8/3)*hyper((-3/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(11/3))","A",0
400,1,39,0,1.942685," ","integrate(x**4*(b*x**3+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)}"," ",0,"a**(3/2)*x**5*gamma(5/3)*hyper((-3/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3))","A",0
401,1,39,0,2.348468," ","integrate(x*(b*x**3+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"a**(3/2)*x**2*gamma(2/3)*hyper((-3/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3))","A",0
402,1,41,0,1.368877," ","integrate((b*x**3+a)**(3/2)/x**2,x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)}"," ",0,"a**(3/2)*gamma(-1/3)*hyper((-3/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3))","A",0
403,1,46,0,2.641109," ","integrate((b*x**3+a)**(3/2)/x**5,x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{4}{3} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"a**(3/2)*gamma(-4/3)*hyper((-3/2, -4/3), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3))","A",0
404,1,94,0,3.616903," ","integrate(x**11/(b*x**3+a)**(1/2),x)","\begin{cases} - \frac{32 a^{3} \sqrt{a + b x^{3}}}{105 b^{4}} + \frac{16 a^{2} x^{3} \sqrt{a + b x^{3}}}{105 b^{3}} - \frac{4 a x^{6} \sqrt{a + b x^{3}}}{35 b^{2}} + \frac{2 x^{9} \sqrt{a + b x^{3}}}{21 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*a**3*sqrt(a + b*x**3)/(105*b**4) + 16*a**2*x**3*sqrt(a + b*x**3)/(105*b**3) - 4*a*x**6*sqrt(a + b*x**3)/(35*b**2) + 2*x**9*sqrt(a + b*x**3)/(21*b), Ne(b, 0)), (x**12/(12*sqrt(a)), True))","A",0
405,1,70,0,2.848371," ","integrate(x**8/(b*x**3+a)**(1/2),x)","\begin{cases} \frac{16 a^{2} \sqrt{a + b x^{3}}}{45 b^{3}} - \frac{8 a x^{3} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15 b} & \text{for}\: b \neq 0 \\\frac{x^{9}}{9 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**2*sqrt(a + b*x**3)/(45*b**3) - 8*a*x**3*sqrt(a + b*x**3)/(45*b**2) + 2*x**6*sqrt(a + b*x**3)/(15*b), Ne(b, 0)), (x**9/(9*sqrt(a)), True))","A",0
406,1,46,0,1.728353," ","integrate(x**5/(b*x**3+a)**(1/2),x)","\begin{cases} - \frac{4 a \sqrt{a + b x^{3}}}{9 b^{2}} + \frac{2 x^{3} \sqrt{a + b x^{3}}}{9 b} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a*sqrt(a + b*x**3)/(9*b**2) + 2*x**3*sqrt(a + b*x**3)/(9*b), Ne(b, 0)), (x**6/(6*sqrt(a)), True))","A",0
407,1,24,0,0.844084," ","integrate(x**2/(b*x**3+a)**(1/2),x)","\begin{cases} \frac{2 \sqrt{a + b x^{3}}}{3 b} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(a + b*x**3)/(3*b), Ne(b, 0)), (x**3/(3*sqrt(a)), True))","A",0
408,1,26,0,3.239255," ","integrate(1/x/(b*x**3+a)**(1/2),x)","- \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 \sqrt{a}}"," ",0,"-2*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*sqrt(a))","A",0
409,1,49,0,5.728731," ","integrate(1/x**4/(b*x**3+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{3}} + 1}}{3 a x^{\frac{3}{2}}} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 a^{\frac{3}{2}}}"," ",0,"-sqrt(b)*sqrt(a/(b*x**3) + 1)/(3*a*x**(3/2)) + b*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*a**(3/2))","A",0
410,1,104,0,10.874908," ","integrate(1/x**7/(b*x**3+a)**(1/2),x)","- \frac{1}{6 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{\sqrt{b}}{12 a x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{b^{\frac{3}{2}}}{4 a^{2} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{4 a^{\frac{5}{2}}}"," ",0,"-1/(6*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) + sqrt(b)/(12*a*x**(9/2)*sqrt(a/(b*x**3) + 1)) + b**(3/2)/(4*a**2*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b**2*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(4*a**(5/2))","A",0
411,1,37,0,2.005864," ","integrate(x**6/(b*x**3+a)**(1/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{10}{3}\right)}"," ",0,"x**7*gamma(7/3)*hyper((1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(10/3))","A",0
412,1,37,0,1.450634," ","integrate(x**3/(b*x**3+a)**(1/2),x)","\frac{x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{7}{3}\right)}"," ",0,"x**4*gamma(4/3)*hyper((1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(7/3))","A",0
413,1,36,0,1.643724," ","integrate(1/(b*x**3+a)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3))","A",0
414,1,41,0,1.589620," ","integrate(1/x**3/(b*x**3+a)**(1/2),x)","\frac{\Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"gamma(-2/3)*hyper((-2/3, 1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*x**2*gamma(1/3))","A",0
415,1,44,0,2.592464," ","integrate(1/x**6/(b*x**3+a)**(1/2),x)","\frac{\Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} x^{5} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"gamma(-5/3)*hyper((-5/3, 1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*x**5*gamma(-2/3))","A",0
416,1,37,0,2.309187," ","integrate(x**7/(b*x**3+a)**(1/2),x)","\frac{x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{11}{3}\right)}"," ",0,"x**8*gamma(8/3)*hyper((1/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(11/3))","A",0
417,1,37,0,0.964051," ","integrate(x**4/(b*x**3+a)**(1/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{8}{3}\right)}"," ",0,"x**5*gamma(5/3)*hyper((1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(8/3))","A",0
418,1,37,0,0.970160," ","integrate(x/(b*x**3+a)**(1/2),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3))","A",0
419,1,39,0,1.776161," ","integrate(1/x**2/(b*x**3+a)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} x \Gamma\left(\frac{2}{3}\right)}"," ",0,"gamma(-1/3)*hyper((-1/3, 1/2), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*x*gamma(2/3))","A",0
420,1,44,0,1.429941," ","integrate(1/x**5/(b*x**3+a)**(1/2),x)","\frac{\Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"gamma(-4/3)*hyper((-4/3, 1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*x**4*gamma(-1/3))","A",0
421,1,94,0,4.620254," ","integrate(x**11/(b*x**3+a)**(3/2),x)","\begin{cases} \frac{32 a^{3}}{15 b^{4} \sqrt{a + b x^{3}}} + \frac{16 a^{2} x^{3}}{15 b^{3} \sqrt{a + b x^{3}}} - \frac{4 a x^{6}}{15 b^{2} \sqrt{a + b x^{3}}} + \frac{2 x^{9}}{15 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((32*a**3/(15*b**4*sqrt(a + b*x**3)) + 16*a**2*x**3/(15*b**3*sqrt(a + b*x**3)) - 4*a*x**6/(15*b**2*sqrt(a + b*x**3)) + 2*x**9/(15*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**12/(12*a**(3/2)), True))","A",0
422,1,70,0,4.924478," ","integrate(x**8/(b*x**3+a)**(3/2),x)","\begin{cases} - \frac{16 a^{2}}{9 b^{3} \sqrt{a + b x^{3}}} - \frac{8 a x^{3}}{9 b^{2} \sqrt{a + b x^{3}}} + \frac{2 x^{6}}{9 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{9}}{9 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*a**2/(9*b**3*sqrt(a + b*x**3)) - 8*a*x**3/(9*b**2*sqrt(a + b*x**3)) + 2*x**6/(9*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**9/(9*a**(3/2)), True))","A",0
423,1,46,0,1.157350," ","integrate(x**5/(b*x**3+a)**(3/2),x)","\begin{cases} \frac{4 a}{3 b^{2} \sqrt{a + b x^{3}}} + \frac{2 x^{3}}{3 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a/(3*b**2*sqrt(a + b*x**3)) + 2*x**3/(3*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**6/(6*a**(3/2)), True))","A",0
424,1,26,0,0.671427," ","integrate(x**2/(b*x**3+a)**(3/2),x)","\begin{cases} - \frac{2}{3 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(3*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**3/(3*a**(3/2)), True))","A",0
425,1,184,0,2.529744," ","integrate(1/x/(b*x**3+a)**(3/2),x)","\frac{2 a^{3} \sqrt{1 + \frac{b x^{3}}{a}}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} + \frac{a^{3} \log{\left(\frac{b x^{3}}{a} \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{3}}{a}} + 1 \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} + \frac{a^{2} b x^{3} \log{\left(\frac{b x^{3}}{a} \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} - \frac{2 a^{2} b x^{3} \log{\left(\sqrt{1 + \frac{b x^{3}}{a}} + 1 \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}}"," ",0,"2*a**3*sqrt(1 + b*x**3/a)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) + a**3*log(b*x**3/a)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) - 2*a**3*log(sqrt(1 + b*x**3/a) + 1)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) + a**2*b*x**3*log(b*x**3/a)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) - 2*a**2*b*x**3*log(sqrt(1 + b*x**3/a) + 1)/(3*a**(9/2) + 3*a**(7/2)*b*x**3)","B",0
426,1,75,0,4.175558," ","integrate(1/x**4/(b*x**3+a)**(3/2),x)","- \frac{1}{3 a \sqrt{b} x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{\sqrt{b}}{a^{2} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{a^{\frac{5}{2}}}"," ",0,"-1/(3*a*sqrt(b)*x**(9/2)*sqrt(a/(b*x**3) + 1)) - sqrt(b)/(a**2*x**(3/2)*sqrt(a/(b*x**3) + 1)) + b*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/a**(5/2)","A",0
427,1,112,0,7.235536," ","integrate(1/x**7/(b*x**3+a)**(3/2),x)","- \frac{1}{6 a \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{5 \sqrt{b}}{12 a^{2} x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{5 b^{\frac{3}{2}}}{4 a^{3} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{5 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{4 a^{\frac{7}{2}}}"," ",0,"-1/(6*a*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) + 5*sqrt(b)/(12*a**2*x**(9/2)*sqrt(a/(b*x**3) + 1)) + 5*b**(3/2)/(4*a**3*x**(3/2)*sqrt(a/(b*x**3) + 1)) - 5*b**2*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(4*a**(7/2))","A",0
428,1,37,0,2.735875," ","integrate(x**6/(b*x**3+a)**(3/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{10}{3}\right)}"," ",0,"x**7*gamma(7/3)*hyper((3/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(10/3))","A",0
429,1,37,0,2.000623," ","integrate(x**3/(b*x**3+a)**(3/2),x)","\frac{x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{3}{2} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"x**4*gamma(4/3)*hyper((4/3, 3/2), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(7/3))","A",0
430,1,36,0,1.921439," ","integrate(1/(b*x**3+a)**(3/2),x)","\frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{4}{3}\right)}"," ",0,"x*gamma(1/3)*hyper((1/3, 3/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(4/3))","A",0
431,1,41,0,1.293418," ","integrate(1/x**3/(b*x**3+a)**(3/2),x)","\frac{\Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{3}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"gamma(-2/3)*hyper((-2/3, 3/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*x**2*gamma(1/3))","A",0
432,1,44,0,2.988230," ","integrate(1/x**6/(b*x**3+a)**(3/2),x)","\frac{\Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, \frac{3}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} x^{5} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"gamma(-5/3)*hyper((-5/3, 3/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*x**5*gamma(-2/3))","A",0
433,1,37,0,2.427244," ","integrate(x**7/(b*x**3+a)**(3/2),x)","\frac{x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{11}{3}\right)}"," ",0,"x**8*gamma(8/3)*hyper((3/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(11/3))","A",0
434,1,37,0,2.098455," ","integrate(x**4/(b*x**3+a)**(3/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"x**5*gamma(5/3)*hyper((3/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(8/3))","A",0
435,1,37,0,1.931096," ","integrate(x/(b*x**3+a)**(3/2),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{3}{2} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((2/3, 3/2), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(5/3))","A",0
436,1,39,0,1.989564," ","integrate(1/x**2/(b*x**3+a)**(3/2),x)","\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{3}{2} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} x \Gamma\left(\frac{2}{3}\right)}"," ",0,"gamma(-1/3)*hyper((-1/3, 3/2), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*x*gamma(2/3))","A",0
437,1,44,0,2.300015," ","integrate(1/x**5/(b*x**3+a)**(3/2),x)","\frac{\Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{3}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"gamma(-4/3)*hyper((-4/3, 3/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*x**4*gamma(-1/3))","A",0
438,1,56,0,2.914622," ","integrate(x**11/(x**3+1)**(1/2),x)","\frac{2 x^{9} \sqrt{x^{3} + 1}}{21} - \frac{4 x^{6} \sqrt{x^{3} + 1}}{35} + \frac{16 x^{3} \sqrt{x^{3} + 1}}{105} - \frac{32 \sqrt{x^{3} + 1}}{105}"," ",0,"2*x**9*sqrt(x**3 + 1)/21 - 4*x**6*sqrt(x**3 + 1)/35 + 16*x**3*sqrt(x**3 + 1)/105 - 32*sqrt(x**3 + 1)/105","A",0
439,1,41,0,1.466592," ","integrate(x**8/(x**3+1)**(1/2),x)","\frac{2 x^{6} \sqrt{x^{3} + 1}}{15} - \frac{8 x^{3} \sqrt{x^{3} + 1}}{45} + \frac{16 \sqrt{x^{3} + 1}}{45}"," ",0,"2*x**6*sqrt(x**3 + 1)/15 - 8*x**3*sqrt(x**3 + 1)/45 + 16*sqrt(x**3 + 1)/45","A",0
440,1,26,0,0.393231," ","integrate(x**5/(x**3+1)**(1/2),x)","\frac{2 x^{3} \sqrt{x^{3} + 1}}{9} - \frac{4 \sqrt{x^{3} + 1}}{9}"," ",0,"2*x**3*sqrt(x**3 + 1)/9 - 4*sqrt(x**3 + 1)/9","A",0
441,1,10,0,0.350492," ","integrate(x**2/(x**3+1)**(1/2),x)","\frac{2 \sqrt{x^{3} + 1}}{3}"," ",0,"2*sqrt(x**3 + 1)/3","A",0
442,1,12,0,1.267085," ","integrate(1/x/(x**3+1)**(1/2),x)","- \frac{2 \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3}"," ",0,"-2*asinh(x**(-3/2))/3","A",0
443,1,26,0,2.486816," ","integrate(1/x**4/(x**3+1)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} - \frac{\sqrt{1 + \frac{1}{x^{3}}}}{3 x^{\frac{3}{2}}}"," ",0,"asinh(x**(-3/2))/3 - sqrt(1 + x**(-3))/(3*x**(3/2))","A",0
444,1,65,0,6.950518," ","integrate(1/x**7/(x**3+1)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{4} + \frac{1}{4 x^{\frac{3}{2}} \sqrt{1 + \frac{1}{x^{3}}}} + \frac{1}{12 x^{\frac{9}{2}} \sqrt{1 + \frac{1}{x^{3}}}} - \frac{1}{6 x^{\frac{15}{2}} \sqrt{1 + \frac{1}{x^{3}}}}"," ",0,"-asinh(x**(-3/2))/4 + 1/(4*x**(3/2)*sqrt(1 + x**(-3))) + 1/(12*x**(9/2)*sqrt(1 + x**(-3))) - 1/(6*x**(15/2)*sqrt(1 + x**(-3)))","A",0
445,1,85,0,5.975863," ","integrate(1/x**10/(x**3+1)**(1/2),x)","\frac{5 \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{24} - \frac{5}{24 x^{\frac{3}{2}} \sqrt{1 + \frac{1}{x^{3}}}} - \frac{5}{72 x^{\frac{9}{2}} \sqrt{1 + \frac{1}{x^{3}}}} + \frac{1}{36 x^{\frac{15}{2}} \sqrt{1 + \frac{1}{x^{3}}}} - \frac{1}{9 x^{\frac{21}{2}} \sqrt{1 + \frac{1}{x^{3}}}}"," ",0,"5*asinh(x**(-3/2))/24 - 5/(24*x**(3/2)*sqrt(1 + x**(-3))) - 5/(72*x**(9/2)*sqrt(1 + x**(-3))) + 1/(36*x**(15/2)*sqrt(1 + x**(-3))) - 1/(9*x**(21/2)*sqrt(1 + x**(-3)))","A",0
446,1,29,0,2.111283," ","integrate(x**6/(x**3+1)**(1/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"x**7*gamma(7/3)*hyper((1/2, 7/3), (10/3,), x**3*exp_polar(I*pi))/(3*gamma(10/3))","A",0
447,1,29,0,1.645492," ","integrate(x**3/(x**3+1)**(1/2),x)","\frac{x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"x**4*gamma(4/3)*hyper((1/2, 4/3), (7/3,), x**3*exp_polar(I*pi))/(3*gamma(7/3))","A",0
448,1,27,0,1.502168," ","integrate(1/(x**3+1)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))","A",0
449,1,32,0,1.704780," ","integrate(1/x**3/(x**3+1)**(1/2),x)","\frac{\Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"gamma(-2/3)*hyper((-2/3, 1/2), (1/3,), x**3*exp_polar(I*pi))/(3*x**2*gamma(1/3))","A",0
450,1,36,0,1.970729," ","integrate(1/x**6/(x**3+1)**(1/2),x)","\frac{\Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"gamma(-5/3)*hyper((-5/3, 1/2), (-2/3,), x**3*exp_polar(I*pi))/(3*x**5*gamma(-2/3))","A",0
451,1,29,0,1.438374," ","integrate(x**7/(x**3+1)**(1/2),x)","\frac{x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)}"," ",0,"x**8*gamma(8/3)*hyper((1/2, 8/3), (11/3,), x**3*exp_polar(I*pi))/(3*gamma(11/3))","A",0
452,1,29,0,0.796064," ","integrate(x**4/(x**3+1)**(1/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)}"," ",0,"x**5*gamma(5/3)*hyper((1/2, 5/3), (8/3,), x**3*exp_polar(I*pi))/(3*gamma(8/3))","A",0
453,1,29,0,1.510763," ","integrate(x/(x**3+1)**(1/2),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(I*pi))/(3*gamma(5/3))","A",0
454,1,31,0,1.020233," ","integrate(1/x**2/(x**3+1)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{2}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)}"," ",0,"gamma(-1/3)*hyper((-1/3, 1/2), (2/3,), x**3*exp_polar(I*pi))/(3*x*gamma(2/3))","A",0
455,1,36,0,1.422019," ","integrate(1/x**5/(x**3+1)**(1/2),x)","\frac{\Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"gamma(-4/3)*hyper((-4/3, 1/2), (-1/3,), x**3*exp_polar(I*pi))/(3*x**4*gamma(-1/3))","A",0
456,1,58,0,1.911453," ","integrate(x**11/(-x**3+1)**(1/2),x)","- \frac{2 x^{9} \sqrt{1 - x^{3}}}{21} - \frac{4 x^{6} \sqrt{1 - x^{3}}}{35} - \frac{16 x^{3} \sqrt{1 - x^{3}}}{105} - \frac{32 \sqrt{1 - x^{3}}}{105}"," ",0,"-2*x**9*sqrt(1 - x**3)/21 - 4*x**6*sqrt(1 - x**3)/35 - 16*x**3*sqrt(1 - x**3)/105 - 32*sqrt(1 - x**3)/105","A",0
457,1,42,0,0.783717," ","integrate(x**8/(-x**3+1)**(1/2),x)","- \frac{2 x^{6} \sqrt{1 - x^{3}}}{15} - \frac{8 x^{3} \sqrt{1 - x^{3}}}{45} - \frac{16 \sqrt{1 - x^{3}}}{45}"," ",0,"-2*x**6*sqrt(1 - x**3)/15 - 8*x**3*sqrt(1 - x**3)/45 - 16*sqrt(1 - x**3)/45","A",0
458,1,27,0,0.685568," ","integrate(x**5/(-x**3+1)**(1/2),x)","- \frac{2 x^{3} \sqrt{1 - x^{3}}}{9} - \frac{4 \sqrt{1 - x^{3}}}{9}"," ",0,"-2*x**3*sqrt(1 - x**3)/9 - 4*sqrt(1 - x**3)/9","A",0
459,1,12,0,0.337155," ","integrate(x**2/(-x**3+1)**(1/2),x)","- \frac{2 \sqrt{1 - x^{3}}}{3}"," ",0,"-2*sqrt(1 - x**3)/3","A",0
460,1,31,0,1.950911," ","integrate(1/x/(-x**3+1)**(1/2),x)","\begin{cases} - \frac{2 \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\\frac{2 i \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (2*I*asin(x**(-3/2))/3, True))","A",0
461,1,82,0,3.793196," ","integrate(1/x**4/(-x**3+1)**(1/2),x)","\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} - \frac{\sqrt{-1 + \frac{1}{x^{3}}}}{3 x^{\frac{3}{2}}} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} - \frac{i}{3 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{x^{3}}}} + \frac{i}{3 x^{\frac{9}{2}} \sqrt{1 - \frac{1}{x^{3}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(x**(-3/2))/3 - sqrt(-1 + x**(-3))/(3*x**(3/2)), 1/Abs(x**3) > 1), (I*asin(x**(-3/2))/3 - I/(3*x**(3/2)*sqrt(1 - 1/x**3)) + I/(3*x**(9/2)*sqrt(1 - 1/x**3)), True))","A",0
462,1,138,0,5.109207," ","integrate(1/x**7/(-x**3+1)**(1/2),x)","\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{4} + \frac{1}{4 x^{\frac{3}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} - \frac{1}{12 x^{\frac{9}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} - \frac{1}{6 x^{\frac{15}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{4} - \frac{i}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{x^{3}}}} + \frac{i}{12 x^{\frac{9}{2}} \sqrt{1 - \frac{1}{x^{3}}}} + \frac{i}{6 x^{\frac{15}{2}} \sqrt{1 - \frac{1}{x^{3}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(x**(-3/2))/4 + 1/(4*x**(3/2)*sqrt(-1 + x**(-3))) - 1/(12*x**(9/2)*sqrt(-1 + x**(-3))) - 1/(6*x**(15/2)*sqrt(-1 + x**(-3))), 1/Abs(x**3) > 1), (I*asin(x**(-3/2))/4 - I/(4*x**(3/2)*sqrt(1 - 1/x**3)) + I/(12*x**(9/2)*sqrt(1 - 1/x**3)) + I/(6*x**(15/2)*sqrt(1 - 1/x**3)), True))","A",0
463,1,182,0,6.895405," ","integrate(1/x**10/(-x**3+1)**(1/2),x)","\begin{cases} - \frac{5 \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{24} + \frac{5}{24 x^{\frac{3}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} - \frac{5}{72 x^{\frac{9}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} - \frac{1}{36 x^{\frac{15}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} - \frac{1}{9 x^{\frac{21}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\\frac{5 i \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{24} - \frac{5 i}{24 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{x^{3}}}} + \frac{5 i}{72 x^{\frac{9}{2}} \sqrt{1 - \frac{1}{x^{3}}}} + \frac{i}{36 x^{\frac{15}{2}} \sqrt{1 - \frac{1}{x^{3}}}} + \frac{i}{9 x^{\frac{21}{2}} \sqrt{1 - \frac{1}{x^{3}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*acosh(x**(-3/2))/24 + 5/(24*x**(3/2)*sqrt(-1 + x**(-3))) - 5/(72*x**(9/2)*sqrt(-1 + x**(-3))) - 1/(36*x**(15/2)*sqrt(-1 + x**(-3))) - 1/(9*x**(21/2)*sqrt(-1 + x**(-3))), 1/Abs(x**3) > 1), (5*I*asin(x**(-3/2))/24 - 5*I/(24*x**(3/2)*sqrt(1 - 1/x**3)) + 5*I/(72*x**(9/2)*sqrt(1 - 1/x**3)) + I/(36*x**(15/2)*sqrt(1 - 1/x**3)) + I/(9*x**(21/2)*sqrt(1 - 1/x**3)), True))","A",0
464,1,31,0,1.686886," ","integrate(x**6/(-x**3+1)**(1/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"x**7*gamma(7/3)*hyper((1/2, 7/3), (10/3,), x**3*exp_polar(2*I*pi))/(3*gamma(10/3))","A",0
465,1,31,0,2.079917," ","integrate(x**3/(-x**3+1)**(1/2),x)","\frac{x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"x**4*gamma(4/3)*hyper((1/2, 4/3), (7/3,), x**3*exp_polar(2*I*pi))/(3*gamma(7/3))","A",0
466,1,29,0,1.242684," ","integrate(1/(-x**3+1)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3))","A",0
467,1,34,0,1.562723," ","integrate(1/x**3/(-x**3+1)**(1/2),x)","\frac{\Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"gamma(-2/3)*hyper((-2/3, 1/2), (1/3,), x**3*exp_polar(2*I*pi))/(3*x**2*gamma(1/3))","A",0
468,1,37,0,1.641074," ","integrate(1/x**6/(-x**3+1)**(1/2),x)","\frac{\Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"gamma(-5/3)*hyper((-5/3, 1/2), (-2/3,), x**3*exp_polar(2*I*pi))/(3*x**5*gamma(-2/3))","A",0
469,1,31,0,1.798235," ","integrate(x**7/(-x**3+1)**(1/2),x)","\frac{x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)}"," ",0,"x**8*gamma(8/3)*hyper((1/2, 8/3), (11/3,), x**3*exp_polar(2*I*pi))/(3*gamma(11/3))","A",0
470,1,31,0,1.017493," ","integrate(x**4/(-x**3+1)**(1/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)}"," ",0,"x**5*gamma(5/3)*hyper((1/2, 5/3), (8/3,), x**3*exp_polar(2*I*pi))/(3*gamma(8/3))","A",0
471,1,31,0,0.828226," ","integrate(x/(-x**3+1)**(1/2),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(2*I*pi))/(3*gamma(5/3))","A",0
472,1,32,0,1.356868," ","integrate(1/x**2/(-x**3+1)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{2}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)}"," ",0,"gamma(-1/3)*hyper((-1/3, 1/2), (2/3,), x**3*exp_polar(2*I*pi))/(3*x*gamma(2/3))","A",0
473,1,37,0,1.576450," ","integrate(1/x**5/(-x**3+1)**(1/2),x)","\frac{\Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"gamma(-4/3)*hyper((-4/3, 1/2), (-1/3,), x**3*exp_polar(2*I*pi))/(3*x**4*gamma(-1/3))","A",0
474,1,56,0,3.079915," ","integrate(x**11/(x**3-1)**(1/2),x)","\frac{2 x^{9} \sqrt{x^{3} - 1}}{21} + \frac{4 x^{6} \sqrt{x^{3} - 1}}{35} + \frac{16 x^{3} \sqrt{x^{3} - 1}}{105} + \frac{32 \sqrt{x^{3} - 1}}{105}"," ",0,"2*x**9*sqrt(x**3 - 1)/21 + 4*x**6*sqrt(x**3 - 1)/35 + 16*x**3*sqrt(x**3 - 1)/105 + 32*sqrt(x**3 - 1)/105","A",0
475,1,41,0,1.378391," ","integrate(x**8/(x**3-1)**(1/2),x)","\frac{2 x^{6} \sqrt{x^{3} - 1}}{15} + \frac{8 x^{3} \sqrt{x^{3} - 1}}{45} + \frac{16 \sqrt{x^{3} - 1}}{45}"," ",0,"2*x**6*sqrt(x**3 - 1)/15 + 8*x**3*sqrt(x**3 - 1)/45 + 16*sqrt(x**3 - 1)/45","A",0
476,1,26,0,0.508343," ","integrate(x**5/(x**3-1)**(1/2),x)","\frac{2 x^{3} \sqrt{x^{3} - 1}}{9} + \frac{4 \sqrt{x^{3} - 1}}{9}"," ",0,"2*x**3*sqrt(x**3 - 1)/9 + 4*sqrt(x**3 - 1)/9","A",0
477,1,10,0,0.222545," ","integrate(x**2/(x**3-1)**(1/2),x)","\frac{2 \sqrt{x^{3} - 1}}{3}"," ",0,"2*sqrt(x**3 - 1)/3","A",0
478,1,31,0,1.349968," ","integrate(1/x/(x**3-1)**(1/2),x)","\begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (-2*asin(x**(-3/2))/3, True))","A",0
479,1,82,0,3.639716," ","integrate(1/x**4/(x**3-1)**(1/2),x)","\begin{cases} \frac{i \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} + \frac{i \sqrt{-1 + \frac{1}{x^{3}}}}{3 x^{\frac{3}{2}}} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\- \frac{\operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} + \frac{1}{3 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{x^{3}}}} - \frac{1}{3 x^{\frac{9}{2}} \sqrt{1 - \frac{1}{x^{3}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*acosh(x**(-3/2))/3 + I*sqrt(-1 + x**(-3))/(3*x**(3/2)), 1/Abs(x**3) > 1), (-asin(x**(-3/2))/3 + 1/(3*x**(3/2)*sqrt(1 - 1/x**3)) - 1/(3*x**(9/2)*sqrt(1 - 1/x**3)), True))","A",0
480,1,138,0,3.735258," ","integrate(1/x**7/(x**3-1)**(1/2),x)","\begin{cases} \frac{i \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{4} - \frac{i}{4 x^{\frac{3}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} + \frac{i}{12 x^{\frac{9}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} + \frac{i}{6 x^{\frac{15}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\- \frac{\operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{4} + \frac{1}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{x^{3}}}} - \frac{1}{12 x^{\frac{9}{2}} \sqrt{1 - \frac{1}{x^{3}}}} - \frac{1}{6 x^{\frac{15}{2}} \sqrt{1 - \frac{1}{x^{3}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*acosh(x**(-3/2))/4 - I/(4*x**(3/2)*sqrt(-1 + x**(-3))) + I/(12*x**(9/2)*sqrt(-1 + x**(-3))) + I/(6*x**(15/2)*sqrt(-1 + x**(-3))), 1/Abs(x**3) > 1), (-asin(x**(-3/2))/4 + 1/(4*x**(3/2)*sqrt(1 - 1/x**3)) - 1/(12*x**(9/2)*sqrt(1 - 1/x**3)) - 1/(6*x**(15/2)*sqrt(1 - 1/x**3)), True))","A",0
481,1,182,0,5.567696," ","integrate(1/x**10/(x**3-1)**(1/2),x)","\begin{cases} \frac{5 i \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{24} - \frac{5 i}{24 x^{\frac{3}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} + \frac{5 i}{72 x^{\frac{9}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} + \frac{i}{36 x^{\frac{15}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} + \frac{i}{9 x^{\frac{21}{2}} \sqrt{-1 + \frac{1}{x^{3}}}} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\- \frac{5 \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{24} + \frac{5}{24 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{x^{3}}}} - \frac{5}{72 x^{\frac{9}{2}} \sqrt{1 - \frac{1}{x^{3}}}} - \frac{1}{36 x^{\frac{15}{2}} \sqrt{1 - \frac{1}{x^{3}}}} - \frac{1}{9 x^{\frac{21}{2}} \sqrt{1 - \frac{1}{x^{3}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*I*acosh(x**(-3/2))/24 - 5*I/(24*x**(3/2)*sqrt(-1 + x**(-3))) + 5*I/(72*x**(9/2)*sqrt(-1 + x**(-3))) + I/(36*x**(15/2)*sqrt(-1 + x**(-3))) + I/(9*x**(21/2)*sqrt(-1 + x**(-3))), 1/Abs(x**3) > 1), (-5*asin(x**(-3/2))/24 + 5/(24*x**(3/2)*sqrt(1 - 1/x**3)) - 5/(72*x**(9/2)*sqrt(1 - 1/x**3)) - 1/(36*x**(15/2)*sqrt(1 - 1/x**3)) - 1/(9*x**(21/2)*sqrt(1 - 1/x**3)), True))","A",0
482,1,27,0,0.990337," ","integrate(x**6/(x**3-1)**(1/2),x)","- \frac{i x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"-I*x**7*gamma(7/3)*hyper((1/2, 7/3), (10/3,), x**3)/(3*gamma(10/3))","A",0
483,1,27,0,1.754565," ","integrate(x**3/(x**3-1)**(1/2),x)","- \frac{i x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"-I*x**4*gamma(4/3)*hyper((1/2, 4/3), (7/3,), x**3)/(3*gamma(7/3))","A",0
484,1,26,0,0.994884," ","integrate(1/(x**3-1)**(1/2),x)","- \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"-I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3))","A",0
485,1,31,0,1.579081," ","integrate(1/x**3/(x**3-1)**(1/2),x)","- \frac{i \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"-I*gamma(-2/3)*hyper((-2/3, 1/2), (1/3,), x**3)/(3*x**2*gamma(1/3))","A",0
486,1,34,0,2.202418," ","integrate(1/x**6/(x**3-1)**(1/2),x)","- \frac{i \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"-I*gamma(-5/3)*hyper((-5/3, 1/2), (-2/3,), x**3)/(3*x**5*gamma(-2/3))","A",0
487,1,27,0,1.644241," ","integrate(x**7/(x**3-1)**(1/2),x)","- \frac{i x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)}"," ",0,"-I*x**8*gamma(8/3)*hyper((1/2, 8/3), (11/3,), x**3)/(3*gamma(11/3))","A",0
488,1,27,0,1.280335," ","integrate(x**4/(x**3-1)**(1/2),x)","- \frac{i x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)}"," ",0,"-I*x**5*gamma(5/3)*hyper((1/2, 5/3), (8/3,), x**3)/(3*gamma(8/3))","A",0
489,1,27,0,1.121175," ","integrate(x/(x**3-1)**(1/2),x)","- \frac{i x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"-I*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3)/(3*gamma(5/3))","A",0
490,1,29,0,0.936761," ","integrate(1/x**2/(x**3-1)**(1/2),x)","- \frac{i \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{2}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)}"," ",0,"-I*gamma(-1/3)*hyper((-1/3, 1/2), (2/3,), x**3)/(3*x*gamma(2/3))","A",0
491,1,34,0,0.996665," ","integrate(1/x**5/(x**3-1)**(1/2),x)","- \frac{i \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"-I*gamma(-4/3)*hyper((-4/3, 1/2), (-1/3,), x**3)/(3*x**4*gamma(-1/3))","A",0
492,1,63,0,1.902243," ","integrate(x**11/(-x**3-1)**(1/2),x)","- \frac{2 x^{9} \sqrt{- x^{3} - 1}}{21} + \frac{4 x^{6} \sqrt{- x^{3} - 1}}{35} - \frac{16 x^{3} \sqrt{- x^{3} - 1}}{105} + \frac{32 \sqrt{- x^{3} - 1}}{105}"," ",0,"-2*x**9*sqrt(-x**3 - 1)/21 + 4*x**6*sqrt(-x**3 - 1)/35 - 16*x**3*sqrt(-x**3 - 1)/105 + 32*sqrt(-x**3 - 1)/105","A",0
493,1,46,0,0.811343," ","integrate(x**8/(-x**3-1)**(1/2),x)","- \frac{2 x^{6} \sqrt{- x^{3} - 1}}{15} + \frac{8 x^{3} \sqrt{- x^{3} - 1}}{45} - \frac{16 \sqrt{- x^{3} - 1}}{45}"," ",0,"-2*x**6*sqrt(-x**3 - 1)/15 + 8*x**3*sqrt(-x**3 - 1)/45 - 16*sqrt(-x**3 - 1)/45","A",0
494,1,29,0,0.664250," ","integrate(x**5/(-x**3-1)**(1/2),x)","- \frac{2 x^{3} \sqrt{- x^{3} - 1}}{9} + \frac{4 \sqrt{- x^{3} - 1}}{9}"," ",0,"-2*x**3*sqrt(-x**3 - 1)/9 + 4*sqrt(-x**3 - 1)/9","A",0
495,1,14,0,0.206778," ","integrate(x**2/(-x**3-1)**(1/2),x)","- \frac{2 \sqrt{- x^{3} - 1}}{3}"," ",0,"-2*sqrt(-x**3 - 1)/3","A",0
496,1,12,0,1.591280," ","integrate(1/x/(-x**3-1)**(1/2),x)","\frac{2 i \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3}"," ",0,"2*I*asinh(x**(-3/2))/3","C",0
497,1,29,0,2.146219," ","integrate(1/x**4/(-x**3-1)**(1/2),x)","- \frac{i \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} + \frac{i \sqrt{1 + \frac{1}{x^{3}}}}{3 x^{\frac{3}{2}}}"," ",0,"-I*asinh(x**(-3/2))/3 + I*sqrt(1 + x**(-3))/(3*x**(3/2))","C",0
498,1,66,0,4.738812," ","integrate(1/x**7/(-x**3-1)**(1/2),x)","\frac{i \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{4} - \frac{i}{4 x^{\frac{3}{2}} \sqrt{1 + \frac{1}{x^{3}}}} - \frac{i}{12 x^{\frac{9}{2}} \sqrt{1 + \frac{1}{x^{3}}}} + \frac{i}{6 x^{\frac{15}{2}} \sqrt{1 + \frac{1}{x^{3}}}}"," ",0,"I*asinh(x**(-3/2))/4 - I/(4*x**(3/2)*sqrt(1 + x**(-3))) - I/(12*x**(9/2)*sqrt(1 + x**(-3))) + I/(6*x**(15/2)*sqrt(1 + x**(-3)))","C",0
499,1,90,0,8.482255," ","integrate(1/x**10/(-x**3-1)**(1/2),x)","- \frac{5 i \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{24} + \frac{5 i}{24 x^{\frac{3}{2}} \sqrt{1 + \frac{1}{x^{3}}}} + \frac{5 i}{72 x^{\frac{9}{2}} \sqrt{1 + \frac{1}{x^{3}}}} - \frac{i}{36 x^{\frac{15}{2}} \sqrt{1 + \frac{1}{x^{3}}}} + \frac{i}{9 x^{\frac{21}{2}} \sqrt{1 + \frac{1}{x^{3}}}}"," ",0,"-5*I*asinh(x**(-3/2))/24 + 5*I/(24*x**(3/2)*sqrt(1 + x**(-3))) + 5*I/(72*x**(9/2)*sqrt(1 + x**(-3))) - I/(36*x**(15/2)*sqrt(1 + x**(-3))) + I/(9*x**(21/2)*sqrt(1 + x**(-3)))","C",0
500,1,32,0,1.196376," ","integrate(x**6/(-x**3-1)**(1/2),x)","- \frac{i x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)}"," ",0,"-I*x**7*gamma(7/3)*hyper((1/2, 7/3), (10/3,), x**3*exp_polar(I*pi))/(3*gamma(10/3))","A",0
501,1,32,0,1.514154," ","integrate(x**3/(-x**3-1)**(1/2),x)","- \frac{i x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"-I*x**4*gamma(4/3)*hyper((1/2, 4/3), (7/3,), x**3*exp_polar(I*pi))/(3*gamma(7/3))","A",0
502,1,31,0,1.195139," ","integrate(1/(-x**3-1)**(1/2),x)","- \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"-I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))","A",0
503,1,36,0,0.958089," ","integrate(1/x**3/(-x**3-1)**(1/2),x)","- \frac{i \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"-I*gamma(-2/3)*hyper((-2/3, 1/2), (1/3,), x**3*exp_polar(I*pi))/(3*x**2*gamma(1/3))","A",0
504,1,39,0,1.995969," ","integrate(1/x**6/(-x**3-1)**(1/2),x)","- \frac{i \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"-I*gamma(-5/3)*hyper((-5/3, 1/2), (-2/3,), x**3*exp_polar(I*pi))/(3*x**5*gamma(-2/3))","A",0
505,1,32,0,1.271520," ","integrate(x**7/(-x**3-1)**(1/2),x)","- \frac{i x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)}"," ",0,"-I*x**8*gamma(8/3)*hyper((1/2, 8/3), (11/3,), x**3*exp_polar(I*pi))/(3*gamma(11/3))","A",0
506,1,32,0,1.322535," ","integrate(x**4/(-x**3-1)**(1/2),x)","- \frac{i x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)}"," ",0,"-I*x**5*gamma(5/3)*hyper((1/2, 5/3), (8/3,), x**3*exp_polar(I*pi))/(3*gamma(8/3))","A",0
507,1,32,0,0.842306," ","integrate(x/(-x**3-1)**(1/2),x)","- \frac{i x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"-I*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(I*pi))/(3*gamma(5/3))","A",0
508,1,34,0,1.719805," ","integrate(1/x**2/(-x**3-1)**(1/2),x)","- \frac{i \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{2}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)}"," ",0,"-I*gamma(-1/3)*hyper((-1/3, 1/2), (2/3,), x**3*exp_polar(I*pi))/(3*x*gamma(2/3))","A",0
509,1,39,0,1.689407," ","integrate(1/x**5/(-x**3-1)**(1/2),x)","- \frac{i \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"-I*gamma(-4/3)*hyper((-4/3, 1/2), (-1/3,), x**3*exp_polar(I*pi))/(3*x**4*gamma(-1/3))","A",0
510,1,110,0,5.548305," ","integrate(x**11*(b*x**3+a)**(1/3),x)","\begin{cases} - \frac{81 a^{4} \sqrt[3]{a + b x^{3}}}{1820 b^{4}} + \frac{27 a^{3} x^{3} \sqrt[3]{a + b x^{3}}}{1820 b^{3}} - \frac{9 a^{2} x^{6} \sqrt[3]{a + b x^{3}}}{910 b^{2}} + \frac{a x^{9} \sqrt[3]{a + b x^{3}}}{130 b} + \frac{x^{12} \sqrt[3]{a + b x^{3}}}{13} & \text{for}\: b \neq 0 \\\frac{\sqrt[3]{a} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-81*a**4*(a + b*x**3)**(1/3)/(1820*b**4) + 27*a**3*x**3*(a + b*x**3)**(1/3)/(1820*b**3) - 9*a**2*x**6*(a + b*x**3)**(1/3)/(910*b**2) + a*x**9*(a + b*x**3)**(1/3)/(130*b) + x**12*(a + b*x**3)**(1/3)/13, Ne(b, 0)), (a**(1/3)*x**12/12, True))","A",0
511,1,87,0,4.465858," ","integrate(x**8*(b*x**3+a)**(1/3),x)","\begin{cases} \frac{9 a^{3} \sqrt[3]{a + b x^{3}}}{140 b^{3}} - \frac{3 a^{2} x^{3} \sqrt[3]{a + b x^{3}}}{140 b^{2}} + \frac{a x^{6} \sqrt[3]{a + b x^{3}}}{70 b} + \frac{x^{9} \sqrt[3]{a + b x^{3}}}{10} & \text{for}\: b \neq 0 \\\frac{\sqrt[3]{a} x^{9}}{9} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a**3*(a + b*x**3)**(1/3)/(140*b**3) - 3*a**2*x**3*(a + b*x**3)**(1/3)/(140*b**2) + a*x**6*(a + b*x**3)**(1/3)/(70*b) + x**9*(a + b*x**3)**(1/3)/10, Ne(b, 0)), (a**(1/3)*x**9/9, True))","A",0
512,1,63,0,1.820719," ","integrate(x**5*(b*x**3+a)**(1/3),x)","\begin{cases} - \frac{3 a^{2} \sqrt[3]{a + b x^{3}}}{28 b^{2}} + \frac{a x^{3} \sqrt[3]{a + b x^{3}}}{28 b} + \frac{x^{6} \sqrt[3]{a + b x^{3}}}{7} & \text{for}\: b \neq 0 \\\frac{\sqrt[3]{a} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a**2*(a + b*x**3)**(1/3)/(28*b**2) + a*x**3*(a + b*x**3)**(1/3)/(28*b) + x**6*(a + b*x**3)**(1/3)/7, Ne(b, 0)), (a**(1/3)*x**6/6, True))","A",0
513,1,39,0,0.490853," ","integrate(x**2*(b*x**3+a)**(1/3),x)","\begin{cases} \frac{a \sqrt[3]{a + b x^{3}}}{4 b} + \frac{x^{3} \sqrt[3]{a + b x^{3}}}{4} & \text{for}\: b \neq 0 \\\frac{\sqrt[3]{a} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*(a + b*x**3)**(1/3)/(4*b) + x**3*(a + b*x**3)**(1/3)/4, Ne(b, 0)), (a**(1/3)*x**3/3, True))","A",0
514,1,42,0,2.309393," ","integrate((b*x**3+a)**(1/3)/x,x)","- \frac{\sqrt[3]{b} x \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{3}}} \right)}}{3 \Gamma\left(\frac{2}{3}\right)}"," ",0,"-b**(1/3)*x*gamma(-1/3)*hyper((-1/3, -1/3), (2/3,), a*exp_polar(I*pi)/(b*x**3))/(3*gamma(2/3))","C",0
515,1,41,0,2.622540," ","integrate((b*x**3+a)**(1/3)/x**4,x)","- \frac{\sqrt[3]{b} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{3}}} \right)}}{3 x^{2} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-b**(1/3)*gamma(2/3)*hyper((-1/3, 2/3), (5/3,), a*exp_polar(I*pi)/(b*x**3))/(3*x**2*gamma(5/3))","C",0
516,1,39,0,1.623555," ","integrate(x**4*(b*x**3+a)**(1/3),x)","\frac{\sqrt[3]{a} x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)}"," ",0,"a**(1/3)*x**5*gamma(5/3)*hyper((-1/3, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3))","C",0
517,1,39,0,1.208553," ","integrate(x*(b*x**3+a)**(1/3),x)","\frac{\sqrt[3]{a} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"a**(1/3)*x**2*gamma(2/3)*hyper((-1/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3))","C",0
518,1,41,0,2.211471," ","integrate((b*x**3+a)**(1/3)/x**2,x)","\frac{\sqrt[3]{a} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)}"," ",0,"a**(1/3)*gamma(-1/3)*hyper((-1/3, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3))","C",0
519,1,68,0,1.469900," ","integrate((b*x**3+a)**(1/3)/x**5,x)","\frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{4}{3}\right)}{3 x^{3} \Gamma\left(- \frac{1}{3}\right)} + \frac{b^{\frac{4}{3}} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{4}{3}\right)}{3 a \Gamma\left(- \frac{1}{3}\right)}"," ",0,"b**(1/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-4/3)/(3*x**3*gamma(-1/3)) + b**(4/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-4/3)/(3*a*gamma(-1/3))","B",0
520,1,109,0,1.230658," ","integrate((b*x**3+a)**(1/3)/x**8,x)","- \frac{4 \sqrt[3]{b} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{7}{3}\right)}{9 x^{6} \Gamma\left(- \frac{1}{3}\right)} - \frac{b^{\frac{4}{3}} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{7}{3}\right)}{9 a x^{3} \Gamma\left(- \frac{1}{3}\right)} + \frac{b^{\frac{7}{3}} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{7}{3}\right)}{3 a^{2} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"-4*b**(1/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-7/3)/(9*x**6*gamma(-1/3)) - b**(4/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-7/3)/(9*a*x**3*gamma(-1/3)) + b**(7/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-7/3)/(3*a**2*gamma(-1/3))","B",0
521,1,520,0,3.233612," ","integrate((b*x**3+a)**(1/3)/x**11,x)","\frac{28 a^{5} b^{\frac{13}{3}} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{1}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{1}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{1}{3}\right)} + \frac{60 a^{4} b^{\frac{16}{3}} x^{3} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{1}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{1}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{1}{3}\right)} + \frac{30 a^{3} b^{\frac{19}{3}} x^{6} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{1}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{1}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{1}{3}\right)} + \frac{10 a^{2} b^{\frac{22}{3}} x^{9} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{1}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{1}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{1}{3}\right)} + \frac{30 a b^{\frac{25}{3}} x^{12} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{1}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{1}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{1}{3}\right)} + \frac{18 b^{\frac{28}{3}} x^{15} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{1}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{1}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"28*a**5*b**(13/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(27*a**5*b**4*x**9*gamma(-1/3) + 54*a**4*b**5*x**12*gamma(-1/3) + 27*a**3*b**6*x**15*gamma(-1/3)) + 60*a**4*b**(16/3)*x**3*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(27*a**5*b**4*x**9*gamma(-1/3) + 54*a**4*b**5*x**12*gamma(-1/3) + 27*a**3*b**6*x**15*gamma(-1/3)) + 30*a**3*b**(19/3)*x**6*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(27*a**5*b**4*x**9*gamma(-1/3) + 54*a**4*b**5*x**12*gamma(-1/3) + 27*a**3*b**6*x**15*gamma(-1/3)) + 10*a**2*b**(22/3)*x**9*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(27*a**5*b**4*x**9*gamma(-1/3) + 54*a**4*b**5*x**12*gamma(-1/3) + 27*a**3*b**6*x**15*gamma(-1/3)) + 30*a*b**(25/3)*x**12*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(27*a**5*b**4*x**9*gamma(-1/3) + 54*a**4*b**5*x**12*gamma(-1/3) + 27*a**3*b**6*x**15*gamma(-1/3)) + 18*b**(28/3)*x**15*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(27*a**5*b**4*x**9*gamma(-1/3) + 54*a**4*b**5*x**12*gamma(-1/3) + 27*a**3*b**6*x**15*gamma(-1/3))","B",0
522,1,847,0,2.813819," ","integrate((b*x**3+a)**(1/3)/x**14,x)","- \frac{280 a^{7} b^{\frac{28}{3}} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{13}{3}\right)}{81 a^{7} b^{9} x^{12} \Gamma\left(- \frac{1}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(- \frac{1}{3}\right) + 243 a^{5} b^{11} x^{18} \Gamma\left(- \frac{1}{3}\right) + 81 a^{4} b^{12} x^{21} \Gamma\left(- \frac{1}{3}\right)} - \frac{868 a^{6} b^{\frac{31}{3}} x^{3} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{13}{3}\right)}{81 a^{7} b^{9} x^{12} \Gamma\left(- \frac{1}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(- \frac{1}{3}\right) + 243 a^{5} b^{11} x^{18} \Gamma\left(- \frac{1}{3}\right) + 81 a^{4} b^{12} x^{21} \Gamma\left(- \frac{1}{3}\right)} - \frac{888 a^{5} b^{\frac{34}{3}} x^{6} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{13}{3}\right)}{81 a^{7} b^{9} x^{12} \Gamma\left(- \frac{1}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(- \frac{1}{3}\right) + 243 a^{5} b^{11} x^{18} \Gamma\left(- \frac{1}{3}\right) + 81 a^{4} b^{12} x^{21} \Gamma\left(- \frac{1}{3}\right)} - \frac{310 a^{4} b^{\frac{37}{3}} x^{9} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{13}{3}\right)}{81 a^{7} b^{9} x^{12} \Gamma\left(- \frac{1}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(- \frac{1}{3}\right) + 243 a^{5} b^{11} x^{18} \Gamma\left(- \frac{1}{3}\right) + 81 a^{4} b^{12} x^{21} \Gamma\left(- \frac{1}{3}\right)} + \frac{80 a^{3} b^{\frac{40}{3}} x^{12} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{13}{3}\right)}{81 a^{7} b^{9} x^{12} \Gamma\left(- \frac{1}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(- \frac{1}{3}\right) + 243 a^{5} b^{11} x^{18} \Gamma\left(- \frac{1}{3}\right) + 81 a^{4} b^{12} x^{21} \Gamma\left(- \frac{1}{3}\right)} + \frac{360 a^{2} b^{\frac{43}{3}} x^{15} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{13}{3}\right)}{81 a^{7} b^{9} x^{12} \Gamma\left(- \frac{1}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(- \frac{1}{3}\right) + 243 a^{5} b^{11} x^{18} \Gamma\left(- \frac{1}{3}\right) + 81 a^{4} b^{12} x^{21} \Gamma\left(- \frac{1}{3}\right)} + \frac{432 a b^{\frac{46}{3}} x^{18} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{13}{3}\right)}{81 a^{7} b^{9} x^{12} \Gamma\left(- \frac{1}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(- \frac{1}{3}\right) + 243 a^{5} b^{11} x^{18} \Gamma\left(- \frac{1}{3}\right) + 81 a^{4} b^{12} x^{21} \Gamma\left(- \frac{1}{3}\right)} + \frac{162 b^{\frac{49}{3}} x^{21} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{13}{3}\right)}{81 a^{7} b^{9} x^{12} \Gamma\left(- \frac{1}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(- \frac{1}{3}\right) + 243 a^{5} b^{11} x^{18} \Gamma\left(- \frac{1}{3}\right) + 81 a^{4} b^{12} x^{21} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"-280*a**7*b**(28/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-13/3)/(81*a**7*b**9*x**12*gamma(-1/3) + 243*a**6*b**10*x**15*gamma(-1/3) + 243*a**5*b**11*x**18*gamma(-1/3) + 81*a**4*b**12*x**21*gamma(-1/3)) - 868*a**6*b**(31/3)*x**3*(a/(b*x**3) + 1)**(1/3)*gamma(-13/3)/(81*a**7*b**9*x**12*gamma(-1/3) + 243*a**6*b**10*x**15*gamma(-1/3) + 243*a**5*b**11*x**18*gamma(-1/3) + 81*a**4*b**12*x**21*gamma(-1/3)) - 888*a**5*b**(34/3)*x**6*(a/(b*x**3) + 1)**(1/3)*gamma(-13/3)/(81*a**7*b**9*x**12*gamma(-1/3) + 243*a**6*b**10*x**15*gamma(-1/3) + 243*a**5*b**11*x**18*gamma(-1/3) + 81*a**4*b**12*x**21*gamma(-1/3)) - 310*a**4*b**(37/3)*x**9*(a/(b*x**3) + 1)**(1/3)*gamma(-13/3)/(81*a**7*b**9*x**12*gamma(-1/3) + 243*a**6*b**10*x**15*gamma(-1/3) + 243*a**5*b**11*x**18*gamma(-1/3) + 81*a**4*b**12*x**21*gamma(-1/3)) + 80*a**3*b**(40/3)*x**12*(a/(b*x**3) + 1)**(1/3)*gamma(-13/3)/(81*a**7*b**9*x**12*gamma(-1/3) + 243*a**6*b**10*x**15*gamma(-1/3) + 243*a**5*b**11*x**18*gamma(-1/3) + 81*a**4*b**12*x**21*gamma(-1/3)) + 360*a**2*b**(43/3)*x**15*(a/(b*x**3) + 1)**(1/3)*gamma(-13/3)/(81*a**7*b**9*x**12*gamma(-1/3) + 243*a**6*b**10*x**15*gamma(-1/3) + 243*a**5*b**11*x**18*gamma(-1/3) + 81*a**4*b**12*x**21*gamma(-1/3)) + 432*a*b**(46/3)*x**18*(a/(b*x**3) + 1)**(1/3)*gamma(-13/3)/(81*a**7*b**9*x**12*gamma(-1/3) + 243*a**6*b**10*x**15*gamma(-1/3) + 243*a**5*b**11*x**18*gamma(-1/3) + 81*a**4*b**12*x**21*gamma(-1/3)) + 162*b**(49/3)*x**21*(a/(b*x**3) + 1)**(1/3)*gamma(-13/3)/(81*a**7*b**9*x**12*gamma(-1/3) + 243*a**6*b**10*x**15*gamma(-1/3) + 243*a**5*b**11*x**18*gamma(-1/3) + 81*a**4*b**12*x**21*gamma(-1/3))","B",0
523,1,39,0,1.829435," ","integrate(x**3*(b*x**3+a)**(1/3),x)","\frac{\sqrt[3]{a} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"a**(1/3)*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3))","C",0
524,1,37,0,0.981229," ","integrate((b*x**3+a)**(1/3),x)","\frac{\sqrt[3]{a} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"a**(1/3)*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3))","C",0
525,1,42,0,1.517874," ","integrate((b*x**3+a)**(1/3)/x**3,x)","\frac{\sqrt[3]{a} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{3} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"a**(1/3)*gamma(-2/3)*hyper((-2/3, -1/3), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3))","C",0
526,1,42,0,1.173585," ","integrate((b*x**3+a)**(1/3)/x**6,x)","\frac{\sqrt[3]{b} \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{3}}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"b**(1/3)*gamma(-4/3)*hyper((-1/3, 4/3), (7/3,), a*exp_polar(I*pi)/(b*x**3))/(3*x**4*gamma(-1/3))","C",0
527,1,110,0,12.615357," ","integrate(x**11*(b*x**3+a)**(2/3),x)","\begin{cases} - \frac{81 a^{4} \left(a + b x^{3}\right)^{\frac{2}{3}}}{3080 b^{4}} + \frac{27 a^{3} x^{3} \left(a + b x^{3}\right)^{\frac{2}{3}}}{1540 b^{3}} - \frac{9 a^{2} x^{6} \left(a + b x^{3}\right)^{\frac{2}{3}}}{616 b^{2}} + \frac{a x^{9} \left(a + b x^{3}\right)^{\frac{2}{3}}}{77 b} + \frac{x^{12} \left(a + b x^{3}\right)^{\frac{2}{3}}}{14} & \text{for}\: b \neq 0 \\\frac{a^{\frac{2}{3}} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-81*a**4*(a + b*x**3)**(2/3)/(3080*b**4) + 27*a**3*x**3*(a + b*x**3)**(2/3)/(1540*b**3) - 9*a**2*x**6*(a + b*x**3)**(2/3)/(616*b**2) + a*x**9*(a + b*x**3)**(2/3)/(77*b) + x**12*(a + b*x**3)**(2/3)/14, Ne(b, 0)), (a**(2/3)*x**12/12, True))","A",0
528,1,87,0,4.212102," ","integrate(x**8*(b*x**3+a)**(2/3),x)","\begin{cases} \frac{9 a^{3} \left(a + b x^{3}\right)^{\frac{2}{3}}}{220 b^{3}} - \frac{3 a^{2} x^{3} \left(a + b x^{3}\right)^{\frac{2}{3}}}{110 b^{2}} + \frac{a x^{6} \left(a + b x^{3}\right)^{\frac{2}{3}}}{44 b} + \frac{x^{9} \left(a + b x^{3}\right)^{\frac{2}{3}}}{11} & \text{for}\: b \neq 0 \\\frac{a^{\frac{2}{3}} x^{9}}{9} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a**3*(a + b*x**3)**(2/3)/(220*b**3) - 3*a**2*x**3*(a + b*x**3)**(2/3)/(110*b**2) + a*x**6*(a + b*x**3)**(2/3)/(44*b) + x**9*(a + b*x**3)**(2/3)/11, Ne(b, 0)), (a**(2/3)*x**9/9, True))","A",0
529,1,63,0,1.938237," ","integrate(x**5*(b*x**3+a)**(2/3),x)","\begin{cases} - \frac{3 a^{2} \left(a + b x^{3}\right)^{\frac{2}{3}}}{40 b^{2}} + \frac{a x^{3} \left(a + b x^{3}\right)^{\frac{2}{3}}}{20 b} + \frac{x^{6} \left(a + b x^{3}\right)^{\frac{2}{3}}}{8} & \text{for}\: b \neq 0 \\\frac{a^{\frac{2}{3}} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a**2*(a + b*x**3)**(2/3)/(40*b**2) + a*x**3*(a + b*x**3)**(2/3)/(20*b) + x**6*(a + b*x**3)**(2/3)/8, Ne(b, 0)), (a**(2/3)*x**6/6, True))","A",0
530,1,39,0,0.931330," ","integrate(x**2*(b*x**3+a)**(2/3),x)","\begin{cases} \frac{a \left(a + b x^{3}\right)^{\frac{2}{3}}}{5 b} + \frac{x^{3} \left(a + b x^{3}\right)^{\frac{2}{3}}}{5} & \text{for}\: b \neq 0 \\\frac{a^{\frac{2}{3}} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*(a + b*x**3)**(2/3)/(5*b) + x**3*(a + b*x**3)**(2/3)/5, Ne(b, 0)), (a**(2/3)*x**3/3, True))","A",0
531,1,44,0,2.190618," ","integrate((b*x**3+a)**(2/3)/x,x)","- \frac{b^{\frac{2}{3}} x^{2} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{2}{3} \\ \frac{1}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{3}}} \right)}}{3 \Gamma\left(\frac{1}{3}\right)}"," ",0,"-b**(2/3)*x**2*gamma(-2/3)*hyper((-2/3, -2/3), (1/3,), a*exp_polar(I*pi)/(b*x**3))/(3*gamma(1/3))","C",0
532,1,39,0,1.347714," ","integrate((b*x**3+a)**(2/3)/x**4,x)","- \frac{b^{\frac{2}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{3}}} \right)}}{3 x \Gamma\left(\frac{4}{3}\right)}"," ",0,"-b**(2/3)*gamma(1/3)*hyper((-2/3, 1/3), (4/3,), a*exp_polar(I*pi)/(b*x**3))/(3*x*gamma(4/3))","C",0
533,1,39,0,2.049271," ","integrate(x**4*(b*x**3+a)**(2/3),x)","\frac{a^{\frac{2}{3}} x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)}"," ",0,"a**(2/3)*x**5*gamma(5/3)*hyper((-2/3, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3))","C",0
534,1,39,0,1.370937," ","integrate(x*(b*x**3+a)**(2/3),x)","\frac{a^{\frac{2}{3}} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"a**(2/3)*x**2*gamma(2/3)*hyper((-2/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3))","C",0
535,1,41,0,1.556361," ","integrate((b*x**3+a)**(2/3)/x**2,x)","\frac{a^{\frac{2}{3}} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)}"," ",0,"a**(2/3)*gamma(-1/3)*hyper((-2/3, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3))","C",0
536,1,46,0,1.324174," ","integrate((b*x**3+a)**(2/3)/x**5,x)","\frac{a^{\frac{2}{3}} \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{2}{3} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"a**(2/3)*gamma(-4/3)*hyper((-4/3, -2/3), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3))","C",0
537,1,39,0,2.495163," ","integrate(x**3*(b*x**3+a)**(2/3),x)","\frac{a^{\frac{2}{3}} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"a**(2/3)*x**4*gamma(4/3)*hyper((-2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3))","C",0
538,1,37,0,2.193766," ","integrate((b*x**3+a)**(2/3),x)","\frac{a^{\frac{2}{3}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"a**(2/3)*x*gamma(1/3)*hyper((-2/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3))","C",0
539,1,42,0,2.097322," ","integrate((b*x**3+a)**(2/3)/x**3,x)","\frac{a^{\frac{2}{3}} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{2}{3} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"a**(2/3)*gamma(-2/3)*hyper((-2/3, -2/3), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3))","C",0
540,1,68,0,1.274401," ","integrate((b*x**3+a)**(2/3)/x**6,x)","\frac{b^{\frac{2}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{5}{3}\right)}{3 x^{3} \Gamma\left(- \frac{2}{3}\right)} + \frac{b^{\frac{5}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{5}{3}\right)}{3 a \Gamma\left(- \frac{2}{3}\right)}"," ",0,"b**(2/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-5/3)/(3*x**3*gamma(-2/3)) + b**(5/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-5/3)/(3*a*gamma(-2/3))","B",0
541,1,110,0,1.991888," ","integrate((b*x**3+a)**(2/3)/x**9,x)","- \frac{5 b^{\frac{2}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{8}{3}\right)}{9 x^{6} \Gamma\left(- \frac{2}{3}\right)} - \frac{2 b^{\frac{5}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{8}{3}\right)}{9 a x^{3} \Gamma\left(- \frac{2}{3}\right)} + \frac{b^{\frac{8}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{8}{3}\right)}{3 a^{2} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"-5*b**(2/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-8/3)/(9*x**6*gamma(-2/3)) - 2*b**(5/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-8/3)/(9*a*x**3*gamma(-2/3)) + b**(8/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-8/3)/(3*a**2*gamma(-2/3))","B",0
542,1,520,0,2.232348," ","integrate((b*x**3+a)**(2/3)/x**12,x)","\frac{40 a^{5} b^{\frac{14}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{2}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{2}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{2}{3}\right)} + \frac{90 a^{4} b^{\frac{17}{3}} x^{3} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{2}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{2}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{2}{3}\right)} + \frac{48 a^{3} b^{\frac{20}{3}} x^{6} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{2}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{2}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{2}{3}\right)} + \frac{4 a^{2} b^{\frac{23}{3}} x^{9} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{2}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{2}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{2}{3}\right)} + \frac{24 a b^{\frac{26}{3}} x^{12} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{2}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{2}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{2}{3}\right)} + \frac{18 b^{\frac{29}{3}} x^{15} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{27 a^{5} b^{4} x^{9} \Gamma\left(- \frac{2}{3}\right) + 54 a^{4} b^{5} x^{12} \Gamma\left(- \frac{2}{3}\right) + 27 a^{3} b^{6} x^{15} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"40*a**5*b**(14/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(27*a**5*b**4*x**9*gamma(-2/3) + 54*a**4*b**5*x**12*gamma(-2/3) + 27*a**3*b**6*x**15*gamma(-2/3)) + 90*a**4*b**(17/3)*x**3*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(27*a**5*b**4*x**9*gamma(-2/3) + 54*a**4*b**5*x**12*gamma(-2/3) + 27*a**3*b**6*x**15*gamma(-2/3)) + 48*a**3*b**(20/3)*x**6*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(27*a**5*b**4*x**9*gamma(-2/3) + 54*a**4*b**5*x**12*gamma(-2/3) + 27*a**3*b**6*x**15*gamma(-2/3)) + 4*a**2*b**(23/3)*x**9*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(27*a**5*b**4*x**9*gamma(-2/3) + 54*a**4*b**5*x**12*gamma(-2/3) + 27*a**3*b**6*x**15*gamma(-2/3)) + 24*a*b**(26/3)*x**12*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(27*a**5*b**4*x**9*gamma(-2/3) + 54*a**4*b**5*x**12*gamma(-2/3) + 27*a**3*b**6*x**15*gamma(-2/3)) + 18*b**(29/3)*x**15*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(27*a**5*b**4*x**9*gamma(-2/3) + 54*a**4*b**5*x**12*gamma(-2/3) + 27*a**3*b**6*x**15*gamma(-2/3))","B",0
543,1,71,0,16.996607," ","integrate(x**8*(-x**3+1)**(6/5),x)","- \frac{5 x^{12} \sqrt[5]{1 - x^{3}}}{63} + \frac{55 x^{9} \sqrt[5]{1 - x^{3}}}{504} - \frac{5 x^{6} \sqrt[5]{1 - x^{3}}}{1848} - \frac{25 x^{3} \sqrt[5]{1 - x^{3}}}{5544} - \frac{125 \sqrt[5]{1 - x^{3}}}{5544}"," ",0,"-5*x**12*(1 - x**3)**(1/5)/63 + 55*x**9*(1 - x**3)**(1/5)/504 - 5*x**6*(1 - x**3)**(1/5)/1848 - 25*x**3*(1 - x**3)**(1/5)/5544 - 125*(1 - x**3)**(1/5)/5544","B",0
544,1,92,0,3.305577," ","integrate(x**11/(b*x**3+a)**(1/3),x)","\begin{cases} - \frac{81 a^{3} \left(a + b x^{3}\right)^{\frac{2}{3}}}{440 b^{4}} + \frac{27 a^{2} x^{3} \left(a + b x^{3}\right)^{\frac{2}{3}}}{220 b^{3}} - \frac{9 a x^{6} \left(a + b x^{3}\right)^{\frac{2}{3}}}{88 b^{2}} + \frac{x^{9} \left(a + b x^{3}\right)^{\frac{2}{3}}}{11 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 \sqrt[3]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-81*a**3*(a + b*x**3)**(2/3)/(440*b**4) + 27*a**2*x**3*(a + b*x**3)**(2/3)/(220*b**3) - 9*a*x**6*(a + b*x**3)**(2/3)/(88*b**2) + x**9*(a + b*x**3)**(2/3)/(11*b), Ne(b, 0)), (x**12/(12*a**(1/3)), True))","A",0
545,1,68,0,2.729137," ","integrate(x**8/(b*x**3+a)**(1/3),x)","\begin{cases} \frac{9 a^{2} \left(a + b x^{3}\right)^{\frac{2}{3}}}{40 b^{3}} - \frac{3 a x^{3} \left(a + b x^{3}\right)^{\frac{2}{3}}}{20 b^{2}} + \frac{x^{6} \left(a + b x^{3}\right)^{\frac{2}{3}}}{8 b} & \text{for}\: b \neq 0 \\\frac{x^{9}}{9 \sqrt[3]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a**2*(a + b*x**3)**(2/3)/(40*b**3) - 3*a*x**3*(a + b*x**3)**(2/3)/(20*b**2) + x**6*(a + b*x**3)**(2/3)/(8*b), Ne(b, 0)), (x**9/(9*a**(1/3)), True))","A",0
546,1,44,0,1.397428," ","integrate(x**5/(b*x**3+a)**(1/3),x)","\begin{cases} - \frac{3 a \left(a + b x^{3}\right)^{\frac{2}{3}}}{10 b^{2}} + \frac{x^{3} \left(a + b x^{3}\right)^{\frac{2}{3}}}{5 b} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 \sqrt[3]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a*(a + b*x**3)**(2/3)/(10*b**2) + x**3*(a + b*x**3)**(2/3)/(5*b), Ne(b, 0)), (x**6/(6*a**(1/3)), True))","A",0
547,1,22,0,0.489045," ","integrate(x**2/(b*x**3+a)**(1/3),x)","\begin{cases} \frac{\left(a + b x^{3}\right)^{\frac{2}{3}}}{2 b} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 \sqrt[3]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a + b*x**3)**(2/3)/(2*b), Ne(b, 0)), (x**3/(3*a**(1/3)), True))","A",0
548,1,37,0,1.107294," ","integrate(1/x/(b*x**3+a)**(1/3),x)","- \frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{3}}} \right)}}{3 \sqrt[3]{b} x \Gamma\left(\frac{4}{3}\right)}"," ",0,"-gamma(1/3)*hyper((1/3, 1/3), (4/3,), a*exp_polar(I*pi)/(b*x**3))/(3*b**(1/3)*x*gamma(4/3))","C",0
549,1,39,0,1.807713," ","integrate(1/x**4/(b*x**3+a)**(1/3),x)","- \frac{\Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{3}}} \right)}}{3 \sqrt[3]{b} x^{4} \Gamma\left(\frac{7}{3}\right)}"," ",0,"-gamma(4/3)*hyper((1/3, 4/3), (7/3,), a*exp_polar(I*pi)/(b*x**3))/(3*b**(1/3)*x**4*gamma(7/3))","C",0
550,1,37,0,1.851527," ","integrate(x**7/(b*x**3+a)**(1/3),x)","\frac{x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{11}{3}\right)}"," ",0,"x**8*gamma(8/3)*hyper((1/3, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(11/3))","C",0
551,1,37,0,1.416514," ","integrate(x**4/(b*x**3+a)**(1/3),x)","\frac{x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{8}{3}\right)}"," ",0,"x**5*gamma(5/3)*hyper((1/3, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(8/3))","C",0
552,1,37,0,1.423102," ","integrate(x/(b*x**3+a)**(1/3),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((1/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(5/3))","C",0
553,1,39,0,1.544903," ","integrate(1/x**2/(b*x**3+a)**(1/3),x)","\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} x \Gamma\left(\frac{2}{3}\right)}"," ",0,"gamma(-1/3)*hyper((-1/3, 1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*x*gamma(2/3))","C",0
554,1,44,0,1.227260," ","integrate(1/x**5/(b*x**3+a)**(1/3),x)","\frac{\Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{1}{3} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} x^{4} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"gamma(-4/3)*hyper((-4/3, 1/3), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*x**4*gamma(-1/3))","C",0
555,1,37,0,1.326420," ","integrate(x**3/(b*x**3+a)**(1/3),x)","\frac{x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{7}{3}\right)}"," ",0,"x**4*gamma(4/3)*hyper((1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(7/3))","C",0
556,1,36,0,1.798767," ","integrate(1/(b*x**3+a)**(1/3),x)","\frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(4/3))","C",0
557,1,31,0,1.288141," ","integrate(1/x**3/(b*x**3+a)**(1/3),x)","\frac{b^{\frac{2}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{2}{3}\right)}{3 a \Gamma\left(\frac{1}{3}\right)}"," ",0,"b**(2/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-2/3)/(3*a*gamma(1/3))","A",0
558,1,70,0,2.033498," ","integrate(1/x**6/(b*x**3+a)**(1/3),x)","- \frac{2 b^{\frac{2}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{5}{3}\right)}{9 a x^{3} \Gamma\left(\frac{1}{3}\right)} + \frac{b^{\frac{5}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{5}{3}\right)}{3 a^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"-2*b**(2/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-5/3)/(9*a*x**3*gamma(1/3)) + b**(5/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-5/3)/(3*a**2*gamma(1/3))","A",0
559,1,406,0,2.584770," ","integrate(1/x**9/(b*x**3+a)**(1/3),x)","\frac{10 a^{4} b^{\frac{14}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{8}{3}\right)}{27 a^{5} b^{4} x^{6} \Gamma\left(\frac{1}{3}\right) + 54 a^{4} b^{5} x^{9} \Gamma\left(\frac{1}{3}\right) + 27 a^{3} b^{6} x^{12} \Gamma\left(\frac{1}{3}\right)} + \frac{8 a^{3} b^{\frac{17}{3}} x^{3} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{8}{3}\right)}{27 a^{5} b^{4} x^{6} \Gamma\left(\frac{1}{3}\right) + 54 a^{4} b^{5} x^{9} \Gamma\left(\frac{1}{3}\right) + 27 a^{3} b^{6} x^{12} \Gamma\left(\frac{1}{3}\right)} + \frac{4 a^{2} b^{\frac{20}{3}} x^{6} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{8}{3}\right)}{27 a^{5} b^{4} x^{6} \Gamma\left(\frac{1}{3}\right) + 54 a^{4} b^{5} x^{9} \Gamma\left(\frac{1}{3}\right) + 27 a^{3} b^{6} x^{12} \Gamma\left(\frac{1}{3}\right)} + \frac{24 a b^{\frac{23}{3}} x^{9} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{8}{3}\right)}{27 a^{5} b^{4} x^{6} \Gamma\left(\frac{1}{3}\right) + 54 a^{4} b^{5} x^{9} \Gamma\left(\frac{1}{3}\right) + 27 a^{3} b^{6} x^{12} \Gamma\left(\frac{1}{3}\right)} + \frac{18 b^{\frac{26}{3}} x^{12} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{8}{3}\right)}{27 a^{5} b^{4} x^{6} \Gamma\left(\frac{1}{3}\right) + 54 a^{4} b^{5} x^{9} \Gamma\left(\frac{1}{3}\right) + 27 a^{3} b^{6} x^{12} \Gamma\left(\frac{1}{3}\right)}"," ",0,"10*a**4*b**(14/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-8/3)/(27*a**5*b**4*x**6*gamma(1/3) + 54*a**4*b**5*x**9*gamma(1/3) + 27*a**3*b**6*x**12*gamma(1/3)) + 8*a**3*b**(17/3)*x**3*(a/(b*x**3) + 1)**(2/3)*gamma(-8/3)/(27*a**5*b**4*x**6*gamma(1/3) + 54*a**4*b**5*x**9*gamma(1/3) + 27*a**3*b**6*x**12*gamma(1/3)) + 4*a**2*b**(20/3)*x**6*(a/(b*x**3) + 1)**(2/3)*gamma(-8/3)/(27*a**5*b**4*x**6*gamma(1/3) + 54*a**4*b**5*x**9*gamma(1/3) + 27*a**3*b**6*x**12*gamma(1/3)) + 24*a*b**(23/3)*x**9*(a/(b*x**3) + 1)**(2/3)*gamma(-8/3)/(27*a**5*b**4*x**6*gamma(1/3) + 54*a**4*b**5*x**9*gamma(1/3) + 27*a**3*b**6*x**12*gamma(1/3)) + 18*b**(26/3)*x**12*(a/(b*x**3) + 1)**(2/3)*gamma(-8/3)/(27*a**5*b**4*x**6*gamma(1/3) + 54*a**4*b**5*x**9*gamma(1/3) + 27*a**3*b**6*x**12*gamma(1/3))","B",0
560,1,692,0,3.439376," ","integrate(1/x**12/(b*x**3+a)**(1/3),x)","- \frac{80 a^{6} b^{\frac{29}{3}} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{1}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{1}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{1}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{1}{3}\right)} - \frac{150 a^{5} b^{\frac{32}{3}} x^{3} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{1}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{1}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{1}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{1}{3}\right)} - \frac{78 a^{4} b^{\frac{35}{3}} x^{6} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{1}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{1}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{1}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{1}{3}\right)} + \frac{28 a^{3} b^{\frac{38}{3}} x^{9} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{1}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{1}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{1}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{1}{3}\right)} + \frac{252 a^{2} b^{\frac{41}{3}} x^{12} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{1}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{1}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{1}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{1}{3}\right)} + \frac{378 a b^{\frac{44}{3}} x^{15} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{1}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{1}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{1}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{1}{3}\right)} + \frac{162 b^{\frac{47}{3}} x^{18} \left(\frac{a}{b x^{3}} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{11}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{1}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{1}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{1}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{1}{3}\right)}"," ",0,"-80*a**6*b**(29/3)*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(81*a**7*b**9*x**9*gamma(1/3) + 243*a**6*b**10*x**12*gamma(1/3) + 243*a**5*b**11*x**15*gamma(1/3) + 81*a**4*b**12*x**18*gamma(1/3)) - 150*a**5*b**(32/3)*x**3*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(81*a**7*b**9*x**9*gamma(1/3) + 243*a**6*b**10*x**12*gamma(1/3) + 243*a**5*b**11*x**15*gamma(1/3) + 81*a**4*b**12*x**18*gamma(1/3)) - 78*a**4*b**(35/3)*x**6*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(81*a**7*b**9*x**9*gamma(1/3) + 243*a**6*b**10*x**12*gamma(1/3) + 243*a**5*b**11*x**15*gamma(1/3) + 81*a**4*b**12*x**18*gamma(1/3)) + 28*a**3*b**(38/3)*x**9*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(81*a**7*b**9*x**9*gamma(1/3) + 243*a**6*b**10*x**12*gamma(1/3) + 243*a**5*b**11*x**15*gamma(1/3) + 81*a**4*b**12*x**18*gamma(1/3)) + 252*a**2*b**(41/3)*x**12*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(81*a**7*b**9*x**9*gamma(1/3) + 243*a**6*b**10*x**12*gamma(1/3) + 243*a**5*b**11*x**15*gamma(1/3) + 81*a**4*b**12*x**18*gamma(1/3)) + 378*a*b**(44/3)*x**15*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(81*a**7*b**9*x**9*gamma(1/3) + 243*a**6*b**10*x**12*gamma(1/3) + 243*a**5*b**11*x**15*gamma(1/3) + 81*a**4*b**12*x**18*gamma(1/3)) + 162*b**(47/3)*x**18*(a/(b*x**3) + 1)**(2/3)*gamma(-11/3)/(81*a**7*b**9*x**9*gamma(1/3) + 243*a**6*b**10*x**12*gamma(1/3) + 243*a**5*b**11*x**15*gamma(1/3) + 81*a**4*b**12*x**18*gamma(1/3))","B",0
561,1,92,0,3.359299," ","integrate(x**11/(b*x**3+a)**(2/3),x)","\begin{cases} - \frac{81 a^{3} \sqrt[3]{a + b x^{3}}}{140 b^{4}} + \frac{27 a^{2} x^{3} \sqrt[3]{a + b x^{3}}}{140 b^{3}} - \frac{9 a x^{6} \sqrt[3]{a + b x^{3}}}{70 b^{2}} + \frac{x^{9} \sqrt[3]{a + b x^{3}}}{10 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 a^{\frac{2}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-81*a**3*(a + b*x**3)**(1/3)/(140*b**4) + 27*a**2*x**3*(a + b*x**3)**(1/3)/(140*b**3) - 9*a*x**6*(a + b*x**3)**(1/3)/(70*b**2) + x**9*(a + b*x**3)**(1/3)/(10*b), Ne(b, 0)), (x**12/(12*a**(2/3)), True))","A",0
562,1,68,0,2.117728," ","integrate(x**8/(b*x**3+a)**(2/3),x)","\begin{cases} \frac{9 a^{2} \sqrt[3]{a + b x^{3}}}{14 b^{3}} - \frac{3 a x^{3} \sqrt[3]{a + b x^{3}}}{14 b^{2}} + \frac{x^{6} \sqrt[3]{a + b x^{3}}}{7 b} & \text{for}\: b \neq 0 \\\frac{x^{9}}{9 a^{\frac{2}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a**2*(a + b*x**3)**(1/3)/(14*b**3) - 3*a*x**3*(a + b*x**3)**(1/3)/(14*b**2) + x**6*(a + b*x**3)**(1/3)/(7*b), Ne(b, 0)), (x**9/(9*a**(2/3)), True))","A",0
563,1,44,0,0.899537," ","integrate(x**5/(b*x**3+a)**(2/3),x)","\begin{cases} - \frac{3 a \sqrt[3]{a + b x^{3}}}{4 b^{2}} + \frac{x^{3} \sqrt[3]{a + b x^{3}}}{4 b} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{2}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a*(a + b*x**3)**(1/3)/(4*b**2) + x**3*(a + b*x**3)**(1/3)/(4*b), Ne(b, 0)), (x**6/(6*a**(2/3)), True))","A",0
564,1,20,0,0.758044," ","integrate(x**2/(b*x**3+a)**(2/3),x)","\begin{cases} \frac{\sqrt[3]{a + b x^{3}}}{b} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{\frac{2}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a + b*x**3)**(1/3)/b, Ne(b, 0)), (x**3/(3*a**(2/3)), True))","A",0
565,1,39,0,1.763823," ","integrate(1/x/(b*x**3+a)**(2/3),x)","- \frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{3}}} \right)}}{3 b^{\frac{2}{3}} x^{2} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-gamma(2/3)*hyper((2/3, 2/3), (5/3,), a*exp_polar(I*pi)/(b*x**3))/(3*b**(2/3)*x**2*gamma(5/3))","C",0
566,1,39,0,2.261658," ","integrate(1/x**4/(b*x**3+a)**(2/3),x)","- \frac{\Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{3}}} \right)}}{3 b^{\frac{2}{3}} x^{5} \Gamma\left(\frac{8}{3}\right)}"," ",0,"-gamma(5/3)*hyper((2/3, 5/3), (8/3,), a*exp_polar(I*pi)/(b*x**3))/(3*b**(2/3)*x**5*gamma(8/3))","C",0
567,1,37,0,2.844259," ","integrate(x**7/(b*x**3+a)**(2/3),x)","\frac{x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{11}{3}\right)}"," ",0,"x**8*gamma(8/3)*hyper((2/3, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(11/3))","C",0
568,1,37,0,2.764242," ","integrate(x**4/(b*x**3+a)**(2/3),x)","\frac{x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"x**5*gamma(5/3)*hyper((2/3, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(8/3))","C",0
569,1,37,0,2.517786," ","integrate(x/(b*x**3+a)**(2/3),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((2/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(5/3))","C",0
570,1,31,0,1.150612," ","integrate(1/x**2/(b*x**3+a)**(2/3),x)","\frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)}"," ",0,"b**(1/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-1/3)/(3*a*gamma(2/3))","B",0
571,1,68,0,1.541604," ","integrate(1/x**5/(b*x**3+a)**(2/3),x)","- \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{4}{3}\right)}{9 a x^{3} \Gamma\left(\frac{2}{3}\right)} + \frac{b^{\frac{4}{3}} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{4}{3}\right)}{3 a^{2} \Gamma\left(\frac{2}{3}\right)}"," ",0,"-b**(1/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-4/3)/(9*a*x**3*gamma(2/3)) + b**(4/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-4/3)/(3*a**2*gamma(2/3))","A",0
572,1,406,0,3.048162," ","integrate(1/x**8/(b*x**3+a)**(2/3),x)","\frac{4 a^{4} b^{\frac{13}{3}} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{7}{3}\right)}{27 a^{5} b^{4} x^{6} \Gamma\left(\frac{2}{3}\right) + 54 a^{4} b^{5} x^{9} \Gamma\left(\frac{2}{3}\right) + 27 a^{3} b^{6} x^{12} \Gamma\left(\frac{2}{3}\right)} + \frac{2 a^{3} b^{\frac{16}{3}} x^{3} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{7}{3}\right)}{27 a^{5} b^{4} x^{6} \Gamma\left(\frac{2}{3}\right) + 54 a^{4} b^{5} x^{9} \Gamma\left(\frac{2}{3}\right) + 27 a^{3} b^{6} x^{12} \Gamma\left(\frac{2}{3}\right)} + \frac{10 a^{2} b^{\frac{19}{3}} x^{6} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{7}{3}\right)}{27 a^{5} b^{4} x^{6} \Gamma\left(\frac{2}{3}\right) + 54 a^{4} b^{5} x^{9} \Gamma\left(\frac{2}{3}\right) + 27 a^{3} b^{6} x^{12} \Gamma\left(\frac{2}{3}\right)} + \frac{30 a b^{\frac{22}{3}} x^{9} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{7}{3}\right)}{27 a^{5} b^{4} x^{6} \Gamma\left(\frac{2}{3}\right) + 54 a^{4} b^{5} x^{9} \Gamma\left(\frac{2}{3}\right) + 27 a^{3} b^{6} x^{12} \Gamma\left(\frac{2}{3}\right)} + \frac{18 b^{\frac{25}{3}} x^{12} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{7}{3}\right)}{27 a^{5} b^{4} x^{6} \Gamma\left(\frac{2}{3}\right) + 54 a^{4} b^{5} x^{9} \Gamma\left(\frac{2}{3}\right) + 27 a^{3} b^{6} x^{12} \Gamma\left(\frac{2}{3}\right)}"," ",0,"4*a**4*b**(13/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-7/3)/(27*a**5*b**4*x**6*gamma(2/3) + 54*a**4*b**5*x**9*gamma(2/3) + 27*a**3*b**6*x**12*gamma(2/3)) + 2*a**3*b**(16/3)*x**3*(a/(b*x**3) + 1)**(1/3)*gamma(-7/3)/(27*a**5*b**4*x**6*gamma(2/3) + 54*a**4*b**5*x**9*gamma(2/3) + 27*a**3*b**6*x**12*gamma(2/3)) + 10*a**2*b**(19/3)*x**6*(a/(b*x**3) + 1)**(1/3)*gamma(-7/3)/(27*a**5*b**4*x**6*gamma(2/3) + 54*a**4*b**5*x**9*gamma(2/3) + 27*a**3*b**6*x**12*gamma(2/3)) + 30*a*b**(22/3)*x**9*(a/(b*x**3) + 1)**(1/3)*gamma(-7/3)/(27*a**5*b**4*x**6*gamma(2/3) + 54*a**4*b**5*x**9*gamma(2/3) + 27*a**3*b**6*x**12*gamma(2/3)) + 18*b**(25/3)*x**12*(a/(b*x**3) + 1)**(1/3)*gamma(-7/3)/(27*a**5*b**4*x**6*gamma(2/3) + 54*a**4*b**5*x**9*gamma(2/3) + 27*a**3*b**6*x**12*gamma(2/3))","B",0
573,1,692,0,3.183221," ","integrate(1/x**11/(b*x**3+a)**(2/3),x)","- \frac{28 a^{6} b^{\frac{28}{3}} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} - \frac{48 a^{5} b^{\frac{31}{3}} x^{3} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} - \frac{30 a^{4} b^{\frac{34}{3}} x^{6} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} + \frac{80 a^{3} b^{\frac{37}{3}} x^{9} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} + \frac{360 a^{2} b^{\frac{40}{3}} x^{12} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} + \frac{432 a b^{\frac{43}{3}} x^{15} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} + \frac{162 b^{\frac{46}{3}} x^{18} \sqrt[3]{\frac{a}{b x^{3}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{9} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{12} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{15} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)}"," ",0,"-28*a**6*b**(28/3)*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**9*gamma(2/3) + 243*a**6*b**10*x**12*gamma(2/3) + 243*a**5*b**11*x**15*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) - 48*a**5*b**(31/3)*x**3*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**9*gamma(2/3) + 243*a**6*b**10*x**12*gamma(2/3) + 243*a**5*b**11*x**15*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) - 30*a**4*b**(34/3)*x**6*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**9*gamma(2/3) + 243*a**6*b**10*x**12*gamma(2/3) + 243*a**5*b**11*x**15*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) + 80*a**3*b**(37/3)*x**9*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**9*gamma(2/3) + 243*a**6*b**10*x**12*gamma(2/3) + 243*a**5*b**11*x**15*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) + 360*a**2*b**(40/3)*x**12*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**9*gamma(2/3) + 243*a**6*b**10*x**12*gamma(2/3) + 243*a**5*b**11*x**15*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) + 432*a*b**(43/3)*x**15*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**9*gamma(2/3) + 243*a**6*b**10*x**12*gamma(2/3) + 243*a**5*b**11*x**15*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) + 162*b**(46/3)*x**18*(a/(b*x**3) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**9*gamma(2/3) + 243*a**6*b**10*x**12*gamma(2/3) + 243*a**5*b**11*x**15*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3))","B",0
574,1,37,0,1.483471," ","integrate(x**6/(b*x**3+a)**(2/3),x)","\frac{x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{10}{3}\right)}"," ",0,"x**7*gamma(7/3)*hyper((2/3, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(10/3))","C",0
575,1,37,0,1.382646," ","integrate(x**3/(b*x**3+a)**(2/3),x)","\frac{x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"x**4*gamma(4/3)*hyper((2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(7/3))","C",0
576,1,36,0,0.901937," ","integrate(1/(b*x**3+a)**(2/3),x)","\frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{2}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)}"," ",0,"x*gamma(1/3)*hyper((1/3, 2/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(4/3))","C",0
577,1,41,0,1.180083," ","integrate(1/x**3/(b*x**3+a)**(2/3),x)","\frac{\Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{2}{3} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} x^{2} \Gamma\left(\frac{1}{3}\right)}"," ",0,"gamma(-2/3)*hyper((-2/3, 2/3), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*x**2*gamma(1/3))","C",0
578,1,44,0,1.590782," ","integrate(1/x**6/(b*x**3+a)**(2/3),x)","\frac{\Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, \frac{2}{3} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} x^{5} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"gamma(-5/3)*hyper((-5/3, 2/3), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*x**5*gamma(-2/3))","C",0
579,1,37,0,1.726819," ","integrate(1/(-b*x**3+a)**(1/3),x)","\frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*a**(1/3)*gamma(4/3))","C",0
580,1,34,0,1.805459," ","integrate(1/(x**3+2)**(1/3),x)","\frac{2^{\frac{2}{3}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3} e^{i \pi}}{2}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}"," ",0,"2**(2/3)*x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), x**3*exp_polar(I*pi)/2)/(6*gamma(4/3))","C",0
581,1,31,0,2.014459," ","integrate(x/(-x**3+1)**(2/3),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((2/3, 2/3), (5/3,), x**3*exp_polar(2*I*pi))/(3*gamma(5/3))","C",0
582,1,10,0,0.717988," ","integrate(x**2/(x**3+2)**(1/4),x)","\frac{4 \left(x^{3} + 2\right)^{\frac{3}{4}}}{9}"," ",0,"4*(x**3 + 2)**(3/4)/9","A",0
583,1,5902,0,47.373837," ","integrate(x**m*(b*x**3+a)**8,x)","\begin{cases} - \frac{a^{8}}{24 x^{24}} - \frac{8 a^{7} b}{21 x^{21}} - \frac{14 a^{6} b^{2}}{9 x^{18}} - \frac{56 a^{5} b^{3}}{15 x^{15}} - \frac{35 a^{4} b^{4}}{6 x^{12}} - \frac{56 a^{3} b^{5}}{9 x^{9}} - \frac{14 a^{2} b^{6}}{3 x^{6}} - \frac{8 a b^{7}}{3 x^{3}} + b^{8} \log{\left(x \right)} & \text{for}\: m = -25 \\- \frac{a^{8}}{21 x^{21}} - \frac{4 a^{7} b}{9 x^{18}} - \frac{28 a^{6} b^{2}}{15 x^{15}} - \frac{14 a^{5} b^{3}}{3 x^{12}} - \frac{70 a^{4} b^{4}}{9 x^{9}} - \frac{28 a^{3} b^{5}}{3 x^{6}} - \frac{28 a^{2} b^{6}}{3 x^{3}} + 8 a b^{7} \log{\left(x \right)} + \frac{b^{8} x^{3}}{3} & \text{for}\: m = -22 \\- \frac{a^{8}}{18 x^{18}} - \frac{8 a^{7} b}{15 x^{15}} - \frac{7 a^{6} b^{2}}{3 x^{12}} - \frac{56 a^{5} b^{3}}{9 x^{9}} - \frac{35 a^{4} b^{4}}{3 x^{6}} - \frac{56 a^{3} b^{5}}{3 x^{3}} + 28 a^{2} b^{6} \log{\left(x \right)} + \frac{8 a b^{7} x^{3}}{3} + \frac{b^{8} x^{6}}{6} & \text{for}\: m = -19 \\- \frac{a^{8}}{15 x^{15}} - \frac{2 a^{7} b}{3 x^{12}} - \frac{28 a^{6} b^{2}}{9 x^{9}} - \frac{28 a^{5} b^{3}}{3 x^{6}} - \frac{70 a^{4} b^{4}}{3 x^{3}} + 56 a^{3} b^{5} \log{\left(x \right)} + \frac{28 a^{2} b^{6} x^{3}}{3} + \frac{4 a b^{7} x^{6}}{3} + \frac{b^{8} x^{9}}{9} & \text{for}\: m = -16 \\- \frac{a^{8}}{12 x^{12}} - \frac{8 a^{7} b}{9 x^{9}} - \frac{14 a^{6} b^{2}}{3 x^{6}} - \frac{56 a^{5} b^{3}}{3 x^{3}} + 70 a^{4} b^{4} \log{\left(x \right)} + \frac{56 a^{3} b^{5} x^{3}}{3} + \frac{14 a^{2} b^{6} x^{6}}{3} + \frac{8 a b^{7} x^{9}}{9} + \frac{b^{8} x^{12}}{12} & \text{for}\: m = -13 \\- \frac{a^{8}}{9 x^{9}} - \frac{4 a^{7} b}{3 x^{6}} - \frac{28 a^{6} b^{2}}{3 x^{3}} + 56 a^{5} b^{3} \log{\left(x \right)} + \frac{70 a^{4} b^{4} x^{3}}{3} + \frac{28 a^{3} b^{5} x^{6}}{3} + \frac{28 a^{2} b^{6} x^{9}}{9} + \frac{2 a b^{7} x^{12}}{3} + \frac{b^{8} x^{15}}{15} & \text{for}\: m = -10 \\- \frac{a^{8}}{6 x^{6}} - \frac{8 a^{7} b}{3 x^{3}} + 28 a^{6} b^{2} \log{\left(x \right)} + \frac{56 a^{5} b^{3} x^{3}}{3} + \frac{35 a^{4} b^{4} x^{6}}{3} + \frac{56 a^{3} b^{5} x^{9}}{9} + \frac{7 a^{2} b^{6} x^{12}}{3} + \frac{8 a b^{7} x^{15}}{15} + \frac{b^{8} x^{18}}{18} & \text{for}\: m = -7 \\- \frac{a^{8}}{3 x^{3}} + 8 a^{7} b \log{\left(x \right)} + \frac{28 a^{6} b^{2} x^{3}}{3} + \frac{28 a^{5} b^{3} x^{6}}{3} + \frac{70 a^{4} b^{4} x^{9}}{9} + \frac{14 a^{3} b^{5} x^{12}}{3} + \frac{28 a^{2} b^{6} x^{15}}{15} + \frac{4 a b^{7} x^{18}}{9} + \frac{b^{8} x^{21}}{21} & \text{for}\: m = -4 \\a^{8} \log{\left(x \right)} + \frac{8 a^{7} b x^{3}}{3} + \frac{14 a^{6} b^{2} x^{6}}{3} + \frac{56 a^{5} b^{3} x^{9}}{9} + \frac{35 a^{4} b^{4} x^{12}}{6} + \frac{56 a^{3} b^{5} x^{15}}{15} + \frac{14 a^{2} b^{6} x^{18}}{9} + \frac{8 a b^{7} x^{21}}{21} + \frac{b^{8} x^{24}}{24} & \text{for}\: m = -1 \\\frac{a^{8} m^{8} x x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{116 a^{8} m^{7} x x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{5698 a^{8} m^{6} x x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{154280 a^{8} m^{5} x x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{2508289 a^{8} m^{4} x x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{24950324 a^{8} m^{3} x x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{147373372 a^{8} m^{2} x x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{468851120 a^{8} m x x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{608608000 a^{8} x x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{8 a^{7} b m^{8} x^{4} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{904 a^{7} b m^{7} x^{4} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{42896 a^{7} b m^{6} x^{4} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{1108240 a^{7} b m^{5} x^{4} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{16867592 a^{7} b m^{4} x^{4} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{152198536 a^{7} b m^{3} x^{4} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{769795424 a^{7} b m^{2} x^{4} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{1850614240 a^{7} b m x^{4} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{1217216000 a^{7} b x^{4} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{28 a^{6} b^{2} m^{8} x^{7} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{3080 a^{6} b^{2} m^{7} x^{7} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{141232 a^{6} b^{2} m^{6} x^{7} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{3490760 a^{6} b^{2} m^{5} x^{7} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{50116612 a^{6} b^{2} m^{4} x^{7} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{418024880 a^{6} b^{2} m^{3} x^{7} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{1898889328 a^{6} b^{2} m^{2} x^{7} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{3962060480 a^{6} b^{2} m x^{7} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{2434432000 a^{6} b^{2} x^{7} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{56 a^{5} b^{3} m^{8} x^{10} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{5992 a^{5} b^{3} m^{7} x^{10} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{265664 a^{5} b^{3} m^{6} x^{10} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{6302128 a^{5} b^{3} m^{5} x^{10} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{86082584 a^{5} b^{3} m^{4} x^{10} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{676856488 a^{5} b^{3} m^{3} x^{10} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{2881562096 a^{5} b^{3} m^{2} x^{10} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{5692950592 a^{5} b^{3} m x^{10} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{3408204800 a^{5} b^{3} x^{10} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{70 a^{4} b^{4} m^{8} x^{13} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{7280 a^{4} b^{4} m^{7} x^{13} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{312340 a^{4} b^{4} m^{6} x^{13} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{7138040 a^{4} b^{4} m^{5} x^{13} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{93585310 a^{4} b^{4} m^{4} x^{13} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{705493880 a^{4} b^{4} m^{3} x^{13} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{2891238280 a^{4} b^{4} m^{2} x^{13} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{5549616800 a^{4} b^{4} m x^{13} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{3277120000 a^{4} b^{4} x^{13} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{56 a^{3} b^{5} m^{8} x^{16} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{5656 a^{3} b^{5} m^{7} x^{16} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{235088 a^{3} b^{5} m^{6} x^{16} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{5197360 a^{3} b^{5} m^{5} x^{16} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{65946104 a^{3} b^{5} m^{4} x^{16} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{482544664 a^{3} b^{5} m^{3} x^{16} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{1929412352 a^{3} b^{5} m^{2} x^{16} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{3637973920 a^{3} b^{5} m x^{16} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{2130128000 a^{3} b^{5} x^{16} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{28 a^{2} b^{6} m^{8} x^{19} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{2744 a^{2} b^{6} m^{7} x^{19} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{110656 a^{2} b^{6} m^{6} x^{19} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{2376920 a^{2} b^{6} m^{5} x^{19} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{29390452 a^{2} b^{6} m^{4} x^{19} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{210422576 a^{2} b^{6} m^{3} x^{19} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{827034544 a^{2} b^{6} m^{2} x^{19} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{1540629440 a^{2} b^{6} m x^{19} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{896896000 a^{2} b^{6} x^{19} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{8 a b^{7} m^{8} x^{22} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{760 a b^{7} m^{7} x^{22} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{29792 a b^{7} m^{6} x^{22} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{624400 a b^{7} m^{5} x^{22} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{7563752 a b^{7} m^{4} x^{22} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{53266360 a b^{7} m^{3} x^{22} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{206729648 a b^{7} m^{2} x^{22} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{381743680 a b^{7} m x^{22} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{221312000 a b^{7} x^{22} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{b^{8} m^{8} x^{25} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{92 b^{8} m^{7} x^{25} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{3514 b^{8} m^{6} x^{25} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{72128 b^{8} m^{5} x^{25} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{859369 b^{8} m^{4} x^{25} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{5974388 b^{8} m^{3} x^{25} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{22963996 b^{8} m^{2} x^{25} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{42124592 b^{8} m x^{25} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} + \frac{24344320 b^{8} x^{25} x^{m}}{m^{9} + 117 m^{8} + 5814 m^{7} + 159978 m^{6} + 2662569 m^{5} + 27458613 m^{4} + 172323696 m^{3} + 616224492 m^{2} + 1077459120 m + 608608000} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**8/(24*x**24) - 8*a**7*b/(21*x**21) - 14*a**6*b**2/(9*x**18) - 56*a**5*b**3/(15*x**15) - 35*a**4*b**4/(6*x**12) - 56*a**3*b**5/(9*x**9) - 14*a**2*b**6/(3*x**6) - 8*a*b**7/(3*x**3) + b**8*log(x), Eq(m, -25)), (-a**8/(21*x**21) - 4*a**7*b/(9*x**18) - 28*a**6*b**2/(15*x**15) - 14*a**5*b**3/(3*x**12) - 70*a**4*b**4/(9*x**9) - 28*a**3*b**5/(3*x**6) - 28*a**2*b**6/(3*x**3) + 8*a*b**7*log(x) + b**8*x**3/3, Eq(m, -22)), (-a**8/(18*x**18) - 8*a**7*b/(15*x**15) - 7*a**6*b**2/(3*x**12) - 56*a**5*b**3/(9*x**9) - 35*a**4*b**4/(3*x**6) - 56*a**3*b**5/(3*x**3) + 28*a**2*b**6*log(x) + 8*a*b**7*x**3/3 + b**8*x**6/6, Eq(m, -19)), (-a**8/(15*x**15) - 2*a**7*b/(3*x**12) - 28*a**6*b**2/(9*x**9) - 28*a**5*b**3/(3*x**6) - 70*a**4*b**4/(3*x**3) + 56*a**3*b**5*log(x) + 28*a**2*b**6*x**3/3 + 4*a*b**7*x**6/3 + b**8*x**9/9, Eq(m, -16)), (-a**8/(12*x**12) - 8*a**7*b/(9*x**9) - 14*a**6*b**2/(3*x**6) - 56*a**5*b**3/(3*x**3) + 70*a**4*b**4*log(x) + 56*a**3*b**5*x**3/3 + 14*a**2*b**6*x**6/3 + 8*a*b**7*x**9/9 + b**8*x**12/12, Eq(m, -13)), (-a**8/(9*x**9) - 4*a**7*b/(3*x**6) - 28*a**6*b**2/(3*x**3) + 56*a**5*b**3*log(x) + 70*a**4*b**4*x**3/3 + 28*a**3*b**5*x**6/3 + 28*a**2*b**6*x**9/9 + 2*a*b**7*x**12/3 + b**8*x**15/15, Eq(m, -10)), (-a**8/(6*x**6) - 8*a**7*b/(3*x**3) + 28*a**6*b**2*log(x) + 56*a**5*b**3*x**3/3 + 35*a**4*b**4*x**6/3 + 56*a**3*b**5*x**9/9 + 7*a**2*b**6*x**12/3 + 8*a*b**7*x**15/15 + b**8*x**18/18, Eq(m, -7)), (-a**8/(3*x**3) + 8*a**7*b*log(x) + 28*a**6*b**2*x**3/3 + 28*a**5*b**3*x**6/3 + 70*a**4*b**4*x**9/9 + 14*a**3*b**5*x**12/3 + 28*a**2*b**6*x**15/15 + 4*a*b**7*x**18/9 + b**8*x**21/21, Eq(m, -4)), (a**8*log(x) + 8*a**7*b*x**3/3 + 14*a**6*b**2*x**6/3 + 56*a**5*b**3*x**9/9 + 35*a**4*b**4*x**12/6 + 56*a**3*b**5*x**15/15 + 14*a**2*b**6*x**18/9 + 8*a*b**7*x**21/21 + b**8*x**24/24, Eq(m, -1)), (a**8*m**8*x*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 116*a**8*m**7*x*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 5698*a**8*m**6*x*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 154280*a**8*m**5*x*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 2508289*a**8*m**4*x*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 24950324*a**8*m**3*x*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 147373372*a**8*m**2*x*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 468851120*a**8*m*x*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 608608000*a**8*x*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 8*a**7*b*m**8*x**4*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 904*a**7*b*m**7*x**4*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 42896*a**7*b*m**6*x**4*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 1108240*a**7*b*m**5*x**4*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 16867592*a**7*b*m**4*x**4*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 152198536*a**7*b*m**3*x**4*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 769795424*a**7*b*m**2*x**4*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 1850614240*a**7*b*m*x**4*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 1217216000*a**7*b*x**4*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 28*a**6*b**2*m**8*x**7*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 3080*a**6*b**2*m**7*x**7*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 141232*a**6*b**2*m**6*x**7*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 3490760*a**6*b**2*m**5*x**7*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 50116612*a**6*b**2*m**4*x**7*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 418024880*a**6*b**2*m**3*x**7*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 1898889328*a**6*b**2*m**2*x**7*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 3962060480*a**6*b**2*m*x**7*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 2434432000*a**6*b**2*x**7*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 56*a**5*b**3*m**8*x**10*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 5992*a**5*b**3*m**7*x**10*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 265664*a**5*b**3*m**6*x**10*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 6302128*a**5*b**3*m**5*x**10*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 86082584*a**5*b**3*m**4*x**10*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 676856488*a**5*b**3*m**3*x**10*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 2881562096*a**5*b**3*m**2*x**10*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 5692950592*a**5*b**3*m*x**10*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 3408204800*a**5*b**3*x**10*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 70*a**4*b**4*m**8*x**13*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 7280*a**4*b**4*m**7*x**13*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 312340*a**4*b**4*m**6*x**13*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 7138040*a**4*b**4*m**5*x**13*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 93585310*a**4*b**4*m**4*x**13*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 705493880*a**4*b**4*m**3*x**13*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 2891238280*a**4*b**4*m**2*x**13*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 5549616800*a**4*b**4*m*x**13*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 3277120000*a**4*b**4*x**13*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 56*a**3*b**5*m**8*x**16*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 5656*a**3*b**5*m**7*x**16*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 235088*a**3*b**5*m**6*x**16*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 5197360*a**3*b**5*m**5*x**16*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 65946104*a**3*b**5*m**4*x**16*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 482544664*a**3*b**5*m**3*x**16*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 1929412352*a**3*b**5*m**2*x**16*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 3637973920*a**3*b**5*m*x**16*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 2130128000*a**3*b**5*x**16*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 28*a**2*b**6*m**8*x**19*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 2744*a**2*b**6*m**7*x**19*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 110656*a**2*b**6*m**6*x**19*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 2376920*a**2*b**6*m**5*x**19*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 29390452*a**2*b**6*m**4*x**19*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 210422576*a**2*b**6*m**3*x**19*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 827034544*a**2*b**6*m**2*x**19*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 1540629440*a**2*b**6*m*x**19*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 896896000*a**2*b**6*x**19*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 8*a*b**7*m**8*x**22*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 760*a*b**7*m**7*x**22*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 29792*a*b**7*m**6*x**22*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 624400*a*b**7*m**5*x**22*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 7563752*a*b**7*m**4*x**22*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 53266360*a*b**7*m**3*x**22*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 206729648*a*b**7*m**2*x**22*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 381743680*a*b**7*m*x**22*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 221312000*a*b**7*x**22*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + b**8*m**8*x**25*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 92*b**8*m**7*x**25*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 3514*b**8*m**6*x**25*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 72128*b**8*m**5*x**25*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 859369*b**8*m**4*x**25*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 5974388*b**8*m**3*x**25*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 22963996*b**8*m**2*x**25*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 42124592*b**8*m*x**25*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000) + 24344320*b**8*x**25*x**m/(m**9 + 117*m**8 + 5814*m**7 + 159978*m**6 + 2662569*m**5 + 27458613*m**4 + 172323696*m**3 + 616224492*m**2 + 1077459120*m + 608608000), True))","A",0
584,1,2006,0,14.930542," ","integrate(x**m*(b*x**3+a)**5,x)","\begin{cases} - \frac{a^{5}}{15 x^{15}} - \frac{5 a^{4} b}{12 x^{12}} - \frac{10 a^{3} b^{2}}{9 x^{9}} - \frac{5 a^{2} b^{3}}{3 x^{6}} - \frac{5 a b^{4}}{3 x^{3}} + b^{5} \log{\left(x \right)} & \text{for}\: m = -16 \\- \frac{a^{5}}{12 x^{12}} - \frac{5 a^{4} b}{9 x^{9}} - \frac{5 a^{3} b^{2}}{3 x^{6}} - \frac{10 a^{2} b^{3}}{3 x^{3}} + 5 a b^{4} \log{\left(x \right)} + \frac{b^{5} x^{3}}{3} & \text{for}\: m = -13 \\- \frac{a^{5}}{9 x^{9}} - \frac{5 a^{4} b}{6 x^{6}} - \frac{10 a^{3} b^{2}}{3 x^{3}} + 10 a^{2} b^{3} \log{\left(x \right)} + \frac{5 a b^{4} x^{3}}{3} + \frac{b^{5} x^{6}}{6} & \text{for}\: m = -10 \\- \frac{a^{5}}{6 x^{6}} - \frac{5 a^{4} b}{3 x^{3}} + 10 a^{3} b^{2} \log{\left(x \right)} + \frac{10 a^{2} b^{3} x^{3}}{3} + \frac{5 a b^{4} x^{6}}{6} + \frac{b^{5} x^{9}}{9} & \text{for}\: m = -7 \\- \frac{a^{5}}{3 x^{3}} + 5 a^{4} b \log{\left(x \right)} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{6}}{3} + \frac{5 a b^{4} x^{9}}{9} + \frac{b^{5} x^{12}}{12} & \text{for}\: m = -4 \\a^{5} \log{\left(x \right)} + \frac{5 a^{4} b x^{3}}{3} + \frac{5 a^{3} b^{2} x^{6}}{3} + \frac{10 a^{2} b^{3} x^{9}}{9} + \frac{5 a b^{4} x^{12}}{12} + \frac{b^{5} x^{15}}{15} & \text{for}\: m = -1 \\\frac{a^{5} m^{5} x x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{50 a^{5} m^{4} x x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{955 a^{5} m^{3} x x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{8650 a^{5} m^{2} x x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{36824 a^{5} m x x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{58240 a^{5} x x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{5 a^{4} b m^{5} x^{4} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{235 a^{4} b m^{4} x^{4} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{4085 a^{4} b m^{3} x^{4} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{31685 a^{4} b m^{2} x^{4} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{100630 a^{4} b m x^{4} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{72800 a^{4} b x^{4} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{10 a^{3} b^{2} m^{5} x^{7} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{440 a^{3} b^{2} m^{4} x^{7} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{6970 a^{3} b^{2} m^{3} x^{7} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{47260 a^{3} b^{2} m^{2} x^{7} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{123920 a^{3} b^{2} m x^{7} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{83200 a^{3} b^{2} x^{7} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{10 a^{2} b^{3} m^{5} x^{10} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{410 a^{2} b^{3} m^{4} x^{10} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{5950 a^{2} b^{3} m^{3} x^{10} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{36550 a^{2} b^{3} m^{2} x^{10} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{89240 a^{2} b^{3} m x^{10} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{58240 a^{2} b^{3} x^{10} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{5 a b^{4} m^{5} x^{13} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{190 a b^{4} m^{4} x^{13} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{2555 a b^{4} m^{3} x^{13} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{14810 a b^{4} m^{2} x^{13} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{34840 a b^{4} m x^{13} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{22400 a b^{4} x^{13} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{b^{5} m^{5} x^{16} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{35 b^{5} m^{4} x^{16} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{445 b^{5} m^{3} x^{16} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{2485 b^{5} m^{2} x^{16} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{5714 b^{5} m x^{16} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} + \frac{3640 b^{5} x^{16} x^{m}}{m^{6} + 51 m^{5} + 1005 m^{4} + 9605 m^{3} + 45474 m^{2} + 95064 m + 58240} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**5/(15*x**15) - 5*a**4*b/(12*x**12) - 10*a**3*b**2/(9*x**9) - 5*a**2*b**3/(3*x**6) - 5*a*b**4/(3*x**3) + b**5*log(x), Eq(m, -16)), (-a**5/(12*x**12) - 5*a**4*b/(9*x**9) - 5*a**3*b**2/(3*x**6) - 10*a**2*b**3/(3*x**3) + 5*a*b**4*log(x) + b**5*x**3/3, Eq(m, -13)), (-a**5/(9*x**9) - 5*a**4*b/(6*x**6) - 10*a**3*b**2/(3*x**3) + 10*a**2*b**3*log(x) + 5*a*b**4*x**3/3 + b**5*x**6/6, Eq(m, -10)), (-a**5/(6*x**6) - 5*a**4*b/(3*x**3) + 10*a**3*b**2*log(x) + 10*a**2*b**3*x**3/3 + 5*a*b**4*x**6/6 + b**5*x**9/9, Eq(m, -7)), (-a**5/(3*x**3) + 5*a**4*b*log(x) + 10*a**3*b**2*x**3/3 + 5*a**2*b**3*x**6/3 + 5*a*b**4*x**9/9 + b**5*x**12/12, Eq(m, -4)), (a**5*log(x) + 5*a**4*b*x**3/3 + 5*a**3*b**2*x**6/3 + 10*a**2*b**3*x**9/9 + 5*a*b**4*x**12/12 + b**5*x**15/15, Eq(m, -1)), (a**5*m**5*x*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 50*a**5*m**4*x*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 955*a**5*m**3*x*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 8650*a**5*m**2*x*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 36824*a**5*m*x*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 58240*a**5*x*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 5*a**4*b*m**5*x**4*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 235*a**4*b*m**4*x**4*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 4085*a**4*b*m**3*x**4*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 31685*a**4*b*m**2*x**4*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 100630*a**4*b*m*x**4*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 72800*a**4*b*x**4*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 10*a**3*b**2*m**5*x**7*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 440*a**3*b**2*m**4*x**7*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 6970*a**3*b**2*m**3*x**7*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 47260*a**3*b**2*m**2*x**7*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 123920*a**3*b**2*m*x**7*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 83200*a**3*b**2*x**7*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 10*a**2*b**3*m**5*x**10*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 410*a**2*b**3*m**4*x**10*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 5950*a**2*b**3*m**3*x**10*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 36550*a**2*b**3*m**2*x**10*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 89240*a**2*b**3*m*x**10*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 58240*a**2*b**3*x**10*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 5*a*b**4*m**5*x**13*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 190*a*b**4*m**4*x**13*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 2555*a*b**4*m**3*x**13*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 14810*a*b**4*m**2*x**13*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 34840*a*b**4*m*x**13*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 22400*a*b**4*x**13*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + b**5*m**5*x**16*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 35*b**5*m**4*x**16*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 445*b**5*m**3*x**16*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 2485*b**5*m**2*x**16*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 5714*b**5*m*x**16*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240) + 3640*b**5*x**16*x**m/(m**6 + 51*m**5 + 1005*m**4 + 9605*m**3 + 45474*m**2 + 95064*m + 58240), True))","A",0
585,1,666,0,4.186254," ","integrate(x**m*(b*x**3+a)**3,x)","\begin{cases} - \frac{a^{3}}{9 x^{9}} - \frac{a^{2} b}{2 x^{6}} - \frac{a b^{2}}{x^{3}} + b^{3} \log{\left(x \right)} & \text{for}\: m = -10 \\- \frac{a^{3}}{6 x^{6}} - \frac{a^{2} b}{x^{3}} + 3 a b^{2} \log{\left(x \right)} + \frac{b^{3} x^{3}}{3} & \text{for}\: m = -7 \\- \frac{a^{3}}{3 x^{3}} + 3 a^{2} b \log{\left(x \right)} + a b^{2} x^{3} + \frac{b^{3} x^{6}}{6} & \text{for}\: m = -4 \\a^{3} \log{\left(x \right)} + a^{2} b x^{3} + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{9}}{9} & \text{for}\: m = -1 \\\frac{a^{3} m^{3} x x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{21 a^{3} m^{2} x x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{138 a^{3} m x x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{280 a^{3} x x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{3 a^{2} b m^{3} x^{4} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{54 a^{2} b m^{2} x^{4} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{261 a^{2} b m x^{4} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{210 a^{2} b x^{4} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{3 a b^{2} m^{3} x^{7} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{45 a b^{2} m^{2} x^{7} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{162 a b^{2} m x^{7} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{120 a b^{2} x^{7} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{b^{3} m^{3} x^{10} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{12 b^{3} m^{2} x^{10} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{39 b^{3} m x^{10} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} + \frac{28 b^{3} x^{10} x^{m}}{m^{4} + 22 m^{3} + 159 m^{2} + 418 m + 280} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3/(9*x**9) - a**2*b/(2*x**6) - a*b**2/x**3 + b**3*log(x), Eq(m, -10)), (-a**3/(6*x**6) - a**2*b/x**3 + 3*a*b**2*log(x) + b**3*x**3/3, Eq(m, -7)), (-a**3/(3*x**3) + 3*a**2*b*log(x) + a*b**2*x**3 + b**3*x**6/6, Eq(m, -4)), (a**3*log(x) + a**2*b*x**3 + a*b**2*x**6/2 + b**3*x**9/9, Eq(m, -1)), (a**3*m**3*x*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 21*a**3*m**2*x*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 138*a**3*m*x*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 280*a**3*x*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 3*a**2*b*m**3*x**4*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 54*a**2*b*m**2*x**4*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 261*a**2*b*m*x**4*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 210*a**2*b*x**4*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 3*a*b**2*m**3*x**7*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 45*a*b**2*m**2*x**7*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 162*a*b**2*m*x**7*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 120*a*b**2*x**7*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + b**3*m**3*x**10*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 12*b**3*m**2*x**10*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 39*b**3*m*x**10*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280) + 28*b**3*x**10*x**m/(m**4 + 22*m**3 + 159*m**2 + 418*m + 280), True))","A",0
586,1,313,0,2.719423," ","integrate(x**m*(b*x**3+a)**2,x)","\begin{cases} - \frac{a^{2}}{6 x^{6}} - \frac{2 a b}{3 x^{3}} + b^{2} \log{\left(x \right)} & \text{for}\: m = -7 \\- \frac{a^{2}}{3 x^{3}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{3}}{3} & \text{for}\: m = -4 \\a^{2} \log{\left(x \right)} + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{6}}{6} & \text{for}\: m = -1 \\\frac{a^{2} m^{2} x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{11 a^{2} m x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{28 a^{2} x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{2 a b m^{2} x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{16 a b m x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{14 a b x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{b^{2} m^{2} x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{5 b^{2} m x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{4 b^{2} x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(6*x**6) - 2*a*b/(3*x**3) + b**2*log(x), Eq(m, -7)), (-a**2/(3*x**3) + 2*a*b*log(x) + b**2*x**3/3, Eq(m, -4)), (a**2*log(x) + 2*a*b*x**3/3 + b**2*x**6/6, Eq(m, -1)), (a**2*m**2*x*x**m/(m**3 + 12*m**2 + 39*m + 28) + 11*a**2*m*x*x**m/(m**3 + 12*m**2 + 39*m + 28) + 28*a**2*x*x**m/(m**3 + 12*m**2 + 39*m + 28) + 2*a*b*m**2*x**4*x**m/(m**3 + 12*m**2 + 39*m + 28) + 16*a*b*m*x**4*x**m/(m**3 + 12*m**2 + 39*m + 28) + 14*a*b*x**4*x**m/(m**3 + 12*m**2 + 39*m + 28) + b**2*m**2*x**7*x**m/(m**3 + 12*m**2 + 39*m + 28) + 5*b**2*m*x**7*x**m/(m**3 + 12*m**2 + 39*m + 28) + 4*b**2*x**7*x**m/(m**3 + 12*m**2 + 39*m + 28), True))","A",0
587,1,94,0,1.092457," ","integrate(x**m*(b*x**3+a),x)","\begin{cases} - \frac{a}{3 x^{3}} + b \log{\left(x \right)} & \text{for}\: m = -4 \\a \log{\left(x \right)} + \frac{b x^{3}}{3} & \text{for}\: m = -1 \\\frac{a m x x^{m}}{m^{2} + 5 m + 4} + \frac{4 a x x^{m}}{m^{2} + 5 m + 4} + \frac{b m x^{4} x^{m}}{m^{2} + 5 m + 4} + \frac{b x^{4} x^{m}}{m^{2} + 5 m + 4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(3*x**3) + b*log(x), Eq(m, -4)), (a*log(x) + b*x**3/3, Eq(m, -1)), (a*m*x*x**m/(m**2 + 5*m + 4) + 4*a*x*x**m/(m**2 + 5*m + 4) + b*m*x**4*x**m/(m**2 + 5*m + 4) + b*x**4*x**m/(m**2 + 5*m + 4), True))","A",0
588,1,88,0,8.745532," ","integrate(x**m/(b*x**3+a),x)","\frac{m x x^{m} \Phi\left(\frac{b x^{3} e^{i \pi}}{a}, 1, \frac{m}{3} + \frac{1}{3}\right) \Gamma\left(\frac{m}{3} + \frac{1}{3}\right)}{9 a \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)} + \frac{x x^{m} \Phi\left(\frac{b x^{3} e^{i \pi}}{a}, 1, \frac{m}{3} + \frac{1}{3}\right) \Gamma\left(\frac{m}{3} + \frac{1}{3}\right)}{9 a \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)}"," ",0,"m*x*x**m*lerchphi(b*x**3*exp_polar(I*pi)/a, 1, m/3 + 1/3)*gamma(m/3 + 1/3)/(9*a*gamma(m/3 + 4/3)) + x*x**m*lerchphi(b*x**3*exp_polar(I*pi)/a, 1, m/3 + 1/3)*gamma(m/3 + 1/3)/(9*a*gamma(m/3 + 4/3))","C",0
589,1,515,0,88.023937," ","integrate(x**m/(b*x**3+a)**2,x)","- \frac{a m^{2} x x^{m} \Phi\left(\frac{b x^{3} e^{i \pi}}{a}, 1, \frac{m}{3} + \frac{1}{3}\right) \Gamma\left(\frac{m}{3} + \frac{1}{3}\right)}{27 a^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right) + 27 a^{2} b x^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)} + \frac{a m x x^{m} \Phi\left(\frac{b x^{3} e^{i \pi}}{a}, 1, \frac{m}{3} + \frac{1}{3}\right) \Gamma\left(\frac{m}{3} + \frac{1}{3}\right)}{27 a^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right) + 27 a^{2} b x^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)} + \frac{3 a m x x^{m} \Gamma\left(\frac{m}{3} + \frac{1}{3}\right)}{27 a^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right) + 27 a^{2} b x^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)} + \frac{2 a x x^{m} \Phi\left(\frac{b x^{3} e^{i \pi}}{a}, 1, \frac{m}{3} + \frac{1}{3}\right) \Gamma\left(\frac{m}{3} + \frac{1}{3}\right)}{27 a^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right) + 27 a^{2} b x^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)} + \frac{3 a x x^{m} \Gamma\left(\frac{m}{3} + \frac{1}{3}\right)}{27 a^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right) + 27 a^{2} b x^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)} - \frac{b m^{2} x^{4} x^{m} \Phi\left(\frac{b x^{3} e^{i \pi}}{a}, 1, \frac{m}{3} + \frac{1}{3}\right) \Gamma\left(\frac{m}{3} + \frac{1}{3}\right)}{27 a^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right) + 27 a^{2} b x^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)} + \frac{b m x^{4} x^{m} \Phi\left(\frac{b x^{3} e^{i \pi}}{a}, 1, \frac{m}{3} + \frac{1}{3}\right) \Gamma\left(\frac{m}{3} + \frac{1}{3}\right)}{27 a^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right) + 27 a^{2} b x^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)} + \frac{2 b x^{4} x^{m} \Phi\left(\frac{b x^{3} e^{i \pi}}{a}, 1, \frac{m}{3} + \frac{1}{3}\right) \Gamma\left(\frac{m}{3} + \frac{1}{3}\right)}{27 a^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right) + 27 a^{2} b x^{3} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)}"," ",0,"-a*m**2*x*x**m*lerchphi(b*x**3*exp_polar(I*pi)/a, 1, m/3 + 1/3)*gamma(m/3 + 1/3)/(27*a**3*gamma(m/3 + 4/3) + 27*a**2*b*x**3*gamma(m/3 + 4/3)) + a*m*x*x**m*lerchphi(b*x**3*exp_polar(I*pi)/a, 1, m/3 + 1/3)*gamma(m/3 + 1/3)/(27*a**3*gamma(m/3 + 4/3) + 27*a**2*b*x**3*gamma(m/3 + 4/3)) + 3*a*m*x*x**m*gamma(m/3 + 1/3)/(27*a**3*gamma(m/3 + 4/3) + 27*a**2*b*x**3*gamma(m/3 + 4/3)) + 2*a*x*x**m*lerchphi(b*x**3*exp_polar(I*pi)/a, 1, m/3 + 1/3)*gamma(m/3 + 1/3)/(27*a**3*gamma(m/3 + 4/3) + 27*a**2*b*x**3*gamma(m/3 + 4/3)) + 3*a*x*x**m*gamma(m/3 + 1/3)/(27*a**3*gamma(m/3 + 4/3) + 27*a**2*b*x**3*gamma(m/3 + 4/3)) - b*m**2*x**4*x**m*lerchphi(b*x**3*exp_polar(I*pi)/a, 1, m/3 + 1/3)*gamma(m/3 + 1/3)/(27*a**3*gamma(m/3 + 4/3) + 27*a**2*b*x**3*gamma(m/3 + 4/3)) + b*m*x**4*x**m*lerchphi(b*x**3*exp_polar(I*pi)/a, 1, m/3 + 1/3)*gamma(m/3 + 1/3)/(27*a**3*gamma(m/3 + 4/3) + 27*a**2*b*x**3*gamma(m/3 + 4/3)) + 2*b*x**4*x**m*lerchphi(b*x**3*exp_polar(I*pi)/a, 1, m/3 + 1/3)*gamma(m/3 + 1/3)/(27*a**3*gamma(m/3 + 4/3) + 27*a**2*b*x**3*gamma(m/3 + 4/3))","C",0
590,-1,0,0,0.000000," ","integrate(x**m/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,1,54,0,4.349632," ","integrate(x**m*(b*x**3+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x x^{m} \Gamma\left(\frac{m}{3} + \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{m}{3} + \frac{1}{3} \\ \frac{m}{3} + \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)}"," ",0,"a**(3/2)*x*x**m*gamma(m/3 + 1/3)*hyper((-3/2, m/3 + 1/3), (m/3 + 4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(m/3 + 4/3))","C",0
592,1,54,0,1.839683," ","integrate(x**m*(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} x x^{m} \Gamma\left(\frac{m}{3} + \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{3} + \frac{1}{3} \\ \frac{m}{3} + \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)}"," ",0,"sqrt(a)*x*x**m*gamma(m/3 + 1/3)*hyper((-1/2, m/3 + 1/3), (m/3 + 4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(m/3 + 4/3))","C",0
593,1,53,0,2.030313," ","integrate(x**m/(b*x**3+a)**(1/2),x)","\frac{x x^{m} \Gamma\left(\frac{m}{3} + \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{3} + \frac{1}{3} \\ \frac{m}{3} + \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)}"," ",0,"x*x**m*gamma(m/3 + 1/3)*hyper((1/2, m/3 + 1/3), (m/3 + 4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(m/3 + 4/3))","C",0
594,1,53,0,2.062289," ","integrate(x**m/(b*x**3+a)**(3/2),x)","\frac{x x^{m} \Gamma\left(\frac{m}{3} + \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{3} + \frac{1}{3} \\ \frac{m}{3} + \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)}"," ",0,"x*x**m*gamma(m/3 + 1/3)*hyper((3/2, m/3 + 1/3), (m/3 + 4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(m/3 + 4/3))","C",0
595,1,58,0,12.598254," ","integrate((c*x)**m*(b*x**3+a)**(4/3),x)","\frac{a^{\frac{4}{3}} c^{m} x x^{m} \Gamma\left(\frac{m}{3} + \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{m}{3} + \frac{1}{3} \\ \frac{m}{3} + \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)}"," ",0,"a**(4/3)*c**m*x*x**m*gamma(m/3 + 1/3)*hyper((-4/3, m/3 + 1/3), (m/3 + 4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(m/3 + 4/3))","C",0
596,1,58,0,2.785952," ","integrate((c*x)**m*(b*x**3+a)**(2/3),x)","\frac{a^{\frac{2}{3}} c^{m} x x^{m} \Gamma\left(\frac{m}{3} + \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{m}{3} + \frac{1}{3} \\ \frac{m}{3} + \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)}"," ",0,"a**(2/3)*c**m*x*x**m*gamma(m/3 + 1/3)*hyper((-2/3, m/3 + 1/3), (m/3 + 4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(m/3 + 4/3))","C",0
597,1,58,0,2.552734," ","integrate((c*x)**m*(b*x**3+a)**(1/3),x)","\frac{\sqrt[3]{a} c^{m} x x^{m} \Gamma\left(\frac{m}{3} + \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{m}{3} + \frac{1}{3} \\ \frac{m}{3} + \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{m}{3} + \frac{4}{3}\right)}"," ",0,"a**(1/3)*c**m*x*x**m*gamma(m/3 + 1/3)*hyper((-1/3, m/3 + 1/3), (m/3 + 4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(m/3 + 4/3))","C",0
598,-1,0,0,0.000000," ","integrate((c*x)**m*(b*x**3+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,1,134,0,2.125461," ","integrate(x**2*(b*x**3+a)**p,x)","\begin{cases} \frac{x^{3}}{3 a} & \text{for}\: b = 0 \wedge p = -1 \\\frac{a^{p} x^{3}}{3} & \text{for}\: b = 0 \\\frac{\log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{3 b} + \frac{\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 b} & \text{for}\: p = -1 \\\frac{a \left(a + b x^{3}\right)^{p}}{3 b p + 3 b} + \frac{b x^{3} \left(a + b x^{3}\right)^{p}}{3 b p + 3 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**3/(3*a), Eq(b, 0) & Eq(p, -1)), (a**p*x**3/3, Eq(b, 0)), (log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(3*b) + 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*b), Eq(p, -1)), (a*(a + b*x**3)**p/(3*b*p + 3*b) + b*x**3*(a + b*x**3)**p/(3*b*p + 3*b), True))","A",0
600,1,524,0,8.074851," ","integrate(x**5*(b*x**3+a)**p,x)","\begin{cases} \frac{a^{p} x^{6}}{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 = -2 \\- \frac{a \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{3 b^{2}} - \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 b^{2}} + \frac{x^{3}}{3 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{3}\right)^{p}}{3 b^{2} p^{2} + 9 b^{2} p + 6 b^{2}} + \frac{a b p x^{3} \left(a + b x^{3}\right)^{p}}{3 b^{2} p^{2} + 9 b^{2} p + 6 b^{2}} + \frac{b^{2} p x^{6} \left(a + b x^{3}\right)^{p}}{3 b^{2} p^{2} + 9 b^{2} p + 6 b^{2}} + \frac{b^{2} x^{6} \left(a + b x^{3}\right)^{p}}{3 b^{2} p^{2} + 9 b^{2} p + 6 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**p*x**6/6, 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, -2)), (-a*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(3*b**2) - 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*b**2) + x**3/(3*b), Eq(p, -1)), (-a**2*(a + b*x**3)**p/(3*b**2*p**2 + 9*b**2*p + 6*b**2) + a*b*p*x**3*(a + b*x**3)**p/(3*b**2*p**2 + 9*b**2*p + 6*b**2) + b**2*p*x**6*(a + b*x**3)**p/(3*b**2*p**2 + 9*b**2*p + 6*b**2) + b**2*x**6*(a + b*x**3)**p/(3*b**2*p**2 + 9*b**2*p + 6*b**2), True))","A",0
601,1,1370,0,32.724033," ","integrate(x**8*(b*x**3+a)**p,x)","\begin{cases} \frac{a^{p} x^{9}}{9} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} + \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)}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} - \frac{4 a^{2} \log{\left(2 \right)}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} + \frac{3 a^{2}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} + \frac{4 a b x^{3} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} + \frac{4 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)}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} - \frac{8 a b x^{3} \log{\left(2 \right)}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} + \frac{4 a b x^{3}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} + \frac{2 b^{2} x^{6} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} + \frac{2 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)}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} - \frac{4 b^{2} x^{6} \log{\left(2 \right)}}{6 a^{2} b^{3} + 12 a b^{4} x^{3} + 6 b^{5} x^{6}} & \text{for}\: p = -3 \\- \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 = -2 \\\frac{a^{2} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{3 b^{3}} + \frac{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 b^{3}} - \frac{a x^{3}}{3 b^{2}} + \frac{x^{6}}{6 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{3}\right)^{p}}{3 b^{3} p^{3} + 18 b^{3} p^{2} + 33 b^{3} p + 18 b^{3}} - \frac{2 a^{2} b p x^{3} \left(a + b x^{3}\right)^{p}}{3 b^{3} p^{3} + 18 b^{3} p^{2} + 33 b^{3} p + 18 b^{3}} + \frac{a b^{2} p^{2} x^{6} \left(a + b x^{3}\right)^{p}}{3 b^{3} p^{3} + 18 b^{3} p^{2} + 33 b^{3} p + 18 b^{3}} + \frac{a b^{2} p x^{6} \left(a + b x^{3}\right)^{p}}{3 b^{3} p^{3} + 18 b^{3} p^{2} + 33 b^{3} p + 18 b^{3}} + \frac{b^{3} p^{2} x^{9} \left(a + b x^{3}\right)^{p}}{3 b^{3} p^{3} + 18 b^{3} p^{2} + 33 b^{3} p + 18 b^{3}} + \frac{3 b^{3} p x^{9} \left(a + b x^{3}\right)^{p}}{3 b^{3} p^{3} + 18 b^{3} p^{2} + 33 b^{3} p + 18 b^{3}} + \frac{2 b^{3} x^{9} \left(a + b x^{3}\right)^{p}}{3 b^{3} p^{3} + 18 b^{3} p^{2} + 33 b^{3} p + 18 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**p*x**9/9, Eq(b, 0)), (2*a**2*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) + 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)/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) - 4*a**2*log(2)/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) + 3*a**2/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) + 4*a*b*x**3*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) + 4*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)/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) - 8*a*b*x**3*log(2)/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) + 4*a*b*x**3/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) + 2*b**2*x**6*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) + 2*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)/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6) - 4*b**2*x**6*log(2)/(6*a**2*b**3 + 12*a*b**4*x**3 + 6*b**5*x**6), Eq(p, -3)), (-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, -2)), (a**2*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(3*b**3) + 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*b**3) - a*x**3/(3*b**2) + x**6/(6*b), Eq(p, -1)), (2*a**3*(a + b*x**3)**p/(3*b**3*p**3 + 18*b**3*p**2 + 33*b**3*p + 18*b**3) - 2*a**2*b*p*x**3*(a + b*x**3)**p/(3*b**3*p**3 + 18*b**3*p**2 + 33*b**3*p + 18*b**3) + a*b**2*p**2*x**6*(a + b*x**3)**p/(3*b**3*p**3 + 18*b**3*p**2 + 33*b**3*p + 18*b**3) + a*b**2*p*x**6*(a + b*x**3)**p/(3*b**3*p**3 + 18*b**3*p**2 + 33*b**3*p + 18*b**3) + b**3*p**2*x**9*(a + b*x**3)**p/(3*b**3*p**3 + 18*b**3*p**2 + 33*b**3*p + 18*b**3) + 3*b**3*p*x**9*(a + b*x**3)**p/(3*b**3*p**3 + 18*b**3*p**2 + 33*b**3*p + 18*b**3) + 2*b**3*x**9*(a + b*x**3)**p/(3*b**3*p**3 + 18*b**3*p**2 + 33*b**3*p + 18*b**3), True))","A",0
602,1,2773,0,80.687112," ","integrate(x**11*(b*x**3+a)**p,x)","\begin{cases} \frac{a^{p} x^{12}}{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 = -4 \\- \frac{6 a^{3} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} - \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^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} - \frac{9 a^{3}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} + \frac{12 a^{3} \log{\left(2 \right)}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} - \frac{12 a^{2} b x^{3} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} - \frac{12 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^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} - \frac{12 a^{2} b x^{3}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} + \frac{24 a^{2} b x^{3} \log{\left(2 \right)}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} - \frac{6 a b^{2} x^{6} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} - \frac{6 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)}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} + \frac{12 a b^{2} x^{6} \log{\left(2 \right)}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} + \frac{2 b^{3} x^{9}}{6 a^{2} b^{4} + 12 a b^{5} x^{3} + 6 b^{6} x^{6}} & \text{for}\: p = -3 \\\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 = -2 \\- \frac{a^{3} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{3 b^{4}} - \frac{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)}}{3 b^{4}} + \frac{a^{2} x^{3}}{3 b^{3}} - \frac{a x^{6}}{6 b^{2}} + \frac{x^{9}}{9 b} & \text{for}\: p = -1 \\- \frac{6 a^{4} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} + \frac{6 a^{3} b p x^{3} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} - \frac{3 a^{2} b^{2} p^{2} x^{6} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} - \frac{3 a^{2} b^{2} p x^{6} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} + \frac{a b^{3} p^{3} x^{9} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} + \frac{3 a b^{3} p^{2} x^{9} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} + \frac{2 a b^{3} p x^{9} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} + \frac{b^{4} p^{3} x^{12} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} + \frac{6 b^{4} p^{2} x^{12} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} + \frac{11 b^{4} p x^{12} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} + \frac{6 b^{4} x^{12} \left(a + b x^{3}\right)^{p}}{3 b^{4} p^{4} + 30 b^{4} p^{3} + 105 b^{4} p^{2} + 150 b^{4} p + 72 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**p*x**12/12, 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, -4)), (-6*a**3*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) - 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**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) - 9*a**3/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) + 12*a**3*log(2)/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) - 12*a**2*b*x**3*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) - 12*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**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) - 12*a**2*b*x**3/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) + 24*a**2*b*x**3*log(2)/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) - 6*a*b**2*x**6*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) - 6*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)/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) + 12*a*b**2*x**6*log(2)/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6) + 2*b**3*x**9/(6*a**2*b**4 + 12*a*b**5*x**3 + 6*b**6*x**6), Eq(p, -3)), (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, -2)), (-a**3*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(3*b**4) - 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)/(3*b**4) + a**2*x**3/(3*b**3) - a*x**6/(6*b**2) + x**9/(9*b), Eq(p, -1)), (-6*a**4*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4) + 6*a**3*b*p*x**3*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4) - 3*a**2*b**2*p**2*x**6*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4) - 3*a**2*b**2*p*x**6*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4) + a*b**3*p**3*x**9*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4) + 3*a*b**3*p**2*x**9*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4) + 2*a*b**3*p*x**9*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4) + b**4*p**3*x**12*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4) + 6*b**4*p**2*x**12*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4) + 11*b**4*p*x**12*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4) + 6*b**4*x**12*(a + b*x**3)**p/(3*b**4*p**4 + 30*b**4*p**3 + 105*b**4*p**2 + 150*b**4*p + 72*b**4), True))","A",0
603,1,94,0,1.304410," ","integrate(x**m*(b*x**4+a),x)","\begin{cases} - \frac{a}{4 x^{4}} + b \log{\left(x \right)} & \text{for}\: m = -5 \\a \log{\left(x \right)} + \frac{b x^{4}}{4} & \text{for}\: m = -1 \\\frac{a m x x^{m}}{m^{2} + 6 m + 5} + \frac{5 a x x^{m}}{m^{2} + 6 m + 5} + \frac{b m x^{5} x^{m}}{m^{2} + 6 m + 5} + \frac{b x^{5} x^{m}}{m^{2} + 6 m + 5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(4*x**4) + b*log(x), Eq(m, -5)), (a*log(x) + b*x**4/4, Eq(m, -1)), (a*m*x*x**m/(m**2 + 6*m + 5) + 5*a*x*x**m/(m**2 + 6*m + 5) + b*m*x**5*x**m/(m**2 + 6*m + 5) + b*x**5*x**m/(m**2 + 6*m + 5), True))","A",0
604,1,12,0,0.083819," ","integrate(x**5*(b*x**4+a),x)","\frac{a x^{6}}{6} + \frac{b x^{10}}{10}"," ",0,"a*x**6/6 + b*x**10/10","A",0
605,1,12,0,0.076817," ","integrate(x**4*(b*x**4+a),x)","\frac{a x^{5}}{5} + \frac{b x^{9}}{9}"," ",0,"a*x**5/5 + b*x**9/9","A",0
606,1,12,0,0.176833," ","integrate(x**3*(b*x**4+a),x)","\frac{a x^{4}}{4} + \frac{b x^{8}}{8}"," ",0,"a*x**4/4 + b*x**8/8","A",0
607,1,12,0,0.065809," ","integrate(x**2*(b*x**4+a),x)","\frac{a x^{3}}{3} + \frac{b x^{7}}{7}"," ",0,"a*x**3/3 + b*x**7/7","A",0
608,1,12,0,0.077594," ","integrate(x*(b*x**4+a),x)","\frac{a x^{2}}{2} + \frac{b x^{6}}{6}"," ",0,"a*x**2/2 + b*x**6/6","A",0
609,1,8,0,0.101165," ","integrate(b*x**4+a,x)","a x + \frac{b x^{5}}{5}"," ",0,"a*x + b*x**5/5","A",0
610,1,10,0,0.095330," ","integrate((b*x**4+a)/x,x)","a \log{\left(x \right)} + \frac{b x^{4}}{4}"," ",0,"a*log(x) + b*x**4/4","A",0
611,1,8,0,0.135394," ","integrate((b*x**4+a)/x**2,x)","- \frac{a}{x} + \frac{b x^{3}}{3}"," ",0,"-a/x + b*x**3/3","A",0
612,1,12,0,0.165246," ","integrate((b*x**4+a)/x**3,x)","- \frac{a}{2 x^{2}} + \frac{b x^{2}}{2}"," ",0,"-a/(2*x**2) + b*x**2/2","A",0
613,1,8,0,0.220461," ","integrate((b*x**4+a)/x**4,x)","- \frac{a}{3 x^{3}} + b x"," ",0,"-a/(3*x**3) + b*x","A",0
614,1,10,0,0.255025," ","integrate((b*x**4+a)/x**5,x)","- \frac{a}{4 x^{4}} + b \log{\left(x \right)}"," ",0,"-a/(4*x**4) + b*log(x)","A",0
615,1,14,0,0.386117," ","integrate((b*x**4+a)/x**6,x)","\frac{- a - 5 b x^{4}}{5 x^{5}}"," ",0,"(-a - 5*b*x**4)/(5*x**5)","A",0
616,1,14,0,0.373914," ","integrate((b*x**4+a)/x**7,x)","\frac{- a - 3 b x^{4}}{6 x^{6}}"," ",0,"(-a - 3*b*x**4)/(6*x**6)","A",0
617,1,15,0,0.317582," ","integrate((b*x**4+a)/x**8,x)","\frac{- 3 a - 7 b x^{4}}{21 x^{7}}"," ",0,"(-3*a - 7*b*x**4)/(21*x**7)","A",0
618,1,14,0,0.180551," ","integrate((b*x**4+a)/x**9,x)","\frac{- a - 2 b x^{4}}{8 x^{8}}"," ",0,"(-a - 2*b*x**4)/(8*x**8)","A",0
619,1,15,0,0.207516," ","integrate((b*x**4+a)/x**10,x)","\frac{- 5 a - 9 b x^{4}}{45 x^{9}}"," ",0,"(-5*a - 9*b*x**4)/(45*x**9)","A",0
620,1,309,0,3.935881," ","integrate(x**m*(b*x**4+a)**2,x)","\begin{cases} - \frac{a^{2}}{8 x^{8}} - \frac{a b}{2 x^{4}} + b^{2} \log{\left(x \right)} & \text{for}\: m = -9 \\- \frac{a^{2}}{4 x^{4}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{4}}{4} & \text{for}\: m = -5 \\a^{2} \log{\left(x \right)} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{8}}{8} & \text{for}\: m = -1 \\\frac{a^{2} m^{2} x x^{m}}{m^{3} + 15 m^{2} + 59 m + 45} + \frac{14 a^{2} m x x^{m}}{m^{3} + 15 m^{2} + 59 m + 45} + \frac{45 a^{2} x x^{m}}{m^{3} + 15 m^{2} + 59 m + 45} + \frac{2 a b m^{2} x^{5} x^{m}}{m^{3} + 15 m^{2} + 59 m + 45} + \frac{20 a b m x^{5} x^{m}}{m^{3} + 15 m^{2} + 59 m + 45} + \frac{18 a b x^{5} x^{m}}{m^{3} + 15 m^{2} + 59 m + 45} + \frac{b^{2} m^{2} x^{9} x^{m}}{m^{3} + 15 m^{2} + 59 m + 45} + \frac{6 b^{2} m x^{9} x^{m}}{m^{3} + 15 m^{2} + 59 m + 45} + \frac{5 b^{2} x^{9} x^{m}}{m^{3} + 15 m^{2} + 59 m + 45} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(8*x**8) - a*b/(2*x**4) + b**2*log(x), Eq(m, -9)), (-a**2/(4*x**4) + 2*a*b*log(x) + b**2*x**4/4, Eq(m, -5)), (a**2*log(x) + a*b*x**4/2 + b**2*x**8/8, Eq(m, -1)), (a**2*m**2*x*x**m/(m**3 + 15*m**2 + 59*m + 45) + 14*a**2*m*x*x**m/(m**3 + 15*m**2 + 59*m + 45) + 45*a**2*x*x**m/(m**3 + 15*m**2 + 59*m + 45) + 2*a*b*m**2*x**5*x**m/(m**3 + 15*m**2 + 59*m + 45) + 20*a*b*m*x**5*x**m/(m**3 + 15*m**2 + 59*m + 45) + 18*a*b*x**5*x**m/(m**3 + 15*m**2 + 59*m + 45) + b**2*m**2*x**9*x**m/(m**3 + 15*m**2 + 59*m + 45) + 6*b**2*m*x**9*x**m/(m**3 + 15*m**2 + 59*m + 45) + 5*b**2*x**9*x**m/(m**3 + 15*m**2 + 59*m + 45), True))","A",0
621,1,24,0,0.101025," ","integrate(x**5*(b*x**4+a)**2,x)","\frac{a^{2} x^{6}}{6} + \frac{a b x^{10}}{5} + \frac{b^{2} x^{14}}{14}"," ",0,"a**2*x**6/6 + a*b*x**10/5 + b**2*x**14/14","A",0
622,1,26,0,0.070509," ","integrate(x**4*(b*x**4+a)**2,x)","\frac{a^{2} x^{5}}{5} + \frac{2 a b x^{9}}{9} + \frac{b^{2} x^{13}}{13}"," ",0,"a**2*x**5/5 + 2*a*b*x**9/9 + b**2*x**13/13","A",0
623,1,24,0,0.198246," ","integrate(x**3*(b*x**4+a)**2,x)","\frac{a^{2} x^{4}}{4} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{12}}{12}"," ",0,"a**2*x**4/4 + a*b*x**8/4 + b**2*x**12/12","B",0
624,1,26,0,0.084232," ","integrate(x**2*(b*x**4+a)**2,x)","\frac{a^{2} x^{3}}{3} + \frac{2 a b x^{7}}{7} + \frac{b^{2} x^{11}}{11}"," ",0,"a**2*x**3/3 + 2*a*b*x**7/7 + b**2*x**11/11","A",0
625,1,24,0,0.088673," ","integrate(x*(b*x**4+a)**2,x)","\frac{a^{2} x^{2}}{2} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{10}}{10}"," ",0,"a**2*x**2/2 + a*b*x**6/3 + b**2*x**10/10","A",0
626,1,22,0,0.091980," ","integrate((b*x**4+a)**2,x)","a^{2} x + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{9}}{9}"," ",0,"a**2*x + 2*a*b*x**5/5 + b**2*x**9/9","A",0
627,1,22,0,0.181880," ","integrate((b*x**4+a)**2/x,x)","a^{2} \log{\left(x \right)} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{8}}{8}"," ",0,"a**2*log(x) + a*b*x**4/2 + b**2*x**8/8","A",0
628,1,22,0,0.195879," ","integrate((b*x**4+a)**2/x**2,x)","- \frac{a^{2}}{x} + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{7}}{7}"," ",0,"-a**2/x + 2*a*b*x**3/3 + b**2*x**7/7","A",0
629,1,22,0,0.161868," ","integrate((b*x**4+a)**2/x**3,x)","- \frac{a^{2}}{2 x^{2}} + a b x^{2} + \frac{b^{2} x^{6}}{6}"," ",0,"-a**2/(2*x**2) + a*b*x**2 + b**2*x**6/6","A",0
630,1,22,0,0.191517," ","integrate((b*x**4+a)**2/x**4,x)","- \frac{a^{2}}{3 x^{3}} + 2 a b x + \frac{b^{2} x^{5}}{5}"," ",0,"-a**2/(3*x**3) + 2*a*b*x + b**2*x**5/5","A",0
631,1,24,0,0.195274," ","integrate((b*x**4+a)**2/x**5,x)","- \frac{a^{2}}{4 x^{4}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{4}}{4}"," ",0,"-a**2/(4*x**4) + 2*a*b*log(x) + b**2*x**4/4","A",0
632,1,683,0,7.362136," ","integrate(x**m*(b*x**4+a)**3,x)","\begin{cases} - \frac{a^{3}}{12 x^{12}} - \frac{3 a^{2} b}{8 x^{8}} - \frac{3 a b^{2}}{4 x^{4}} + b^{3} \log{\left(x \right)} & \text{for}\: m = -13 \\- \frac{a^{3}}{8 x^{8}} - \frac{3 a^{2} b}{4 x^{4}} + 3 a b^{2} \log{\left(x \right)} + \frac{b^{3} x^{4}}{4} & \text{for}\: m = -9 \\- \frac{a^{3}}{4 x^{4}} + 3 a^{2} b \log{\left(x \right)} + \frac{3 a b^{2} x^{4}}{4} + \frac{b^{3} x^{8}}{8} & \text{for}\: m = -5 \\a^{3} \log{\left(x \right)} + \frac{3 a^{2} b x^{4}}{4} + \frac{3 a b^{2} x^{8}}{8} + \frac{b^{3} x^{12}}{12} & \text{for}\: m = -1 \\\frac{a^{3} m^{3} x x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{27 a^{3} m^{2} x x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{227 a^{3} m x x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{585 a^{3} x x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{3 a^{2} b m^{3} x^{5} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{69 a^{2} b m^{2} x^{5} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{417 a^{2} b m x^{5} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{351 a^{2} b x^{5} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{3 a b^{2} m^{3} x^{9} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{57 a b^{2} m^{2} x^{9} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{249 a b^{2} m x^{9} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{195 a b^{2} x^{9} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{b^{3} m^{3} x^{13} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{15 b^{3} m^{2} x^{13} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{59 b^{3} m x^{13} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} + \frac{45 b^{3} x^{13} x^{m}}{m^{4} + 28 m^{3} + 254 m^{2} + 812 m + 585} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3/(12*x**12) - 3*a**2*b/(8*x**8) - 3*a*b**2/(4*x**4) + b**3*log(x), Eq(m, -13)), (-a**3/(8*x**8) - 3*a**2*b/(4*x**4) + 3*a*b**2*log(x) + b**3*x**4/4, Eq(m, -9)), (-a**3/(4*x**4) + 3*a**2*b*log(x) + 3*a*b**2*x**4/4 + b**3*x**8/8, Eq(m, -5)), (a**3*log(x) + 3*a**2*b*x**4/4 + 3*a*b**2*x**8/8 + b**3*x**12/12, Eq(m, -1)), (a**3*m**3*x*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 27*a**3*m**2*x*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 227*a**3*m*x*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 585*a**3*x*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 3*a**2*b*m**3*x**5*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 69*a**2*b*m**2*x**5*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 417*a**2*b*m*x**5*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 351*a**2*b*x**5*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 3*a*b**2*m**3*x**9*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 57*a*b**2*m**2*x**9*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 249*a*b**2*m*x**9*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 195*a*b**2*x**9*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + b**3*m**3*x**13*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 15*b**3*m**2*x**13*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 59*b**3*m*x**13*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585) + 45*b**3*x**13*x**m/(m**4 + 28*m**3 + 254*m**2 + 812*m + 585), True))","A",0
633,1,39,0,0.321179," ","integrate(x**5*(b*x**4+a)**3,x)","\frac{a^{3} x^{6}}{6} + \frac{3 a^{2} b x^{10}}{10} + \frac{3 a b^{2} x^{14}}{14} + \frac{b^{3} x^{18}}{18}"," ",0,"a**3*x**6/6 + 3*a**2*b*x**10/10 + 3*a*b**2*x**14/14 + b**3*x**18/18","A",0
634,1,37,0,0.126717," ","integrate(x**4*(b*x**4+a)**3,x)","\frac{a^{3} x^{5}}{5} + \frac{a^{2} b x^{9}}{3} + \frac{3 a b^{2} x^{13}}{13} + \frac{b^{3} x^{17}}{17}"," ",0,"a**3*x**5/5 + a**2*b*x**9/3 + 3*a*b**2*x**13/13 + b**3*x**17/17","A",0
635,1,37,0,0.089234," ","integrate(x**3*(b*x**4+a)**3,x)","\frac{a^{3} x^{4}}{4} + \frac{3 a^{2} b x^{8}}{8} + \frac{a b^{2} x^{12}}{4} + \frac{b^{3} x^{16}}{16}"," ",0,"a**3*x**4/4 + 3*a**2*b*x**8/8 + a*b**2*x**12/4 + b**3*x**16/16","B",0
636,1,39,0,0.082917," ","integrate(x**2*(b*x**4+a)**3,x)","\frac{a^{3} x^{3}}{3} + \frac{3 a^{2} b x^{7}}{7} + \frac{3 a b^{2} x^{11}}{11} + \frac{b^{3} x^{15}}{15}"," ",0,"a**3*x**3/3 + 3*a**2*b*x**7/7 + 3*a*b**2*x**11/11 + b**3*x**15/15","A",0
637,1,37,0,0.086862," ","integrate(x*(b*x**4+a)**3,x)","\frac{a^{3} x^{2}}{2} + \frac{a^{2} b x^{6}}{2} + \frac{3 a b^{2} x^{10}}{10} + \frac{b^{3} x^{14}}{14}"," ",0,"a**3*x**2/2 + a**2*b*x**6/2 + 3*a*b**2*x**10/10 + b**3*x**14/14","A",0
638,1,34,0,0.083424," ","integrate((b*x**4+a)**3,x)","a^{3} x + \frac{3 a^{2} b x^{5}}{5} + \frac{a b^{2} x^{9}}{3} + \frac{b^{3} x^{13}}{13}"," ",0,"a**3*x + 3*a**2*b*x**5/5 + a*b**2*x**9/3 + b**3*x**13/13","A",0
639,1,37,0,0.140481," ","integrate((b*x**4+a)**3/x,x)","a^{3} \log{\left(x \right)} + \frac{3 a^{2} b x^{4}}{4} + \frac{3 a b^{2} x^{8}}{8} + \frac{b^{3} x^{12}}{12}"," ",0,"a**3*log(x) + 3*a**2*b*x**4/4 + 3*a*b**2*x**8/8 + b**3*x**12/12","A",0
640,1,32,0,0.153076," ","integrate((b*x**4+a)**3/x**2,x)","- \frac{a^{3}}{x} + a^{2} b x^{3} + \frac{3 a b^{2} x^{7}}{7} + \frac{b^{3} x^{11}}{11}"," ",0,"-a**3/x + a**2*b*x**3 + 3*a*b**2*x**7/7 + b**3*x**11/11","A",0
641,1,37,0,0.310394," ","integrate((b*x**4+a)**3/x**3,x)","- \frac{a^{3}}{2 x^{2}} + \frac{3 a^{2} b x^{2}}{2} + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{10}}{10}"," ",0,"-a**3/(2*x**2) + 3*a**2*b*x**2/2 + a*b**2*x**6/2 + b**3*x**10/10","A",0
642,1,36,0,0.302552," ","integrate((b*x**4+a)**3/x**4,x)","- \frac{a^{3}}{3 x^{3}} + 3 a^{2} b x + \frac{3 a b^{2} x^{5}}{5} + \frac{b^{3} x^{9}}{9}"," ",0,"-a**3/(3*x**3) + 3*a**2*b*x + 3*a*b**2*x**5/5 + b**3*x**9/9","A",0
643,1,37,0,0.316718," ","integrate((b*x**4+a)**3/x**5,x)","- \frac{a^{3}}{4 x^{4}} + 3 a^{2} b \log{\left(x \right)} + \frac{3 a b^{2} x^{4}}{4} + \frac{b^{3} x^{8}}{8}"," ",0,"-a**3/(4*x**4) + 3*a**2*b*log(x) + 3*a*b**2*x**4/4 + b**3*x**8/8","A",0
644,1,87,0,0.281998," ","integrate(x**9/(c*x**4+a),x)","- \frac{a x^{2}}{2 c^{2}} - \frac{\sqrt{- \frac{a^{3}}{c^{5}}} \log{\left(x^{2} - \frac{c^{2} \sqrt{- \frac{a^{3}}{c^{5}}}}{a} \right)}}{4} + \frac{\sqrt{- \frac{a^{3}}{c^{5}}} \log{\left(x^{2} + \frac{c^{2} \sqrt{- \frac{a^{3}}{c^{5}}}}{a} \right)}}{4} + \frac{x^{6}}{6 c}"," ",0,"-a*x**2/(2*c**2) - sqrt(-a**3/c**5)*log(x**2 - c**2*sqrt(-a**3/c**5)/a)/4 + sqrt(-a**3/c**5)*log(x**2 + c**2*sqrt(-a**3/c**5)/a)/4 + x**6/(6*c)","B",0
645,1,20,0,0.239199," ","integrate(x**7/(c*x**4+a),x)","- \frac{a \log{\left(a + c x^{4} \right)}}{4 c^{2}} + \frac{x^{4}}{4 c}"," ",0,"-a*log(a + c*x**4)/(4*c**2) + x**4/(4*c)","A",0
646,1,63,0,0.319810," ","integrate(x**5/(c*x**4+a),x)","\frac{\sqrt{- \frac{a}{c^{3}}} \log{\left(- c \sqrt{- \frac{a}{c^{3}}} + x^{2} \right)}}{4} - \frac{\sqrt{- \frac{a}{c^{3}}} \log{\left(c \sqrt{- \frac{a}{c^{3}}} + x^{2} \right)}}{4} + \frac{x^{2}}{2 c}"," ",0,"sqrt(-a/c**3)*log(-c*sqrt(-a/c**3) + x**2)/4 - sqrt(-a/c**3)*log(c*sqrt(-a/c**3) + x**2)/4 + x**2/(2*c)","A",0
647,1,10,0,0.190038," ","integrate(x**3/(c*x**4+a),x)","\frac{\log{\left(a + c x^{4} \right)}}{4 c}"," ",0,"log(a + c*x**4)/(4*c)","A",0
648,1,56,0,0.223379," ","integrate(x/(c*x**4+a),x)","- \frac{\sqrt{- \frac{1}{a c}} \log{\left(- a \sqrt{- \frac{1}{a c}} + x^{2} \right)}}{4} + \frac{\sqrt{- \frac{1}{a c}} \log{\left(a \sqrt{- \frac{1}{a c}} + x^{2} \right)}}{4}"," ",0,"-sqrt(-1/(a*c))*log(-a*sqrt(-1/(a*c)) + x**2)/4 + sqrt(-1/(a*c))*log(a*sqrt(-1/(a*c)) + x**2)/4","B",0
649,1,15,0,0.610476," ","integrate(1/x/(c*x**4+a),x)","\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{c} + x^{4} \right)}}{4 a}"," ",0,"log(x)/a - log(a/c + x**4)/(4*a)","A",0
650,1,71,0,0.465119," ","integrate(1/x**3/(c*x**4+a),x)","\frac{\sqrt{- \frac{c}{a^{3}}} \log{\left(- \frac{a^{2} \sqrt{- \frac{c}{a^{3}}}}{c} + x^{2} \right)}}{4} - \frac{\sqrt{- \frac{c}{a^{3}}} \log{\left(\frac{a^{2} \sqrt{- \frac{c}{a^{3}}}}{c} + x^{2} \right)}}{4} - \frac{1}{2 a x^{2}}"," ",0,"sqrt(-c/a**3)*log(-a**2*sqrt(-c/a**3)/c + x**2)/4 - sqrt(-c/a**3)*log(a**2*sqrt(-c/a**3)/c + x**2)/4 - 1/(2*a*x**2)","A",0
651,1,31,0,0.833971," ","integrate(1/x**5/(c*x**4+a),x)","- \frac{1}{4 a x^{4}} - \frac{c \log{\left(x \right)}}{a^{2}} + \frac{c \log{\left(\frac{a}{c} + x^{4} \right)}}{4 a^{2}}"," ",0,"-1/(4*a*x**4) - c*log(x)/a**2 + c*log(a/c + x**4)/(4*a**2)","A",0
652,1,90,0,0.525400," ","integrate(1/x**7/(c*x**4+a),x)","- \frac{\sqrt{- \frac{c^{3}}{a^{5}}} \log{\left(- \frac{a^{3} \sqrt{- \frac{c^{3}}{a^{5}}}}{c^{2}} + x^{2} \right)}}{4} + \frac{\sqrt{- \frac{c^{3}}{a^{5}}} \log{\left(\frac{a^{3} \sqrt{- \frac{c^{3}}{a^{5}}}}{c^{2}} + x^{2} \right)}}{4} + \frac{- a + 3 c x^{4}}{6 a^{2} x^{6}}"," ",0,"-sqrt(-c**3/a**5)*log(-a**3*sqrt(-c**3/a**5)/c**2 + x**2)/4 + sqrt(-c**3/a**5)*log(a**3*sqrt(-c**3/a**5)/c**2 + x**2)/4 + (-a + 3*c*x**4)/(6*a**2*x**6)","B",0
653,1,22,0,0.231025," ","integrate(x**4/(c*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} c^{5} + a, \left( t \mapsto t \log{\left(- 4 t c + x \right)} \right)\right)} + \frac{x}{c}"," ",0,"RootSum(256*_t**4*c**5 + a, Lambda(_t, _t*log(-4*_t*c + x))) + x/c","A",0
654,1,26,0,0.223754," ","integrate(x**2/(c*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a c^{3} + 1, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} + x \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a*c**3 + 1, Lambda(_t, _t*log(64*_t**3*a*c**2 + x)))","A",0
655,1,20,0,0.238291," ","integrate(1/(c*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} c + 1, \left( t \mapsto t \log{\left(4 t a + x \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a**3*c + 1, Lambda(_t, _t*log(4*_t*a + x)))","A",0
656,1,29,0,0.269239," ","integrate(1/x**2/(c*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{5} + c, \left( t \mapsto t \log{\left(- \frac{64 t^{3} a^{4}}{c} + x \right)} \right)\right)} - \frac{1}{a x}"," ",0,"RootSum(256*_t**4*a**5 + c, Lambda(_t, _t*log(-64*_t**3*a**4/c + x))) - 1/(a*x)","A",0
657,1,32,0,0.335571," ","integrate(1/x**4/(c*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{7} + c^{3}, \left( t \mapsto t \log{\left(- \frac{4 t a^{2}}{c} + x \right)} \right)\right)} - \frac{1}{3 a x^{3}}"," ",0,"RootSum(256*_t**4*a**7 + c**3, Lambda(_t, _t*log(-4*_t*a**2/c + x))) - 1/(3*a*x**3)","A",0
658,1,41,0,0.521309," ","integrate(x**11/(c*x**4+a)**2,x)","- \frac{a^{2}}{4 a c^{3} + 4 c^{4} x^{4}} - \frac{a \log{\left(a + c x^{4} \right)}}{2 c^{3}} + \frac{x^{4}}{4 c^{2}}"," ",0,"-a**2/(4*a*c**3 + 4*c**4*x**4) - a*log(a + c*x**4)/(2*c**3) + x**4/(4*c**2)","A",0
659,1,92,0,0.852738," ","integrate(x**9/(c*x**4+a)**2,x)","\frac{a x^{2}}{4 a c^{2} + 4 c^{3} x^{4}} + \frac{3 \sqrt{- \frac{a}{c^{5}}} \log{\left(- c^{2} \sqrt{- \frac{a}{c^{5}}} + x^{2} \right)}}{8} - \frac{3 \sqrt{- \frac{a}{c^{5}}} \log{\left(c^{2} \sqrt{- \frac{a}{c^{5}}} + x^{2} \right)}}{8} + \frac{x^{2}}{2 c^{2}}"," ",0,"a*x**2/(4*a*c**2 + 4*c**3*x**4) + 3*sqrt(-a/c**5)*log(-c**2*sqrt(-a/c**5) + x**2)/8 - 3*sqrt(-a/c**5)*log(c**2*sqrt(-a/c**5) + x**2)/8 + x**2/(2*c**2)","A",0
660,1,29,0,0.336833," ","integrate(x**7/(c*x**4+a)**2,x)","\frac{a}{4 a c^{2} + 4 c^{3} x^{4}} + \frac{\log{\left(a + c x^{4} \right)}}{4 c^{2}}"," ",0,"a/(4*a*c**2 + 4*c**3*x**4) + log(a + c*x**4)/(4*c**2)","A",0
661,1,83,0,0.483381," ","integrate(x**5/(c*x**4+a)**2,x)","- \frac{x^{2}}{4 a c + 4 c^{2} x^{4}} - \frac{\sqrt{- \frac{1}{a c^{3}}} \log{\left(- a c \sqrt{- \frac{1}{a c^{3}}} + x^{2} \right)}}{8} + \frac{\sqrt{- \frac{1}{a c^{3}}} \log{\left(a c \sqrt{- \frac{1}{a c^{3}}} + x^{2} \right)}}{8}"," ",0,"-x**2/(4*a*c + 4*c**2*x**4) - sqrt(-1/(a*c**3))*log(-a*c*sqrt(-1/(a*c**3)) + x**2)/8 + sqrt(-1/(a*c**3))*log(a*c*sqrt(-1/(a*c**3)) + x**2)/8","B",0
662,1,15,0,0.645963," ","integrate(x**3/(c*x**4+a)**2,x)","- \frac{1}{4 a c + 4 c^{2} x^{4}}"," ",0,"-1/(4*a*c + 4*c**2*x**4)","A",0
663,1,83,0,0.531100," ","integrate(x/(c*x**4+a)**2,x)","\frac{x^{2}}{4 a^{2} + 4 a c x^{4}} - \frac{\sqrt{- \frac{1}{a^{3} c}} \log{\left(- a^{2} \sqrt{- \frac{1}{a^{3} c}} + x^{2} \right)}}{8} + \frac{\sqrt{- \frac{1}{a^{3} c}} \log{\left(a^{2} \sqrt{- \frac{1}{a^{3} c}} + x^{2} \right)}}{8}"," ",0,"x**2/(4*a**2 + 4*a*c*x**4) - sqrt(-1/(a**3*c))*log(-a**2*sqrt(-1/(a**3*c)) + x**2)/8 + sqrt(-1/(a**3*c))*log(a**2*sqrt(-1/(a**3*c)) + x**2)/8","B",0
664,1,34,0,0.570339," ","integrate(1/x/(c*x**4+a)**2,x)","\frac{1}{4 a^{2} + 4 a c x^{4}} + \frac{\log{\left(x \right)}}{a^{2}} - \frac{\log{\left(\frac{a}{c} + x^{4} \right)}}{4 a^{2}}"," ",0,"1/(4*a**2 + 4*a*c*x**4) + log(x)/a**2 - log(a/c + x**4)/(4*a**2)","A",0
665,1,97,0,0.872075," ","integrate(1/x**3/(c*x**4+a)**2,x)","\frac{3 \sqrt{- \frac{c}{a^{5}}} \log{\left(- \frac{a^{3} \sqrt{- \frac{c}{a^{5}}}}{c} + x^{2} \right)}}{8} - \frac{3 \sqrt{- \frac{c}{a^{5}}} \log{\left(\frac{a^{3} \sqrt{- \frac{c}{a^{5}}}}{c} + x^{2} \right)}}{8} + \frac{- 2 a - 3 c x^{4}}{4 a^{3} x^{2} + 4 a^{2} c x^{6}}"," ",0,"3*sqrt(-c/a**5)*log(-a**3*sqrt(-c/a**5)/c + x**2)/8 - 3*sqrt(-c/a**5)*log(a**3*sqrt(-c/a**5)/c + x**2)/8 + (-2*a - 3*c*x**4)/(4*a**3*x**2 + 4*a**2*c*x**6)","A",0
666,1,44,0,0.370639," ","integrate(x**6/(c*x**4+a)**2,x)","- \frac{x^{3}}{4 a c + 4 c^{2} x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} a c^{7} + 81, \left( t \mapsto t \log{\left(\frac{4096 t^{3} a c^{5}}{27} + x \right)} \right)\right)}"," ",0,"-x**3/(4*a*c + 4*c**2*x**4) + RootSum(65536*_t**4*a*c**7 + 81, Lambda(_t, _t*log(4096*_t**3*a*c**5/27 + x)))","A",0
667,1,39,0,0.536416," ","integrate(x**4/(c*x**4+a)**2,x)","- \frac{x}{4 a c + 4 c^{2} x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} a^{3} c^{5} + 1, \left( t \mapsto t \log{\left(16 t a c + x \right)} \right)\right)}"," ",0,"-x/(4*a*c + 4*c**2*x**4) + RootSum(65536*_t**4*a**3*c**5 + 1, Lambda(_t, _t*log(16*_t*a*c + x)))","A",0
668,1,46,0,0.644372," ","integrate(x**2/(c*x**4+a)**2,x)","\frac{x^{3}}{4 a^{2} + 4 a c x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} a^{5} c^{3} + 1, \left( t \mapsto t \log{\left(4096 t^{3} a^{4} c^{2} + x \right)} \right)\right)}"," ",0,"x**3/(4*a**2 + 4*a*c*x**4) + RootSum(65536*_t**4*a**5*c**3 + 1, Lambda(_t, _t*log(4096*_t**3*a**4*c**2 + x)))","A",0
669,1,39,0,0.403331," ","integrate(1/(c*x**4+a)**2,x)","\frac{x}{4 a^{2} + 4 a c x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} a^{7} c + 81, \left( t \mapsto t \log{\left(\frac{16 t a^{2}}{3} + x \right)} \right)\right)}"," ",0,"x/(4*a**2 + 4*a*c*x**4) + RootSum(65536*_t**4*a**7*c + 81, Lambda(_t, _t*log(16*_t*a**2/3 + x)))","A",0
670,1,56,0,0.712650," ","integrate(1/x**2/(c*x**4+a)**2,x)","\frac{- 4 a - 5 c x^{4}}{4 a^{3} x + 4 a^{2} c x^{5}} + \operatorname{RootSum} {\left(65536 t^{4} a^{9} + 625 c, \left( t \mapsto t \log{\left(- \frac{4096 t^{3} a^{7}}{125 c} + x \right)} \right)\right)}"," ",0,"(-4*a - 5*c*x**4)/(4*a**3*x + 4*a**2*c*x**5) + RootSum(65536*_t**4*a**9 + 625*c, Lambda(_t, _t*log(-4096*_t**3*a**7/(125*c) + x)))","A",0
671,1,58,0,0.883514," ","integrate(1/x**4/(c*x**4+a)**2,x)","\frac{- 4 a - 7 c x^{4}}{12 a^{3} x^{3} + 12 a^{2} c x^{7}} + \operatorname{RootSum} {\left(65536 t^{4} a^{11} + 2401 c^{3}, \left( t \mapsto t \log{\left(- \frac{16 t a^{3}}{7 c} + x \right)} \right)\right)}"," ",0,"(-4*a - 7*c*x**4)/(12*a**3*x**3 + 12*a**2*c*x**7) + RootSum(65536*_t**4*a**11 + 2401*c**3, Lambda(_t, _t*log(-16*_t*a**3/(7*c) + x)))","A",0
672,1,53,0,0.742652," ","integrate(x**11/(c*x**4+a)**3,x)","\frac{3 a^{2} + 4 a c x^{4}}{8 a^{2} c^{3} + 16 a c^{4} x^{4} + 8 c^{5} x^{8}} + \frac{\log{\left(a + c x^{4} \right)}}{4 c^{3}}"," ",0,"(3*a**2 + 4*a*c*x**4)/(8*a**2*c**3 + 16*a*c**4*x**4 + 8*c**5*x**8) + log(a + c*x**4)/(4*c**3)","A",0
673,1,116,0,1.039250," ","integrate(x**9/(c*x**4+a)**3,x)","- \frac{3 \sqrt{- \frac{1}{a c^{5}}} \log{\left(- a c^{2} \sqrt{- \frac{1}{a c^{5}}} + x^{2} \right)}}{32} + \frac{3 \sqrt{- \frac{1}{a c^{5}}} \log{\left(a c^{2} \sqrt{- \frac{1}{a c^{5}}} + x^{2} \right)}}{32} + \frac{- 3 a x^{2} - 5 c x^{6}}{16 a^{2} c^{2} + 32 a c^{3} x^{4} + 16 c^{4} x^{8}}"," ",0,"-3*sqrt(-1/(a*c**5))*log(-a*c**2*sqrt(-1/(a*c**5)) + x**2)/32 + 3*sqrt(-1/(a*c**5))*log(a*c**2*sqrt(-1/(a*c**5)) + x**2)/32 + (-3*a*x**2 - 5*c*x**6)/(16*a**2*c**2 + 32*a*c**3*x**4 + 16*c**4*x**8)","A",0
674,1,36,0,0.504236," ","integrate(x**7/(c*x**4+a)**3,x)","\frac{- a - 2 c x^{4}}{8 a^{2} c^{2} + 16 a c^{3} x^{4} + 8 c^{4} x^{8}}"," ",0,"(-a - 2*c*x**4)/(8*a**2*c**2 + 16*a*c**3*x**4 + 8*c**4*x**8)","B",0
675,1,116,0,0.806138," ","integrate(x**5/(c*x**4+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{3} c^{3}}} \log{\left(- a^{2} c \sqrt{- \frac{1}{a^{3} c^{3}}} + x^{2} \right)}}{32} + \frac{\sqrt{- \frac{1}{a^{3} c^{3}}} \log{\left(a^{2} c \sqrt{- \frac{1}{a^{3} c^{3}}} + x^{2} \right)}}{32} + \frac{- a x^{2} + c x^{6}}{16 a^{3} c + 32 a^{2} c^{2} x^{4} + 16 a c^{3} x^{8}}"," ",0,"-sqrt(-1/(a**3*c**3))*log(-a**2*c*sqrt(-1/(a**3*c**3)) + x**2)/32 + sqrt(-1/(a**3*c**3))*log(a**2*c*sqrt(-1/(a**3*c**3)) + x**2)/32 + (-a*x**2 + c*x**6)/(16*a**3*c + 32*a**2*c**2*x**4 + 16*a*c**3*x**8)","B",0
676,1,27,0,0.480875," ","integrate(x**3/(c*x**4+a)**3,x)","- \frac{1}{8 a^{2} c + 16 a c^{2} x^{4} + 8 c^{3} x^{8}}"," ",0,"-1/(8*a**2*c + 16*a*c**2*x**4 + 8*c**3*x**8)","A",0
677,1,110,0,0.581582," ","integrate(x/(c*x**4+a)**3,x)","- \frac{3 \sqrt{- \frac{1}{a^{5} c}} \log{\left(- a^{3} \sqrt{- \frac{1}{a^{5} c}} + x^{2} \right)}}{32} + \frac{3 \sqrt{- \frac{1}{a^{5} c}} \log{\left(a^{3} \sqrt{- \frac{1}{a^{5} c}} + x^{2} \right)}}{32} + \frac{5 a x^{2} + 3 c x^{6}}{16 a^{4} + 32 a^{3} c x^{4} + 16 a^{2} c^{2} x^{8}}"," ",0,"-3*sqrt(-1/(a**5*c))*log(-a**3*sqrt(-1/(a**5*c)) + x**2)/32 + 3*sqrt(-1/(a**5*c))*log(a**3*sqrt(-1/(a**5*c)) + x**2)/32 + (5*a*x**2 + 3*c*x**6)/(16*a**4 + 32*a**3*c*x**4 + 16*a**2*c**2*x**8)","A",0
678,1,56,0,0.779005," ","integrate(1/x/(c*x**4+a)**3,x)","\frac{3 a + 2 c x^{4}}{8 a^{4} + 16 a^{3} c x^{4} + 8 a^{2} c^{2} x^{8}} + \frac{\log{\left(x \right)}}{a^{3}} - \frac{\log{\left(\frac{a}{c} + x^{4} \right)}}{4 a^{3}}"," ",0,"(3*a + 2*c*x**4)/(8*a**4 + 16*a**3*c*x**4 + 8*a**2*c**2*x**8) + log(x)/a**3 - log(a/c + x**4)/(4*a**3)","A",0
679,1,121,0,0.820556," ","integrate(1/x**3/(c*x**4+a)**3,x)","\frac{15 \sqrt{- \frac{c}{a^{7}}} \log{\left(- \frac{a^{4} \sqrt{- \frac{c}{a^{7}}}}{c} + x^{2} \right)}}{32} - \frac{15 \sqrt{- \frac{c}{a^{7}}} \log{\left(\frac{a^{4} \sqrt{- \frac{c}{a^{7}}}}{c} + x^{2} \right)}}{32} + \frac{- 8 a^{2} - 25 a c x^{4} - 15 c^{2} x^{8}}{16 a^{5} x^{2} + 32 a^{4} c x^{6} + 16 a^{3} c^{2} x^{10}}"," ",0,"15*sqrt(-c/a**7)*log(-a**4*sqrt(-c/a**7)/c + x**2)/32 - 15*sqrt(-c/a**7)*log(a**4*sqrt(-c/a**7)/c + x**2)/32 + (-8*a**2 - 25*a*c*x**4 - 15*c**2*x**8)/(16*a**5*x**2 + 32*a**4*c*x**6 + 16*a**3*c**2*x**10)","A",0
680,1,70,0,0.684361," ","integrate(x**10/(c*x**4+a)**3,x)","\frac{- 7 a x^{3} - 11 c x^{7}}{32 a^{2} c^{2} + 64 a c^{3} x^{4} + 32 c^{4} x^{8}} + \operatorname{RootSum} {\left(268435456 t^{4} a c^{11} + 194481, \left( t \mapsto t \log{\left(\frac{2097152 t^{3} a c^{8}}{9261} + x \right)} \right)\right)}"," ",0,"(-7*a*x**3 - 11*c*x**7)/(32*a**2*c**2 + 64*a*c**3*x**4 + 32*c**4*x**8) + RootSum(268435456*_t**4*a*c**11 + 194481, Lambda(_t, _t*log(2097152*_t**3*a*c**8/9261 + x)))","A",0
681,1,68,0,0.958774," ","integrate(x**8/(c*x**4+a)**3,x)","\frac{- 5 a x - 9 c x^{5}}{32 a^{2} c^{2} + 64 a c^{3} x^{4} + 32 c^{4} x^{8}} + \operatorname{RootSum} {\left(268435456 t^{4} a^{3} c^{9} + 625, \left( t \mapsto t \log{\left(\frac{128 t a c^{2}}{5} + x \right)} \right)\right)}"," ",0,"(-5*a*x - 9*c*x**5)/(32*a**2*c**2 + 64*a*c**3*x**4 + 32*c**4*x**8) + RootSum(268435456*_t**4*a**3*c**9 + 625, Lambda(_t, _t*log(128*_t*a*c**2/5 + x)))","A",0
682,1,71,0,0.976217," ","integrate(x**6/(c*x**4+a)**3,x)","\frac{- a x^{3} + 3 c x^{7}}{32 a^{3} c + 64 a^{2} c^{2} x^{4} + 32 a c^{3} x^{8}} + \operatorname{RootSum} {\left(268435456 t^{4} a^{5} c^{7} + 81, \left( t \mapsto t \log{\left(\frac{2097152 t^{3} a^{4} c^{5}}{27} + x \right)} \right)\right)}"," ",0,"(-a*x**3 + 3*c*x**7)/(32*a**3*c + 64*a**2*c**2*x**4 + 32*a*c**3*x**8) + RootSum(268435456*_t**4*a**5*c**7 + 81, Lambda(_t, _t*log(2097152*_t**3*a**4*c**5/27 + x)))","A",0
683,1,66,0,0.848124," ","integrate(x**4/(c*x**4+a)**3,x)","\frac{- 3 a x + c x^{5}}{32 a^{3} c + 64 a^{2} c^{2} x^{4} + 32 a c^{3} x^{8}} + \operatorname{RootSum} {\left(268435456 t^{4} a^{7} c^{5} + 81, \left( t \mapsto t \log{\left(\frac{128 t a^{2} c}{3} + x \right)} \right)\right)}"," ",0,"(-3*a*x + c*x**5)/(32*a**3*c + 64*a**2*c**2*x**4 + 32*a*c**3*x**8) + RootSum(268435456*_t**4*a**7*c**5 + 81, Lambda(_t, _t*log(128*_t*a**2*c/3 + x)))","A",0
684,1,71,0,0.575220," ","integrate(x**2/(c*x**4+a)**3,x)","\frac{9 a x^{3} + 5 c x^{7}}{32 a^{4} + 64 a^{3} c x^{4} + 32 a^{2} c^{2} x^{8}} + \operatorname{RootSum} {\left(268435456 t^{4} a^{9} c^{3} + 625, \left( t \mapsto t \log{\left(\frac{2097152 t^{3} a^{7} c^{2}}{125} + x \right)} \right)\right)}"," ",0,"(9*a*x**3 + 5*c*x**7)/(32*a**4 + 64*a**3*c*x**4 + 32*a**2*c**2*x**8) + RootSum(268435456*_t**4*a**9*c**3 + 625, Lambda(_t, _t*log(2097152*_t**3*a**7*c**2/125 + x)))","A",0
685,1,63,0,0.575261," ","integrate(1/(c*x**4+a)**3,x)","\frac{11 a x + 7 c x^{5}}{32 a^{4} + 64 a^{3} c x^{4} + 32 a^{2} c^{2} x^{8}} + \operatorname{RootSum} {\left(268435456 t^{4} a^{11} c + 194481, \left( t \mapsto t \log{\left(\frac{128 t a^{3}}{21} + x \right)} \right)\right)}"," ",0,"(11*a*x + 7*c*x**5)/(32*a**4 + 64*a**3*c*x**4 + 32*a**2*c**2*x**8) + RootSum(268435456*_t**4*a**11*c + 194481, Lambda(_t, _t*log(128*_t*a**3/21 + x)))","A",0
686,1,80,0,1.038141," ","integrate(1/x**2/(c*x**4+a)**3,x)","\frac{- 32 a^{2} - 81 a c x^{4} - 45 c^{2} x^{8}}{32 a^{5} x + 64 a^{4} c x^{5} + 32 a^{3} c^{2} x^{9}} + \operatorname{RootSum} {\left(268435456 t^{4} a^{13} + 4100625 c, \left( t \mapsto t \log{\left(- \frac{2097152 t^{3} a^{10}}{91125 c} + x \right)} \right)\right)}"," ",0,"(-32*a**2 - 81*a*c*x**4 - 45*c**2*x**8)/(32*a**5*x + 64*a**4*c*x**5 + 32*a**3*c**2*x**9) + RootSum(268435456*_t**4*a**13 + 4100625*c, Lambda(_t, _t*log(-2097152*_t**3*a**10/(91125*c) + x)))","A",0
687,1,27,0,0.242374," ","integrate(x**9/(3*x**4+2),x)","\frac{x^{6}}{18} - \frac{x^{2}}{9} + \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x^{2}}{2} \right)}}{27}"," ",0,"x**6/18 - x**2/9 + sqrt(6)*atan(sqrt(6)*x**2/2)/27","A",0
688,1,14,0,0.245007," ","integrate(x**7/(3*x**4+2),x)","\frac{x^{4}}{12} - \frac{\log{\left(3 x^{4} + 2 \right)}}{18}"," ",0,"x**4/12 - log(3*x**4 + 2)/18","A",0
689,1,22,0,0.159288," ","integrate(x**5/(3*x**4+2),x)","\frac{x^{2}}{6} - \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x^{2}}{2} \right)}}{18}"," ",0,"x**2/6 - sqrt(6)*atan(sqrt(6)*x**2/2)/18","A",0
690,1,8,0,0.095357," ","integrate(x**3/(3*x**4+2),x)","\frac{\log{\left(3 x^{4} + 2 \right)}}{12}"," ",0,"log(3*x**4 + 2)/12","A",0
691,1,17,0,0.121748," ","integrate(x/(3*x**4+2),x)","\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x^{2}}{2} \right)}}{12}"," ",0,"sqrt(6)*atan(sqrt(6)*x**2/2)/12","A",0
692,1,14,0,0.118710," ","integrate(1/x/(3*x**4+2),x)","\frac{\log{\left(x \right)}}{2} - \frac{\log{\left(3 x^{4} + 2 \right)}}{8}"," ",0,"log(x)/2 - log(3*x**4 + 2)/8","A",0
693,1,26,0,0.148753," ","integrate(1/x**3/(3*x**4+2),x)","- \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x^{2}}{2} \right)}}{8} - \frac{1}{4 x^{2}}"," ",0,"-sqrt(6)*atan(sqrt(6)*x**2/2)/8 - 1/(4*x**2)","A",0
694,1,92,0,0.465771," ","integrate(x**6/(3*x**4+2),x)","\frac{x^{3}}{9} - \frac{\sqrt[4]{6} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{36} + \frac{\sqrt[4]{6} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{36} - \frac{\sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{18} - \frac{\sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{18}"," ",0,"x**3/9 - 6**(1/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/36 + 6**(1/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/36 - 6**(1/4)*atan(6**(1/4)*x - 1)/18 - 6**(1/4)*atan(6**(1/4)*x + 1)/18","A",0
695,1,90,0,0.494638," ","integrate(x**4/(3*x**4+2),x)","\frac{x}{3} + \frac{6^{\frac{3}{4}} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{72} - \frac{6^{\frac{3}{4}} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{72} - \frac{6^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{36} - \frac{6^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{36}"," ",0,"x/3 + 6**(3/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/72 - 6**(3/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/72 - 6**(3/4)*atan(6**(1/4)*x - 1)/36 - 6**(3/4)*atan(6**(1/4)*x + 1)/36","A",0
696,1,87,0,0.477065," ","integrate(x**2/(3*x**4+2),x)","\frac{\sqrt[4]{6} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{24} - \frac{\sqrt[4]{6} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{24} + \frac{\sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{12} + \frac{\sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{12}"," ",0,"6**(1/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/24 - 6**(1/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/24 + 6**(1/4)*atan(6**(1/4)*x - 1)/12 + 6**(1/4)*atan(6**(1/4)*x + 1)/12","A",0
697,1,87,0,0.471318," ","integrate(1/(3*x**4+2),x)","- \frac{6^{\frac{3}{4}} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{48} + \frac{6^{\frac{3}{4}} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{48} + \frac{6^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{24} + \frac{6^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{24}"," ",0,"-6**(3/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/48 + 6**(3/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/48 + 6**(3/4)*atan(6**(1/4)*x - 1)/24 + 6**(3/4)*atan(6**(1/4)*x + 1)/24","A",0
698,1,92,0,0.473558," ","integrate(1/x**2/(3*x**4+2),x)","- \frac{\sqrt[4]{6} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{16} + \frac{\sqrt[4]{6} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{16} - \frac{\sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{8} - \frac{\sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{8} - \frac{1}{2 x}"," ",0,"-6**(1/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/16 + 6**(1/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/16 - 6**(1/4)*atan(6**(1/4)*x - 1)/8 - 6**(1/4)*atan(6**(1/4)*x + 1)/8 - 1/(2*x)","A",0
699,1,8,0,0.178875," ","integrate(x**3/(3*x**4+2)**2,x)","- \frac{1}{36 x^{4} + 24}"," ",0,"-1/(36*x**4 + 24)","A",0
700,1,27,0,0.173891," ","integrate(x/(3*x**4+2)**2,x)","\frac{x^{2}}{24 x^{4} + 16} + \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x^{2}}{2} \right)}}{48}"," ",0,"x**2/(24*x**4 + 16) + sqrt(6)*atan(sqrt(6)*x**2/2)/48","A",0
701,1,22,0,0.169157," ","integrate(1/x/(3*x**4+2)**2,x)","\frac{\log{\left(x \right)}}{4} - \frac{\log{\left(3 x^{4} + 2 \right)}}{16} + \frac{1}{24 x^{4} + 16}"," ",0,"log(x)/4 - log(3*x**4 + 2)/16 + 1/(24*x**4 + 16)","A",0
702,1,37,0,0.297508," ","integrate(1/x**3/(3*x**4+2)**2,x)","\frac{- 9 x^{4} - 4}{48 x^{6} + 32 x^{2}} - \frac{3 \sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x^{2}}{2} \right)}}{32}"," ",0,"(-9*x**4 - 4)/(48*x**6 + 32*x**2) - 3*sqrt(6)*atan(sqrt(6)*x**2/2)/32","A",0
703,1,95,0,0.785779," ","integrate(x**4/(3*x**4+2)**2,x)","- \frac{x}{36 x^{4} + 24} - \frac{6^{\frac{3}{4}} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{576} + \frac{6^{\frac{3}{4}} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{576} + \frac{6^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{288} + \frac{6^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{288}"," ",0,"-x/(36*x**4 + 24) - 6**(3/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/576 + 6**(3/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/576 + 6**(3/4)*atan(6**(1/4)*x - 1)/288 + 6**(3/4)*atan(6**(1/4)*x + 1)/288","A",0
704,1,97,0,0.475731," ","integrate(x**2/(3*x**4+2)**2,x)","\frac{x^{3}}{24 x^{4} + 16} + \frac{\sqrt[4]{6} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{192} - \frac{\sqrt[4]{6} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{192} + \frac{\sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{96} + \frac{\sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{96}"," ",0,"x**3/(24*x**4 + 16) + 6**(1/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/192 - 6**(1/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/192 + 6**(1/4)*atan(6**(1/4)*x - 1)/96 + 6**(1/4)*atan(6**(1/4)*x + 1)/96","A",0
705,1,95,0,0.599175," ","integrate(1/(3*x**4+2)**2,x)","\frac{x}{24 x^{4} + 16} - \frac{6^{\frac{3}{4}} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{128} + \frac{6^{\frac{3}{4}} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{128} + \frac{6^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{64} + \frac{6^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{64}"," ",0,"x/(24*x**4 + 16) - 6**(3/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/128 + 6**(3/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/128 + 6**(3/4)*atan(6**(1/4)*x - 1)/64 + 6**(3/4)*atan(6**(1/4)*x + 1)/64","A",0
706,1,110,0,0.667672," ","integrate(1/x**2/(3*x**4+2)**2,x)","\frac{- 15 x^{4} - 8}{48 x^{5} + 32 x} - \frac{5 \sqrt[4]{6} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{128} + \frac{5 \sqrt[4]{6} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{128} - \frac{5 \sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{64} - \frac{5 \sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{64}"," ",0,"(-15*x**4 - 8)/(48*x**5 + 32*x) - 5*6**(1/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/128 + 5*6**(1/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/128 - 5*6**(1/4)*atan(6**(1/4)*x - 1)/64 - 5*6**(1/4)*atan(6**(1/4)*x + 1)/64","A",0
707,1,124,0,0.471786," ","integrate(x**2/(x**4+3),x)","\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \log{\left(x^{2} - \sqrt{2} \sqrt[4]{3} x + \sqrt{3} \right)}}{24} - \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \log{\left(x^{2} + \sqrt{2} \sqrt[4]{3} x + \sqrt{3} \right)}}{24} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} x}{3} - 1 \right)}}{12} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} x}{3} + 1 \right)}}{12}"," ",0,"sqrt(2)*3**(3/4)*log(x**2 - sqrt(2)*3**(1/4)*x + sqrt(3))/24 - sqrt(2)*3**(3/4)*log(x**2 + sqrt(2)*3**(1/4)*x + sqrt(3))/24 + sqrt(2)*3**(3/4)*atan(sqrt(2)*3**(3/4)*x/3 - 1)/12 + sqrt(2)*3**(3/4)*atan(sqrt(2)*3**(3/4)*x/3 + 1)/12","A",0
708,1,32,0,0.493968," ","integrate(1/(1+a+(-1+a)*x**4),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{4} + 512 a^{3} - 512 a - 256\right) + 1, \left( t \mapsto t \log{\left(4 t a + 4 t + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**4 + 512*a**3 - 512*a - 256) + 1, Lambda(_t, _t*log(4*_t*a + 4*_t + x)))","A",0
709,1,42,0,0.431705," ","integrate(1/(x**4+2*a+2*b),x)","\operatorname{RootSum} {\left(t^{4} \left(2048 a^{3} + 6144 a^{2} b + 6144 a b^{2} + 2048 b^{3}\right) + 1, \left( t \mapsto t \log{\left(8 t a + 8 t b + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(2048*a**3 + 6144*a**2*b + 6144*a*b**2 + 2048*b**3) + 1, Lambda(_t, _t*log(8*_t*a + 8*_t*b + x)))","A",0
710,1,42,0,0.547763," ","integrate(1/(x**4+2*a+2*b),x)","\operatorname{RootSum} {\left(t^{4} \left(2048 a^{3} + 6144 a^{2} b + 6144 a b^{2} + 2048 b^{3}\right) + 1, \left( t \mapsto t \log{\left(8 t a + 8 t b + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(2048*a**3 + 6144*a**2*b + 6144*a*b**2 + 2048*b**3) + 1, Lambda(_t, _t*log(8*_t*a + 8*_t*b + x)))","A",0
711,1,110,0,0.490501," ","integrate(x/(x**4+2*a+2*b),x)","- \frac{\sqrt{2} \sqrt{- \frac{1}{a + b}} \log{\left(- \sqrt{2} a \sqrt{- \frac{1}{a + b}} - \sqrt{2} b \sqrt{- \frac{1}{a + b}} + x^{2} \right)}}{8} + \frac{\sqrt{2} \sqrt{- \frac{1}{a + b}} \log{\left(\sqrt{2} a \sqrt{- \frac{1}{a + b}} + \sqrt{2} b \sqrt{- \frac{1}{a + b}} + x^{2} \right)}}{8}"," ",0,"-sqrt(2)*sqrt(-1/(a + b))*log(-sqrt(2)*a*sqrt(-1/(a + b)) - sqrt(2)*b*sqrt(-1/(a + b)) + x**2)/8 + sqrt(2)*sqrt(-1/(a + b))*log(sqrt(2)*a*sqrt(-1/(a + b)) + sqrt(2)*b*sqrt(-1/(a + b)) + x**2)/8","B",0
712,1,110,0,0.292295," ","integrate(x/(x**4+2*a+2*b),x)","- \frac{\sqrt{2} \sqrt{- \frac{1}{a + b}} \log{\left(- \sqrt{2} a \sqrt{- \frac{1}{a + b}} - \sqrt{2} b \sqrt{- \frac{1}{a + b}} + x^{2} \right)}}{8} + \frac{\sqrt{2} \sqrt{- \frac{1}{a + b}} \log{\left(\sqrt{2} a \sqrt{- \frac{1}{a + b}} + \sqrt{2} b \sqrt{- \frac{1}{a + b}} + x^{2} \right)}}{8}"," ",0,"-sqrt(2)*sqrt(-1/(a + b))*log(-sqrt(2)*a*sqrt(-1/(a + b)) - sqrt(2)*b*sqrt(-1/(a + b)) + x**2)/8 + sqrt(2)*sqrt(-1/(a + b))*log(sqrt(2)*a*sqrt(-1/(a + b)) + sqrt(2)*b*sqrt(-1/(a + b)) + x**2)/8","B",0
713,1,29,0,0.283641," ","integrate(x**2/(x**4+2*a+2*b),x)","\operatorname{RootSum} {\left(t^{4} \left(512 a + 512 b\right) + 1, \left( t \mapsto t \log{\left(128 t^{3} a + 128 t^{3} b + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(512*a + 512*b) + 1, Lambda(_t, _t*log(128*_t**3*a + 128*_t**3*b + x)))","A",0
714,1,29,0,0.491366," ","integrate(x**2/(x**4+2*a+2*b),x)","\operatorname{RootSum} {\left(t^{4} \left(512 a + 512 b\right) + 1, \left( t \mapsto t \log{\left(128 t^{3} a + 128 t^{3} b + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(512*a + 512*b) + 1, Lambda(_t, _t*log(128*_t**3*a + 128*_t**3*b + x)))","A",0
715,1,12,0,0.460176," ","integrate(x**3/(x**4+2*a+2*b),x)","\frac{\log{\left(2 a + 2 b + x^{4} \right)}}{4}"," ",0,"log(2*a + 2*b + x**4)/4","A",0
716,1,12,0,0.207137," ","integrate(x**3/(x**4+2*a+2*b),x)","\frac{\log{\left(2 a + 2 b + x^{4} \right)}}{4}"," ",0,"log(2*a + 2*b + x**4)/4","A",0
717,1,19,0,7.941257," ","integrate(x**(5/2)*(c*x**4+a),x)","\frac{2 a x^{\frac{7}{2}}}{7} + \frac{2 c x^{\frac{15}{2}}}{15}"," ",0,"2*a*x**(7/2)/7 + 2*c*x**(15/2)/15","A",0
718,1,19,0,4.008275," ","integrate(x**(3/2)*(c*x**4+a),x)","\frac{2 a x^{\frac{5}{2}}}{5} + \frac{2 c x^{\frac{13}{2}}}{13}"," ",0,"2*a*x**(5/2)/5 + 2*c*x**(13/2)/13","A",0
719,1,19,0,2.778684," ","integrate((c*x**4+a)*x**(1/2),x)","\frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 c x^{\frac{11}{2}}}{11}"," ",0,"2*a*x**(3/2)/3 + 2*c*x**(11/2)/11","A",0
720,1,17,0,1.690926," ","integrate((c*x**4+a)/x**(1/2),x)","2 a \sqrt{x} + \frac{2 c x^{\frac{9}{2}}}{9}"," ",0,"2*a*sqrt(x) + 2*c*x**(9/2)/9","A",0
721,1,17,0,1.658037," ","integrate((c*x**4+a)/x**(3/2),x)","- \frac{2 a}{\sqrt{x}} + \frac{2 c x^{\frac{7}{2}}}{7}"," ",0,"-2*a/sqrt(x) + 2*c*x**(7/2)/7","A",0
722,1,19,0,1.556138," ","integrate((c*x**4+a)/x**(5/2),x)","- \frac{2 a}{3 x^{\frac{3}{2}}} + \frac{2 c x^{\frac{5}{2}}}{5}"," ",0,"-2*a/(3*x**(3/2)) + 2*c*x**(5/2)/5","A",0
723,1,19,0,3.379235," ","integrate((c*x**4+a)/x**(7/2),x)","- \frac{2 a}{5 x^{\frac{5}{2}}} + \frac{2 c x^{\frac{3}{2}}}{3}"," ",0,"-2*a/(5*x**(5/2)) + 2*c*x**(3/2)/3","A",0
724,1,34,0,24.246981," ","integrate(x**(5/2)*(c*x**4+a)**2,x)","\frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a c x^{\frac{15}{2}}}{15} + \frac{2 c^{2} x^{\frac{23}{2}}}{23}"," ",0,"2*a**2*x**(7/2)/7 + 4*a*c*x**(15/2)/15 + 2*c**2*x**(23/2)/23","A",0
725,1,34,0,17.037518," ","integrate(x**(3/2)*(c*x**4+a)**2,x)","\frac{2 a^{2} x^{\frac{5}{2}}}{5} + \frac{4 a c x^{\frac{13}{2}}}{13} + \frac{2 c^{2} x^{\frac{21}{2}}}{21}"," ",0,"2*a**2*x**(5/2)/5 + 4*a*c*x**(13/2)/13 + 2*c**2*x**(21/2)/21","A",0
726,1,34,0,2.960834," ","integrate((c*x**4+a)**2*x**(1/2),x)","\frac{2 a^{2} x^{\frac{3}{2}}}{3} + \frac{4 a c x^{\frac{11}{2}}}{11} + \frac{2 c^{2} x^{\frac{19}{2}}}{19}"," ",0,"2*a**2*x**(3/2)/3 + 4*a*c*x**(11/2)/11 + 2*c**2*x**(19/2)/19","A",0
727,1,32,0,7.336140," ","integrate((c*x**4+a)**2/x**(1/2),x)","2 a^{2} \sqrt{x} + \frac{4 a c x^{\frac{9}{2}}}{9} + \frac{2 c^{2} x^{\frac{17}{2}}}{17}"," ",0,"2*a**2*sqrt(x) + 4*a*c*x**(9/2)/9 + 2*c**2*x**(17/2)/17","A",0
728,1,32,0,5.886678," ","integrate((c*x**4+a)**2/x**(3/2),x)","- \frac{2 a^{2}}{\sqrt{x}} + \frac{4 a c x^{\frac{7}{2}}}{7} + \frac{2 c^{2} x^{\frac{15}{2}}}{15}"," ",0,"-2*a**2/sqrt(x) + 4*a*c*x**(7/2)/7 + 2*c**2*x**(15/2)/15","A",0
729,1,34,0,7.430844," ","integrate((c*x**4+a)**2/x**(5/2),x)","- \frac{2 a^{2}}{3 x^{\frac{3}{2}}} + \frac{4 a c x^{\frac{5}{2}}}{5} + \frac{2 c^{2} x^{\frac{13}{2}}}{13}"," ",0,"-2*a**2/(3*x**(3/2)) + 4*a*c*x**(5/2)/5 + 2*c**2*x**(13/2)/13","A",0
730,1,34,0,8.957574," ","integrate((c*x**4+a)**2/x**(7/2),x)","- \frac{2 a^{2}}{5 x^{\frac{5}{2}}} + \frac{4 a c x^{\frac{3}{2}}}{3} + \frac{2 c^{2} x^{\frac{11}{2}}}{11}"," ",0,"-2*a**2/(5*x**(5/2)) + 4*a*c*x**(3/2)/3 + 2*c**2*x**(11/2)/11","A",0
731,1,49,0,70.177654," ","integrate(x**(5/2)*(c*x**4+a)**3,x)","\frac{2 a^{3} x^{\frac{7}{2}}}{7} + \frac{2 a^{2} c x^{\frac{15}{2}}}{5} + \frac{6 a c^{2} x^{\frac{23}{2}}}{23} + \frac{2 c^{3} x^{\frac{31}{2}}}{31}"," ",0,"2*a**3*x**(7/2)/7 + 2*a**2*c*x**(15/2)/5 + 6*a*c**2*x**(23/2)/23 + 2*c**3*x**(31/2)/31","A",0
732,1,49,0,48.123675," ","integrate(x**(3/2)*(c*x**4+a)**3,x)","\frac{2 a^{3} x^{\frac{5}{2}}}{5} + \frac{6 a^{2} c x^{\frac{13}{2}}}{13} + \frac{2 a c^{2} x^{\frac{21}{2}}}{7} + \frac{2 c^{3} x^{\frac{29}{2}}}{29}"," ",0,"2*a**3*x**(5/2)/5 + 6*a**2*c*x**(13/2)/13 + 2*a*c**2*x**(21/2)/7 + 2*c**3*x**(29/2)/29","A",0
733,1,49,0,5.952011," ","integrate((c*x**4+a)**3*x**(1/2),x)","\frac{2 a^{3} x^{\frac{3}{2}}}{3} + \frac{6 a^{2} c x^{\frac{11}{2}}}{11} + \frac{6 a c^{2} x^{\frac{19}{2}}}{19} + \frac{2 c^{3} x^{\frac{27}{2}}}{27}"," ",0,"2*a**3*x**(3/2)/3 + 6*a**2*c*x**(11/2)/11 + 6*a*c**2*x**(19/2)/19 + 2*c**3*x**(27/2)/27","A",0
734,1,48,0,24.751905," ","integrate((c*x**4+a)**3/x**(1/2),x)","2 a^{3} \sqrt{x} + \frac{2 a^{2} c x^{\frac{9}{2}}}{3} + \frac{6 a c^{2} x^{\frac{17}{2}}}{17} + \frac{2 c^{3} x^{\frac{25}{2}}}{25}"," ",0,"2*a**3*sqrt(x) + 2*a**2*c*x**(9/2)/3 + 6*a*c**2*x**(17/2)/17 + 2*c**3*x**(25/2)/25","A",0
735,1,48,0,27.823785," ","integrate((c*x**4+a)**3/x**(3/2),x)","- \frac{2 a^{3}}{\sqrt{x}} + \frac{6 a^{2} c x^{\frac{7}{2}}}{7} + \frac{2 a c^{2} x^{\frac{15}{2}}}{5} + \frac{2 c^{3} x^{\frac{23}{2}}}{23}"," ",0,"-2*a**3/sqrt(x) + 6*a**2*c*x**(7/2)/7 + 2*a*c**2*x**(15/2)/5 + 2*c**3*x**(23/2)/23","A",0
736,1,49,0,37.073075," ","integrate((c*x**4+a)**3/x**(5/2),x)","- \frac{2 a^{3}}{3 x^{\frac{3}{2}}} + \frac{6 a^{2} c x^{\frac{5}{2}}}{5} + \frac{6 a c^{2} x^{\frac{13}{2}}}{13} + \frac{2 c^{3} x^{\frac{21}{2}}}{21}"," ",0,"-2*a**3/(3*x**(3/2)) + 6*a**2*c*x**(5/2)/5 + 6*a*c**2*x**(13/2)/13 + 2*c**3*x**(21/2)/21","A",0
737,1,48,0,37.209733," ","integrate((c*x**4+a)**3/x**(7/2),x)","- \frac{2 a^{3}}{5 x^{\frac{5}{2}}} + 2 a^{2} c x^{\frac{3}{2}} + \frac{6 a c^{2} x^{\frac{11}{2}}}{11} + \frac{2 c^{3} x^{\frac{19}{2}}}{19}"," ",0,"-2*a**3/(5*x**(5/2)) + 2*a**2*c*x**(3/2) + 6*a*c**2*x**(11/2)/11 + 2*c**3*x**(19/2)/19","A",0
738,-1,0,0,0.000000," ","integrate(x**(9/2)/(c*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
739,1,459,0,168.071847," ","integrate(x**(7/2)/(c*x**4+a),x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: a = 0 \wedge c = 0 \\\frac{2 x^{\frac{9}{2}}}{9 a} & \text{for}\: c = 0 \\\frac{2 \sqrt{x}}{c} & \text{for}\: a = 0 \\\frac{\sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} \log{\left(- \sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 c} - \frac{\sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} \log{\left(\sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 c} + \frac{\sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} \log{\left(- 4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 c} - \frac{\sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} \log{\left(4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 c} + \frac{\sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{7}{8}} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{2 c} - \frac{\sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} \operatorname{atan}{\left(1 - \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 c} + \frac{\sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} \operatorname{atan}{\left(1 + \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 c} + \frac{2 \sqrt{x}}{c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(c, 0)), (2*x**(9/2)/(9*a), Eq(c, 0)), (2*sqrt(x)/c, Eq(a, 0)), ((-1)**(1/8)*a**(1/8)*(1/c)**(1/8)*log(-(-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*c) - (-1)**(1/8)*a**(1/8)*(1/c)**(1/8)*log((-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*c) + (-1)**(1/8)*sqrt(2)*a**(1/8)*(1/c)**(1/8)*log(-4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*c) - (-1)**(1/8)*sqrt(2)*a**(1/8)*(1/c)**(1/8)*log(4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*c) + (-1)**(1/8)*a**(1/8)*(1/c)**(1/8)*atan((-1)**(7/8)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(2*c) - (-1)**(1/8)*sqrt(2)*a**(1/8)*(1/c)**(1/8)*atan(1 - (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*c) + (-1)**(1/8)*sqrt(2)*a**(1/8)*(1/c)**(1/8)*atan(1 + (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*c) + 2*sqrt(x)/c, True))","A",0
740,1,452,0,94.125490," ","integrate(x**(5/2)/(c*x**4+a),x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge c = 0 \\\frac{2 x^{\frac{7}{2}}}{7 a} & \text{for}\: c = 0 \\- \frac{2}{c \sqrt{x}} & \text{for}\: a = 0 \\- \frac{\left(-1\right)^{\frac{7}{8}} \log{\left(- \sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 \sqrt[8]{a} c \sqrt[8]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{7}{8}} \log{\left(\sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 \sqrt[8]{a} c \sqrt[8]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \log{\left(- 4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 \sqrt[8]{a} c \sqrt[8]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \log{\left(4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 \sqrt[8]{a} c \sqrt[8]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{7}{8}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{7}{8}} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{2 \sqrt[8]{a} c \sqrt[8]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \operatorname{atan}{\left(1 - \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 \sqrt[8]{a} c \sqrt[8]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \operatorname{atan}{\left(1 + \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 \sqrt[8]{a} c \sqrt[8]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(c, 0)), (2*x**(7/2)/(7*a), Eq(c, 0)), (-2/(c*sqrt(x)), Eq(a, 0)), (-(-1)**(7/8)*log(-(-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*a**(1/8)*c*(1/c)**(1/8)) + (-1)**(7/8)*log((-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*a**(1/8)*c*(1/c)**(1/8)) - (-1)**(7/8)*sqrt(2)*log(-4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*a**(1/8)*c*(1/c)**(1/8)) + (-1)**(7/8)*sqrt(2)*log(4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*a**(1/8)*c*(1/c)**(1/8)) + (-1)**(7/8)*atan((-1)**(7/8)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(2*a**(1/8)*c*(1/c)**(1/8)) - (-1)**(7/8)*sqrt(2)*atan(1 - (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*a**(1/8)*c*(1/c)**(1/8)) + (-1)**(7/8)*sqrt(2)*atan(1 + (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*a**(1/8)*c*(1/c)**(1/8)), True))","A",0
741,1,454,0,74.187138," ","integrate(x**(3/2)/(c*x**4+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge c = 0 \\\frac{2 x^{\frac{5}{2}}}{5 a} & \text{for}\: c = 0 \\- \frac{2}{3 c x^{\frac{3}{2}}} & \text{for}\: a = 0 \\- \frac{\left(-1\right)^{\frac{5}{8}} \log{\left(- \sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 a^{\frac{3}{8}} c \left(\frac{1}{c}\right)^{\frac{3}{8}}} + \frac{\left(-1\right)^{\frac{5}{8}} \log{\left(\sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 a^{\frac{3}{8}} c \left(\frac{1}{c}\right)^{\frac{3}{8}}} + \frac{\left(-1\right)^{\frac{5}{8}} \sqrt{2} \log{\left(- 4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 a^{\frac{3}{8}} c \left(\frac{1}{c}\right)^{\frac{3}{8}}} - \frac{\left(-1\right)^{\frac{5}{8}} \sqrt{2} \log{\left(4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 a^{\frac{3}{8}} c \left(\frac{1}{c}\right)^{\frac{3}{8}}} - \frac{\left(-1\right)^{\frac{5}{8}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{7}{8}} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{2 a^{\frac{3}{8}} c \left(\frac{1}{c}\right)^{\frac{3}{8}}} - \frac{\left(-1\right)^{\frac{5}{8}} \sqrt{2} \operatorname{atan}{\left(1 - \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 a^{\frac{3}{8}} c \left(\frac{1}{c}\right)^{\frac{3}{8}}} + \frac{\left(-1\right)^{\frac{5}{8}} \sqrt{2} \operatorname{atan}{\left(1 + \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 a^{\frac{3}{8}} c \left(\frac{1}{c}\right)^{\frac{3}{8}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(c, 0)), (2*x**(5/2)/(5*a), Eq(c, 0)), (-2/(3*c*x**(3/2)), Eq(a, 0)), (-(-1)**(5/8)*log(-(-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*a**(3/8)*c*(1/c)**(3/8)) + (-1)**(5/8)*log((-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*a**(3/8)*c*(1/c)**(3/8)) + (-1)**(5/8)*sqrt(2)*log(-4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*a**(3/8)*c*(1/c)**(3/8)) - (-1)**(5/8)*sqrt(2)*log(4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*a**(3/8)*c*(1/c)**(3/8)) - (-1)**(5/8)*atan((-1)**(7/8)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(2*a**(3/8)*c*(1/c)**(3/8)) - (-1)**(5/8)*sqrt(2)*atan(1 - (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*a**(3/8)*c*(1/c)**(3/8)) + (-1)**(5/8)*sqrt(2)*atan(1 + (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*a**(3/8)*c*(1/c)**(3/8)), True))","A",0
742,1,442,0,40.999191," ","integrate(x**(1/2)/(c*x**4+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge c = 0 \\\frac{2 x^{\frac{3}{2}}}{3 a} & \text{for}\: c = 0 \\- \frac{2}{5 c x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{\left(-1\right)^{\frac{3}{8}} \left(\frac{1}{c}\right)^{\frac{3}{8}} \log{\left(- \sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 a^{\frac{5}{8}}} + \frac{\left(-1\right)^{\frac{3}{8}} \left(\frac{1}{c}\right)^{\frac{3}{8}} \log{\left(\sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 a^{\frac{5}{8}}} + \frac{\left(-1\right)^{\frac{3}{8}} \sqrt{2} \left(\frac{1}{c}\right)^{\frac{3}{8}} \log{\left(- 4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 a^{\frac{5}{8}}} - \frac{\left(-1\right)^{\frac{3}{8}} \sqrt{2} \left(\frac{1}{c}\right)^{\frac{3}{8}} \log{\left(4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 a^{\frac{5}{8}}} + \frac{\left(-1\right)^{\frac{3}{8}} \left(\frac{1}{c}\right)^{\frac{3}{8}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{7}{8}} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{2 a^{\frac{5}{8}}} + \frac{\left(-1\right)^{\frac{3}{8}} \sqrt{2} \left(\frac{1}{c}\right)^{\frac{3}{8}} \operatorname{atan}{\left(1 - \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 a^{\frac{5}{8}}} - \frac{\left(-1\right)^{\frac{3}{8}} \sqrt{2} \left(\frac{1}{c}\right)^{\frac{3}{8}} \operatorname{atan}{\left(1 + \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 a^{\frac{5}{8}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(c, 0)), (2*x**(3/2)/(3*a), Eq(c, 0)), (-2/(5*c*x**(5/2)), Eq(a, 0)), (-(-1)**(3/8)*(1/c)**(3/8)*log(-(-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*a**(5/8)) + (-1)**(3/8)*(1/c)**(3/8)*log((-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*a**(5/8)) + (-1)**(3/8)*sqrt(2)*(1/c)**(3/8)*log(-4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*a**(5/8)) - (-1)**(3/8)*sqrt(2)*(1/c)**(3/8)*log(4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*a**(5/8)) + (-1)**(3/8)*(1/c)**(3/8)*atan((-1)**(7/8)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(2*a**(5/8)) + (-1)**(3/8)*sqrt(2)*(1/c)**(3/8)*atan(1 - (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*a**(5/8)) - (-1)**(3/8)*sqrt(2)*(1/c)**(3/8)*atan(1 + (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*a**(5/8)), True))","A",0
743,1,440,0,58.917377," ","integrate(1/(c*x**4+a)/x**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge c = 0 \\\frac{2 \sqrt{x}}{a} & \text{for}\: c = 0 \\- \frac{2}{7 c x^{\frac{7}{2}}} & \text{for}\: a = 0 \\- \frac{\sqrt[8]{-1} \sqrt[8]{\frac{1}{c}} \log{\left(- \sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 a^{\frac{7}{8}}} + \frac{\sqrt[8]{-1} \sqrt[8]{\frac{1}{c}} \log{\left(\sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 a^{\frac{7}{8}}} - \frac{\sqrt[8]{-1} \sqrt{2} \sqrt[8]{\frac{1}{c}} \log{\left(- 4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 a^{\frac{7}{8}}} + \frac{\sqrt[8]{-1} \sqrt{2} \sqrt[8]{\frac{1}{c}} \log{\left(4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 a^{\frac{7}{8}}} - \frac{\sqrt[8]{-1} \sqrt[8]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{7}{8}} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{2 a^{\frac{7}{8}}} + \frac{\sqrt[8]{-1} \sqrt{2} \sqrt[8]{\frac{1}{c}} \operatorname{atan}{\left(1 - \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 a^{\frac{7}{8}}} - \frac{\sqrt[8]{-1} \sqrt{2} \sqrt[8]{\frac{1}{c}} \operatorname{atan}{\left(1 + \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 a^{\frac{7}{8}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(c, 0)), (2*sqrt(x)/a, Eq(c, 0)), (-2/(7*c*x**(7/2)), Eq(a, 0)), (-(-1)**(1/8)*(1/c)**(1/8)*log(-(-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*a**(7/8)) + (-1)**(1/8)*(1/c)**(1/8)*log((-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*a**(7/8)) - (-1)**(1/8)*sqrt(2)*(1/c)**(1/8)*log(-4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*a**(7/8)) + (-1)**(1/8)*sqrt(2)*(1/c)**(1/8)*log(4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*a**(7/8)) - (-1)**(1/8)*(1/c)**(1/8)*atan((-1)**(7/8)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(2*a**(7/8)) + (-1)**(1/8)*sqrt(2)*(1/c)**(1/8)*atan(1 - (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*a**(7/8)) - (-1)**(1/8)*sqrt(2)*(1/c)**(1/8)*atan(1 + (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*a**(7/8)), True))","A",0
744,1,450,0,148.288913," ","integrate(1/x**(3/2)/(c*x**4+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{9}{2}}} & \text{for}\: a = 0 \wedge c = 0 \\- \frac{2}{9 c x^{\frac{9}{2}}} & \text{for}\: a = 0 \\- \frac{2}{a \sqrt{x}} & \text{for}\: c = 0 \\- \frac{2}{a \sqrt{x}} + \frac{\left(-1\right)^{\frac{7}{8}} \log{\left(- \sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 a^{\frac{9}{8}} \sqrt[8]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{7}{8}} \log{\left(\sqrt[8]{-1} \sqrt[8]{a} \sqrt[8]{\frac{1}{c}} + \sqrt{x} \right)}}{4 a^{\frac{9}{8}} \sqrt[8]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \log{\left(- 4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 a^{\frac{9}{8}} \sqrt[8]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \log{\left(4 \sqrt[8]{-1} \sqrt{2} \sqrt[8]{a} \sqrt{x} \sqrt[8]{\frac{1}{c}} + 4 \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + 4 x \right)}}{8 a^{\frac{9}{8}} \sqrt[8]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{7}{8}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{7}{8}} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{2 a^{\frac{9}{8}} \sqrt[8]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \operatorname{atan}{\left(1 - \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 a^{\frac{9}{8}} \sqrt[8]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \operatorname{atan}{\left(1 + \frac{\left(-1\right)^{\frac{7}{8}} \sqrt{2} \sqrt{x}}{\sqrt[8]{a} \sqrt[8]{\frac{1}{c}}} \right)}}{4 a^{\frac{9}{8}} \sqrt[8]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(9/2), Eq(a, 0) & Eq(c, 0)), (-2/(9*c*x**(9/2)), Eq(a, 0)), (-2/(a*sqrt(x)), Eq(c, 0)), (-2/(a*sqrt(x)) + (-1)**(7/8)*log(-(-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*a**(9/8)*(1/c)**(1/8)) - (-1)**(7/8)*log((-1)**(1/8)*a**(1/8)*(1/c)**(1/8) + sqrt(x))/(4*a**(9/8)*(1/c)**(1/8)) + (-1)**(7/8)*sqrt(2)*log(-4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*a**(9/8)*(1/c)**(1/8)) - (-1)**(7/8)*sqrt(2)*log(4*(-1)**(1/8)*sqrt(2)*a**(1/8)*sqrt(x)*(1/c)**(1/8) + 4*(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + 4*x)/(8*a**(9/8)*(1/c)**(1/8)) - (-1)**(7/8)*atan((-1)**(7/8)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(2*a**(9/8)*(1/c)**(1/8)) + (-1)**(7/8)*sqrt(2)*atan(1 - (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*a**(9/8)*(1/c)**(1/8)) - (-1)**(7/8)*sqrt(2)*atan(1 + (-1)**(7/8)*sqrt(2)*sqrt(x)/(a**(1/8)*(1/c)**(1/8)))/(4*a**(9/8)*(1/c)**(1/8)), True))","A",0
745,-1,0,0,0.000000," ","integrate(1/x**(5/2)/(c*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,-1,0,0,0.000000," ","integrate(x**(13/2)/(c*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
747,-1,0,0,0.000000," ","integrate(x**(11/2)/(c*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
748,-1,0,0,0.000000," ","integrate(x**(9/2)/(c*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
749,-1,0,0,0.000000," ","integrate(x**(7/2)/(c*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,-1,0,0,0.000000," ","integrate(x**(5/2)/(c*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,-1,0,0,0.000000," ","integrate(x**(3/2)/(c*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
752,-1,0,0,0.000000," ","integrate(x**(1/2)/(c*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
753,-1,0,0,0.000000," ","integrate(1/(c*x**4+a)**2/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
754,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(c*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
755,-1,0,0,0.000000," ","integrate(x**(15/2)/(c*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
756,-1,0,0,0.000000," ","integrate(x**(13/2)/(c*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,-1,0,0,0.000000," ","integrate(x**(11/2)/(c*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,-1,0,0,0.000000," ","integrate(x**(9/2)/(c*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,-1,0,0,0.000000," ","integrate(x**(7/2)/(c*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
760,-1,0,0,0.000000," ","integrate(x**(5/2)/(c*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
761,-1,0,0,0.000000," ","integrate(x**(3/2)/(c*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
762,-1,0,0,0.000000," ","integrate(x**(1/2)/(c*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,-1,0,0,0.000000," ","integrate(1/(c*x**4+a)**3/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
764,1,87,0,3.788996," ","integrate(x**11*(c*x**4+a)**(1/2),x)","\begin{cases} \frac{4 a^{3} \sqrt{a + c x^{4}}}{105 c^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + c x^{4}}}{105 c^{2}} + \frac{a x^{8} \sqrt{a + c x^{4}}}{70 c} + \frac{x^{12} \sqrt{a + c x^{4}}}{14} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a**3*sqrt(a + c*x**4)/(105*c**3) - 2*a**2*x**4*sqrt(a + c*x**4)/(105*c**2) + a*x**8*sqrt(a + c*x**4)/(70*c) + x**12*sqrt(a + c*x**4)/14, Ne(c, 0)), (sqrt(a)*x**12/12, True))","A",0
765,1,61,0,2.898610," ","integrate(x**7*(c*x**4+a)**(1/2),x)","\begin{cases} - \frac{a^{2} \sqrt{a + c x^{4}}}{15 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{4}}}{30 c} + \frac{x^{8} \sqrt{a + c x^{4}}}{10} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*sqrt(a + c*x**4)/(15*c**2) + a*x**4*sqrt(a + c*x**4)/(30*c) + x**8*sqrt(a + c*x**4)/10, Ne(c, 0)), (sqrt(a)*x**8/8, True))","A",0
766,1,39,0,0.395894," ","integrate(x**3*(c*x**4+a)**(1/2),x)","\begin{cases} \frac{a \sqrt{a + c x^{4}}}{6 c} + \frac{x^{4} \sqrt{a + c x^{4}}}{6} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*sqrt(a + c*x**4)/(6*c) + x**4*sqrt(a + c*x**4)/6, Ne(c, 0)), (sqrt(a)*x**4/4, True))","A",0
767,1,66,0,2.358938," ","integrate((c*x**4+a)**(1/2)/x,x)","- \frac{\sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x^{2}} \right)}}{2} + \frac{a}{2 \sqrt{c} x^{2} \sqrt{\frac{a}{c x^{4}} + 1}} + \frac{\sqrt{c} x^{2}}{2 \sqrt{\frac{a}{c x^{4}} + 1}}"," ",0,"-sqrt(a)*asinh(sqrt(a)/(sqrt(c)*x**2))/2 + a/(2*sqrt(c)*x**2*sqrt(a/(c*x**4) + 1)) + sqrt(c)*x**2/(2*sqrt(a/(c*x**4) + 1))","A",0
768,1,46,0,4.062556," ","integrate((c*x**4+a)**(1/2)/x**5,x)","- \frac{\sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{4 x^{2}} - \frac{c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x^{2}} \right)}}{4 \sqrt{a}}"," ",0,"-sqrt(c)*sqrt(a/(c*x**4) + 1)/(4*x**2) - c*asinh(sqrt(a)/(sqrt(c)*x**2))/(4*sqrt(a))","A",0
769,1,95,0,5.093976," ","integrate((c*x**4+a)**(1/2)/x**9,x)","- \frac{a}{8 \sqrt{c} x^{10} \sqrt{\frac{a}{c x^{4}} + 1}} - \frac{3 \sqrt{c}}{16 x^{6} \sqrt{\frac{a}{c x^{4}} + 1}} - \frac{c^{\frac{3}{2}}}{16 a x^{2} \sqrt{\frac{a}{c x^{4}} + 1}} + \frac{c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x^{2}} \right)}}{16 a^{\frac{3}{2}}}"," ",0,"-a/(8*sqrt(c)*x**10*sqrt(a/(c*x**4) + 1)) - 3*sqrt(c)/(16*x**6*sqrt(a/(c*x**4) + 1)) - c**(3/2)/(16*a*x**2*sqrt(a/(c*x**4) + 1)) + c**2*asinh(sqrt(a)/(sqrt(c)*x**2))/(16*a**(3/2))","A",0
770,1,95,0,5.167027," ","integrate(x**5*(c*x**4+a)**(1/2),x)","\frac{a^{\frac{3}{2}} x^{2}}{16 c \sqrt{1 + \frac{c x^{4}}{a}}} + \frac{3 \sqrt{a} x^{6}}{16 \sqrt{1 + \frac{c x^{4}}{a}}} - \frac{a^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} + \frac{c x^{10}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{4}}{a}}}"," ",0,"a**(3/2)*x**2/(16*c*sqrt(1 + c*x**4/a)) + 3*sqrt(a)*x**6/(16*sqrt(1 + c*x**4/a)) - a**2*asinh(sqrt(c)*x**2/sqrt(a))/(16*c**(3/2)) + c*x**10/(8*sqrt(a)*sqrt(1 + c*x**4/a))","A",0
771,1,44,0,3.534558," ","integrate(x*(c*x**4+a)**(1/2),x)","\frac{\sqrt{a} x^{2} \sqrt{1 + \frac{c x^{4}}{a}}}{4} + \frac{a \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{4 \sqrt{c}}"," ",0,"sqrt(a)*x**2*sqrt(1 + c*x**4/a)/4 + a*asinh(sqrt(c)*x**2/sqrt(a))/(4*sqrt(c))","A",0
772,1,66,0,3.178147," ","integrate((c*x**4+a)**(1/2)/x**3,x)","- \frac{\sqrt{a}}{2 x^{2} \sqrt{1 + \frac{c x^{4}}{a}}} + \frac{\sqrt{c} \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{2} - \frac{c x^{2}}{2 \sqrt{a} \sqrt{1 + \frac{c x^{4}}{a}}}"," ",0,"-sqrt(a)/(2*x**2*sqrt(1 + c*x**4/a)) + sqrt(c)*asinh(sqrt(c)*x**2/sqrt(a))/2 - c*x**2/(2*sqrt(a)*sqrt(1 + c*x**4/a))","A",0
773,1,42,0,1.625461," ","integrate((c*x**4+a)**(1/2)/x**7,x)","- \frac{\sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{6 x^{4}} - \frac{c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{6 a}"," ",0,"-sqrt(c)*sqrt(a/(c*x**4) + 1)/(6*x**4) - c**(3/2)*sqrt(a/(c*x**4) + 1)/(6*a)","B",0
774,1,66,0,2.347341," ","integrate((c*x**4+a)**(1/2)/x**11,x)","- \frac{\sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{10 x^{8}} - \frac{c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{30 a x^{4}} + \frac{c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{15 a^{2}}"," ",0,"-sqrt(c)*sqrt(a/(c*x**4) + 1)/(10*x**8) - c**(3/2)*sqrt(a/(c*x**4) + 1)/(30*a*x**4) + c**(5/2)*sqrt(a/(c*x**4) + 1)/(15*a**2)","A",0
775,1,359,0,3.434223," ","integrate((c*x**4+a)**(1/2)/x**15,x)","- \frac{15 a^{5} c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{210 a^{5} c^{4} x^{12} + 420 a^{4} c^{5} x^{16} + 210 a^{3} c^{6} x^{20}} - \frac{33 a^{4} c^{\frac{11}{2}} x^{4} \sqrt{\frac{a}{c x^{4}} + 1}}{210 a^{5} c^{4} x^{12} + 420 a^{4} c^{5} x^{16} + 210 a^{3} c^{6} x^{20}} - \frac{17 a^{3} c^{\frac{13}{2}} x^{8} \sqrt{\frac{a}{c x^{4}} + 1}}{210 a^{5} c^{4} x^{12} + 420 a^{4} c^{5} x^{16} + 210 a^{3} c^{6} x^{20}} - \frac{3 a^{2} c^{\frac{15}{2}} x^{12} \sqrt{\frac{a}{c x^{4}} + 1}}{210 a^{5} c^{4} x^{12} + 420 a^{4} c^{5} x^{16} + 210 a^{3} c^{6} x^{20}} - \frac{12 a c^{\frac{17}{2}} x^{16} \sqrt{\frac{a}{c x^{4}} + 1}}{210 a^{5} c^{4} x^{12} + 420 a^{4} c^{5} x^{16} + 210 a^{3} c^{6} x^{20}} - \frac{8 c^{\frac{19}{2}} x^{20} \sqrt{\frac{a}{c x^{4}} + 1}}{210 a^{5} c^{4} x^{12} + 420 a^{4} c^{5} x^{16} + 210 a^{3} c^{6} x^{20}}"," ",0,"-15*a**5*c**(9/2)*sqrt(a/(c*x**4) + 1)/(210*a**5*c**4*x**12 + 420*a**4*c**5*x**16 + 210*a**3*c**6*x**20) - 33*a**4*c**(11/2)*x**4*sqrt(a/(c*x**4) + 1)/(210*a**5*c**4*x**12 + 420*a**4*c**5*x**16 + 210*a**3*c**6*x**20) - 17*a**3*c**(13/2)*x**8*sqrt(a/(c*x**4) + 1)/(210*a**5*c**4*x**12 + 420*a**4*c**5*x**16 + 210*a**3*c**6*x**20) - 3*a**2*c**(15/2)*x**12*sqrt(a/(c*x**4) + 1)/(210*a**5*c**4*x**12 + 420*a**4*c**5*x**16 + 210*a**3*c**6*x**20) - 12*a*c**(17/2)*x**16*sqrt(a/(c*x**4) + 1)/(210*a**5*c**4*x**12 + 420*a**4*c**5*x**16 + 210*a**3*c**6*x**20) - 8*c**(19/2)*x**20*sqrt(a/(c*x**4) + 1)/(210*a**5*c**4*x**12 + 420*a**4*c**5*x**16 + 210*a**3*c**6*x**20)","B",0
776,1,39,0,2.033826," ","integrate(x**4*(c*x**4+a)**(1/2),x)","\frac{\sqrt{a} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"sqrt(a)*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4))","C",0
777,1,37,0,1.817328," ","integrate((c*x**4+a)**(1/2),x)","\frac{\sqrt{a} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(a)*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4))","C",0
778,1,42,0,1.624074," ","integrate((c*x**4+a)**(1/2)/x**4,x)","\frac{\sqrt{a} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"sqrt(a)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), c*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4))","C",0
779,1,46,0,1.386998," ","integrate((c*x**4+a)**(1/2)/x**8,x)","\frac{\sqrt{a} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"sqrt(a)*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), c*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4))","C",0
780,1,39,0,1.764683," ","integrate(x**2*(c*x**4+a)**(1/2),x)","\frac{\sqrt{a} x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(a)*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4))","C",0
781,1,41,0,1.440272," ","integrate((c*x**4+a)**(1/2)/x**2,x)","\frac{\sqrt{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"sqrt(a)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4))","C",0
782,1,46,0,2.208320," ","integrate((c*x**4+a)**(1/2)/x**6,x)","\frac{\sqrt{a} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"sqrt(a)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), c*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4))","C",0
783,1,109,0,11.027647," ","integrate(x**11*(c*x**4+a)**(3/2),x)","\begin{cases} \frac{4 a^{4} \sqrt{a + c x^{4}}}{315 c^{3}} - \frac{2 a^{3} x^{4} \sqrt{a + c x^{4}}}{315 c^{2}} + \frac{a^{2} x^{8} \sqrt{a + c x^{4}}}{210 c} + \frac{5 a x^{12} \sqrt{a + c x^{4}}}{63} + \frac{c x^{16} \sqrt{a + c x^{4}}}{18} & \text{for}\: c \neq 0 \\\frac{a^{\frac{3}{2}} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a**4*sqrt(a + c*x**4)/(315*c**3) - 2*a**3*x**4*sqrt(a + c*x**4)/(315*c**2) + a**2*x**8*sqrt(a + c*x**4)/(210*c) + 5*a*x**12*sqrt(a + c*x**4)/63 + c*x**16*sqrt(a + c*x**4)/18, Ne(c, 0)), (a**(3/2)*x**12/12, True))","A",0
784,1,83,0,5.423015," ","integrate(x**7*(c*x**4+a)**(3/2),x)","\begin{cases} - \frac{a^{3} \sqrt{a + c x^{4}}}{35 c^{2}} + \frac{a^{2} x^{4} \sqrt{a + c x^{4}}}{70 c} + \frac{4 a x^{8} \sqrt{a + c x^{4}}}{35} + \frac{c x^{12} \sqrt{a + c x^{4}}}{14} & \text{for}\: c \neq 0 \\\frac{a^{\frac{3}{2}} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*sqrt(a + c*x**4)/(35*c**2) + a**2*x**4*sqrt(a + c*x**4)/(70*c) + 4*a*x**8*sqrt(a + c*x**4)/35 + c*x**12*sqrt(a + c*x**4)/14, Ne(c, 0)), (a**(3/2)*x**8/8, True))","A",0
785,1,60,0,1.208267," ","integrate(x**3*(c*x**4+a)**(3/2),x)","\begin{cases} \frac{a^{2} \sqrt{a + c x^{4}}}{10 c} + \frac{a x^{4} \sqrt{a + c x^{4}}}{5} + \frac{c x^{8} \sqrt{a + c x^{4}}}{10} & \text{for}\: c \neq 0 \\\frac{a^{\frac{3}{2}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*sqrt(a + c*x**4)/(10*c) + a*x**4*sqrt(a + c*x**4)/5 + c*x**8*sqrt(a + c*x**4)/10, Ne(c, 0)), (a**(3/2)*x**4/4, True))","A",0
786,1,80,0,3.642014," ","integrate((c*x**4+a)**(3/2)/x,x)","\frac{2 a^{\frac{3}{2}} \sqrt{1 + \frac{c x^{4}}{a}}}{3} + \frac{a^{\frac{3}{2}} \log{\left(\frac{c x^{4}}{a} \right)}}{4} - \frac{a^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{c x^{4}}{a}} + 1 \right)}}{2} + \frac{\sqrt{a} c x^{4} \sqrt{1 + \frac{c x^{4}}{a}}}{6}"," ",0,"2*a**(3/2)*sqrt(1 + c*x**4/a)/3 + a**(3/2)*log(c*x**4/a)/4 - a**(3/2)*log(sqrt(1 + c*x**4/a) + 1)/2 + sqrt(a)*c*x**4*sqrt(1 + c*x**4/a)/6","A",0
787,1,95,0,4.611104," ","integrate((c*x**4+a)**(3/2)/x**5,x)","- \frac{3 \sqrt{a} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x^{2}} \right)}}{4} - \frac{a^{2}}{4 \sqrt{c} x^{6} \sqrt{\frac{a}{c x^{4}} + 1}} + \frac{a \sqrt{c}}{4 x^{2} \sqrt{\frac{a}{c x^{4}} + 1}} + \frac{c^{\frac{3}{2}} x^{2}}{2 \sqrt{\frac{a}{c x^{4}} + 1}}"," ",0,"-3*sqrt(a)*c*asinh(sqrt(a)/(sqrt(c)*x**2))/4 - a**2/(4*sqrt(c)*x**6*sqrt(a/(c*x**4) + 1)) + a*sqrt(c)/(4*x**2*sqrt(a/(c*x**4) + 1)) + c**(3/2)*x**2/(2*sqrt(a/(c*x**4) + 1))","A",0
788,1,75,0,4.984889," ","integrate((c*x**4+a)**(3/2)/x**9,x)","- \frac{a \sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{8 x^{6}} - \frac{5 c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{16 x^{2}} - \frac{3 c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x^{2}} \right)}}{16 \sqrt{a}}"," ",0,"-a*sqrt(c)*sqrt(a/(c*x**4) + 1)/(8*x**6) - 5*c**(3/2)*sqrt(a/(c*x**4) + 1)/(16*x**2) - 3*c**2*asinh(sqrt(a)/(sqrt(c)*x**2))/(16*sqrt(a))","A",0
789,1,122,0,6.344846," ","integrate(x**5*(c*x**4+a)**(3/2),x)","\frac{a^{\frac{5}{2}} x^{2}}{32 c \sqrt{1 + \frac{c x^{4}}{a}}} + \frac{17 a^{\frac{3}{2}} x^{6}}{96 \sqrt{1 + \frac{c x^{4}}{a}}} + \frac{11 \sqrt{a} c x^{10}}{48 \sqrt{1 + \frac{c x^{4}}{a}}} - \frac{a^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{32 c^{\frac{3}{2}}} + \frac{c^{2} x^{14}}{12 \sqrt{a} \sqrt{1 + \frac{c x^{4}}{a}}}"," ",0,"a**(5/2)*x**2/(32*c*sqrt(1 + c*x**4/a)) + 17*a**(3/2)*x**6/(96*sqrt(1 + c*x**4/a)) + 11*sqrt(a)*c*x**10/(48*sqrt(1 + c*x**4/a)) - a**3*asinh(sqrt(c)*x**2/sqrt(a))/(32*c**(3/2)) + c**2*x**14/(12*sqrt(a)*sqrt(1 + c*x**4/a))","A",0
790,1,73,0,4.593322," ","integrate(x*(c*x**4+a)**(3/2),x)","\frac{5 a^{\frac{3}{2}} x^{2} \sqrt{1 + \frac{c x^{4}}{a}}}{16} + \frac{\sqrt{a} c x^{6} \sqrt{1 + \frac{c x^{4}}{a}}}{8} + \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{16 \sqrt{c}}"," ",0,"5*a**(3/2)*x**2*sqrt(1 + c*x**4/a)/16 + sqrt(a)*c*x**6*sqrt(1 + c*x**4/a)/8 + 3*a**2*asinh(sqrt(c)*x**2/sqrt(a))/(16*sqrt(c))","A",0
791,1,95,0,2.879571," ","integrate((c*x**4+a)**(3/2)/x**3,x)","- \frac{a^{\frac{3}{2}}}{2 x^{2} \sqrt{1 + \frac{c x^{4}}{a}}} - \frac{\sqrt{a} c x^{2}}{4 \sqrt{1 + \frac{c x^{4}}{a}}} + \frac{3 a \sqrt{c} \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{4} + \frac{c^{2} x^{6}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{4}}{a}}}"," ",0,"-a**(3/2)/(2*x**2*sqrt(1 + c*x**4/a)) - sqrt(a)*c*x**2/(4*sqrt(1 + c*x**4/a)) + 3*a*sqrt(c)*asinh(sqrt(c)*x**2/sqrt(a))/4 + c**2*x**6/(4*sqrt(a)*sqrt(1 + c*x**4/a))","A",0
792,1,80,0,4.477273," ","integrate((c*x**4+a)**(3/2)/x**7,x)","- \frac{a \sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{6 x^{4}} - \frac{2 c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{3} - \frac{c^{\frac{3}{2}} \log{\left(\frac{a}{c x^{4}} \right)}}{4} + \frac{c^{\frac{3}{2}} \log{\left(\sqrt{\frac{a}{c x^{4}} + 1} + 1 \right)}}{2}"," ",0,"-a*sqrt(c)*sqrt(a/(c*x**4) + 1)/(6*x**4) - 2*c**(3/2)*sqrt(a/(c*x**4) + 1)/3 - c**(3/2)*log(a/(c*x**4))/4 + c**(3/2)*log(sqrt(a/(c*x**4) + 1) + 1)/2","A",0
793,1,66,0,2.495741," ","integrate((c*x**4+a)**(3/2)/x**11,x)","- \frac{a \sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{10 x^{8}} - \frac{c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{5 x^{4}} - \frac{c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{10 a}"," ",0,"-a*sqrt(c)*sqrt(a/(c*x**4) + 1)/(10*x**8) - c**(3/2)*sqrt(a/(c*x**4) + 1)/(5*x**4) - c**(5/2)*sqrt(a/(c*x**4) + 1)/(10*a)","B",0
794,1,92,0,2.346852," ","integrate((c*x**4+a)**(3/2)/x**15,x)","- \frac{a \sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{14 x^{12}} - \frac{4 c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{35 x^{8}} - \frac{c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{70 a x^{4}} + \frac{c^{\frac{7}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{35 a^{2}}"," ",0,"-a*sqrt(c)*sqrt(a/(c*x**4) + 1)/(14*x**12) - 4*c**(3/2)*sqrt(a/(c*x**4) + 1)/(35*x**8) - c**(5/2)*sqrt(a/(c*x**4) + 1)/(70*a*x**4) + c**(7/2)*sqrt(a/(c*x**4) + 1)/(35*a**2)","B",0
795,1,420,0,5.408663," ","integrate((c*x**4+a)**(3/2)/x**19,x)","- \frac{35 a^{6} c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{120 a^{5} c^{\frac{11}{2}} x^{4} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{138 a^{4} c^{\frac{13}{2}} x^{8} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{52 a^{3} c^{\frac{15}{2}} x^{12} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{3 a^{2} c^{\frac{17}{2}} x^{16} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{12 a c^{\frac{19}{2}} x^{20} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{8 c^{\frac{21}{2}} x^{24} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}}"," ",0,"-35*a**6*c**(9/2)*sqrt(a/(c*x**4) + 1)/(630*a**5*c**4*x**16 + 1260*a**4*c**5*x**20 + 630*a**3*c**6*x**24) - 120*a**5*c**(11/2)*x**4*sqrt(a/(c*x**4) + 1)/(630*a**5*c**4*x**16 + 1260*a**4*c**5*x**20 + 630*a**3*c**6*x**24) - 138*a**4*c**(13/2)*x**8*sqrt(a/(c*x**4) + 1)/(630*a**5*c**4*x**16 + 1260*a**4*c**5*x**20 + 630*a**3*c**6*x**24) - 52*a**3*c**(15/2)*x**12*sqrt(a/(c*x**4) + 1)/(630*a**5*c**4*x**16 + 1260*a**4*c**5*x**20 + 630*a**3*c**6*x**24) - 3*a**2*c**(17/2)*x**16*sqrt(a/(c*x**4) + 1)/(630*a**5*c**4*x**16 + 1260*a**4*c**5*x**20 + 630*a**3*c**6*x**24) - 12*a*c**(19/2)*x**20*sqrt(a/(c*x**4) + 1)/(630*a**5*c**4*x**16 + 1260*a**4*c**5*x**20 + 630*a**3*c**6*x**24) - 8*c**(21/2)*x**24*sqrt(a/(c*x**4) + 1)/(630*a**5*c**4*x**16 + 1260*a**4*c**5*x**20 + 630*a**3*c**6*x**24)","B",0
796,1,39,0,1.767802," ","integrate(x**4*(c*x**4+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**(3/2)*x**5*gamma(5/4)*hyper((-3/2, 5/4), (9/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4))","C",0
797,1,37,0,1.245465," ","integrate((c*x**4+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**(3/2)*x*gamma(1/4)*hyper((-3/2, 1/4), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4))","C",0
798,1,42,0,2.121644," ","integrate((c*x**4+a)**(3/2)/x**4,x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"a**(3/2)*gamma(-3/4)*hyper((-3/2, -3/4), (1/4,), c*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4))","C",0
799,1,46,0,2.471056," ","integrate((c*x**4+a)**(3/2)/x**8,x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{3}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"a**(3/2)*gamma(-7/4)*hyper((-7/4, -3/2), (-3/4,), c*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4))","C",0
800,1,39,0,1.869694," ","integrate(x**2*(c*x**4+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**(3/2)*x**3*gamma(3/4)*hyper((-3/2, 3/4), (7/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4))","C",0
801,1,41,0,1.652385," ","integrate((c*x**4+a)**(3/2)/x**2,x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"a**(3/2)*gamma(-1/4)*hyper((-3/2, -1/4), (3/4,), c*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4))","C",0
802,1,46,0,1.435320," ","integrate((c*x**4+a)**(3/2)/x**6,x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{5}{4} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"a**(3/2)*gamma(-5/4)*hyper((-3/2, -5/4), (-1/4,), c*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4))","C",0
803,1,29,0,1.006551," ","integrate((x**4+1)**(3/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((-3/2, 1/4), (5/4,), x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
804,1,31,0,1.313175," ","integrate((-x**4+1)**(3/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((-3/2, 1/4), (5/4,), x**4*exp_polar(2*I*pi))/(4*gamma(5/4))","A",0
805,1,42,0,0.854088," ","integrate(x**7*(3*x**4+5)**(1/2),x)","\frac{x^{8} \sqrt{3 x^{4} + 5}}{10} + \frac{x^{4} \sqrt{3 x^{4} + 5}}{18} - \frac{5 \sqrt{3 x^{4} + 5}}{27}"," ",0,"x**8*sqrt(3*x**4 + 5)/10 + x**4*sqrt(3*x**4 + 5)/18 - 5*sqrt(3*x**4 + 5)/27","A",0
806,1,24,0,0.324969," ","integrate(x**3*(x**4+5)**(1/2),x)","\frac{x^{4} \sqrt{x^{4} + 5}}{6} + \frac{5 \sqrt{x^{4} + 5}}{6}"," ",0,"x**4*sqrt(x**4 + 5)/6 + 5*sqrt(x**4 + 5)/6","B",0
807,1,51,0,2.763987," ","integrate(x*(2*x**4+3)**(1/2),x)","\frac{x^{6}}{2 \sqrt{2 x^{4} + 3}} + \frac{3 x^{2}}{4 \sqrt{2 x^{4} + 3}} + \frac{3 \sqrt{2} \operatorname{asinh}{\left(\frac{\sqrt{6} x^{2}}{3} \right)}}{8}"," ",0,"x**6/(2*sqrt(2*x**4 + 3)) + 3*x**2/(4*sqrt(2*x**4 + 3)) + 3*sqrt(2)*asinh(sqrt(6)*x**2/3)/8","A",0
808,1,90,0,2.963927," ","integrate(x*(x**4-2)**(1/2),x)","\begin{cases} \frac{x^{6}}{4 \sqrt{x^{4} - 2}} - \frac{x^{2}}{2 \sqrt{x^{4} - 2}} - \frac{\operatorname{acosh}{\left(\frac{\sqrt{2} x^{2}}{2} \right)}}{2} & \text{for}\: \frac{\left|{x^{4}}\right|}{2} > 1 \\- \frac{i x^{6}}{4 \sqrt{2 - x^{4}}} + \frac{i x^{2}}{2 \sqrt{2 - x^{4}}} + \frac{i \operatorname{asin}{\left(\frac{\sqrt{2} x^{2}}{2} \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**6/(4*sqrt(x**4 - 2)) - x**2/(2*sqrt(x**4 - 2)) - acosh(sqrt(2)*x**2/2)/2, Abs(x**4)/2 > 1), (-I*x**6/(4*sqrt(2 - x**4)) + I*x**2/(2*sqrt(2 - x**4)) + I*asin(sqrt(2)*x**2/2)/2, True))","A",0
809,1,29,0,1.434168," ","integrate((x**4+1)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
810,1,31,0,1.561019," ","integrate((-x**4+1)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), x**4*exp_polar(2*I*pi))/(4*gamma(5/4))","A",0
811,1,68,0,5.089453," ","integrate(x**11/(b*x**4+a)**(1/2),x)","\begin{cases} \frac{4 a^{2} \sqrt{a + b x^{4}}}{15 b^{3}} - \frac{2 a x^{4} \sqrt{a + b x^{4}}}{15 b^{2}} + \frac{x^{8} \sqrt{a + b x^{4}}}{10 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a**2*sqrt(a + b*x**4)/(15*b**3) - 2*a*x**4*sqrt(a + b*x**4)/(15*b**2) + x**8*sqrt(a + b*x**4)/(10*b), Ne(b, 0)), (x**12/(12*sqrt(a)), True))","A",0
812,1,42,0,1.937784," ","integrate(x**7/(b*x**4+a)**(1/2),x)","\begin{cases} - \frac{a \sqrt{a + b x^{4}}}{3 b^{2}} + \frac{x^{4} \sqrt{a + b x^{4}}}{6 b} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*sqrt(a + b*x**4)/(3*b**2) + x**4*sqrt(a + b*x**4)/(6*b), Ne(b, 0)), (x**8/(8*sqrt(a)), True))","A",0
813,1,22,0,0.837059," ","integrate(x**3/(b*x**4+a)**(1/2),x)","\begin{cases} \frac{\sqrt{a + b x^{4}}}{2 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(a + b*x**4)/(2*b), Ne(b, 0)), (x**4/(4*sqrt(a)), True))","A",0
814,1,22,0,1.595961," ","integrate(1/x/(b*x**4+a)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2 \sqrt{a}}"," ",0,"-asinh(sqrt(a)/(sqrt(b)*x**2))/(2*sqrt(a))","A",0
815,1,46,0,4.216709," ","integrate(1/x**5/(b*x**4+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{4}} + 1}}{4 a x^{2}} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4 a^{\frac{3}{2}}}"," ",0,"-sqrt(b)*sqrt(a/(b*x**4) + 1)/(4*a*x**2) + b*asinh(sqrt(a)/(sqrt(b)*x**2))/(4*a**(3/2))","A",0
816,1,46,0,4.173546," ","integrate(x**5/(b*x**4+a)**(1/2),x)","\frac{\sqrt{a} x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4 b} - \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}}"," ",0,"sqrt(a)*x**2*sqrt(1 + b*x**4/a)/(4*b) - a*asinh(sqrt(b)*x**2/sqrt(a))/(4*b**(3/2))","A",0
817,1,20,0,1.938637," ","integrate(x/(b*x**4+a)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}}"," ",0,"asinh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b))","A",0
818,1,20,0,0.976482," ","integrate(1/x**3/(b*x**4+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{4}} + 1}}{2 a}"," ",0,"-sqrt(b)*sqrt(a/(b*x**4) + 1)/(2*a)","A",0
819,1,44,0,1.333036," ","integrate(1/x**7/(b*x**4+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{4}} + 1}}{6 a x^{4}} + \frac{b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{4}} + 1}}{3 a^{2}}"," ",0,"-sqrt(b)*sqrt(a/(b*x**4) + 1)/(6*a*x**4) + b**(3/2)*sqrt(a/(b*x**4) + 1)/(3*a**2)","A",0
820,1,298,0,2.915107," ","integrate(1/x**11/(b*x**4+a)**(1/2),x)","- \frac{3 a^{4} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} + 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{2 a^{3} b^{\frac{11}{2}} x^{4} \sqrt{\frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} + 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{3 a^{2} b^{\frac{13}{2}} x^{8} \sqrt{\frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} + 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{12 a b^{\frac{15}{2}} x^{12} \sqrt{\frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} + 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{8 b^{\frac{17}{2}} x^{16} \sqrt{\frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} + 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}}"," ",0,"-3*a**4*b**(9/2)*sqrt(a/(b*x**4) + 1)/(30*a**5*b**4*x**8 + 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) - 2*a**3*b**(11/2)*x**4*sqrt(a/(b*x**4) + 1)/(30*a**5*b**4*x**8 + 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) - 3*a**2*b**(13/2)*x**8*sqrt(a/(b*x**4) + 1)/(30*a**5*b**4*x**8 + 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) - 12*a*b**(15/2)*x**12*sqrt(a/(b*x**4) + 1)/(30*a**5*b**4*x**8 + 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) - 8*b**(17/2)*x**16*sqrt(a/(b*x**4) + 1)/(30*a**5*b**4*x**8 + 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16)","B",0
821,1,37,0,1.342549," ","integrate(x**8/(b*x**4+a)**(1/2),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((1/2, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(13/4))","C",0
822,1,37,0,1.594816," ","integrate(x**4/(b*x**4+a)**(1/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(9/4))","C",0
823,1,36,0,1.494563," ","integrate(1/(b*x**4+a)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4))","C",0
824,1,41,0,2.045015," ","integrate(1/x**4/(b*x**4+a)**(1/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x**3*gamma(1/4))","C",0
825,1,44,0,2.280832," ","integrate(1/x**8/(b*x**4+a)**(1/2),x)","\frac{\Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"gamma(-7/4)*hyper((-7/4, 1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x**7*gamma(-3/4))","C",0
826,1,37,0,1.380458," ","integrate(x**10/(b*x**4+a)**(1/2),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((1/2, 11/4), (15/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(15/4))","C",0
827,1,37,0,1.707724," ","integrate(x**6/(b*x**4+a)**(1/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(11/4))","C",0
828,1,37,0,1.488137," ","integrate(x**2/(b*x**4+a)**(1/2),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(7/4))","C",0
829,1,39,0,2.125721," ","integrate(1/x**2/(b*x**4+a)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x*gamma(3/4))","C",0
830,1,44,0,2.311546," ","integrate(1/x**6/(b*x**4+a)**(1/2),x)","\frac{\Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x^{5} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"gamma(-5/4)*hyper((-5/4, 1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x**5*gamma(-1/4))","C",0
831,1,70,0,3.250734," ","integrate(x**11/(-b*x**4+a)**(1/2),x)","\begin{cases} - \frac{4 a^{2} \sqrt{a - b x^{4}}}{15 b^{3}} - \frac{2 a x^{4} \sqrt{a - b x^{4}}}{15 b^{2}} - \frac{x^{8} \sqrt{a - b x^{4}}}{10 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**2*sqrt(a - b*x**4)/(15*b**3) - 2*a*x**4*sqrt(a - b*x**4)/(15*b**2) - x**8*sqrt(a - b*x**4)/(10*b), Ne(b, 0)), (x**12/(12*sqrt(a)), True))","A",0
832,1,44,0,1.605164," ","integrate(x**7/(-b*x**4+a)**(1/2),x)","\begin{cases} - \frac{a \sqrt{a - b x^{4}}}{3 b^{2}} - \frac{x^{4} \sqrt{a - b x^{4}}}{6 b} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*sqrt(a - b*x**4)/(3*b**2) - x**4*sqrt(a - b*x**4)/(6*b), Ne(b, 0)), (x**8/(8*sqrt(a)), True))","A",0
833,1,24,0,1.029399," ","integrate(x**3/(-b*x**4+a)**(1/2),x)","\begin{cases} - \frac{\sqrt{a - b x^{4}}}{2 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(a - b*x**4)/(2*b), Ne(b, 0)), (x**4/(4*sqrt(a)), True))","A",0
834,1,53,0,2.208715," ","integrate(1/x/(-b*x**4+a)**(1/2),x)","\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2 \sqrt{a}} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\\frac{i \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(sqrt(a)/(sqrt(b)*x**2))/(2*sqrt(a)), Abs(a/(b*x**4)) > 1), (I*asin(sqrt(a)/(sqrt(b)*x**2))/(2*sqrt(a)), True))","A",0
835,1,129,0,5.231232," ","integrate(1/x**5/(-b*x**4+a)**(1/2),x)","\begin{cases} - \frac{\sqrt{b} \sqrt{\frac{a}{b x^{4}} - 1}}{4 a x^{2}} - \frac{b \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4 a^{\frac{3}{2}}} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\\frac{i}{4 \sqrt{b} x^{6} \sqrt{- \frac{a}{b x^{4}} + 1}} - \frac{i \sqrt{b}}{4 a x^{2} \sqrt{- \frac{a}{b x^{4}} + 1}} + \frac{i b \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(b)*sqrt(a/(b*x**4) - 1)/(4*a*x**2) - b*acosh(sqrt(a)/(sqrt(b)*x**2))/(4*a**(3/2)), Abs(a/(b*x**4)) > 1), (I/(4*sqrt(b)*x**6*sqrt(-a/(b*x**4) + 1)) - I*sqrt(b)/(4*a*x**2*sqrt(-a/(b*x**4) + 1)) + I*b*asin(sqrt(a)/(sqrt(b)*x**2))/(4*a**(3/2)), True))","A",0
836,1,128,0,4.380761," ","integrate(x**5/(-b*x**4+a)**(1/2),x)","\begin{cases} - \frac{i \sqrt{a} x^{2} \sqrt{-1 + \frac{b x^{4}}{a}}}{4 b} - \frac{i a \operatorname{acosh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}} & \text{for}\: \left|{\frac{b x^{4}}{a}}\right| > 1 \\- \frac{\sqrt{a} x^{2}}{4 b \sqrt{1 - \frac{b x^{4}}{a}}} + \frac{a \operatorname{asin}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}} + \frac{x^{6}}{4 \sqrt{a} \sqrt{1 - \frac{b x^{4}}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*sqrt(a)*x**2*sqrt(-1 + b*x**4/a)/(4*b) - I*a*acosh(sqrt(b)*x**2/sqrt(a))/(4*b**(3/2)), Abs(b*x**4/a) > 1), (-sqrt(a)*x**2/(4*b*sqrt(1 - b*x**4/a)) + a*asin(sqrt(b)*x**2/sqrt(a))/(4*b**(3/2)) + x**6/(4*sqrt(a)*sqrt(1 - b*x**4/a)), True))","A",0
837,1,53,0,1.640067," ","integrate(x/(-b*x**4+a)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} & \text{for}\: \left|{\frac{b x^{4}}{a}}\right| > 1 \\\frac{\operatorname{asin}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)), Abs(b*x**4/a) > 1), (asin(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)), True))","A",0
838,1,51,0,1.771027," ","integrate(1/x**3/(-b*x**4+a)**(1/2),x)","\begin{cases} - \frac{\sqrt{b} \sqrt{\frac{a}{b x^{4}} - 1}}{2 a} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{i \sqrt{b} \sqrt{- \frac{a}{b x^{4}} + 1}}{2 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(b)*sqrt(a/(b*x**4) - 1)/(2*a), Abs(a/(b*x**4)) > 1), (-I*sqrt(b)*sqrt(-a/(b*x**4) + 1)/(2*a), True))","A",0
839,1,189,0,1.740249," ","integrate(1/x**7/(-b*x**4+a)**(1/2),x)","\begin{cases} - \frac{\sqrt{b} \sqrt{\frac{a}{b x^{4}} - 1}}{6 a x^{4}} - \frac{b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{4}} - 1}}{3 a^{2}} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\\frac{i a^{2} b^{\frac{3}{2}} \sqrt{- \frac{a}{b x^{4}} + 1}}{- 6 a^{3} b x^{4} + 6 a^{2} b^{2} x^{8}} + \frac{i a b^{\frac{5}{2}} x^{4} \sqrt{- \frac{a}{b x^{4}} + 1}}{- 6 a^{3} b x^{4} + 6 a^{2} b^{2} x^{8}} - \frac{2 i b^{\frac{7}{2}} x^{8} \sqrt{- \frac{a}{b x^{4}} + 1}}{- 6 a^{3} b x^{4} + 6 a^{2} b^{2} x^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(b)*sqrt(a/(b*x**4) - 1)/(6*a*x**4) - b**(3/2)*sqrt(a/(b*x**4) - 1)/(3*a**2), Abs(a/(b*x**4)) > 1), (I*a**2*b**(3/2)*sqrt(-a/(b*x**4) + 1)/(-6*a**3*b*x**4 + 6*a**2*b**2*x**8) + I*a*b**(5/2)*x**4*sqrt(-a/(b*x**4) + 1)/(-6*a**3*b*x**4 + 6*a**2*b**2*x**8) - 2*I*b**(7/2)*x**8*sqrt(-a/(b*x**4) + 1)/(-6*a**3*b*x**4 + 6*a**2*b**2*x**8), True))","A",0
840,1,609,0,5.277305," ","integrate(1/x**11/(-b*x**4+a)**(1/2),x)","\begin{cases} - \frac{3 a^{4} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{4}} - 1}}{30 a^{5} b^{4} x^{8} - 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} + \frac{2 a^{3} b^{\frac{11}{2}} x^{4} \sqrt{\frac{a}{b x^{4}} - 1}}{30 a^{5} b^{4} x^{8} - 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{3 a^{2} b^{\frac{13}{2}} x^{8} \sqrt{\frac{a}{b x^{4}} - 1}}{30 a^{5} b^{4} x^{8} - 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} + \frac{12 a b^{\frac{15}{2}} x^{12} \sqrt{\frac{a}{b x^{4}} - 1}}{30 a^{5} b^{4} x^{8} - 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{8 b^{\frac{17}{2}} x^{16} \sqrt{\frac{a}{b x^{4}} - 1}}{30 a^{5} b^{4} x^{8} - 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{3 i a^{4} b^{\frac{9}{2}} \sqrt{- \frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} - 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} + \frac{2 i a^{3} b^{\frac{11}{2}} x^{4} \sqrt{- \frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} - 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{3 i a^{2} b^{\frac{13}{2}} x^{8} \sqrt{- \frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} - 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} + \frac{12 i a b^{\frac{15}{2}} x^{12} \sqrt{- \frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} - 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{8 i b^{\frac{17}{2}} x^{16} \sqrt{- \frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} - 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a**4*b**(9/2)*sqrt(a/(b*x**4) - 1)/(30*a**5*b**4*x**8 - 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) + 2*a**3*b**(11/2)*x**4*sqrt(a/(b*x**4) - 1)/(30*a**5*b**4*x**8 - 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) - 3*a**2*b**(13/2)*x**8*sqrt(a/(b*x**4) - 1)/(30*a**5*b**4*x**8 - 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) + 12*a*b**(15/2)*x**12*sqrt(a/(b*x**4) - 1)/(30*a**5*b**4*x**8 - 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) - 8*b**(17/2)*x**16*sqrt(a/(b*x**4) - 1)/(30*a**5*b**4*x**8 - 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16), Abs(a/(b*x**4)) > 1), (-3*I*a**4*b**(9/2)*sqrt(-a/(b*x**4) + 1)/(30*a**5*b**4*x**8 - 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) + 2*I*a**3*b**(11/2)*x**4*sqrt(-a/(b*x**4) + 1)/(30*a**5*b**4*x**8 - 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) - 3*I*a**2*b**(13/2)*x**8*sqrt(-a/(b*x**4) + 1)/(30*a**5*b**4*x**8 - 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) + 12*I*a*b**(15/2)*x**12*sqrt(-a/(b*x**4) + 1)/(30*a**5*b**4*x**8 - 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16) - 8*I*b**(17/2)*x**16*sqrt(-a/(b*x**4) + 1)/(30*a**5*b**4*x**8 - 60*a**4*b**5*x**12 + 30*a**3*b**6*x**16), True))","B",0
841,1,39,0,2.105037," ","integrate(x**8/(-b*x**4+a)**(1/2),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((1/2, 9/4), (13/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(13/4))","A",0
842,1,39,0,1.783573," ","integrate(x**4/(-b*x**4+a)**(1/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(9/4))","A",0
843,1,37,0,1.002916," ","integrate(1/(-b*x**4+a)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(5/4))","A",0
844,1,42,0,1.981307," ","integrate(1/x**4/(-b*x**4+a)**(1/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*x**3*gamma(1/4))","A",0
845,1,46,0,1.402491," ","integrate(1/x**8/(-b*x**4+a)**(1/2),x)","\frac{\Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"gamma(-7/4)*hyper((-7/4, 1/2), (-3/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*x**7*gamma(-3/4))","A",0
846,1,39,0,2.250386," ","integrate(x**10/(-b*x**4+a)**(1/2),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((1/2, 11/4), (15/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(15/4))","A",0
847,1,39,0,2.031974," ","integrate(x**6/(-b*x**4+a)**(1/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(11/4))","A",0
848,1,39,0,0.855266," ","integrate(x**2/(-b*x**4+a)**(1/2),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(7/4))","A",0
849,1,41,0,2.035158," ","integrate(1/x**2/(-b*x**4+a)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*x*gamma(3/4))","A",0
850,1,39,0,1.480479," ","integrate(1/x**6/(-b*x**4+a)**(1/2),x)","- \frac{i \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{4 \sqrt{b} x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"-I*gamma(-7/4)*hyper((1/2, 7/4), (11/4,), a/(b*x**4))/(4*sqrt(b)*x**7*gamma(-3/4))","A",0
851,1,68,0,3.566763," ","integrate(x**11/(b*x**4+a)**(3/2),x)","\begin{cases} - \frac{4 a^{2}}{3 b^{3} \sqrt{a + b x^{4}}} - \frac{2 a x^{4}}{3 b^{2} \sqrt{a + b x^{4}}} + \frac{x^{8}}{6 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**2/(3*b**3*sqrt(a + b*x**4)) - 2*a*x**4/(3*b**2*sqrt(a + b*x**4)) + x**8/(6*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**12/(12*a**(3/2)), True))","A",0
852,1,41,0,2.476102," ","integrate(x**7/(b*x**4+a)**(3/2),x)","\begin{cases} \frac{a}{b^{2} \sqrt{a + b x^{4}}} + \frac{x^{4}}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a/(b**2*sqrt(a + b*x**4)) + x**4/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**8/(8*a**(3/2)), True))","A",0
853,1,26,0,1.116776," ","integrate(x**3/(b*x**4+a)**(3/2),x)","\begin{cases} - \frac{1}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**4/(4*a**(3/2)), True))","A",0
854,1,184,0,3.788241," ","integrate(1/x/(b*x**4+a)**(3/2),x)","\frac{2 a^{3} \sqrt{1 + \frac{b x^{4}}{a}}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} + \frac{a^{3} \log{\left(\frac{b x^{4}}{a} \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{4}}{a}} + 1 \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} + \frac{a^{2} b x^{4} \log{\left(\frac{b x^{4}}{a} \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} - \frac{2 a^{2} b x^{4} \log{\left(\sqrt{1 + \frac{b x^{4}}{a}} + 1 \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}}"," ",0,"2*a**3*sqrt(1 + b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) + a**3*log(b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) - 2*a**3*log(sqrt(1 + b*x**4/a) + 1)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) + a**2*b*x**4*log(b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) - 2*a**2*b*x**4*log(sqrt(1 + b*x**4/a) + 1)/(4*a**(9/2) + 4*a**(7/2)*b*x**4)","B",0
855,1,76,0,6.881946," ","integrate(1/x**5/(b*x**4+a)**(3/2),x)","- \frac{1}{4 a \sqrt{b} x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{3 \sqrt{b}}{4 a^{2} x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{3 b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4 a^{\frac{5}{2}}}"," ",0,"-1/(4*a*sqrt(b)*x**6*sqrt(a/(b*x**4) + 1)) - 3*sqrt(b)/(4*a**2*x**2*sqrt(a/(b*x**4) + 1)) + 3*b*asinh(sqrt(a)/(sqrt(b)*x**2))/(4*a**(5/2))","A",0
856,1,75,0,4.270482," ","integrate(x**9/(b*x**4+a)**(3/2),x)","\frac{3 \sqrt{a} x^{2}}{4 b^{2} \sqrt{1 + \frac{b x^{4}}{a}}} - \frac{3 a \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 b^{\frac{5}{2}}} + \frac{x^{6}}{4 \sqrt{a} b \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"3*sqrt(a)*x**2/(4*b**2*sqrt(1 + b*x**4/a)) - 3*a*asinh(sqrt(b)*x**2/sqrt(a))/(4*b**(5/2)) + x**6/(4*sqrt(a)*b*sqrt(1 + b*x**4/a))","A",0
857,1,44,0,3.319461," ","integrate(x**5/(b*x**4+a)**(3/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} - \frac{x^{2}}{2 \sqrt{a} b \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"asinh(sqrt(b)*x**2/sqrt(a))/(2*b**(3/2)) - x**2/(2*sqrt(a)*b*sqrt(1 + b*x**4/a))","A",0
858,1,20,0,1.039428," ","integrate(x/(b*x**4+a)**(3/2),x)","\frac{x^{2}}{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"x**2/(2*a**(3/2)*sqrt(1 + b*x**4/a))","A",0
859,1,46,0,1.336783," ","integrate(1/x**3/(b*x**4+a)**(3/2),x)","- \frac{1}{2 a \sqrt{b} x^{4} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{\sqrt{b}}{a^{2} \sqrt{\frac{a}{b x^{4}} + 1}}"," ",0,"-1/(2*a*sqrt(b)*x**4*sqrt(a/(b*x**4) + 1)) - sqrt(b)/(a**2*sqrt(a/(b*x**4) + 1))","A",0
860,1,233,0,2.659854," ","integrate(1/x**7/(b*x**4+a)**(3/2),x)","- \frac{a^{3} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{4}} + 1}}{6 a^{5} b^{4} x^{4} + 12 a^{4} b^{5} x^{8} + 6 a^{3} b^{6} x^{12}} + \frac{3 a^{2} b^{\frac{11}{2}} x^{4} \sqrt{\frac{a}{b x^{4}} + 1}}{6 a^{5} b^{4} x^{4} + 12 a^{4} b^{5} x^{8} + 6 a^{3} b^{6} x^{12}} + \frac{12 a b^{\frac{13}{2}} x^{8} \sqrt{\frac{a}{b x^{4}} + 1}}{6 a^{5} b^{4} x^{4} + 12 a^{4} b^{5} x^{8} + 6 a^{3} b^{6} x^{12}} + \frac{8 b^{\frac{15}{2}} x^{12} \sqrt{\frac{a}{b x^{4}} + 1}}{6 a^{5} b^{4} x^{4} + 12 a^{4} b^{5} x^{8} + 6 a^{3} b^{6} x^{12}}"," ",0,"-a**3*b**(9/2)*sqrt(a/(b*x**4) + 1)/(6*a**5*b**4*x**4 + 12*a**4*b**5*x**8 + 6*a**3*b**6*x**12) + 3*a**2*b**(11/2)*x**4*sqrt(a/(b*x**4) + 1)/(6*a**5*b**4*x**4 + 12*a**4*b**5*x**8 + 6*a**3*b**6*x**12) + 12*a*b**(13/2)*x**8*sqrt(a/(b*x**4) + 1)/(6*a**5*b**4*x**4 + 12*a**4*b**5*x**8 + 6*a**3*b**6*x**12) + 8*b**(15/2)*x**12*sqrt(a/(b*x**4) + 1)/(6*a**5*b**4*x**4 + 12*a**4*b**5*x**8 + 6*a**3*b**6*x**12)","B",0
861,1,37,0,2.467479," ","integrate(x**12/(b*x**4+a)**(3/2),x)","\frac{x^{13} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{17}{4}\right)}"," ",0,"x**13*gamma(13/4)*hyper((3/2, 13/4), (17/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(17/4))","C",0
862,1,37,0,2.213024," ","integrate(x**8/(b*x**4+a)**(3/2),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((3/2, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(13/4))","C",0
863,1,37,0,1.992990," ","integrate(x**4/(b*x**4+a)**(3/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(9/4))","C",0
864,1,36,0,0.896126," ","integrate(1/(b*x**4+a)**(3/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(5/4))","C",0
865,1,41,0,1.912189," ","integrate(1/x**4/(b*x**4+a)**(3/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 3/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*x**3*gamma(1/4))","C",0
866,1,44,0,1.561916," ","integrate(1/x**8/(b*x**4+a)**(3/2),x)","\frac{\Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{3}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"gamma(-7/4)*hyper((-7/4, 3/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*x**7*gamma(-3/4))","C",0
867,1,37,0,1.880900," ","integrate(x**14/(b*x**4+a)**(3/2),x)","\frac{x^{15} \Gamma\left(\frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{15}{4} \\ \frac{19}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{19}{4}\right)}"," ",0,"x**15*gamma(15/4)*hyper((3/2, 15/4), (19/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(19/4))","C",0
868,1,37,0,1.632303," ","integrate(x**10/(b*x**4+a)**(3/2),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((3/2, 11/4), (15/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(15/4))","C",0
869,1,37,0,1.224809," ","integrate(x**6/(b*x**4+a)**(3/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((3/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(11/4))","C",0
870,1,37,0,0.994457," ","integrate(x**2/(b*x**4+a)**(3/2),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((3/4, 3/2), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(7/4))","C",0
871,1,39,0,1.793903," ","integrate(1/x**2/(b*x**4+a)**(3/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*x*gamma(3/4))","C",0
872,1,44,0,1.799103," ","integrate(1/x**6/(b*x**4+a)**(3/2),x)","\frac{\Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} x^{5} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"gamma(-5/4)*hyper((-5/4, 3/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*x**5*gamma(-1/4))","C",0
873,1,36,0,1.333081," ","integrate(1/(b*x**4+a)**(5/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 5/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/2)*gamma(5/4))","C",0
874,1,41,0,1.563998," ","integrate(x**11/(-x**4+1)**(1/2),x)","- \frac{x^{8} \sqrt{1 - x^{4}}}{10} - \frac{2 x^{4} \sqrt{1 - x^{4}}}{15} - \frac{4 \sqrt{1 - x^{4}}}{15}"," ",0,"-x**8*sqrt(1 - x**4)/10 - 2*x**4*sqrt(1 - x**4)/15 - 4*sqrt(1 - x**4)/15","A",0
875,1,24,0,1.130503," ","integrate(x**7/(-x**4+1)**(1/2),x)","- \frac{x^{4} \sqrt{1 - x^{4}}}{6} - \frac{\sqrt{1 - x^{4}}}{3}"," ",0,"-x**4*sqrt(1 - x**4)/6 - sqrt(1 - x**4)/3","A",0
876,1,10,0,0.340994," ","integrate(x**3/(-x**4+1)**(1/2),x)","- \frac{\sqrt{1 - x^{4}}}{2}"," ",0,"-sqrt(1 - x**4)/2","A",0
877,1,24,0,1.918344," ","integrate(1/x/(-x**4+1)**(1/2),x)","\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{1}{x^{2}} \right)}}{2} & \text{for}\: \frac{1}{\left|{x^{4}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{1}{x^{2}} \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(x**(-2))/2, 1/Abs(x**4) > 1), (I*asin(x**(-2))/2, True))","A",0
878,1,73,0,2.197314," ","integrate(1/x**5/(-x**4+1)**(1/2),x)","\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{1}{x^{2}} \right)}}{4} - \frac{\sqrt{-1 + \frac{1}{x^{4}}}}{4 x^{2}} & \text{for}\: \frac{1}{\left|{x^{4}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{1}{x^{2}} \right)}}{4} - \frac{i}{4 x^{2} \sqrt{1 - \frac{1}{x^{4}}}} + \frac{i}{4 x^{6} \sqrt{1 - \frac{1}{x^{4}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(x**(-2))/4 - sqrt(-1 + x**(-4))/(4*x**2), 1/Abs(x**4) > 1), (I*asin(x**(-2))/4 - I/(4*x**2*sqrt(1 - 1/x**4)) + I/(4*x**6*sqrt(1 - 1/x**4)), True))","A",0
879,1,61,0,3.176759," ","integrate(x**5/(-x**4+1)**(1/2),x)","\begin{cases} - \frac{i x^{2} \sqrt{x^{4} - 1}}{4} - \frac{i \operatorname{acosh}{\left(x^{2} \right)}}{4} & \text{for}\: \left|{x^{4}}\right| > 1 \\\frac{x^{6}}{4 \sqrt{1 - x^{4}}} - \frac{x^{2}}{4 \sqrt{1 - x^{4}}} + \frac{\operatorname{asin}{\left(x^{2} \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*x**2*sqrt(x**4 - 1)/4 - I*acosh(x**2)/4, Abs(x**4) > 1), (x**6/(4*sqrt(1 - x**4)) - x**2/(4*sqrt(1 - x**4)) + asin(x**2)/4, True))","A",0
880,1,19,0,1.803380," ","integrate(x/(-x**4+1)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(x^{2} \right)}}{2} & \text{for}\: \left|{x^{4}}\right| > 1 \\\frac{\operatorname{asin}{\left(x^{2} \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(x**2)/2, Abs(x**4) > 1), (asin(x**2)/2, True))","A",0
881,1,34,0,1.182819," ","integrate(1/x**3/(-x**4+1)**(1/2),x)","\begin{cases} - \frac{i \sqrt{x^{4} - 1}}{2 x^{2}} & \text{for}\: \left|{x^{4}}\right| > 1 \\- \frac{\sqrt{1 - x^{4}}}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*sqrt(x**4 - 1)/(2*x**2), Abs(x**4) > 1), (-sqrt(1 - x**4)/(2*x**2), True))","A",0
882,1,63,0,2.245205," ","integrate(1/x**7/(-x**4+1)**(1/2),x)","\begin{cases} - \frac{i \sqrt{x^{4} - 1}}{3 x^{2}} - \frac{i \sqrt{x^{4} - 1}}{6 x^{6}} & \text{for}\: \left|{x^{4}}\right| > 1 \\- \frac{\sqrt{1 - x^{4}}}{3 x^{2}} - \frac{\sqrt{1 - x^{4}}}{6 x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*sqrt(x**4 - 1)/(3*x**2) - I*sqrt(x**4 - 1)/(6*x**6), Abs(x**4) > 1), (-sqrt(1 - x**4)/(3*x**2) - sqrt(1 - x**4)/(6*x**6), True))","A",0
883,1,104,0,1.689010," ","integrate(1/x**11/(-x**4+1)**(1/2),x)","\begin{cases} - \frac{4 \sqrt{-1 + \frac{1}{x^{4}}}}{15} - \frac{2 \sqrt{-1 + \frac{1}{x^{4}}}}{15 x^{4}} - \frac{\sqrt{-1 + \frac{1}{x^{4}}}}{10 x^{8}} & \text{for}\: \frac{1}{\left|{x^{4}}\right|} > 1 \\- \frac{4 i \sqrt{1 - \frac{1}{x^{4}}}}{15} - \frac{2 i \sqrt{1 - \frac{1}{x^{4}}}}{15 x^{4}} - \frac{i \sqrt{1 - \frac{1}{x^{4}}}}{10 x^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*sqrt(-1 + x**(-4))/15 - 2*sqrt(-1 + x**(-4))/(15*x**4) - sqrt(-1 + x**(-4))/(10*x**8), 1/Abs(x**4) > 1), (-4*I*sqrt(1 - 1/x**4)/15 - 2*I*sqrt(1 - 1/x**4)/(15*x**4) - I*sqrt(1 - 1/x**4)/(10*x**8), True))","A",0
884,1,31,0,1.011333," ","integrate(x**8/(-x**4+1)**(1/2),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((1/2, 9/4), (13/4,), x**4*exp_polar(2*I*pi))/(4*gamma(13/4))","A",0
885,1,31,0,1.165381," ","integrate(x**4/(-x**4+1)**(1/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), x**4*exp_polar(2*I*pi))/(4*gamma(9/4))","B",0
886,1,29,0,0.830239," ","integrate(1/(-x**4+1)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), x**4*exp_polar(2*I*pi))/(4*gamma(5/4))","B",0
887,1,34,0,0.965115," ","integrate(1/x**4/(-x**4+1)**(1/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), x**4*exp_polar(2*I*pi))/(4*x**3*gamma(1/4))","A",0
888,1,37,0,1.962882," ","integrate(1/x**8/(-x**4+1)**(1/2),x)","\frac{\Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"gamma(-7/4)*hyper((-7/4, 1/2), (-3/4,), x**4*exp_polar(2*I*pi))/(4*x**7*gamma(-3/4))","A",0
889,1,31,0,1.209810," ","integrate(x**10/(-x**4+1)**(1/2),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((1/2, 11/4), (15/4,), x**4*exp_polar(2*I*pi))/(4*gamma(15/4))","A",0
890,1,31,0,1.545394," ","integrate(x**6/(-x**4+1)**(1/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), x**4*exp_polar(2*I*pi))/(4*gamma(11/4))","A",0
891,1,31,0,1.536615," ","integrate(x**2/(-x**4+1)**(1/2),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), x**4*exp_polar(2*I*pi))/(4*gamma(7/4))","B",0
892,1,32,0,1.128301," ","integrate(1/x**2/(-x**4+1)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), x**4*exp_polar(2*I*pi))/(4*x*gamma(3/4))","B",0
893,1,37,0,1.013370," ","integrate(1/x**6/(-x**4+1)**(1/2),x)","\frac{\Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"gamma(-5/4)*hyper((-5/4, 1/2), (-1/4,), x**4*exp_polar(2*I*pi))/(4*x**5*gamma(-1/4))","A",0
894,1,39,0,1.721717," ","integrate(x**11/(-x**4+1)**(3/2),x)","- \frac{x^{8}}{6 \sqrt{1 - x^{4}}} - \frac{2 x^{4}}{3 \sqrt{1 - x^{4}}} + \frac{4}{3 \sqrt{1 - x^{4}}}"," ",0,"-x**8/(6*sqrt(1 - x**4)) - 2*x**4/(3*sqrt(1 - x**4)) + 4/(3*sqrt(1 - x**4))","A",0
895,1,22,0,1.202343," ","integrate(x**7/(-x**4+1)**(3/2),x)","- \frac{x^{4}}{2 \sqrt{1 - x^{4}}} + \frac{1}{\sqrt{1 - x^{4}}}"," ",0,"-x**4/(2*sqrt(1 - x**4)) + 1/sqrt(1 - x**4)","A",0
896,1,10,0,0.585151," ","integrate(x**3/(-x**4+1)**(3/2),x)","\frac{1}{2 \sqrt{1 - x^{4}}}"," ",0,"1/(2*sqrt(1 - x**4))","A",0
897,1,228,0,2.698120," ","integrate(1/x/(-x**4+1)**(3/2),x)","\begin{cases} \frac{2 x^{4} \log{\left(x^{2} \right)}}{4 - 4 x^{4}} - \frac{x^{4} \log{\left(x^{4} \right)}}{4 - 4 x^{4}} - \frac{2 i x^{4} \operatorname{asin}{\left(\frac{1}{x^{2}} \right)}}{4 - 4 x^{4}} + \frac{2 i \sqrt{x^{4} - 1}}{4 - 4 x^{4}} - \frac{2 \log{\left(x^{2} \right)}}{4 - 4 x^{4}} + \frac{\log{\left(x^{4} \right)}}{4 - 4 x^{4}} + \frac{2 i \operatorname{asin}{\left(\frac{1}{x^{2}} \right)}}{4 - 4 x^{4}} & \text{for}\: \left|{x^{4}}\right| > 1 \\- \frac{x^{4} \log{\left(x^{4} \right)}}{4 - 4 x^{4}} + \frac{2 x^{4} \log{\left(\sqrt{1 - x^{4}} + 1 \right)}}{4 - 4 x^{4}} - \frac{i \pi x^{4}}{4 - 4 x^{4}} + \frac{2 \sqrt{1 - x^{4}}}{4 - 4 x^{4}} + \frac{\log{\left(x^{4} \right)}}{4 - 4 x^{4}} - \frac{2 \log{\left(\sqrt{1 - x^{4}} + 1 \right)}}{4 - 4 x^{4}} + \frac{i \pi}{4 - 4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x**4*log(x**2)/(4 - 4*x**4) - x**4*log(x**4)/(4 - 4*x**4) - 2*I*x**4*asin(x**(-2))/(4 - 4*x**4) + 2*I*sqrt(x**4 - 1)/(4 - 4*x**4) - 2*log(x**2)/(4 - 4*x**4) + log(x**4)/(4 - 4*x**4) + 2*I*asin(x**(-2))/(4 - 4*x**4), Abs(x**4) > 1), (-x**4*log(x**4)/(4 - 4*x**4) + 2*x**4*log(sqrt(1 - x**4) + 1)/(4 - 4*x**4) - I*pi*x**4/(4 - 4*x**4) + 2*sqrt(1 - x**4)/(4 - 4*x**4) + log(x**4)/(4 - 4*x**4) - 2*log(sqrt(1 - x**4) + 1)/(4 - 4*x**4) + I*pi/(4 - 4*x**4), True))","C",0
898,1,95,0,4.870330," ","integrate(1/x**5/(-x**4+1)**(3/2),x)","\begin{cases} - \frac{3 \operatorname{acosh}{\left(\frac{1}{x^{2}} \right)}}{4} + \frac{3}{4 x^{2} \sqrt{-1 + \frac{1}{x^{4}}}} - \frac{1}{4 x^{6} \sqrt{-1 + \frac{1}{x^{4}}}} & \text{for}\: \frac{1}{\left|{x^{4}}\right|} > 1 \\\frac{3 i \operatorname{asin}{\left(\frac{1}{x^{2}} \right)}}{4} - \frac{3 i}{4 x^{2} \sqrt{1 - \frac{1}{x^{4}}}} + \frac{i}{4 x^{6} \sqrt{1 - \frac{1}{x^{4}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*acosh(x**(-2))/4 + 3/(4*x**2*sqrt(-1 + x**(-4))) - 1/(4*x**6*sqrt(-1 + x**(-4))), 1/Abs(x**4) > 1), (3*I*asin(x**(-2))/4 - 3*I/(4*x**2*sqrt(1 - 1/x**4)) + I/(4*x**6*sqrt(1 - 1/x**4)), True))","A",0
899,1,82,0,4.161651," ","integrate(x**9/(-x**4+1)**(3/2),x)","\begin{cases} \frac{i x^{6}}{4 \sqrt{x^{4} - 1}} - \frac{3 i x^{2}}{4 \sqrt{x^{4} - 1}} + \frac{3 i \operatorname{acosh}{\left(x^{2} \right)}}{4} & \text{for}\: \left|{x^{4}}\right| > 1 \\- \frac{x^{6}}{4 \sqrt{1 - x^{4}}} + \frac{3 x^{2}}{4 \sqrt{1 - x^{4}}} - \frac{3 \operatorname{asin}{\left(x^{2} \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x**6/(4*sqrt(x**4 - 1)) - 3*I*x**2/(4*sqrt(x**4 - 1)) + 3*I*acosh(x**2)/4, Abs(x**4) > 1), (-x**6/(4*sqrt(1 - x**4)) + 3*x**2/(4*sqrt(1 - x**4)) - 3*asin(x**2)/4, True))","A",0
900,1,46,0,2.293700," ","integrate(x**5/(-x**4+1)**(3/2),x)","\begin{cases} - \frac{i x^{2}}{2 \sqrt{x^{4} - 1}} + \frac{i \operatorname{acosh}{\left(x^{2} \right)}}{2} & \text{for}\: \left|{x^{4}}\right| > 1 \\\frac{x^{2}}{2 \sqrt{1 - x^{4}}} - \frac{\operatorname{asin}{\left(x^{2} \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*x**2/(2*sqrt(x**4 - 1)) + I*acosh(x**2)/2, Abs(x**4) > 1), (x**2/(2*sqrt(1 - x**4)) - asin(x**2)/2, True))","A",0
901,1,32,0,1.404981," ","integrate(x/(-x**4+1)**(3/2),x)","\begin{cases} - \frac{i x^{2}}{2 \sqrt{x^{4} - 1}} & \text{for}\: \left|{x^{4}}\right| > 1 \\\frac{x^{2}}{2 \sqrt{1 - x^{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*x**2/(2*sqrt(x**4 - 1)), Abs(x**4) > 1), (x**2/(2*sqrt(1 - x**4)), True))","A",0
902,1,90,0,1.863213," ","integrate(1/x**3/(-x**4+1)**(3/2),x)","\begin{cases} - \frac{2 i x^{4} \sqrt{x^{4} - 1}}{2 x^{6} - 2 x^{2}} + \frac{i \sqrt{x^{4} - 1}}{2 x^{6} - 2 x^{2}} & \text{for}\: \left|{x^{4}}\right| > 1 \\- \frac{2 x^{4} \sqrt{1 - x^{4}}}{2 x^{6} - 2 x^{2}} + \frac{\sqrt{1 - x^{4}}}{2 x^{6} - 2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*x**4*sqrt(x**4 - 1)/(2*x**6 - 2*x**2) + I*sqrt(x**4 - 1)/(2*x**6 - 2*x**2), Abs(x**4) > 1), (-2*x**4*sqrt(1 - x**4)/(2*x**6 - 2*x**2) + sqrt(1 - x**4)/(2*x**6 - 2*x**2), True))","A",0
903,1,151,0,2.359580," ","integrate(1/x**7/(-x**4+1)**(3/2),x)","\begin{cases} - \frac{8 x^{8} \sqrt{-1 + \frac{1}{x^{4}}}}{6 x^{8} - 6 x^{4}} + \frac{4 x^{4} \sqrt{-1 + \frac{1}{x^{4}}}}{6 x^{8} - 6 x^{4}} + \frac{\sqrt{-1 + \frac{1}{x^{4}}}}{6 x^{8} - 6 x^{4}} & \text{for}\: \frac{1}{\left|{x^{4}}\right|} > 1 \\- \frac{8 i x^{8} \sqrt{1 - \frac{1}{x^{4}}}}{6 x^{8} - 6 x^{4}} + \frac{4 i x^{4} \sqrt{1 - \frac{1}{x^{4}}}}{6 x^{8} - 6 x^{4}} + \frac{i \sqrt{1 - \frac{1}{x^{4}}}}{6 x^{8} - 6 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*x**8*sqrt(-1 + x**(-4))/(6*x**8 - 6*x**4) + 4*x**4*sqrt(-1 + x**(-4))/(6*x**8 - 6*x**4) + sqrt(-1 + x**(-4))/(6*x**8 - 6*x**4), 1/Abs(x**4) > 1), (-8*I*x**8*sqrt(1 - 1/x**4)/(6*x**8 - 6*x**4) + 4*I*x**4*sqrt(1 - 1/x**4)/(6*x**8 - 6*x**4) + I*sqrt(1 - 1/x**4)/(6*x**8 - 6*x**4), True))","A",0
904,1,31,0,1.736280," ","integrate(x**12/(-x**4+1)**(3/2),x)","\frac{x^{13} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{17}{4}\right)}"," ",0,"x**13*gamma(13/4)*hyper((3/2, 13/4), (17/4,), x**4*exp_polar(2*I*pi))/(4*gamma(17/4))","A",0
905,1,31,0,1.142914," ","integrate(x**8/(-x**4+1)**(3/2),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((3/2, 9/4), (13/4,), x**4*exp_polar(2*I*pi))/(4*gamma(13/4))","A",0
906,1,31,0,1.278026," ","integrate(x**4/(-x**4+1)**(3/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), x**4*exp_polar(2*I*pi))/(4*gamma(9/4))","B",0
907,1,29,0,1.017818," ","integrate(1/(-x**4+1)**(3/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), x**4*exp_polar(2*I*pi))/(4*gamma(5/4))","A",0
908,1,34,0,1.393312," ","integrate(1/x**4/(-x**4+1)**(3/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{1}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 3/2), (1/4,), x**4*exp_polar(2*I*pi))/(4*x**3*gamma(1/4))","A",0
909,1,37,0,1.500447," ","integrate(1/x**8/(-x**4+1)**(3/2),x)","\frac{\Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{3}{2} \\ - \frac{3}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"gamma(-7/4)*hyper((-7/4, 3/2), (-3/4,), x**4*exp_polar(2*I*pi))/(4*x**7*gamma(-3/4))","A",0
910,1,31,0,1.657811," ","integrate(x**14/(-x**4+1)**(3/2),x)","\frac{x^{15} \Gamma\left(\frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{15}{4} \\ \frac{19}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{19}{4}\right)}"," ",0,"x**15*gamma(15/4)*hyper((3/2, 15/4), (19/4,), x**4*exp_polar(2*I*pi))/(4*gamma(19/4))","A",0
911,1,31,0,1.631169," ","integrate(x**10/(-x**4+1)**(3/2),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((3/2, 11/4), (15/4,), x**4*exp_polar(2*I*pi))/(4*gamma(15/4))","A",0
912,1,31,0,1.985914," ","integrate(x**6/(-x**4+1)**(3/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((3/2, 7/4), (11/4,), x**4*exp_polar(2*I*pi))/(4*gamma(11/4))","A",0
913,1,31,0,0.857456," ","integrate(x**2/(-x**4+1)**(3/2),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((3/4, 3/2), (7/4,), x**4*exp_polar(2*I*pi))/(4*gamma(7/4))","A",0
914,1,32,0,1.262241," ","integrate(1/x**2/(-x**4+1)**(3/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), x**4*exp_polar(2*I*pi))/(4*x*gamma(3/4))","A",0
915,1,37,0,1.480220," ","integrate(1/x**6/(-x**4+1)**(3/2),x)","\frac{\Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{2} \\ - \frac{1}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"gamma(-5/4)*hyper((-5/4, 3/2), (-1/4,), x**4*exp_polar(2*I*pi))/(4*x**5*gamma(-1/4))","A",0
916,1,29,0,1.364547," ","integrate(1/(-x**4+1)**(5/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 5/2), (5/4,), x**4*exp_polar(2*I*pi))/(4*gamma(5/4))","A",0
917,1,39,0,2.189420," ","integrate(x**11/(x**4+1)**(1/2),x)","\frac{x^{8} \sqrt{x^{4} + 1}}{10} - \frac{2 x^{4} \sqrt{x^{4} + 1}}{15} + \frac{4 \sqrt{x^{4} + 1}}{15}"," ",0,"x**8*sqrt(x**4 + 1)/10 - 2*x**4*sqrt(x**4 + 1)/15 + 4*sqrt(x**4 + 1)/15","A",0
918,1,22,0,0.827129," ","integrate(x**7/(x**4+1)**(1/2),x)","\frac{x^{4} \sqrt{x^{4} + 1}}{6} - \frac{\sqrt{x^{4} + 1}}{3}"," ",0,"x**4*sqrt(x**4 + 1)/6 - sqrt(x**4 + 1)/3","A",0
919,1,8,0,0.191537," ","integrate(x**3/(x**4+1)**(1/2),x)","\frac{\sqrt{x^{4} + 1}}{2}"," ",0,"sqrt(x**4 + 1)/2","A",0
920,1,8,0,1.110267," ","integrate(1/x/(x**4+1)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{1}{x^{2}} \right)}}{2}"," ",0,"-asinh(x**(-2))/2","A",0
921,1,22,0,2.101782," ","integrate(1/x**5/(x**4+1)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{1}{x^{2}} \right)}}{4} - \frac{\sqrt{1 + \frac{1}{x^{4}}}}{4 x^{2}}"," ",0,"asinh(x**(-2))/4 - sqrt(1 + x**(-4))/(4*x**2)","A",0
922,1,19,0,2.117215," ","integrate(x**5/(x**4+1)**(1/2),x)","\frac{x^{2} \sqrt{x^{4} + 1}}{4} - \frac{\operatorname{asinh}{\left(x^{2} \right)}}{4}"," ",0,"x**2*sqrt(x**4 + 1)/4 - asinh(x**2)/4","A",0
923,1,5,0,1.022116," ","integrate(x/(x**4+1)**(1/2),x)","\frac{\operatorname{asinh}{\left(x^{2} \right)}}{2}"," ",0,"asinh(x**2)/2","A",0
924,1,12,0,0.790797," ","integrate(1/x**3/(x**4+1)**(1/2),x)","- \frac{\sqrt{1 + \frac{1}{x^{4}}}}{2}"," ",0,"-sqrt(1 + x**(-4))/2","A",0
925,1,26,0,1.067874," ","integrate(1/x**7/(x**4+1)**(1/2),x)","\frac{\sqrt{1 + \frac{1}{x^{4}}}}{3} - \frac{\sqrt{1 + \frac{1}{x^{4}}}}{6 x^{4}}"," ",0,"sqrt(1 + x**(-4))/3 - sqrt(1 + x**(-4))/(6*x**4)","A",0
926,1,44,0,1.544245," ","integrate(1/x**11/(x**4+1)**(1/2),x)","- \frac{4 \sqrt{1 + \frac{1}{x^{4}}}}{15} + \frac{2 \sqrt{1 + \frac{1}{x^{4}}}}{15 x^{4}} - \frac{\sqrt{1 + \frac{1}{x^{4}}}}{10 x^{8}}"," ",0,"-4*sqrt(1 + x**(-4))/15 + 2*sqrt(1 + x**(-4))/(15*x**4) - sqrt(1 + x**(-4))/(10*x**8)","A",0
927,1,29,0,1.540491," ","integrate(x**8/(x**4+1)**(1/2),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((1/2, 9/4), (13/4,), x**4*exp_polar(I*pi))/(4*gamma(13/4))","C",0
928,1,29,0,0.769599," ","integrate(x**4/(x**4+1)**(1/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), x**4*exp_polar(I*pi))/(4*gamma(9/4))","C",0
929,1,27,0,0.792056," ","integrate(1/(x**4+1)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
930,1,32,0,0.901011," ","integrate(1/x**4/(x**4+1)**(1/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), x**4*exp_polar(I*pi))/(4*x**3*gamma(1/4))","C",0
931,1,36,0,1.675822," ","integrate(1/x**8/(x**4+1)**(1/2),x)","\frac{\Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"gamma(-7/4)*hyper((-7/4, 1/2), (-3/4,), x**4*exp_polar(I*pi))/(4*x**7*gamma(-3/4))","C",0
932,1,29,0,1.160666," ","integrate(x**10/(x**4+1)**(1/2),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((1/2, 11/4), (15/4,), x**4*exp_polar(I*pi))/(4*gamma(15/4))","C",0
933,1,29,0,0.907534," ","integrate(x**6/(x**4+1)**(1/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), x**4*exp_polar(I*pi))/(4*gamma(11/4))","C",0
934,1,29,0,0.938445," ","integrate(x**2/(x**4+1)**(1/2),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), x**4*exp_polar(I*pi))/(4*gamma(7/4))","C",0
935,1,31,0,1.278904," ","integrate(1/x**2/(x**4+1)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), x**4*exp_polar(I*pi))/(4*x*gamma(3/4))","C",0
936,1,36,0,1.122964," ","integrate(1/x**6/(x**4+1)**(1/2),x)","\frac{\Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"gamma(-5/4)*hyper((-5/4, 1/2), (-1/4,), x**4*exp_polar(I*pi))/(4*x**5*gamma(-1/4))","C",0
937,1,39,0,2.260958," ","integrate(x**11/(x**4+1)**(3/2),x)","\frac{x^{8}}{6 \sqrt{x^{4} + 1}} - \frac{2 x^{4}}{3 \sqrt{x^{4} + 1}} - \frac{4}{3 \sqrt{x^{4} + 1}}"," ",0,"x**8/(6*sqrt(x**4 + 1)) - 2*x**4/(3*sqrt(x**4 + 1)) - 4/(3*sqrt(x**4 + 1))","A",0
938,1,22,0,1.172446," ","integrate(x**7/(x**4+1)**(3/2),x)","\frac{x^{4}}{2 \sqrt{x^{4} + 1}} + \frac{1}{\sqrt{x^{4} + 1}}"," ",0,"x**4/(2*sqrt(x**4 + 1)) + 1/sqrt(x**4 + 1)","A",0
939,1,12,0,0.434083," ","integrate(x**3/(x**4+1)**(3/2),x)","- \frac{1}{2 \sqrt{x^{4} + 1}}"," ",0,"-1/(2*sqrt(x**4 + 1))","A",0
940,1,87,0,1.890441," ","integrate(1/x/(x**4+1)**(3/2),x)","\frac{x^{4} \log{\left(x^{4} \right)}}{4 x^{4} + 4} - \frac{2 x^{4} \log{\left(\sqrt{x^{4} + 1} + 1 \right)}}{4 x^{4} + 4} + \frac{2 \sqrt{x^{4} + 1}}{4 x^{4} + 4} + \frac{\log{\left(x^{4} \right)}}{4 x^{4} + 4} - \frac{2 \log{\left(\sqrt{x^{4} + 1} + 1 \right)}}{4 x^{4} + 4}"," ",0,"x**4*log(x**4)/(4*x**4 + 4) - 2*x**4*log(sqrt(x**4 + 1) + 1)/(4*x**4 + 4) + 2*sqrt(x**4 + 1)/(4*x**4 + 4) + log(x**4)/(4*x**4 + 4) - 2*log(sqrt(x**4 + 1) + 1)/(4*x**4 + 4)","B",0
941,1,42,0,3.071479," ","integrate(1/x**5/(x**4+1)**(3/2),x)","\frac{3 \operatorname{asinh}{\left(\frac{1}{x^{2}} \right)}}{4} - \frac{3}{4 x^{2} \sqrt{1 + \frac{1}{x^{4}}}} - \frac{1}{4 x^{6} \sqrt{1 + \frac{1}{x^{4}}}}"," ",0,"3*asinh(x**(-2))/4 - 3/(4*x**2*sqrt(1 + x**(-4))) - 1/(4*x**6*sqrt(1 + x**(-4)))","A",0
942,1,36,0,4.011634," ","integrate(x**9/(x**4+1)**(3/2),x)","\frac{x^{6}}{4 \sqrt{x^{4} + 1}} + \frac{3 x^{2}}{4 \sqrt{x^{4} + 1}} - \frac{3 \operatorname{asinh}{\left(x^{2} \right)}}{4}"," ",0,"x**6/(4*sqrt(x**4 + 1)) + 3*x**2/(4*sqrt(x**4 + 1)) - 3*asinh(x**2)/4","A",0
943,1,19,0,2.297050," ","integrate(x**5/(x**4+1)**(3/2),x)","- \frac{x^{2}}{2 \sqrt{x^{4} + 1}} + \frac{\operatorname{asinh}{\left(x^{2} \right)}}{2}"," ",0,"-x**2/(2*sqrt(x**4 + 1)) + asinh(x**2)/2","A",0
944,1,12,0,0.659076," ","integrate(x/(x**4+1)**(3/2),x)","\frac{x^{2}}{2 \sqrt{x^{4} + 1}}"," ",0,"x**2/(2*sqrt(x**4 + 1))","A",0
945,1,42,0,0.896309," ","integrate(1/x**3/(x**4+1)**(3/2),x)","- \frac{2 x^{4} \sqrt{x^{4} + 1}}{2 x^{6} + 2 x^{2}} - \frac{\sqrt{x^{4} + 1}}{2 x^{6} + 2 x^{2}}"," ",0,"-2*x**4*sqrt(x**4 + 1)/(2*x**6 + 2*x**2) - sqrt(x**4 + 1)/(2*x**6 + 2*x**2)","A",0
946,1,70,0,2.251084," ","integrate(1/x**7/(x**4+1)**(3/2),x)","\frac{8 x^{8} \sqrt{1 + \frac{1}{x^{4}}}}{6 x^{8} + 6 x^{4}} + \frac{4 x^{4} \sqrt{1 + \frac{1}{x^{4}}}}{6 x^{8} + 6 x^{4}} - \frac{\sqrt{1 + \frac{1}{x^{4}}}}{6 x^{8} + 6 x^{4}}"," ",0,"8*x**8*sqrt(1 + x**(-4))/(6*x**8 + 6*x**4) + 4*x**4*sqrt(1 + x**(-4))/(6*x**8 + 6*x**4) - sqrt(1 + x**(-4))/(6*x**8 + 6*x**4)","A",0
947,1,29,0,1.941690," ","integrate(x**12/(x**4+1)**(3/2),x)","\frac{x^{13} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{17}{4}\right)}"," ",0,"x**13*gamma(13/4)*hyper((3/2, 13/4), (17/4,), x**4*exp_polar(I*pi))/(4*gamma(17/4))","C",0
948,1,29,0,1.399512," ","integrate(x**8/(x**4+1)**(3/2),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((3/2, 9/4), (13/4,), x**4*exp_polar(I*pi))/(4*gamma(13/4))","C",0
949,1,29,0,0.825138," ","integrate(x**4/(x**4+1)**(3/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), x**4*exp_polar(I*pi))/(4*gamma(9/4))","C",0
950,1,27,0,0.856103," ","integrate(1/(x**4+1)**(3/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
951,1,32,0,1.394393," ","integrate(1/x**4/(x**4+1)**(3/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{1}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 3/2), (1/4,), x**4*exp_polar(I*pi))/(4*x**3*gamma(1/4))","C",0
952,1,36,0,2.060382," ","integrate(1/x**8/(x**4+1)**(3/2),x)","\frac{\Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{3}{2} \\ - \frac{3}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"gamma(-7/4)*hyper((-7/4, 3/2), (-3/4,), x**4*exp_polar(I*pi))/(4*x**7*gamma(-3/4))","C",0
953,1,29,0,2.240735," ","integrate(x**14/(x**4+1)**(3/2),x)","\frac{x^{15} \Gamma\left(\frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{15}{4} \\ \frac{19}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{19}{4}\right)}"," ",0,"x**15*gamma(15/4)*hyper((3/2, 15/4), (19/4,), x**4*exp_polar(I*pi))/(4*gamma(19/4))","C",0
954,1,29,0,1.195134," ","integrate(x**10/(x**4+1)**(3/2),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((3/2, 11/4), (15/4,), x**4*exp_polar(I*pi))/(4*gamma(15/4))","C",0
955,1,29,0,0.968616," ","integrate(x**6/(x**4+1)**(3/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((3/2, 7/4), (11/4,), x**4*exp_polar(I*pi))/(4*gamma(11/4))","C",0
956,1,29,0,0.890464," ","integrate(x**2/(x**4+1)**(3/2),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((3/4, 3/2), (7/4,), x**4*exp_polar(I*pi))/(4*gamma(7/4))","C",0
957,1,31,0,1.462451," ","integrate(1/x**2/(x**4+1)**(3/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), x**4*exp_polar(I*pi))/(4*x*gamma(3/4))","C",0
958,1,36,0,1.822084," ","integrate(1/x**6/(x**4+1)**(3/2),x)","\frac{\Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{2} \\ - \frac{1}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"gamma(-5/4)*hyper((-5/4, 3/2), (-1/4,), x**4*exp_polar(I*pi))/(4*x**5*gamma(-1/4))","C",0
959,1,27,0,1.028146," ","integrate(1/(x**4+1)**(5/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 5/2), (5/4,), x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
960,1,26,0,0.658172," ","integrate(x**7/(-x**4+16)**(1/2),x)","- \frac{x^{4} \sqrt{16 - x^{4}}}{6} - \frac{16 \sqrt{16 - x^{4}}}{3}"," ",0,"-x**4*sqrt(16 - x**4)/6 - 16*sqrt(16 - x**4)/3","A",0
961,1,80,0,2.894170," ","integrate(x**5/(-x**4+16)**(1/2),x)","\begin{cases} - \frac{i x^{6}}{4 \sqrt{x^{4} - 16}} + \frac{4 i x^{2}}{\sqrt{x^{4} - 16}} - 4 i \operatorname{acosh}{\left(\frac{x^{2}}{4} \right)} & \text{for}\: \frac{\left|{x^{4}}\right|}{16} > 1 \\\frac{x^{6}}{4 \sqrt{16 - x^{4}}} - \frac{4 x^{2}}{\sqrt{16 - x^{4}}} + 4 \operatorname{asin}{\left(\frac{x^{2}}{4} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*x**6/(4*sqrt(x**4 - 16)) + 4*I*x**2/sqrt(x**4 - 16) - 4*I*acosh(x**2/4), Abs(x**4)/16 > 1), (x**6/(4*sqrt(16 - x**4)) - 4*x**2/sqrt(16 - x**4) + 4*asin(x**2/4), True))","A",0
962,1,10,0,0.321334," ","integrate(x**3/(-x**4+16)**(1/2),x)","- \frac{\sqrt{16 - x^{4}}}{2}"," ",0,"-sqrt(16 - x**4)/2","A",0
963,1,24,0,1.194875," ","integrate(x/(-x**4+16)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{x^{2}}{4} \right)}}{2} & \text{for}\: \frac{\left|{x^{4}}\right|}{16} > 1 \\\frac{\operatorname{asin}{\left(\frac{x^{2}}{4} \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(x**2/4)/2, Abs(x**4)/16 > 1), (asin(x**2/4)/2, True))","A",0
964,1,24,0,1.873570," ","integrate(1/x/(-x**4+16)**(1/2),x)","\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{4}{x^{2}} \right)}}{8} & \text{for}\: \frac{16}{\left|{x^{4}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{4}{x^{2}} \right)}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(4/x**2)/8, 16/Abs(x**4) > 1), (I*asin(4/x**2)/8, True))","A",0
965,1,32,0,0.872393," ","integrate(1/x**3/(-x**4+16)**(1/2),x)","\begin{cases} - \frac{\sqrt{-1 + \frac{16}{x^{4}}}}{32} & \text{for}\: \frac{16}{\left|{x^{4}}\right|} > 1 \\- \frac{i \sqrt{1 - \frac{16}{x^{4}}}}{32} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(-1 + 16/x**4)/32, 16/Abs(x**4) > 1), (-I*sqrt(1 - 16/x**4)/32, True))","A",0
966,1,73,0,3.011118," ","integrate(1/x**5/(-x**4+16)**(1/2),x)","\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{4}{x^{2}} \right)}}{256} - \frac{\sqrt{-1 + \frac{16}{x^{4}}}}{64 x^{2}} & \text{for}\: \frac{16}{\left|{x^{4}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{4}{x^{2}} \right)}}{256} - \frac{i}{64 x^{2} \sqrt{1 - \frac{16}{x^{4}}}} + \frac{i}{4 x^{6} \sqrt{1 - \frac{16}{x^{4}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(4/x**2)/256 - sqrt(-1 + 16/x**4)/(64*x**2), 16/Abs(x**4) > 1), (I*asin(4/x**2)/256 - I/(64*x**2*sqrt(1 - 16/x**4)) + I/(4*x**6*sqrt(1 - 16/x**4)), True))","A",0
967,1,65,0,1.583728," ","integrate(1/x**7/(-x**4+16)**(1/2),x)","\begin{cases} - \frac{\sqrt{-1 + \frac{16}{x^{4}}}}{768} - \frac{\sqrt{-1 + \frac{16}{x^{4}}}}{96 x^{4}} & \text{for}\: \frac{16}{\left|{x^{4}}\right|} > 1 \\- \frac{i \sqrt{1 - \frac{16}{x^{4}}}}{768} - \frac{i \sqrt{1 - \frac{16}{x^{4}}}}{96 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(-1 + 16/x**4)/768 - sqrt(-1 + 16/x**4)/(96*x**4), 16/Abs(x**4) > 1), (-I*sqrt(1 - 16/x**4)/768 - I*sqrt(1 - 16/x**4)/(96*x**4), True))","A",0
968,1,32,0,0.987406," ","integrate(x**6/(-x**4+16)**(1/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{x^{4} e^{2 i \pi}}{16}} \right)}}{16 \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), x**4*exp_polar(2*I*pi)/16)/(16*gamma(11/4))","A",0
969,1,32,0,0.985079," ","integrate(x**4/(-x**4+16)**(1/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{x^{4} e^{2 i \pi}}{16}} \right)}}{16 \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), x**4*exp_polar(2*I*pi)/16)/(16*gamma(9/4))","A",0
970,1,32,0,1.313814," ","integrate(x**2/(-x**4+16)**(1/2),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{x^{4} e^{2 i \pi}}{16}} \right)}}{16 \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), x**4*exp_polar(2*I*pi)/16)/(16*gamma(7/4))","B",0
971,1,31,0,0.919054," ","integrate(1/(-x**4+16)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{x^{4} e^{2 i \pi}}{16}} \right)}}{16 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), x**4*exp_polar(2*I*pi)/16)/(16*gamma(5/4))","B",0
972,1,34,0,0.980932," ","integrate(1/x**2/(-x**4+16)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{x^{4} e^{2 i \pi}}{16}} \right)}}{16 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), x**4*exp_polar(2*I*pi)/16)/(16*x*gamma(3/4))","A",0
973,1,36,0,1.111952," ","integrate(1/x**4/(-x**4+16)**(1/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{x^{4} e^{2 i \pi}}{16}} \right)}}{16 x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), x**4*exp_polar(2*I*pi)/16)/(16*x**3*gamma(1/4))","A",0
974,1,24,0,1.956643," ","integrate(x/(x**4-4)**(1/2),x)","\begin{cases} \frac{\operatorname{acosh}{\left(\frac{x^{2}}{2} \right)}}{2} & \text{for}\: \frac{\left|{x^{4}}\right|}{4} > 1 \\- \frac{i \operatorname{asin}{\left(\frac{x^{2}}{2} \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((acosh(x**2/2)/2, Abs(x**4)/4 > 1), (-I*asin(x**2/2)/2, True))","A",0
975,1,7,0,1.475743," ","integrate(x/(x**4+4)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{x^{2}}{2} \right)}}{2}"," ",0,"asinh(x**2/2)/2","A",0
976,1,24,0,1.558446," ","integrate(1/x/(x**4-1)**(1/2),x)","\begin{cases} \frac{i \operatorname{acosh}{\left(\frac{1}{x^{2}} \right)}}{2} & \text{for}\: \frac{1}{\left|{x^{4}}\right|} > 1 \\- \frac{\operatorname{asin}{\left(\frac{1}{x^{2}} \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*acosh(x**(-2))/2, 1/Abs(x**4) > 1), (-asin(x**(-2))/2, True))","A",0
977,1,27,0,1.463384," ","integrate(x**4/(x**4-1)**(1/2),x)","- \frac{i x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {x^{4}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"-I*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), x**4)/(4*gamma(9/4))","C",0
978,1,26,0,0.773983," ","integrate(1/(x**4-1)**(1/2),x)","- \frac{i x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {x^{4}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), x**4)/(4*gamma(5/4))","C",0
979,1,31,0,1.575936," ","integrate(1/x**4/(x**4-1)**(1/2),x)","- \frac{i \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {x^{4}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"-I*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), x**4)/(4*x**3*gamma(1/4))","C",0
980,1,27,0,1.006928," ","integrate(x**6/(x**4-1)**(1/2),x)","- \frac{i x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {x^{4}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"-I*x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), x**4)/(4*gamma(11/4))","C",0
981,1,27,0,0.937322," ","integrate(x**2/(x**4-1)**(1/2),x)","- \frac{i x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {x^{4}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"-I*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), x**4)/(4*gamma(7/4))","C",0
982,1,29,0,0.967250," ","integrate(1/x**2/(x**4-1)**(1/2),x)","- \frac{i \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {x^{4}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"-I*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), x**4)/(4*x*gamma(3/4))","C",0
983,1,39,0,1.284457," ","integrate(x**2/(-2*x**4+3)**(1/2),x)","\frac{\sqrt{3} x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{2 x^{4} e^{2 i \pi}}{3}} \right)}}{12 \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(3)*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), 2*x**4*exp_polar(2*I*pi)/3)/(12*gamma(7/4))","A",0
984,1,39,0,1.386470," ","integrate(x**2/(-b*x**4+3)**(1/2),x)","\frac{\sqrt{3} x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{3}} \right)}}{12 \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(3)*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**4*exp_polar(2*I*pi)/3)/(12*gamma(7/4))","A",0
985,1,41,0,1.098583," ","integrate(x**7*(x**4+1)**(1/3),x)","\frac{3 x^{8} \sqrt[3]{x^{4} + 1}}{28} + \frac{3 x^{4} \sqrt[3]{x^{4} + 1}}{112} - \frac{9 \sqrt[3]{x^{4} + 1}}{112}"," ",0,"3*x**8*(x**4 + 1)**(1/3)/28 + 3*x**4*(x**4 + 1)**(1/3)/112 - 9*(x**4 + 1)**(1/3)/112","A",0
986,1,12,0,0.561917," ","integrate(x**3/(x**4+1)**(4/3),x)","- \frac{3}{4 \sqrt[3]{x^{4} + 1}}"," ",0,"-3/(4*(x**4 + 1)**(1/3))","A",0
987,1,10,0,0.197490," ","integrate(x**3/(x**4+1)**(1/3),x)","\frac{3 \left(x^{4} + 1\right)^{\frac{2}{3}}}{8}"," ",0,"3*(x**4 + 1)**(2/3)/8","A",0
988,1,134,0,22.687086," ","integrate(x**19*(b*x**4+a)**(1/4),x)","\begin{cases} \frac{2048 a^{5} \sqrt[4]{a + b x^{4}}}{69615 b^{5}} - \frac{512 a^{4} x^{4} \sqrt[4]{a + b x^{4}}}{69615 b^{4}} + \frac{64 a^{3} x^{8} \sqrt[4]{a + b x^{4}}}{13923 b^{3}} - \frac{16 a^{2} x^{12} \sqrt[4]{a + b x^{4}}}{4641 b^{2}} + \frac{a x^{16} \sqrt[4]{a + b x^{4}}}{357 b} + \frac{x^{20} \sqrt[4]{a + b x^{4}}}{21} & \text{for}\: b \neq 0 \\\frac{\sqrt[4]{a} x^{20}}{20} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2048*a**5*(a + b*x**4)**(1/4)/(69615*b**5) - 512*a**4*x**4*(a + b*x**4)**(1/4)/(69615*b**4) + 64*a**3*x**8*(a + b*x**4)**(1/4)/(13923*b**3) - 16*a**2*x**12*(a + b*x**4)**(1/4)/(4641*b**2) + a*x**16*(a + b*x**4)**(1/4)/(357*b) + x**20*(a + b*x**4)**(1/4)/21, Ne(b, 0)), (a**(1/4)*x**20/20, True))","A",0
989,1,110,0,15.768754," ","integrate(x**15*(b*x**4+a)**(1/4),x)","\begin{cases} - \frac{128 a^{4} \sqrt[4]{a + b x^{4}}}{3315 b^{4}} + \frac{32 a^{3} x^{4} \sqrt[4]{a + b x^{4}}}{3315 b^{3}} - \frac{4 a^{2} x^{8} \sqrt[4]{a + b x^{4}}}{663 b^{2}} + \frac{a x^{12} \sqrt[4]{a + b x^{4}}}{221 b} + \frac{x^{16} \sqrt[4]{a + b x^{4}}}{17} & \text{for}\: b \neq 0 \\\frac{\sqrt[4]{a} x^{16}}{16} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-128*a**4*(a + b*x**4)**(1/4)/(3315*b**4) + 32*a**3*x**4*(a + b*x**4)**(1/4)/(3315*b**3) - 4*a**2*x**8*(a + b*x**4)**(1/4)/(663*b**2) + a*x**12*(a + b*x**4)**(1/4)/(221*b) + x**16*(a + b*x**4)**(1/4)/17, Ne(b, 0)), (a**(1/4)*x**16/16, True))","A",0
990,1,87,0,5.618618," ","integrate(x**11*(b*x**4+a)**(1/4),x)","\begin{cases} \frac{32 a^{3} \sqrt[4]{a + b x^{4}}}{585 b^{3}} - \frac{8 a^{2} x^{4} \sqrt[4]{a + b x^{4}}}{585 b^{2}} + \frac{a x^{8} \sqrt[4]{a + b x^{4}}}{117 b} + \frac{x^{12} \sqrt[4]{a + b x^{4}}}{13} & \text{for}\: b \neq 0 \\\frac{\sqrt[4]{a} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((32*a**3*(a + b*x**4)**(1/4)/(585*b**3) - 8*a**2*x**4*(a + b*x**4)**(1/4)/(585*b**2) + a*x**8*(a + b*x**4)**(1/4)/(117*b) + x**12*(a + b*x**4)**(1/4)/13, Ne(b, 0)), (a**(1/4)*x**12/12, True))","A",0
991,1,63,0,2.884491," ","integrate(x**7*(b*x**4+a)**(1/4),x)","\begin{cases} - \frac{4 a^{2} \sqrt[4]{a + b x^{4}}}{45 b^{2}} + \frac{a x^{4} \sqrt[4]{a + b x^{4}}}{45 b} + \frac{x^{8} \sqrt[4]{a + b x^{4}}}{9} & \text{for}\: b \neq 0 \\\frac{\sqrt[4]{a} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**2*(a + b*x**4)**(1/4)/(45*b**2) + a*x**4*(a + b*x**4)**(1/4)/(45*b) + x**8*(a + b*x**4)**(1/4)/9, Ne(b, 0)), (a**(1/4)*x**8/8, True))","A",0
992,1,39,0,0.902116," ","integrate(x**3*(b*x**4+a)**(1/4),x)","\begin{cases} \frac{a \sqrt[4]{a + b x^{4}}}{5 b} + \frac{x^{4} \sqrt[4]{a + b x^{4}}}{5} & \text{for}\: b \neq 0 \\\frac{\sqrt[4]{a} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*(a + b*x**4)**(1/4)/(5*b) + x**4*(a + b*x**4)**(1/4)/5, Ne(b, 0)), (a**(1/4)*x**4/4, True))","A",0
993,1,42,0,2.245664," ","integrate((b*x**4+a)**(1/4)/x,x)","- \frac{\sqrt[4]{b} x \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}"," ",0,"-b**(1/4)*x*gamma(-1/4)*hyper((-1/4, -1/4), (3/4,), a*exp_polar(I*pi)/(b*x**4))/(4*gamma(3/4))","C",0
994,1,41,0,2.855468," ","integrate((b*x**4+a)**(1/4)/x**5,x)","- \frac{\sqrt[4]{b} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-b**(1/4)*gamma(3/4)*hyper((-1/4, 3/4), (7/4,), a*exp_polar(I*pi)/(b*x**4))/(4*x**3*gamma(7/4))","C",0
995,1,41,0,2.655142," ","integrate((b*x**4+a)**(1/4)/x**9,x)","- \frac{\sqrt[4]{b} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 x^{7} \Gamma\left(\frac{11}{4}\right)}"," ",0,"-b**(1/4)*gamma(7/4)*hyper((-1/4, 7/4), (11/4,), a*exp_polar(I*pi)/(b*x**4))/(4*x**7*gamma(11/4))","C",0
996,1,29,0,1.783962," ","integrate(x**9*(b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{10} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10}"," ",0,"a**(1/4)*x**10*hyper((-1/4, 5/2), (7/2,), b*x**4*exp_polar(I*pi)/a)/10","C",0
997,1,29,0,1.321501," ","integrate(x**5*(b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{6} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6}"," ",0,"a**(1/4)*x**6*hyper((-1/4, 3/2), (5/2,), b*x**4*exp_polar(I*pi)/a)/6","C",0
998,1,29,0,1.849707," ","integrate(x*(b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2}"," ",0,"a**(1/4)*x**2*hyper((-1/4, 1/2), (3/2,), b*x**4*exp_polar(I*pi)/a)/2","C",0
999,1,32,0,1.095547," ","integrate((b*x**4+a)**(1/4)/x**3,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2 x^{2}}"," ",0,"-a**(1/4)*hyper((-1/2, -1/4), (1/2,), b*x**4*exp_polar(I*pi)/a)/(2*x**2)","C",0
1000,1,34,0,2.780352," ","integrate((b*x**4+a)**(1/4)/x**7,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6 x^{6}}"," ",0,"-a**(1/4)*hyper((-3/2, -1/4), (-1/2,), b*x**4*exp_polar(I*pi)/a)/(6*x**6)","C",0
1001,1,34,0,3.448767," ","integrate((b*x**4+a)**(1/4)/x**11,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10 x^{10}}"," ",0,"-a**(1/4)*hyper((-5/2, -1/4), (-3/2,), b*x**4*exp_polar(I*pi)/a)/(10*x**10)","C",0
1002,1,39,0,3.098885," ","integrate(x**6*(b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**(1/4)*x**7*gamma(7/4)*hyper((-1/4, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4))","C",0
1003,1,39,0,1.653173," ","integrate(x**2*(b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**(1/4)*x**3*gamma(3/4)*hyper((-1/4, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4))","C",0
1004,1,41,0,1.949404," ","integrate((b*x**4+a)**(1/4)/x**2,x)","\frac{\sqrt[4]{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"a**(1/4)*gamma(-1/4)*hyper((-1/4, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4))","C",0
1005,1,68,0,1.774667," ","integrate((b*x**4+a)**(1/4)/x**6,x)","\frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{5}{4}\right)}{4 x^{4} \Gamma\left(- \frac{1}{4}\right)} + \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{5}{4}\right)}{4 a \Gamma\left(- \frac{1}{4}\right)}"," ",0,"b**(1/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-5/4)/(4*x**4*gamma(-1/4)) + b**(5/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-5/4)/(4*a*gamma(-1/4))","B",0
1006,1,109,0,2.838327," ","integrate((b*x**4+a)**(1/4)/x**10,x)","- \frac{5 \sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{16 x^{8} \Gamma\left(- \frac{1}{4}\right)} - \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{16 a x^{4} \Gamma\left(- \frac{1}{4}\right)} + \frac{b^{\frac{9}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{4 a^{2} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"-5*b**(1/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(16*x**8*gamma(-1/4)) - b**(5/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(16*a*x**4*gamma(-1/4)) + b**(9/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(4*a**2*gamma(-1/4))","B",0
1007,1,520,0,3.261156," ","integrate((b*x**4+a)**(1/4)/x**14,x)","\frac{45 a^{5} b^{\frac{17}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} + \frac{95 a^{4} b^{\frac{21}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} + \frac{47 a^{3} b^{\frac{25}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} + \frac{21 a^{2} b^{\frac{29}{4}} x^{12} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} + \frac{56 a b^{\frac{33}{4}} x^{16} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} + \frac{32 b^{\frac{37}{4}} x^{20} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"45*a**5*b**(17/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) + 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) + 95*a**4*b**(21/4)*x**4*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) + 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) + 47*a**3*b**(25/4)*x**8*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) + 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) + 21*a**2*b**(29/4)*x**12*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) + 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) + 56*a*b**(33/4)*x**16*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) + 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) + 32*b**(37/4)*x**20*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) + 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4))","B",0
1008,1,847,0,5.852534," ","integrate((b*x**4+a)**(1/4)/x**18,x)","- \frac{585 a^{7} b^{\frac{37}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{1800 a^{6} b^{\frac{41}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{1830 a^{5} b^{\frac{45}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{636 a^{4} b^{\frac{49}{4}} x^{12} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} + \frac{231 a^{3} b^{\frac{53}{4}} x^{16} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} + \frac{924 a^{2} b^{\frac{57}{4}} x^{20} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} + \frac{1056 a b^{\frac{61}{4}} x^{24} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} + \frac{384 b^{\frac{65}{4}} x^{28} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"-585*a**7*b**(37/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) + 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 1800*a**6*b**(41/4)*x**4*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) + 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 1830*a**5*b**(45/4)*x**8*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) + 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 636*a**4*b**(49/4)*x**12*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) + 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) + 231*a**3*b**(53/4)*x**16*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) + 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) + 924*a**2*b**(57/4)*x**20*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) + 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) + 1056*a*b**(61/4)*x**24*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) + 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) + 384*b**(65/4)*x**28*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) + 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4))","B",0
1009,1,39,0,2.914216," ","integrate(x**12*(b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{13} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{17}{4}\right)}"," ",0,"a**(1/4)*x**13*gamma(13/4)*hyper((-1/4, 13/4), (17/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(17/4))","C",0
1010,1,39,0,2.826931," ","integrate(x**8*(b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)}"," ",0,"a**(1/4)*x**9*gamma(9/4)*hyper((-1/4, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(13/4))","C",0
1011,1,39,0,2.041554," ","integrate(x**4*(b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**(1/4)*x**5*gamma(5/4)*hyper((-1/4, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4))","C",0
1012,1,37,0,1.447026," ","integrate((b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**(1/4)*x*gamma(1/4)*hyper((-1/4, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4))","C",0
1013,1,31,0,1.789938," ","integrate((b*x**4+a)**(1/4)/x**4,x)","- \frac{\sqrt[4]{b} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{2 x^{2}}"," ",0,"-b**(1/4)*hyper((-1/4, 1/2), (3/2,), a*exp_polar(I*pi)/(b*x**4))/(2*x**2)","C",0
1014,1,31,0,2.434945," ","integrate((b*x**4+a)**(1/4)/x**8,x)","- \frac{\sqrt[4]{b} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{6 x^{6}}"," ",0,"-b**(1/4)*hyper((-1/4, 3/2), (5/2,), a*exp_polar(I*pi)/(b*x**4))/(6*x**6)","C",0
1015,1,46,0,2.838861," ","integrate((b*x**4+a)**(1/4)/x**12,x)","\frac{\sqrt[4]{a} \Gamma\left(- \frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{11}{4}, - \frac{1}{4} \\ - \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{11} \Gamma\left(- \frac{7}{4}\right)}"," ",0,"a**(1/4)*gamma(-11/4)*hyper((-11/4, -1/4), (-7/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**11*gamma(-7/4))","C",0
1016,1,46,0,4.380033," ","integrate((b*x**4+a)**(1/4)/x**16,x)","\frac{\sqrt[4]{a} \Gamma\left(- \frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{15}{4}, - \frac{1}{4} \\ - \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{15} \Gamma\left(- \frac{11}{4}\right)}"," ",0,"a**(1/4)*gamma(-15/4)*hyper((-15/4, -1/4), (-11/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**15*gamma(-11/4))","C",0
1017,1,136,0,39.716409," ","integrate(x**19*(b*x**4+a)**(3/4),x)","\begin{cases} \frac{2048 a^{5} \left(a + b x^{4}\right)^{\frac{3}{4}}}{168245 b^{5}} - \frac{1536 a^{4} x^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{168245 b^{4}} + \frac{192 a^{3} x^{8} \left(a + b x^{4}\right)^{\frac{3}{4}}}{24035 b^{3}} - \frac{16 a^{2} x^{12} \left(a + b x^{4}\right)^{\frac{3}{4}}}{2185 b^{2}} + \frac{3 a x^{16} \left(a + b x^{4}\right)^{\frac{3}{4}}}{437 b} + \frac{x^{20} \left(a + b x^{4}\right)^{\frac{3}{4}}}{23} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{4}} x^{20}}{20} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2048*a**5*(a + b*x**4)**(3/4)/(168245*b**5) - 1536*a**4*x**4*(a + b*x**4)**(3/4)/(168245*b**4) + 192*a**3*x**8*(a + b*x**4)**(3/4)/(24035*b**3) - 16*a**2*x**12*(a + b*x**4)**(3/4)/(2185*b**2) + 3*a*x**16*(a + b*x**4)**(3/4)/(437*b) + x**20*(a + b*x**4)**(3/4)/23, Ne(b, 0)), (a**(3/4)*x**20/20, True))","A",0
1018,1,110,0,22.762343," ","integrate(x**15*(b*x**4+a)**(3/4),x)","\begin{cases} - \frac{128 a^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{7315 b^{4}} + \frac{96 a^{3} x^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{7315 b^{3}} - \frac{12 a^{2} x^{8} \left(a + b x^{4}\right)^{\frac{3}{4}}}{1045 b^{2}} + \frac{a x^{12} \left(a + b x^{4}\right)^{\frac{3}{4}}}{95 b} + \frac{x^{16} \left(a + b x^{4}\right)^{\frac{3}{4}}}{19} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{4}} x^{16}}{16} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-128*a**4*(a + b*x**4)**(3/4)/(7315*b**4) + 96*a**3*x**4*(a + b*x**4)**(3/4)/(7315*b**3) - 12*a**2*x**8*(a + b*x**4)**(3/4)/(1045*b**2) + a*x**12*(a + b*x**4)**(3/4)/(95*b) + x**16*(a + b*x**4)**(3/4)/19, Ne(b, 0)), (a**(3/4)*x**16/16, True))","A",0
1019,1,87,0,15.892536," ","integrate(x**11*(b*x**4+a)**(3/4),x)","\begin{cases} \frac{32 a^{3} \left(a + b x^{4}\right)^{\frac{3}{4}}}{1155 b^{3}} - \frac{8 a^{2} x^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{385 b^{2}} + \frac{a x^{8} \left(a + b x^{4}\right)^{\frac{3}{4}}}{55 b} + \frac{x^{12} \left(a + b x^{4}\right)^{\frac{3}{4}}}{15} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{4}} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((32*a**3*(a + b*x**4)**(3/4)/(1155*b**3) - 8*a**2*x**4*(a + b*x**4)**(3/4)/(385*b**2) + a*x**8*(a + b*x**4)**(3/4)/(55*b) + x**12*(a + b*x**4)**(3/4)/15, Ne(b, 0)), (a**(3/4)*x**12/12, True))","A",0
1020,1,65,0,8.262524," ","integrate(x**7*(b*x**4+a)**(3/4),x)","\begin{cases} - \frac{4 a^{2} \left(a + b x^{4}\right)^{\frac{3}{4}}}{77 b^{2}} + \frac{3 a x^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{77 b} + \frac{x^{8} \left(a + b x^{4}\right)^{\frac{3}{4}}}{11} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{4}} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**2*(a + b*x**4)**(3/4)/(77*b**2) + 3*a*x**4*(a + b*x**4)**(3/4)/(77*b) + x**8*(a + b*x**4)**(3/4)/11, Ne(b, 0)), (a**(3/4)*x**8/8, True))","A",0
1021,1,39,0,1.797031," ","integrate(x**3*(b*x**4+a)**(3/4),x)","\begin{cases} \frac{a \left(a + b x^{4}\right)^{\frac{3}{4}}}{7 b} + \frac{x^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{7} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{4}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*(a + b*x**4)**(3/4)/(7*b) + x**4*(a + b*x**4)**(3/4)/7, Ne(b, 0)), (a**(3/4)*x**4/4, True))","A",0
1022,1,44,0,1.990639," ","integrate((b*x**4+a)**(3/4)/x,x)","- \frac{b^{\frac{3}{4}} x^{3} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 \Gamma\left(\frac{1}{4}\right)}"," ",0,"-b**(3/4)*x**3*gamma(-3/4)*hyper((-3/4, -3/4), (1/4,), a*exp_polar(I*pi)/(b*x**4))/(4*gamma(1/4))","C",0
1023,1,39,0,3.048014," ","integrate((b*x**4+a)**(3/4)/x**5,x)","- \frac{b^{\frac{3}{4}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 x \Gamma\left(\frac{5}{4}\right)}"," ",0,"-b**(3/4)*gamma(1/4)*hyper((-3/4, 1/4), (5/4,), a*exp_polar(I*pi)/(b*x**4))/(4*x*gamma(5/4))","C",0
1024,1,41,0,2.980807," ","integrate((b*x**4+a)**(3/4)/x**9,x)","- \frac{b^{\frac{3}{4}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 x^{5} \Gamma\left(\frac{9}{4}\right)}"," ",0,"-b**(3/4)*gamma(5/4)*hyper((-3/4, 5/4), (9/4,), a*exp_polar(I*pi)/(b*x**4))/(4*x**5*gamma(9/4))","C",0
1025,1,29,0,2.522963," ","integrate(x**9*(b*x**4+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{10} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10}"," ",0,"a**(3/4)*x**10*hyper((-3/4, 5/2), (7/2,), b*x**4*exp_polar(I*pi)/a)/10","C",0
1026,1,29,0,3.894707," ","integrate(x**5*(b*x**4+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{6} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6}"," ",0,"a**(3/4)*x**6*hyper((-3/4, 3/2), (5/2,), b*x**4*exp_polar(I*pi)/a)/6","C",0
1027,1,29,0,1.899283," ","integrate(x*(b*x**4+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2}"," ",0,"a**(3/4)*x**2*hyper((-3/4, 1/2), (3/2,), b*x**4*exp_polar(I*pi)/a)/2","C",0
1028,1,32,0,1.246444," ","integrate((b*x**4+a)**(3/4)/x**3,x)","- \frac{a^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2 x^{2}}"," ",0,"-a**(3/4)*hyper((-3/4, -1/2), (1/2,), b*x**4*exp_polar(I*pi)/a)/(2*x**2)","C",0
1029,1,34,0,3.166637," ","integrate((b*x**4+a)**(3/4)/x**7,x)","- \frac{a^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6 x^{6}}"," ",0,"-a**(3/4)*hyper((-3/2, -3/4), (-1/2,), b*x**4*exp_polar(I*pi)/a)/(6*x**6)","C",0
1030,1,34,0,2.217495," ","integrate((b*x**4+a)**(3/4)/x**11,x)","- \frac{a^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10 x^{10}}"," ",0,"-a**(3/4)*hyper((-5/2, -3/4), (-3/2,), b*x**4*exp_polar(I*pi)/a)/(10*x**10)","C",0
1031,1,39,0,10.399996," ","integrate(x**12*(b*x**4+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{13} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{17}{4}\right)}"," ",0,"a**(3/4)*x**13*gamma(13/4)*hyper((-3/4, 13/4), (17/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(17/4))","C",0
1032,1,39,0,4.690522," ","integrate(x**8*(b*x**4+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)}"," ",0,"a**(3/4)*x**9*gamma(9/4)*hyper((-3/4, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(13/4))","C",0
1033,1,39,0,4.294406," ","integrate(x**4*(b*x**4+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**(3/4)*x**5*gamma(5/4)*hyper((-3/4, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4))","C",0
1034,1,37,0,1.786289," ","integrate((b*x**4+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**(3/4)*x*gamma(1/4)*hyper((-3/4, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4))","C",0
1035,1,42,0,3.341675," ","integrate((b*x**4+a)**(3/4)/x**4,x)","\frac{a^{\frac{3}{4}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"a**(3/4)*gamma(-3/4)*hyper((-3/4, -3/4), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4))","C",0
1036,1,68,0,3.180358," ","integrate((b*x**4+a)**(3/4)/x**8,x)","\frac{b^{\frac{3}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{4 x^{4} \Gamma\left(- \frac{3}{4}\right)} + \frac{b^{\frac{7}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{4 a \Gamma\left(- \frac{3}{4}\right)}"," ",0,"b**(3/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(4*x**4*gamma(-3/4)) + b**(7/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(4*a*gamma(-3/4))","B",0
1037,1,110,0,3.085855," ","integrate((b*x**4+a)**(3/4)/x**12,x)","- \frac{7 b^{\frac{3}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{16 x^{8} \Gamma\left(- \frac{3}{4}\right)} - \frac{3 b^{\frac{7}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{16 a x^{4} \Gamma\left(- \frac{3}{4}\right)} + \frac{b^{\frac{11}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{4 a^{2} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"-7*b**(3/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(16*x**8*gamma(-3/4)) - 3*b**(7/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(16*a*x**4*gamma(-3/4)) + b**(11/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(4*a**2*gamma(-3/4))","B",0
1038,1,520,0,7.157147," ","integrate((b*x**4+a)**(3/4)/x**16,x)","\frac{77 a^{5} b^{\frac{19}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{3}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{3}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{3}{4}\right)} + \frac{175 a^{4} b^{\frac{23}{4}} x^{4} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{3}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{3}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{3}{4}\right)} + \frac{95 a^{3} b^{\frac{27}{4}} x^{8} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{3}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{3}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{3}{4}\right)} + \frac{5 a^{2} b^{\frac{31}{4}} x^{12} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{3}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{3}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{3}{4}\right)} + \frac{40 a b^{\frac{35}{4}} x^{16} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{3}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{3}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{3}{4}\right)} + \frac{32 b^{\frac{39}{4}} x^{20} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{3}{4}\right) + 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{3}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"77*a**5*b**(19/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(64*a**5*b**4*x**12*gamma(-3/4) + 128*a**4*b**5*x**16*gamma(-3/4) + 64*a**3*b**6*x**20*gamma(-3/4)) + 175*a**4*b**(23/4)*x**4*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(64*a**5*b**4*x**12*gamma(-3/4) + 128*a**4*b**5*x**16*gamma(-3/4) + 64*a**3*b**6*x**20*gamma(-3/4)) + 95*a**3*b**(27/4)*x**8*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(64*a**5*b**4*x**12*gamma(-3/4) + 128*a**4*b**5*x**16*gamma(-3/4) + 64*a**3*b**6*x**20*gamma(-3/4)) + 5*a**2*b**(31/4)*x**12*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(64*a**5*b**4*x**12*gamma(-3/4) + 128*a**4*b**5*x**16*gamma(-3/4) + 64*a**3*b**6*x**20*gamma(-3/4)) + 40*a*b**(35/4)*x**16*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(64*a**5*b**4*x**12*gamma(-3/4) + 128*a**4*b**5*x**16*gamma(-3/4) + 64*a**3*b**6*x**20*gamma(-3/4)) + 32*b**(39/4)*x**20*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(64*a**5*b**4*x**12*gamma(-3/4) + 128*a**4*b**5*x**16*gamma(-3/4) + 64*a**3*b**6*x**20*gamma(-3/4))","B",0
1039,1,847,0,14.530751," ","integrate((b*x**4+a)**(3/4)/x**20,x)","- \frac{1155 a^{7} b^{\frac{39}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{3}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{3}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{3}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{3}{4}\right)} - \frac{3696 a^{6} b^{\frac{43}{4}} x^{4} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{3}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{3}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{3}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{3}{4}\right)} - \frac{3906 a^{5} b^{\frac{47}{4}} x^{8} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{3}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{3}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{3}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{3}{4}\right)} - \frac{1380 a^{4} b^{\frac{51}{4}} x^{12} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{3}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{3}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{3}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{3}{4}\right)} + \frac{45 a^{3} b^{\frac{55}{4}} x^{16} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{3}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{3}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{3}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{3}{4}\right)} + \frac{540 a^{2} b^{\frac{59}{4}} x^{20} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{3}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{3}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{3}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{3}{4}\right)} + \frac{864 a b^{\frac{63}{4}} x^{24} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{3}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{3}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{3}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{3}{4}\right)} + \frac{384 b^{\frac{67}{4}} x^{28} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{3}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{3}{4}\right) + 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{3}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"-1155*a**7*b**(39/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(256*a**7*b**9*x**16*gamma(-3/4) + 768*a**6*b**10*x**20*gamma(-3/4) + 768*a**5*b**11*x**24*gamma(-3/4) + 256*a**4*b**12*x**28*gamma(-3/4)) - 3696*a**6*b**(43/4)*x**4*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(256*a**7*b**9*x**16*gamma(-3/4) + 768*a**6*b**10*x**20*gamma(-3/4) + 768*a**5*b**11*x**24*gamma(-3/4) + 256*a**4*b**12*x**28*gamma(-3/4)) - 3906*a**5*b**(47/4)*x**8*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(256*a**7*b**9*x**16*gamma(-3/4) + 768*a**6*b**10*x**20*gamma(-3/4) + 768*a**5*b**11*x**24*gamma(-3/4) + 256*a**4*b**12*x**28*gamma(-3/4)) - 1380*a**4*b**(51/4)*x**12*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(256*a**7*b**9*x**16*gamma(-3/4) + 768*a**6*b**10*x**20*gamma(-3/4) + 768*a**5*b**11*x**24*gamma(-3/4) + 256*a**4*b**12*x**28*gamma(-3/4)) + 45*a**3*b**(55/4)*x**16*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(256*a**7*b**9*x**16*gamma(-3/4) + 768*a**6*b**10*x**20*gamma(-3/4) + 768*a**5*b**11*x**24*gamma(-3/4) + 256*a**4*b**12*x**28*gamma(-3/4)) + 540*a**2*b**(59/4)*x**20*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(256*a**7*b**9*x**16*gamma(-3/4) + 768*a**6*b**10*x**20*gamma(-3/4) + 768*a**5*b**11*x**24*gamma(-3/4) + 256*a**4*b**12*x**28*gamma(-3/4)) + 864*a*b**(63/4)*x**24*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(256*a**7*b**9*x**16*gamma(-3/4) + 768*a**6*b**10*x**20*gamma(-3/4) + 768*a**5*b**11*x**24*gamma(-3/4) + 256*a**4*b**12*x**28*gamma(-3/4)) + 384*b**(67/4)*x**28*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(256*a**7*b**9*x**16*gamma(-3/4) + 768*a**6*b**10*x**20*gamma(-3/4) + 768*a**5*b**11*x**24*gamma(-3/4) + 256*a**4*b**12*x**28*gamma(-3/4))","B",0
1040,1,39,0,4.843791," ","integrate(x**10*(b*x**4+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{15}{4}\right)}"," ",0,"a**(3/4)*x**11*gamma(11/4)*hyper((-3/4, 11/4), (15/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(15/4))","C",0
1041,1,39,0,3.856280," ","integrate(x**6*(b*x**4+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**(3/4)*x**7*gamma(7/4)*hyper((-3/4, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4))","C",0
1042,1,39,0,2.501628," ","integrate(x**2*(b*x**4+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**(3/4)*x**3*gamma(3/4)*hyper((-3/4, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4))","C",0
1043,1,41,0,2.044091," ","integrate((b*x**4+a)**(3/4)/x**2,x)","\frac{a^{\frac{3}{4}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"a**(3/4)*gamma(-1/4)*hyper((-3/4, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4))","C",0
1044,1,31,0,3.581265," ","integrate((b*x**4+a)**(3/4)/x**6,x)","- \frac{b^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{2 x^{2}}"," ",0,"-b**(3/4)*hyper((-3/4, 1/2), (3/2,), a*exp_polar(I*pi)/(b*x**4))/(2*x**2)","C",0
1045,1,31,0,4.519309," ","integrate((b*x**4+a)**(3/4)/x**10,x)","- \frac{b^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{6 x^{6}}"," ",0,"-b**(3/4)*hyper((-3/4, 3/2), (5/2,), a*exp_polar(I*pi)/(b*x**4))/(6*x**6)","C",0
1046,1,46,0,4.449986," ","integrate((b*x**4+a)**(3/4)/x**14,x)","\frac{a^{\frac{3}{4}} \Gamma\left(- \frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{13}{4}, - \frac{3}{4} \\ - \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{13} \Gamma\left(- \frac{9}{4}\right)}"," ",0,"a**(3/4)*gamma(-13/4)*hyper((-13/4, -3/4), (-9/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**13*gamma(-9/4))","C",0
1047,1,156,0,87.307528," ","integrate(x**19*(b*x**4+a)**(5/4),x)","\begin{cases} \frac{2048 a^{6} \sqrt[4]{a + b x^{4}}}{348075 b^{5}} - \frac{512 a^{5} x^{4} \sqrt[4]{a + b x^{4}}}{348075 b^{4}} + \frac{64 a^{4} x^{8} \sqrt[4]{a + b x^{4}}}{69615 b^{3}} - \frac{16 a^{3} x^{12} \sqrt[4]{a + b x^{4}}}{23205 b^{2}} + \frac{a^{2} x^{16} \sqrt[4]{a + b x^{4}}}{1785 b} + \frac{26 a x^{20} \sqrt[4]{a + b x^{4}}}{525} + \frac{b x^{24} \sqrt[4]{a + b x^{4}}}{25} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{4}} x^{20}}{20} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2048*a**6*(a + b*x**4)**(1/4)/(348075*b**5) - 512*a**5*x**4*(a + b*x**4)**(1/4)/(348075*b**4) + 64*a**4*x**8*(a + b*x**4)**(1/4)/(69615*b**3) - 16*a**3*x**12*(a + b*x**4)**(1/4)/(23205*b**2) + a**2*x**16*(a + b*x**4)**(1/4)/(1785*b) + 26*a*x**20*(a + b*x**4)**(1/4)/525 + b*x**24*(a + b*x**4)**(1/4)/25, Ne(b, 0)), (a**(5/4)*x**20/20, True))","A",0
1048,1,134,0,38.259485," ","integrate(x**15*(b*x**4+a)**(5/4),x)","\begin{cases} - \frac{128 a^{5} \sqrt[4]{a + b x^{4}}}{13923 b^{4}} + \frac{32 a^{4} x^{4} \sqrt[4]{a + b x^{4}}}{13923 b^{3}} - \frac{20 a^{3} x^{8} \sqrt[4]{a + b x^{4}}}{13923 b^{2}} + \frac{5 a^{2} x^{12} \sqrt[4]{a + b x^{4}}}{4641 b} + \frac{22 a x^{16} \sqrt[4]{a + b x^{4}}}{357} + \frac{b x^{20} \sqrt[4]{a + b x^{4}}}{21} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{4}} x^{16}}{16} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-128*a**5*(a + b*x**4)**(1/4)/(13923*b**4) + 32*a**4*x**4*(a + b*x**4)**(1/4)/(13923*b**3) - 20*a**3*x**8*(a + b*x**4)**(1/4)/(13923*b**2) + 5*a**2*x**12*(a + b*x**4)**(1/4)/(4641*b) + 22*a*x**16*(a + b*x**4)**(1/4)/357 + b*x**20*(a + b*x**4)**(1/4)/21, Ne(b, 0)), (a**(5/4)*x**16/16, True))","A",0
1049,1,110,0,25.287635," ","integrate(x**11*(b*x**4+a)**(5/4),x)","\begin{cases} \frac{32 a^{4} \sqrt[4]{a + b x^{4}}}{1989 b^{3}} - \frac{8 a^{3} x^{4} \sqrt[4]{a + b x^{4}}}{1989 b^{2}} + \frac{5 a^{2} x^{8} \sqrt[4]{a + b x^{4}}}{1989 b} + \frac{18 a x^{12} \sqrt[4]{a + b x^{4}}}{221} + \frac{b x^{16} \sqrt[4]{a + b x^{4}}}{17} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{4}} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((32*a**4*(a + b*x**4)**(1/4)/(1989*b**3) - 8*a**3*x**4*(a + b*x**4)**(1/4)/(1989*b**2) + 5*a**2*x**8*(a + b*x**4)**(1/4)/(1989*b) + 18*a*x**12*(a + b*x**4)**(1/4)/221 + b*x**16*(a + b*x**4)**(1/4)/17, Ne(b, 0)), (a**(5/4)*x**12/12, True))","A",0
1050,1,85,0,18.342179," ","integrate(x**7*(b*x**4+a)**(5/4),x)","\begin{cases} - \frac{4 a^{3} \sqrt[4]{a + b x^{4}}}{117 b^{2}} + \frac{a^{2} x^{4} \sqrt[4]{a + b x^{4}}}{117 b} + \frac{14 a x^{8} \sqrt[4]{a + b x^{4}}}{117} + \frac{b x^{12} \sqrt[4]{a + b x^{4}}}{13} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{4}} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**3*(a + b*x**4)**(1/4)/(117*b**2) + a**2*x**4*(a + b*x**4)**(1/4)/(117*b) + 14*a*x**8*(a + b*x**4)**(1/4)/117 + b*x**12*(a + b*x**4)**(1/4)/13, Ne(b, 0)), (a**(5/4)*x**8/8, True))","A",0
1051,1,61,0,11.152153," ","integrate(x**3*(b*x**4+a)**(5/4),x)","\begin{cases} \frac{a^{2} \sqrt[4]{a + b x^{4}}}{9 b} + \frac{2 a x^{4} \sqrt[4]{a + b x^{4}}}{9} + \frac{b x^{8} \sqrt[4]{a + b x^{4}}}{9} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{4}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*(a + b*x**4)**(1/4)/(9*b) + 2*a*x**4*(a + b*x**4)**(1/4)/9 + b*x**8*(a + b*x**4)**(1/4)/9, Ne(b, 0)), (a**(5/4)*x**4/4, True))","A",0
1052,1,48,0,2.762879," ","integrate((b*x**4+a)**(5/4)/x,x)","- \frac{b^{\frac{5}{4}} x^{5} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{5}{4} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 \Gamma\left(- \frac{1}{4}\right)}"," ",0,"-b**(5/4)*x**5*gamma(-5/4)*hyper((-5/4, -5/4), (-1/4,), a*exp_polar(I*pi)/(b*x**4))/(4*gamma(-1/4))","C",0
1053,1,42,0,3.890634," ","integrate((b*x**4+a)**(5/4)/x**5,x)","- \frac{b^{\frac{5}{4}} x \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}"," ",0,"-b**(5/4)*x*gamma(-1/4)*hyper((-5/4, -1/4), (3/4,), a*exp_polar(I*pi)/(b*x**4))/(4*gamma(3/4))","C",0
1054,1,41,0,4.185374," ","integrate((b*x**4+a)**(5/4)/x**9,x)","- \frac{b^{\frac{5}{4}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-b**(5/4)*gamma(3/4)*hyper((-5/4, 3/4), (7/4,), a*exp_polar(I*pi)/(b*x**4))/(4*x**3*gamma(7/4))","C",0
1055,1,29,0,4.833956," ","integrate(x**9*(b*x**4+a)**(5/4),x)","\frac{a^{\frac{5}{4}} x^{10} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10}"," ",0,"a**(5/4)*x**10*hyper((-5/4, 5/2), (7/2,), b*x**4*exp_polar(I*pi)/a)/10","C",0
1056,1,29,0,4.293484," ","integrate(x**5*(b*x**4+a)**(5/4),x)","\frac{a^{\frac{5}{4}} x^{6} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6}"," ",0,"a**(5/4)*x**6*hyper((-5/4, 3/2), (5/2,), b*x**4*exp_polar(I*pi)/a)/6","C",0
1057,1,29,0,2.250769," ","integrate(x*(b*x**4+a)**(5/4),x)","\frac{a^{\frac{5}{4}} x^{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2}"," ",0,"a**(5/4)*x**2*hyper((-5/4, 1/2), (3/2,), b*x**4*exp_polar(I*pi)/a)/2","C",0
1058,1,32,0,1.482761," ","integrate((b*x**4+a)**(5/4)/x**3,x)","- \frac{a^{\frac{5}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2 x^{2}}"," ",0,"-a**(5/4)*hyper((-5/4, -1/2), (1/2,), b*x**4*exp_polar(I*pi)/a)/(2*x**2)","C",0
1059,1,34,0,3.130721," ","integrate((b*x**4+a)**(5/4)/x**7,x)","- \frac{a^{\frac{5}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{5}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6 x^{6}}"," ",0,"-a**(5/4)*hyper((-3/2, -5/4), (-1/2,), b*x**4*exp_polar(I*pi)/a)/(6*x**6)","C",0
1060,1,34,0,6.724141," ","integrate((b*x**4+a)**(5/4)/x**11,x)","- \frac{a^{\frac{5}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{5}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10 x^{10}}"," ",0,"-a**(5/4)*hyper((-5/2, -5/4), (-3/2,), b*x**4*exp_polar(I*pi)/a)/(10*x**10)","C",0
1061,1,34,0,5.553685," ","integrate((b*x**4+a)**(5/4)/x**15,x)","- \frac{a^{\frac{5}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{2}, - \frac{5}{4} \\ - \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{14 x^{14}}"," ",0,"-a**(5/4)*hyper((-7/2, -5/4), (-5/2,), b*x**4*exp_polar(I*pi)/a)/(14*x**14)","C",0
1062,1,39,0,11.435705," ","integrate(x**10*(b*x**4+a)**(5/4),x)","\frac{a^{\frac{5}{4}} x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{15}{4}\right)}"," ",0,"a**(5/4)*x**11*gamma(11/4)*hyper((-5/4, 11/4), (15/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(15/4))","C",0
1063,1,39,0,5.829943," ","integrate(x**6*(b*x**4+a)**(5/4),x)","\frac{a^{\frac{5}{4}} x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**(5/4)*x**7*gamma(7/4)*hyper((-5/4, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4))","C",0
1064,1,39,0,1.936658," ","integrate(x**2*(b*x**4+a)**(5/4),x)","\frac{a^{\frac{5}{4}} x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**(5/4)*x**3*gamma(3/4)*hyper((-5/4, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4))","C",0
1065,1,41,0,3.851902," ","integrate((b*x**4+a)**(5/4)/x**2,x)","\frac{a^{\frac{5}{4}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"a**(5/4)*gamma(-1/4)*hyper((-5/4, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4))","C",0
1066,1,46,0,4.833928," ","integrate((b*x**4+a)**(5/4)/x**6,x)","\frac{a^{\frac{5}{4}} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{5}{4} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"a**(5/4)*gamma(-5/4)*hyper((-5/4, -5/4), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4))","C",0
1067,1,105,0,3.353781," ","integrate((b*x**4+a)**(5/4)/x**10,x)","\frac{a \sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{4 x^{8} \Gamma\left(- \frac{5}{4}\right)} + \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{2 x^{4} \Gamma\left(- \frac{5}{4}\right)} + \frac{b^{\frac{9}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{4 a \Gamma\left(- \frac{5}{4}\right)}"," ",0,"a*b**(1/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(4*x**8*gamma(-5/4)) + b**(5/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(2*x**4*gamma(-5/4)) + b**(9/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(4*a*gamma(-5/4))","B",0
1068,1,148,0,5.332274," ","integrate((b*x**4+a)**(5/4)/x**14,x)","- \frac{9 a \sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{16 x^{12} \Gamma\left(- \frac{5}{4}\right)} - \frac{7 b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{8 x^{8} \Gamma\left(- \frac{5}{4}\right)} - \frac{b^{\frac{9}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{16 a x^{4} \Gamma\left(- \frac{5}{4}\right)} + \frac{b^{\frac{13}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{4 a^{2} \Gamma\left(- \frac{5}{4}\right)}"," ",0,"-9*a*b**(1/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(16*x**12*gamma(-5/4)) - 7*b**(5/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(8*x**8*gamma(-5/4)) - b**(9/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(16*a*x**4*gamma(-5/4)) + b**(13/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(4*a**2*gamma(-5/4))","B",0
1069,1,609,0,11.920732," ","integrate((b*x**4+a)**(5/4)/x**18,x)","\frac{117 a^{6} b^{\frac{17}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{64 a^{5} b^{4} x^{16} \Gamma\left(- \frac{5}{4}\right) + 128 a^{4} b^{5} x^{20} \Gamma\left(- \frac{5}{4}\right) + 64 a^{3} b^{6} x^{24} \Gamma\left(- \frac{5}{4}\right)} + \frac{396 a^{5} b^{\frac{21}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{64 a^{5} b^{4} x^{16} \Gamma\left(- \frac{5}{4}\right) + 128 a^{4} b^{5} x^{20} \Gamma\left(- \frac{5}{4}\right) + 64 a^{3} b^{6} x^{24} \Gamma\left(- \frac{5}{4}\right)} + \frac{446 a^{4} b^{\frac{25}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{64 a^{5} b^{4} x^{16} \Gamma\left(- \frac{5}{4}\right) + 128 a^{4} b^{5} x^{20} \Gamma\left(- \frac{5}{4}\right) + 64 a^{3} b^{6} x^{24} \Gamma\left(- \frac{5}{4}\right)} + \frac{164 a^{3} b^{\frac{29}{4}} x^{12} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{64 a^{5} b^{4} x^{16} \Gamma\left(- \frac{5}{4}\right) + 128 a^{4} b^{5} x^{20} \Gamma\left(- \frac{5}{4}\right) + 64 a^{3} b^{6} x^{24} \Gamma\left(- \frac{5}{4}\right)} + \frac{21 a^{2} b^{\frac{33}{4}} x^{16} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{64 a^{5} b^{4} x^{16} \Gamma\left(- \frac{5}{4}\right) + 128 a^{4} b^{5} x^{20} \Gamma\left(- \frac{5}{4}\right) + 64 a^{3} b^{6} x^{24} \Gamma\left(- \frac{5}{4}\right)} + \frac{56 a b^{\frac{37}{4}} x^{20} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{64 a^{5} b^{4} x^{16} \Gamma\left(- \frac{5}{4}\right) + 128 a^{4} b^{5} x^{20} \Gamma\left(- \frac{5}{4}\right) + 64 a^{3} b^{6} x^{24} \Gamma\left(- \frac{5}{4}\right)} + \frac{32 b^{\frac{41}{4}} x^{24} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{17}{4}\right)}{64 a^{5} b^{4} x^{16} \Gamma\left(- \frac{5}{4}\right) + 128 a^{4} b^{5} x^{20} \Gamma\left(- \frac{5}{4}\right) + 64 a^{3} b^{6} x^{24} \Gamma\left(- \frac{5}{4}\right)}"," ",0,"117*a**6*b**(17/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(64*a**5*b**4*x**16*gamma(-5/4) + 128*a**4*b**5*x**20*gamma(-5/4) + 64*a**3*b**6*x**24*gamma(-5/4)) + 396*a**5*b**(21/4)*x**4*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(64*a**5*b**4*x**16*gamma(-5/4) + 128*a**4*b**5*x**20*gamma(-5/4) + 64*a**3*b**6*x**24*gamma(-5/4)) + 446*a**4*b**(25/4)*x**8*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(64*a**5*b**4*x**16*gamma(-5/4) + 128*a**4*b**5*x**20*gamma(-5/4) + 64*a**3*b**6*x**24*gamma(-5/4)) + 164*a**3*b**(29/4)*x**12*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(64*a**5*b**4*x**16*gamma(-5/4) + 128*a**4*b**5*x**20*gamma(-5/4) + 64*a**3*b**6*x**24*gamma(-5/4)) + 21*a**2*b**(33/4)*x**16*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(64*a**5*b**4*x**16*gamma(-5/4) + 128*a**4*b**5*x**20*gamma(-5/4) + 64*a**3*b**6*x**24*gamma(-5/4)) + 56*a*b**(37/4)*x**20*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(64*a**5*b**4*x**16*gamma(-5/4) + 128*a**4*b**5*x**20*gamma(-5/4) + 64*a**3*b**6*x**24*gamma(-5/4)) + 32*b**(41/4)*x**24*(a/(b*x**4) + 1)**(1/4)*gamma(-17/4)/(64*a**5*b**4*x**16*gamma(-5/4) + 128*a**4*b**5*x**20*gamma(-5/4) + 64*a**3*b**6*x**24*gamma(-5/4))","B",0
1070,1,954,0,15.290126," ","integrate((b*x**4+a)**(5/4)/x**22,x)","- \frac{1989 a^{8} b^{\frac{37}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{21}{4}\right)}{256 a^{7} b^{9} x^{20} \Gamma\left(- \frac{5}{4}\right) + 768 a^{6} b^{10} x^{24} \Gamma\left(- \frac{5}{4}\right) + 768 a^{5} b^{11} x^{28} \Gamma\left(- \frac{5}{4}\right) + 256 a^{4} b^{12} x^{32} \Gamma\left(- \frac{5}{4}\right)} - \frac{8541 a^{7} b^{\frac{41}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{21}{4}\right)}{256 a^{7} b^{9} x^{20} \Gamma\left(- \frac{5}{4}\right) + 768 a^{6} b^{10} x^{24} \Gamma\left(- \frac{5}{4}\right) + 768 a^{5} b^{11} x^{28} \Gamma\left(- \frac{5}{4}\right) + 256 a^{4} b^{12} x^{32} \Gamma\left(- \frac{5}{4}\right)} - \frac{13734 a^{6} b^{\frac{45}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{21}{4}\right)}{256 a^{7} b^{9} x^{20} \Gamma\left(- \frac{5}{4}\right) + 768 a^{6} b^{10} x^{24} \Gamma\left(- \frac{5}{4}\right) + 768 a^{5} b^{11} x^{28} \Gamma\left(- \frac{5}{4}\right) + 256 a^{4} b^{12} x^{32} \Gamma\left(- \frac{5}{4}\right)} - \frac{9786 a^{5} b^{\frac{49}{4}} x^{12} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{21}{4}\right)}{256 a^{7} b^{9} x^{20} \Gamma\left(- \frac{5}{4}\right) + 768 a^{6} b^{10} x^{24} \Gamma\left(- \frac{5}{4}\right) + 768 a^{5} b^{11} x^{28} \Gamma\left(- \frac{5}{4}\right) + 256 a^{4} b^{12} x^{32} \Gamma\left(- \frac{5}{4}\right)} - \frac{2625 a^{4} b^{\frac{53}{4}} x^{16} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{21}{4}\right)}{256 a^{7} b^{9} x^{20} \Gamma\left(- \frac{5}{4}\right) + 768 a^{6} b^{10} x^{24} \Gamma\left(- \frac{5}{4}\right) + 768 a^{5} b^{11} x^{28} \Gamma\left(- \frac{5}{4}\right) + 256 a^{4} b^{12} x^{32} \Gamma\left(- \frac{5}{4}\right)} + \frac{231 a^{3} b^{\frac{57}{4}} x^{20} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{21}{4}\right)}{256 a^{7} b^{9} x^{20} \Gamma\left(- \frac{5}{4}\right) + 768 a^{6} b^{10} x^{24} \Gamma\left(- \frac{5}{4}\right) + 768 a^{5} b^{11} x^{28} \Gamma\left(- \frac{5}{4}\right) + 256 a^{4} b^{12} x^{32} \Gamma\left(- \frac{5}{4}\right)} + \frac{924 a^{2} b^{\frac{61}{4}} x^{24} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{21}{4}\right)}{256 a^{7} b^{9} x^{20} \Gamma\left(- \frac{5}{4}\right) + 768 a^{6} b^{10} x^{24} \Gamma\left(- \frac{5}{4}\right) + 768 a^{5} b^{11} x^{28} \Gamma\left(- \frac{5}{4}\right) + 256 a^{4} b^{12} x^{32} \Gamma\left(- \frac{5}{4}\right)} + \frac{1056 a b^{\frac{65}{4}} x^{28} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{21}{4}\right)}{256 a^{7} b^{9} x^{20} \Gamma\left(- \frac{5}{4}\right) + 768 a^{6} b^{10} x^{24} \Gamma\left(- \frac{5}{4}\right) + 768 a^{5} b^{11} x^{28} \Gamma\left(- \frac{5}{4}\right) + 256 a^{4} b^{12} x^{32} \Gamma\left(- \frac{5}{4}\right)} + \frac{384 b^{\frac{69}{4}} x^{32} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{21}{4}\right)}{256 a^{7} b^{9} x^{20} \Gamma\left(- \frac{5}{4}\right) + 768 a^{6} b^{10} x^{24} \Gamma\left(- \frac{5}{4}\right) + 768 a^{5} b^{11} x^{28} \Gamma\left(- \frac{5}{4}\right) + 256 a^{4} b^{12} x^{32} \Gamma\left(- \frac{5}{4}\right)}"," ",0,"-1989*a**8*b**(37/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-21/4)/(256*a**7*b**9*x**20*gamma(-5/4) + 768*a**6*b**10*x**24*gamma(-5/4) + 768*a**5*b**11*x**28*gamma(-5/4) + 256*a**4*b**12*x**32*gamma(-5/4)) - 8541*a**7*b**(41/4)*x**4*(a/(b*x**4) + 1)**(1/4)*gamma(-21/4)/(256*a**7*b**9*x**20*gamma(-5/4) + 768*a**6*b**10*x**24*gamma(-5/4) + 768*a**5*b**11*x**28*gamma(-5/4) + 256*a**4*b**12*x**32*gamma(-5/4)) - 13734*a**6*b**(45/4)*x**8*(a/(b*x**4) + 1)**(1/4)*gamma(-21/4)/(256*a**7*b**9*x**20*gamma(-5/4) + 768*a**6*b**10*x**24*gamma(-5/4) + 768*a**5*b**11*x**28*gamma(-5/4) + 256*a**4*b**12*x**32*gamma(-5/4)) - 9786*a**5*b**(49/4)*x**12*(a/(b*x**4) + 1)**(1/4)*gamma(-21/4)/(256*a**7*b**9*x**20*gamma(-5/4) + 768*a**6*b**10*x**24*gamma(-5/4) + 768*a**5*b**11*x**28*gamma(-5/4) + 256*a**4*b**12*x**32*gamma(-5/4)) - 2625*a**4*b**(53/4)*x**16*(a/(b*x**4) + 1)**(1/4)*gamma(-21/4)/(256*a**7*b**9*x**20*gamma(-5/4) + 768*a**6*b**10*x**24*gamma(-5/4) + 768*a**5*b**11*x**28*gamma(-5/4) + 256*a**4*b**12*x**32*gamma(-5/4)) + 231*a**3*b**(57/4)*x**20*(a/(b*x**4) + 1)**(1/4)*gamma(-21/4)/(256*a**7*b**9*x**20*gamma(-5/4) + 768*a**6*b**10*x**24*gamma(-5/4) + 768*a**5*b**11*x**28*gamma(-5/4) + 256*a**4*b**12*x**32*gamma(-5/4)) + 924*a**2*b**(61/4)*x**24*(a/(b*x**4) + 1)**(1/4)*gamma(-21/4)/(256*a**7*b**9*x**20*gamma(-5/4) + 768*a**6*b**10*x**24*gamma(-5/4) + 768*a**5*b**11*x**28*gamma(-5/4) + 256*a**4*b**12*x**32*gamma(-5/4)) + 1056*a*b**(65/4)*x**28*(a/(b*x**4) + 1)**(1/4)*gamma(-21/4)/(256*a**7*b**9*x**20*gamma(-5/4) + 768*a**6*b**10*x**24*gamma(-5/4) + 768*a**5*b**11*x**28*gamma(-5/4) + 256*a**4*b**12*x**32*gamma(-5/4)) + 384*b**(69/4)*x**32*(a/(b*x**4) + 1)**(1/4)*gamma(-21/4)/(256*a**7*b**9*x**20*gamma(-5/4) + 768*a**6*b**10*x**24*gamma(-5/4) + 768*a**5*b**11*x**28*gamma(-5/4) + 256*a**4*b**12*x**32*gamma(-5/4))","B",0
1071,1,39,0,3.992120," ","integrate(x**12*(b*x**4+a)**(5/4),x)","\frac{a^{\frac{5}{4}} x^{13} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{17}{4}\right)}"," ",0,"a**(5/4)*x**13*gamma(13/4)*hyper((-5/4, 13/4), (17/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(17/4))","C",0
1072,1,39,0,3.372956," ","integrate(x**8*(b*x**4+a)**(5/4),x)","\frac{a^{\frac{5}{4}} x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)}"," ",0,"a**(5/4)*x**9*gamma(9/4)*hyper((-5/4, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(13/4))","C",0
1073,1,39,0,1.707933," ","integrate(x**4*(b*x**4+a)**(5/4),x)","\frac{a^{\frac{5}{4}} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**(5/4)*x**5*gamma(5/4)*hyper((-5/4, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4))","C",0
1074,1,37,0,2.697856," ","integrate((b*x**4+a)**(5/4),x)","\frac{a^{\frac{5}{4}} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**(5/4)*x*gamma(1/4)*hyper((-5/4, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4))","C",0
1075,1,42,0,2.590269," ","integrate((b*x**4+a)**(5/4)/x**4,x)","\frac{a^{\frac{5}{4}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"a**(5/4)*gamma(-3/4)*hyper((-5/4, -3/4), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4))","C",0
1076,1,31,0,3.391505," ","integrate((b*x**4+a)**(5/4)/x**8,x)","- \frac{b^{\frac{5}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{2 x^{2}}"," ",0,"-b**(5/4)*hyper((-5/4, 1/2), (3/2,), a*exp_polar(I*pi)/(b*x**4))/(2*x**2)","C",0
1077,1,31,0,2.396999," ","integrate((b*x**4+a)**(5/4)/x**12,x)","- \frac{b^{\frac{5}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{6 x^{6}}"," ",0,"-b**(5/4)*hyper((-5/4, 3/2), (5/2,), a*exp_polar(I*pi)/(b*x**4))/(6*x**6)","C",0
1078,1,46,0,6.849778," ","integrate((b*x**4+a)**(5/4)/x**16,x)","\frac{a^{\frac{5}{4}} \Gamma\left(- \frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{15}{4}, - \frac{5}{4} \\ - \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{15} \Gamma\left(- \frac{11}{4}\right)}"," ",0,"a**(5/4)*gamma(-15/4)*hyper((-15/4, -5/4), (-11/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**15*gamma(-11/4))","C",0
1079,1,37,0,2.004936," ","integrate((b*x**4+a)**(7/4),x)","\frac{a^{\frac{7}{4}} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**(7/4)*x*gamma(1/4)*hyper((-7/4, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4))","C",0
1080,1,116,0,24.290913," ","integrate(x**19/(b*x**4+a)**(1/4),x)","\begin{cases} \frac{2048 a^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{21945 b^{5}} - \frac{512 a^{3} x^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{7315 b^{4}} + \frac{64 a^{2} x^{8} \left(a + b x^{4}\right)^{\frac{3}{4}}}{1045 b^{3}} - \frac{16 a x^{12} \left(a + b x^{4}\right)^{\frac{3}{4}}}{285 b^{2}} + \frac{x^{16} \left(a + b x^{4}\right)^{\frac{3}{4}}}{19 b} & \text{for}\: b \neq 0 \\\frac{x^{20}}{20 \sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2048*a**4*(a + b*x**4)**(3/4)/(21945*b**5) - 512*a**3*x**4*(a + b*x**4)**(3/4)/(7315*b**4) + 64*a**2*x**8*(a + b*x**4)**(3/4)/(1045*b**3) - 16*a*x**12*(a + b*x**4)**(3/4)/(285*b**2) + x**16*(a + b*x**4)**(3/4)/(19*b), Ne(b, 0)), (x**20/(20*a**(1/4)), True))","A",0
1081,1,92,0,14.846602," ","integrate(x**15/(b*x**4+a)**(1/4),x)","\begin{cases} - \frac{128 a^{3} \left(a + b x^{4}\right)^{\frac{3}{4}}}{1155 b^{4}} + \frac{32 a^{2} x^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{385 b^{3}} - \frac{4 a x^{8} \left(a + b x^{4}\right)^{\frac{3}{4}}}{55 b^{2}} + \frac{x^{12} \left(a + b x^{4}\right)^{\frac{3}{4}}}{15 b} & \text{for}\: b \neq 0 \\\frac{x^{16}}{16 \sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-128*a**3*(a + b*x**4)**(3/4)/(1155*b**4) + 32*a**2*x**4*(a + b*x**4)**(3/4)/(385*b**3) - 4*a*x**8*(a + b*x**4)**(3/4)/(55*b**2) + x**12*(a + b*x**4)**(3/4)/(15*b), Ne(b, 0)), (x**16/(16*a**(1/4)), True))","A",0
1082,1,68,0,6.348661," ","integrate(x**11/(b*x**4+a)**(1/4),x)","\begin{cases} \frac{32 a^{2} \left(a + b x^{4}\right)^{\frac{3}{4}}}{231 b^{3}} - \frac{8 a x^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{77 b^{2}} + \frac{x^{8} \left(a + b x^{4}\right)^{\frac{3}{4}}}{11 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 \sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((32*a**2*(a + b*x**4)**(3/4)/(231*b**3) - 8*a*x**4*(a + b*x**4)**(3/4)/(77*b**2) + x**8*(a + b*x**4)**(3/4)/(11*b), Ne(b, 0)), (x**12/(12*a**(1/4)), True))","A",0
1083,1,44,0,2.270433," ","integrate(x**7/(b*x**4+a)**(1/4),x)","\begin{cases} - \frac{4 a \left(a + b x^{4}\right)^{\frac{3}{4}}}{21 b^{2}} + \frac{x^{4} \left(a + b x^{4}\right)^{\frac{3}{4}}}{7 b} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 \sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a*(a + b*x**4)**(3/4)/(21*b**2) + x**4*(a + b*x**4)**(3/4)/(7*b), Ne(b, 0)), (x**8/(8*a**(1/4)), True))","A",0
1084,1,22,0,0.895174," ","integrate(x**3/(b*x**4+a)**(1/4),x)","\begin{cases} \frac{\left(a + b x^{4}\right)^{\frac{3}{4}}}{3 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a + b*x**4)**(3/4)/(3*b), Ne(b, 0)), (x**4/(4*a**(1/4)), True))","A",0
1085,1,37,0,1.246229," ","integrate(1/x/(b*x**4+a)**(1/4),x)","- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 \sqrt[4]{b} x \Gamma\left(\frac{5}{4}\right)}"," ",0,"-gamma(1/4)*hyper((1/4, 1/4), (5/4,), a*exp_polar(I*pi)/(b*x**4))/(4*b**(1/4)*x*gamma(5/4))","C",0
1086,1,39,0,2.720301," ","integrate(1/x**5/(b*x**4+a)**(1/4),x)","- \frac{\Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 \sqrt[4]{b} x^{5} \Gamma\left(\frac{9}{4}\right)}"," ",0,"-gamma(5/4)*hyper((1/4, 5/4), (9/4,), a*exp_polar(I*pi)/(b*x**4))/(4*b**(1/4)*x**5*gamma(9/4))","C",0
1087,1,39,0,3.379127," ","integrate(1/x**9/(b*x**4+a)**(1/4),x)","- \frac{\Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 \sqrt[4]{b} x^{9} \Gamma\left(\frac{13}{4}\right)}"," ",0,"-gamma(9/4)*hyper((1/4, 9/4), (13/4,), a*exp_polar(I*pi)/(b*x**4))/(4*b**(1/4)*x**9*gamma(13/4))","C",0
1088,1,27,0,1.632045," ","integrate(x**13/(b*x**4+a)**(1/4),x)","\frac{x^{14} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{14 \sqrt[4]{a}}"," ",0,"x**14*hyper((1/4, 7/2), (9/2,), b*x**4*exp_polar(I*pi)/a)/(14*a**(1/4))","C",0
1089,1,27,0,1.212027," ","integrate(x**9/(b*x**4+a)**(1/4),x)","\frac{x^{10} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10 \sqrt[4]{a}}"," ",0,"x**10*hyper((1/4, 5/2), (7/2,), b*x**4*exp_polar(I*pi)/a)/(10*a**(1/4))","C",0
1090,1,27,0,1.546897," ","integrate(x**5/(b*x**4+a)**(1/4),x)","\frac{x^{6} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6 \sqrt[4]{a}}"," ",0,"x**6*hyper((1/4, 3/2), (5/2,), b*x**4*exp_polar(I*pi)/a)/(6*a**(1/4))","C",0
1091,1,27,0,1.543346," ","integrate(x/(b*x**4+a)**(1/4),x)","\frac{x^{2} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a}}"," ",0,"x**2*hyper((1/4, 1/2), (3/2,), b*x**4*exp_polar(I*pi)/a)/(2*a**(1/4))","C",0
1092,1,31,0,1.768905," ","integrate(1/x**3/(b*x**4+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} x^{2}}"," ",0,"-hyper((-1/2, 1/4), (1/2,), b*x**4*exp_polar(I*pi)/a)/(2*a**(1/4)*x**2)","C",0
1093,1,32,0,2.481151," ","integrate(1/x**7/(b*x**4+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6 \sqrt[4]{a} x^{6}}"," ",0,"-hyper((-3/2, 1/4), (-1/2,), b*x**4*exp_polar(I*pi)/a)/(6*a**(1/4)*x**6)","C",0
1094,1,32,0,2.415097," ","integrate(1/x**11/(b*x**4+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10 \sqrt[4]{a} x^{10}}"," ",0,"-hyper((-5/2, 1/4), (-3/2,), b*x**4*exp_polar(I*pi)/a)/(10*a**(1/4)*x**10)","C",0
1095,1,37,0,2.173088," ","integrate(x**8/(b*x**4+a)**(1/4),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((1/4, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(1/4)*gamma(13/4))","C",0
1096,1,37,0,1.548157," ","integrate(x**4/(b*x**4+a)**(1/4),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((1/4, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(1/4)*gamma(9/4))","C",0
1097,1,36,0,1.230023," ","integrate(1/(b*x**4+a)**(1/4),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(1/4)*gamma(5/4))","C",0
1098,1,31,0,1.060135," ","integrate(1/x**4/(b*x**4+a)**(1/4),x)","\frac{b^{\frac{3}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{3}{4}\right)}{4 a \Gamma\left(\frac{1}{4}\right)}"," ",0,"b**(3/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-3/4)/(4*a*gamma(1/4))","A",0
1099,1,70,0,2.767823," ","integrate(1/x**8/(b*x**4+a)**(1/4),x)","- \frac{3 b^{\frac{3}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{16 a x^{4} \Gamma\left(\frac{1}{4}\right)} + \frac{b^{\frac{7}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{4 a^{2} \Gamma\left(\frac{1}{4}\right)}"," ",0,"-3*b**(3/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(16*a*x**4*gamma(1/4)) + b**(7/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(4*a**2*gamma(1/4))","A",0
1100,1,406,0,3.071223," ","integrate(1/x**12/(b*x**4+a)**(1/4),x)","\frac{21 a^{4} b^{\frac{19}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} \Gamma\left(\frac{1}{4}\right) + 128 a^{4} b^{5} x^{12} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} \Gamma\left(\frac{1}{4}\right)} + \frac{18 a^{3} b^{\frac{23}{4}} x^{4} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} \Gamma\left(\frac{1}{4}\right) + 128 a^{4} b^{5} x^{12} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} \Gamma\left(\frac{1}{4}\right)} + \frac{5 a^{2} b^{\frac{27}{4}} x^{8} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} \Gamma\left(\frac{1}{4}\right) + 128 a^{4} b^{5} x^{12} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} \Gamma\left(\frac{1}{4}\right)} + \frac{40 a b^{\frac{31}{4}} x^{12} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} \Gamma\left(\frac{1}{4}\right) + 128 a^{4} b^{5} x^{12} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} \Gamma\left(\frac{1}{4}\right)} + \frac{32 b^{\frac{35}{4}} x^{16} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} \Gamma\left(\frac{1}{4}\right) + 128 a^{4} b^{5} x^{12} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} \Gamma\left(\frac{1}{4}\right)}"," ",0,"21*a**4*b**(19/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(64*a**5*b**4*x**8*gamma(1/4) + 128*a**4*b**5*x**12*gamma(1/4) + 64*a**3*b**6*x**16*gamma(1/4)) + 18*a**3*b**(23/4)*x**4*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(64*a**5*b**4*x**8*gamma(1/4) + 128*a**4*b**5*x**12*gamma(1/4) + 64*a**3*b**6*x**16*gamma(1/4)) + 5*a**2*b**(27/4)*x**8*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(64*a**5*b**4*x**8*gamma(1/4) + 128*a**4*b**5*x**12*gamma(1/4) + 64*a**3*b**6*x**16*gamma(1/4)) + 40*a*b**(31/4)*x**12*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(64*a**5*b**4*x**8*gamma(1/4) + 128*a**4*b**5*x**12*gamma(1/4) + 64*a**3*b**6*x**16*gamma(1/4)) + 32*b**(35/4)*x**16*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(64*a**5*b**4*x**8*gamma(1/4) + 128*a**4*b**5*x**12*gamma(1/4) + 64*a**3*b**6*x**16*gamma(1/4))","B",0
1101,1,692,0,5.364460," ","integrate(1/x**16/(b*x**4+a)**(1/4),x)","- \frac{231 a^{6} b^{\frac{39}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{1}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{1}{4}\right)} - \frac{441 a^{5} b^{\frac{43}{4}} x^{4} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{1}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{1}{4}\right)} - \frac{225 a^{4} b^{\frac{47}{4}} x^{8} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{1}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{1}{4}\right)} + \frac{45 a^{3} b^{\frac{51}{4}} x^{12} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{1}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{1}{4}\right)} + \frac{540 a^{2} b^{\frac{55}{4}} x^{16} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{1}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{1}{4}\right)} + \frac{864 a b^{\frac{59}{4}} x^{20} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{1}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{1}{4}\right)} + \frac{384 b^{\frac{63}{4}} x^{24} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{1}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{1}{4}\right)}"," ",0,"-231*a**6*b**(39/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(256*a**7*b**9*x**12*gamma(1/4) + 768*a**6*b**10*x**16*gamma(1/4) + 768*a**5*b**11*x**20*gamma(1/4) + 256*a**4*b**12*x**24*gamma(1/4)) - 441*a**5*b**(43/4)*x**4*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(256*a**7*b**9*x**12*gamma(1/4) + 768*a**6*b**10*x**16*gamma(1/4) + 768*a**5*b**11*x**20*gamma(1/4) + 256*a**4*b**12*x**24*gamma(1/4)) - 225*a**4*b**(47/4)*x**8*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(256*a**7*b**9*x**12*gamma(1/4) + 768*a**6*b**10*x**16*gamma(1/4) + 768*a**5*b**11*x**20*gamma(1/4) + 256*a**4*b**12*x**24*gamma(1/4)) + 45*a**3*b**(51/4)*x**12*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(256*a**7*b**9*x**12*gamma(1/4) + 768*a**6*b**10*x**16*gamma(1/4) + 768*a**5*b**11*x**20*gamma(1/4) + 256*a**4*b**12*x**24*gamma(1/4)) + 540*a**2*b**(55/4)*x**16*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(256*a**7*b**9*x**12*gamma(1/4) + 768*a**6*b**10*x**16*gamma(1/4) + 768*a**5*b**11*x**20*gamma(1/4) + 256*a**4*b**12*x**24*gamma(1/4)) + 864*a*b**(59/4)*x**20*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(256*a**7*b**9*x**12*gamma(1/4) + 768*a**6*b**10*x**16*gamma(1/4) + 768*a**5*b**11*x**20*gamma(1/4) + 256*a**4*b**12*x**24*gamma(1/4)) + 384*b**(63/4)*x**24*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(256*a**7*b**9*x**12*gamma(1/4) + 768*a**6*b**10*x**16*gamma(1/4) + 768*a**5*b**11*x**20*gamma(1/4) + 256*a**4*b**12*x**24*gamma(1/4))","B",0
1102,1,1046,0,8.483040," ","integrate(1/x**20/(b*x**4+a)**(1/4),x)","\frac{3465 a^{8} b^{\frac{67}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} \Gamma\left(\frac{1}{4}\right) + 4096 a^{8} b^{17} x^{20} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} \Gamma\left(\frac{1}{4}\right) + 4096 a^{6} b^{19} x^{28} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} \Gamma\left(\frac{1}{4}\right)} + \frac{10164 a^{7} b^{\frac{71}{4}} x^{4} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} \Gamma\left(\frac{1}{4}\right) + 4096 a^{8} b^{17} x^{20} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} \Gamma\left(\frac{1}{4}\right) + 4096 a^{6} b^{19} x^{28} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} \Gamma\left(\frac{1}{4}\right)} + \frac{10038 a^{6} b^{\frac{75}{4}} x^{8} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} \Gamma\left(\frac{1}{4}\right) + 4096 a^{8} b^{17} x^{20} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} \Gamma\left(\frac{1}{4}\right) + 4096 a^{6} b^{19} x^{28} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} \Gamma\left(\frac{1}{4}\right)} + \frac{3204 a^{5} b^{\frac{79}{4}} x^{12} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} \Gamma\left(\frac{1}{4}\right) + 4096 a^{8} b^{17} x^{20} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} \Gamma\left(\frac{1}{4}\right) + 4096 a^{6} b^{19} x^{28} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} \Gamma\left(\frac{1}{4}\right)} + \frac{585 a^{4} b^{\frac{83}{4}} x^{16} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} \Gamma\left(\frac{1}{4}\right) + 4096 a^{8} b^{17} x^{20} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} \Gamma\left(\frac{1}{4}\right) + 4096 a^{6} b^{19} x^{28} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} \Gamma\left(\frac{1}{4}\right)} + \frac{9360 a^{3} b^{\frac{87}{4}} x^{20} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} \Gamma\left(\frac{1}{4}\right) + 4096 a^{8} b^{17} x^{20} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} \Gamma\left(\frac{1}{4}\right) + 4096 a^{6} b^{19} x^{28} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} \Gamma\left(\frac{1}{4}\right)} + \frac{22464 a^{2} b^{\frac{91}{4}} x^{24} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} \Gamma\left(\frac{1}{4}\right) + 4096 a^{8} b^{17} x^{20} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} \Gamma\left(\frac{1}{4}\right) + 4096 a^{6} b^{19} x^{28} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} \Gamma\left(\frac{1}{4}\right)} + \frac{19968 a b^{\frac{95}{4}} x^{28} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} \Gamma\left(\frac{1}{4}\right) + 4096 a^{8} b^{17} x^{20} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} \Gamma\left(\frac{1}{4}\right) + 4096 a^{6} b^{19} x^{28} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} \Gamma\left(\frac{1}{4}\right)} + \frac{6144 b^{\frac{99}{4}} x^{32} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} \Gamma\left(\frac{1}{4}\right) + 4096 a^{8} b^{17} x^{20} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} \Gamma\left(\frac{1}{4}\right) + 4096 a^{6} b^{19} x^{28} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} \Gamma\left(\frac{1}{4}\right)}"," ",0,"3465*a**8*b**(67/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*gamma(1/4) + 4096*a**8*b**17*x**20*gamma(1/4) + 6144*a**7*b**18*x**24*gamma(1/4) + 4096*a**6*b**19*x**28*gamma(1/4) + 1024*a**5*b**20*x**32*gamma(1/4)) + 10164*a**7*b**(71/4)*x**4*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*gamma(1/4) + 4096*a**8*b**17*x**20*gamma(1/4) + 6144*a**7*b**18*x**24*gamma(1/4) + 4096*a**6*b**19*x**28*gamma(1/4) + 1024*a**5*b**20*x**32*gamma(1/4)) + 10038*a**6*b**(75/4)*x**8*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*gamma(1/4) + 4096*a**8*b**17*x**20*gamma(1/4) + 6144*a**7*b**18*x**24*gamma(1/4) + 4096*a**6*b**19*x**28*gamma(1/4) + 1024*a**5*b**20*x**32*gamma(1/4)) + 3204*a**5*b**(79/4)*x**12*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*gamma(1/4) + 4096*a**8*b**17*x**20*gamma(1/4) + 6144*a**7*b**18*x**24*gamma(1/4) + 4096*a**6*b**19*x**28*gamma(1/4) + 1024*a**5*b**20*x**32*gamma(1/4)) + 585*a**4*b**(83/4)*x**16*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*gamma(1/4) + 4096*a**8*b**17*x**20*gamma(1/4) + 6144*a**7*b**18*x**24*gamma(1/4) + 4096*a**6*b**19*x**28*gamma(1/4) + 1024*a**5*b**20*x**32*gamma(1/4)) + 9360*a**3*b**(87/4)*x**20*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*gamma(1/4) + 4096*a**8*b**17*x**20*gamma(1/4) + 6144*a**7*b**18*x**24*gamma(1/4) + 4096*a**6*b**19*x**28*gamma(1/4) + 1024*a**5*b**20*x**32*gamma(1/4)) + 22464*a**2*b**(91/4)*x**24*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*gamma(1/4) + 4096*a**8*b**17*x**20*gamma(1/4) + 6144*a**7*b**18*x**24*gamma(1/4) + 4096*a**6*b**19*x**28*gamma(1/4) + 1024*a**5*b**20*x**32*gamma(1/4)) + 19968*a*b**(95/4)*x**28*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*gamma(1/4) + 4096*a**8*b**17*x**20*gamma(1/4) + 6144*a**7*b**18*x**24*gamma(1/4) + 4096*a**6*b**19*x**28*gamma(1/4) + 1024*a**5*b**20*x**32*gamma(1/4)) + 6144*b**(99/4)*x**32*(a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*gamma(1/4) + 4096*a**8*b**17*x**20*gamma(1/4) + 6144*a**7*b**18*x**24*gamma(1/4) + 4096*a**6*b**19*x**28*gamma(1/4) + 1024*a**5*b**20*x**32*gamma(1/4))","B",0
1103,1,37,0,1.412986," ","integrate(x**10/(b*x**4+a)**(1/4),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((1/4, 11/4), (15/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(1/4)*gamma(15/4))","C",0
1104,1,37,0,1.767183," ","integrate(x**6/(b*x**4+a)**(1/4),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((1/4, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(1/4)*gamma(11/4))","C",0
1105,1,37,0,1.449075," ","integrate(x**2/(b*x**4+a)**(1/4),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((1/4, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(1/4)*gamma(7/4))","C",0
1106,1,39,0,1.548220," ","integrate(1/x**2/(b*x**4+a)**(1/4),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt[4]{a} x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(1/4)*x*gamma(3/4))","C",0
1107,1,29,0,1.733660," ","integrate(1/x**6/(b*x**4+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{6 \sqrt[4]{b} x^{6}}"," ",0,"-hyper((1/4, 3/2), (5/2,), a*exp_polar(I*pi)/(b*x**4))/(6*b**(1/4)*x**6)","C",0
1108,1,44,0,1.824752," ","integrate(1/x**10/(b*x**4+a)**(1/4),x)","\frac{\Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, \frac{1}{4} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt[4]{a} x^{9} \Gamma\left(- \frac{5}{4}\right)}"," ",0,"gamma(-9/4)*hyper((-9/4, 1/4), (-5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(1/4)*x**9*gamma(-5/4))","C",0
1109,1,44,0,3.609107," ","integrate(1/x**14/(b*x**4+a)**(1/4),x)","\frac{\Gamma\left(- \frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{13}{4}, \frac{1}{4} \\ - \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt[4]{a} x^{13} \Gamma\left(- \frac{9}{4}\right)}"," ",0,"gamma(-13/4)*hyper((-13/4, 1/4), (-9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(1/4)*x**13*gamma(-9/4))","C",0
1110,1,116,0,25.210228," ","integrate(x**19/(b*x**4+a)**(3/4),x)","\begin{cases} \frac{2048 a^{4} \sqrt[4]{a + b x^{4}}}{3315 b^{5}} - \frac{512 a^{3} x^{4} \sqrt[4]{a + b x^{4}}}{3315 b^{4}} + \frac{64 a^{2} x^{8} \sqrt[4]{a + b x^{4}}}{663 b^{3}} - \frac{16 a x^{12} \sqrt[4]{a + b x^{4}}}{221 b^{2}} + \frac{x^{16} \sqrt[4]{a + b x^{4}}}{17 b} & \text{for}\: b \neq 0 \\\frac{x^{20}}{20 a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2048*a**4*(a + b*x**4)**(1/4)/(3315*b**5) - 512*a**3*x**4*(a + b*x**4)**(1/4)/(3315*b**4) + 64*a**2*x**8*(a + b*x**4)**(1/4)/(663*b**3) - 16*a*x**12*(a + b*x**4)**(1/4)/(221*b**2) + x**16*(a + b*x**4)**(1/4)/(17*b), Ne(b, 0)), (x**20/(20*a**(3/4)), True))","A",0
1111,1,92,0,10.225019," ","integrate(x**15/(b*x**4+a)**(3/4),x)","\begin{cases} - \frac{128 a^{3} \sqrt[4]{a + b x^{4}}}{195 b^{4}} + \frac{32 a^{2} x^{4} \sqrt[4]{a + b x^{4}}}{195 b^{3}} - \frac{4 a x^{8} \sqrt[4]{a + b x^{4}}}{39 b^{2}} + \frac{x^{12} \sqrt[4]{a + b x^{4}}}{13 b} & \text{for}\: b \neq 0 \\\frac{x^{16}}{16 a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-128*a**3*(a + b*x**4)**(1/4)/(195*b**4) + 32*a**2*x**4*(a + b*x**4)**(1/4)/(195*b**3) - 4*a*x**8*(a + b*x**4)**(1/4)/(39*b**2) + x**12*(a + b*x**4)**(1/4)/(13*b), Ne(b, 0)), (x**16/(16*a**(3/4)), True))","A",0
1112,1,68,0,4.241910," ","integrate(x**11/(b*x**4+a)**(3/4),x)","\begin{cases} \frac{32 a^{2} \sqrt[4]{a + b x^{4}}}{45 b^{3}} - \frac{8 a x^{4} \sqrt[4]{a + b x^{4}}}{45 b^{2}} + \frac{x^{8} \sqrt[4]{a + b x^{4}}}{9 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((32*a**2*(a + b*x**4)**(1/4)/(45*b**3) - 8*a*x**4*(a + b*x**4)**(1/4)/(45*b**2) + x**8*(a + b*x**4)**(1/4)/(9*b), Ne(b, 0)), (x**12/(12*a**(3/4)), True))","A",0
1113,1,44,0,2.276455," ","integrate(x**7/(b*x**4+a)**(3/4),x)","\begin{cases} - \frac{4 a \sqrt[4]{a + b x^{4}}}{5 b^{2}} + \frac{x^{4} \sqrt[4]{a + b x^{4}}}{5 b} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a*(a + b*x**4)**(1/4)/(5*b**2) + x**4*(a + b*x**4)**(1/4)/(5*b), Ne(b, 0)), (x**8/(8*a**(3/4)), True))","A",0
1114,1,20,0,0.927093," ","integrate(x**3/(b*x**4+a)**(3/4),x)","\begin{cases} \frac{\sqrt[4]{a + b x^{4}}}{b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a + b*x**4)**(1/4)/b, Ne(b, 0)), (x**4/(4*a**(3/4)), True))","A",0
1115,1,39,0,2.087609," ","integrate(1/x/(b*x**4+a)**(3/4),x)","- \frac{\Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 b^{\frac{3}{4}} x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-gamma(3/4)*hyper((3/4, 3/4), (7/4,), a*exp_polar(I*pi)/(b*x**4))/(4*b**(3/4)*x**3*gamma(7/4))","C",0
1116,1,39,0,2.465550," ","integrate(1/x**5/(b*x**4+a)**(3/4),x)","- \frac{\Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 b^{\frac{3}{4}} x^{7} \Gamma\left(\frac{11}{4}\right)}"," ",0,"-gamma(7/4)*hyper((3/4, 7/4), (11/4,), a*exp_polar(I*pi)/(b*x**4))/(4*b**(3/4)*x**7*gamma(11/4))","C",0
1117,1,39,0,3.507468," ","integrate(1/x**9/(b*x**4+a)**(3/4),x)","- \frac{\Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 b^{\frac{3}{4}} x^{11} \Gamma\left(\frac{15}{4}\right)}"," ",0,"-gamma(11/4)*hyper((3/4, 11/4), (15/4,), a*exp_polar(I*pi)/(b*x**4))/(4*b**(3/4)*x**11*gamma(15/4))","C",0
1118,1,27,0,2.716482," ","integrate(x**13/(b*x**4+a)**(3/4),x)","\frac{x^{14} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{14 a^{\frac{3}{4}}}"," ",0,"x**14*hyper((3/4, 7/2), (9/2,), b*x**4*exp_polar(I*pi)/a)/(14*a**(3/4))","C",0
1119,1,27,0,2.321490," ","integrate(x**9/(b*x**4+a)**(3/4),x)","\frac{x^{10} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10 a^{\frac{3}{4}}}"," ",0,"x**10*hyper((3/4, 5/2), (7/2,), b*x**4*exp_polar(I*pi)/a)/(10*a**(3/4))","C",0
1120,1,27,0,1.297253," ","integrate(x**5/(b*x**4+a)**(3/4),x)","\frac{x^{6} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6 a^{\frac{3}{4}}}"," ",0,"x**6*hyper((3/4, 3/2), (5/2,), b*x**4*exp_polar(I*pi)/a)/(6*a**(3/4))","C",0
1121,1,27,0,1.211335," ","integrate(x/(b*x**4+a)**(3/4),x)","\frac{x^{2} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}}}"," ",0,"x**2*hyper((1/2, 3/4), (3/2,), b*x**4*exp_polar(I*pi)/a)/(2*a**(3/4))","C",0
1122,1,31,0,1.469393," ","integrate(1/x**3/(b*x**4+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} x^{2}}"," ",0,"-hyper((-1/2, 3/4), (1/2,), b*x**4*exp_polar(I*pi)/a)/(2*a**(3/4)*x**2)","C",0
1123,1,32,0,2.202587," ","integrate(1/x**7/(b*x**4+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6 a^{\frac{3}{4}} x^{6}}"," ",0,"-hyper((-3/2, 3/4), (-1/2,), b*x**4*exp_polar(I*pi)/a)/(6*a**(3/4)*x**6)","C",0
1124,1,32,0,2.712008," ","integrate(1/x**11/(b*x**4+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10 a^{\frac{3}{4}} x^{10}}"," ",0,"-hyper((-5/2, 3/4), (-3/2,), b*x**4*exp_polar(I*pi)/a)/(10*a**(3/4)*x**10)","C",0
1125,1,37,0,2.353950," ","integrate(x**10/(b*x**4+a)**(3/4),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((3/4, 11/4), (15/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/4)*gamma(15/4))","C",0
1126,1,37,0,1.640409," ","integrate(x**6/(b*x**4+a)**(3/4),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((3/4, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/4)*gamma(11/4))","C",0
1127,1,37,0,1.622984," ","integrate(x**2/(b*x**4+a)**(3/4),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((3/4, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/4)*gamma(7/4))","C",0
1128,1,31,0,1.212432," ","integrate(1/x**2/(b*x**4+a)**(3/4),x)","\frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{1}{4}\right)}{4 a \Gamma\left(\frac{3}{4}\right)}"," ",0,"b**(1/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-1/4)/(4*a*gamma(3/4))","B",0
1129,1,68,0,1.324154," ","integrate(1/x**6/(b*x**4+a)**(3/4),x)","- \frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{5}{4}\right)}{16 a x^{4} \Gamma\left(\frac{3}{4}\right)} + \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{5}{4}\right)}{4 a^{2} \Gamma\left(\frac{3}{4}\right)}"," ",0,"-b**(1/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-5/4)/(16*a*x**4*gamma(3/4)) + b**(5/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-5/4)/(4*a**2*gamma(3/4))","A",0
1130,1,406,0,2.630599," ","integrate(1/x**10/(b*x**4+a)**(3/4),x)","\frac{5 a^{4} b^{\frac{17}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} \Gamma\left(\frac{3}{4}\right) + 128 a^{4} b^{5} x^{12} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} \Gamma\left(\frac{3}{4}\right)} + \frac{2 a^{3} b^{\frac{21}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} \Gamma\left(\frac{3}{4}\right) + 128 a^{4} b^{5} x^{12} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} \Gamma\left(\frac{3}{4}\right)} + \frac{21 a^{2} b^{\frac{25}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} \Gamma\left(\frac{3}{4}\right) + 128 a^{4} b^{5} x^{12} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} \Gamma\left(\frac{3}{4}\right)} + \frac{56 a b^{\frac{29}{4}} x^{12} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} \Gamma\left(\frac{3}{4}\right) + 128 a^{4} b^{5} x^{12} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} \Gamma\left(\frac{3}{4}\right)} + \frac{32 b^{\frac{33}{4}} x^{16} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} \Gamma\left(\frac{3}{4}\right) + 128 a^{4} b^{5} x^{12} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} \Gamma\left(\frac{3}{4}\right)}"," ",0,"5*a**4*b**(17/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(64*a**5*b**4*x**8*gamma(3/4) + 128*a**4*b**5*x**12*gamma(3/4) + 64*a**3*b**6*x**16*gamma(3/4)) + 2*a**3*b**(21/4)*x**4*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(64*a**5*b**4*x**8*gamma(3/4) + 128*a**4*b**5*x**12*gamma(3/4) + 64*a**3*b**6*x**16*gamma(3/4)) + 21*a**2*b**(25/4)*x**8*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(64*a**5*b**4*x**8*gamma(3/4) + 128*a**4*b**5*x**12*gamma(3/4) + 64*a**3*b**6*x**16*gamma(3/4)) + 56*a*b**(29/4)*x**12*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(64*a**5*b**4*x**8*gamma(3/4) + 128*a**4*b**5*x**12*gamma(3/4) + 64*a**3*b**6*x**16*gamma(3/4)) + 32*b**(33/4)*x**16*(a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(64*a**5*b**4*x**8*gamma(3/4) + 128*a**4*b**5*x**12*gamma(3/4) + 64*a**3*b**6*x**16*gamma(3/4))","B",0
1131,1,692,0,3.258215," ","integrate(1/x**14/(b*x**4+a)**(3/4),x)","- \frac{45 a^{6} b^{\frac{37}{4}} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{3}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{3}{4}\right)} - \frac{75 a^{5} b^{\frac{41}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{3}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{3}{4}\right)} - \frac{51 a^{4} b^{\frac{45}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{3}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{3}{4}\right)} + \frac{231 a^{3} b^{\frac{49}{4}} x^{12} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{3}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{3}{4}\right)} + \frac{924 a^{2} b^{\frac{53}{4}} x^{16} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{3}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{3}{4}\right)} + \frac{1056 a b^{\frac{57}{4}} x^{20} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{3}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{3}{4}\right)} + \frac{384 b^{\frac{61}{4}} x^{24} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{256 a^{7} b^{9} x^{12} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} \Gamma\left(\frac{3}{4}\right) + 768 a^{5} b^{11} x^{20} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} \Gamma\left(\frac{3}{4}\right)}"," ",0,"-45*a**6*b**(37/4)*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(256*a**7*b**9*x**12*gamma(3/4) + 768*a**6*b**10*x**16*gamma(3/4) + 768*a**5*b**11*x**20*gamma(3/4) + 256*a**4*b**12*x**24*gamma(3/4)) - 75*a**5*b**(41/4)*x**4*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(256*a**7*b**9*x**12*gamma(3/4) + 768*a**6*b**10*x**16*gamma(3/4) + 768*a**5*b**11*x**20*gamma(3/4) + 256*a**4*b**12*x**24*gamma(3/4)) - 51*a**4*b**(45/4)*x**8*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(256*a**7*b**9*x**12*gamma(3/4) + 768*a**6*b**10*x**16*gamma(3/4) + 768*a**5*b**11*x**20*gamma(3/4) + 256*a**4*b**12*x**24*gamma(3/4)) + 231*a**3*b**(49/4)*x**12*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(256*a**7*b**9*x**12*gamma(3/4) + 768*a**6*b**10*x**16*gamma(3/4) + 768*a**5*b**11*x**20*gamma(3/4) + 256*a**4*b**12*x**24*gamma(3/4)) + 924*a**2*b**(53/4)*x**16*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(256*a**7*b**9*x**12*gamma(3/4) + 768*a**6*b**10*x**16*gamma(3/4) + 768*a**5*b**11*x**20*gamma(3/4) + 256*a**4*b**12*x**24*gamma(3/4)) + 1056*a*b**(57/4)*x**20*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(256*a**7*b**9*x**12*gamma(3/4) + 768*a**6*b**10*x**16*gamma(3/4) + 768*a**5*b**11*x**20*gamma(3/4) + 256*a**4*b**12*x**24*gamma(3/4)) + 384*b**(61/4)*x**24*(a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(256*a**7*b**9*x**12*gamma(3/4) + 768*a**6*b**10*x**16*gamma(3/4) + 768*a**5*b**11*x**20*gamma(3/4) + 256*a**4*b**12*x**24*gamma(3/4))","B",0
1132,1,37,0,2.142218," ","integrate(x**12/(b*x**4+a)**(3/4),x)","\frac{x^{13} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{17}{4}\right)}"," ",0,"x**13*gamma(13/4)*hyper((3/4, 13/4), (17/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/4)*gamma(17/4))","C",0
1133,1,37,0,1.552507," ","integrate(x**8/(b*x**4+a)**(3/4),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((3/4, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/4)*gamma(13/4))","C",0
1134,1,37,0,0.973146," ","integrate(x**4/(b*x**4+a)**(3/4),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((3/4, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/4)*gamma(9/4))","C",0
1135,1,36,0,0.914822," ","integrate(1/(b*x**4+a)**(3/4),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 3/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/4)*gamma(5/4))","C",0
1136,1,41,0,1.555452," ","integrate(1/x**4/(b*x**4+a)**(3/4),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 3/4), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/4)*x**3*gamma(1/4))","C",0
1137,1,44,0,1.991367," ","integrate(1/x**8/(b*x**4+a)**(3/4),x)","\frac{\Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{3}{4} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} x^{7} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"gamma(-7/4)*hyper((-7/4, 3/4), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/4)*x**7*gamma(-3/4))","C",0
1138,1,44,0,2.569232," ","integrate(1/x**12/(b*x**4+a)**(3/4),x)","\frac{\Gamma\left(- \frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{11}{4}, \frac{3}{4} \\ - \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} x^{11} \Gamma\left(- \frac{7}{4}\right)}"," ",0,"gamma(-11/4)*hyper((-11/4, 3/4), (-7/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/4)*x**11*gamma(-7/4))","C",0
1139,1,116,0,18.124874," ","integrate(x**19/(b*x**4+a)**(5/4),x)","\begin{cases} - \frac{2048 a^{4}}{1155 b^{5} \sqrt[4]{a + b x^{4}}} - \frac{512 a^{3} x^{4}}{1155 b^{4} \sqrt[4]{a + b x^{4}}} + \frac{64 a^{2} x^{8}}{385 b^{3} \sqrt[4]{a + b x^{4}}} - \frac{16 a x^{12}}{165 b^{2} \sqrt[4]{a + b x^{4}}} + \frac{x^{16}}{15 b \sqrt[4]{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{20}}{20 a^{\frac{5}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2048*a**4/(1155*b**5*(a + b*x**4)**(1/4)) - 512*a**3*x**4/(1155*b**4*(a + b*x**4)**(1/4)) + 64*a**2*x**8/(385*b**3*(a + b*x**4)**(1/4)) - 16*a*x**12/(165*b**2*(a + b*x**4)**(1/4)) + x**16/(15*b*(a + b*x**4)**(1/4)), Ne(b, 0)), (x**20/(20*a**(5/4)), True))","A",0
1140,1,92,0,12.754771," ","integrate(x**15/(b*x**4+a)**(5/4),x)","\begin{cases} \frac{128 a^{3}}{77 b^{4} \sqrt[4]{a + b x^{4}}} + \frac{32 a^{2} x^{4}}{77 b^{3} \sqrt[4]{a + b x^{4}}} - \frac{12 a x^{8}}{77 b^{2} \sqrt[4]{a + b x^{4}}} + \frac{x^{12}}{11 b \sqrt[4]{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{16}}{16 a^{\frac{5}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((128*a**3/(77*b**4*(a + b*x**4)**(1/4)) + 32*a**2*x**4/(77*b**3*(a + b*x**4)**(1/4)) - 12*a*x**8/(77*b**2*(a + b*x**4)**(1/4)) + x**12/(11*b*(a + b*x**4)**(1/4)), Ne(b, 0)), (x**16/(16*a**(5/4)), True))","A",0
1141,1,68,0,5.034470," ","integrate(x**11/(b*x**4+a)**(5/4),x)","\begin{cases} - \frac{32 a^{2}}{21 b^{3} \sqrt[4]{a + b x^{4}}} - \frac{8 a x^{4}}{21 b^{2} \sqrt[4]{a + b x^{4}}} + \frac{x^{8}}{7 b \sqrt[4]{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 a^{\frac{5}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*a**2/(21*b**3*(a + b*x**4)**(1/4)) - 8*a*x**4/(21*b**2*(a + b*x**4)**(1/4)) + x**8/(7*b*(a + b*x**4)**(1/4)), Ne(b, 0)), (x**12/(12*a**(5/4)), True))","A",0
1142,1,44,0,2.096236," ","integrate(x**7/(b*x**4+a)**(5/4),x)","\begin{cases} \frac{4 a}{3 b^{2} \sqrt[4]{a + b x^{4}}} + \frac{x^{4}}{3 b \sqrt[4]{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 a^{\frac{5}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a/(3*b**2*(a + b*x**4)**(1/4)) + x**4/(3*b*(a + b*x**4)**(1/4)), Ne(b, 0)), (x**8/(8*a**(5/4)), True))","A",0
1143,1,24,0,1.298842," ","integrate(x**3/(b*x**4+a)**(5/4),x)","\begin{cases} - \frac{1}{b \sqrt[4]{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{5}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(b*(a + b*x**4)**(1/4)), Ne(b, 0)), (x**4/(4*a**(5/4)), True))","A",0
1144,1,39,0,1.820762," ","integrate(1/x/(b*x**4+a)**(5/4),x)","- \frac{\Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 b^{\frac{5}{4}} x^{5} \Gamma\left(\frac{9}{4}\right)}"," ",0,"-gamma(5/4)*hyper((5/4, 5/4), (9/4,), a*exp_polar(I*pi)/(b*x**4))/(4*b**(5/4)*x**5*gamma(9/4))","C",0
1145,1,39,0,1.828418," ","integrate(1/x**5/(b*x**4+a)**(5/4),x)","- \frac{\Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 b^{\frac{5}{4}} x^{9} \Gamma\left(\frac{13}{4}\right)}"," ",0,"-gamma(9/4)*hyper((5/4, 9/4), (13/4,), a*exp_polar(I*pi)/(b*x**4))/(4*b**(5/4)*x**9*gamma(13/4))","C",0
1146,1,39,0,3.206215," ","integrate(1/x**9/(b*x**4+a)**(5/4),x)","- \frac{\Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 b^{\frac{5}{4}} x^{13} \Gamma\left(\frac{17}{4}\right)}"," ",0,"-gamma(13/4)*hyper((5/4, 13/4), (17/4,), a*exp_polar(I*pi)/(b*x**4))/(4*b**(5/4)*x**13*gamma(17/4))","C",0
1147,1,27,0,2.288448," ","integrate(x**13/(b*x**4+a)**(5/4),x)","\frac{x^{14} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{14 a^{\frac{5}{4}}}"," ",0,"x**14*hyper((5/4, 7/2), (9/2,), b*x**4*exp_polar(I*pi)/a)/(14*a**(5/4))","C",0
1148,1,27,0,1.728684," ","integrate(x**9/(b*x**4+a)**(5/4),x)","\frac{x^{10} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10 a^{\frac{5}{4}}}"," ",0,"x**10*hyper((5/4, 5/2), (7/2,), b*x**4*exp_polar(I*pi)/a)/(10*a**(5/4))","C",0
1149,1,27,0,1.242895," ","integrate(x**5/(b*x**4+a)**(5/4),x)","\frac{x^{6} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6 a^{\frac{5}{4}}}"," ",0,"x**6*hyper((5/4, 3/2), (5/2,), b*x**4*exp_polar(I*pi)/a)/(6*a**(5/4))","C",0
1150,1,27,0,0.942084," ","integrate(x/(b*x**4+a)**(5/4),x)","\frac{x^{2} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}}}"," ",0,"x**2*hyper((1/2, 5/4), (3/2,), b*x**4*exp_polar(I*pi)/a)/(2*a**(5/4))","C",0
1151,1,31,0,1.697217," ","integrate(1/x**3/(b*x**4+a)**(5/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} x^{2}}"," ",0,"-hyper((-1/2, 5/4), (1/2,), b*x**4*exp_polar(I*pi)/a)/(2*a**(5/4)*x**2)","C",0
1152,1,32,0,1.612612," ","integrate(1/x**7/(b*x**4+a)**(5/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{5}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6 a^{\frac{5}{4}} x^{6}}"," ",0,"-hyper((-3/2, 5/4), (-1/2,), b*x**4*exp_polar(I*pi)/a)/(6*a**(5/4)*x**6)","C",0
1153,1,32,0,3.154779," ","integrate(1/x**11/(b*x**4+a)**(5/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{5}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{10 a^{\frac{5}{4}} x^{10}}"," ",0,"-hyper((-5/2, 5/4), (-3/2,), b*x**4*exp_polar(I*pi)/a)/(10*a**(5/4)*x**10)","C",0
1154,1,37,0,2.758720," ","integrate(x**12/(b*x**4+a)**(5/4),x)","\frac{x^{13} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} \Gamma\left(\frac{17}{4}\right)}"," ",0,"x**13*gamma(13/4)*hyper((5/4, 13/4), (17/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*gamma(17/4))","C",0
1155,1,37,0,1.574564," ","integrate(x**8/(b*x**4+a)**(5/4),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((5/4, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*gamma(13/4))","C",0
1156,1,37,0,1.774304," ","integrate(x**4/(b*x**4+a)**(5/4),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((5/4, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*gamma(9/4))","C",0
1157,1,29,0,1.075696," ","integrate(1/(b*x**4+a)**(5/4),x)","\frac{x \Gamma\left(\frac{1}{4}\right)}{4 a^{\frac{5}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)/(4*a**(5/4)*(1 + b*x**4/a)**(1/4)*gamma(5/4))","B",0
1158,1,68,0,1.670291," ","integrate(1/x**4/(b*x**4+a)**(5/4),x)","\frac{\Gamma\left(- \frac{3}{4}\right)}{16 a \sqrt[4]{b} x^{4} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(\frac{5}{4}\right)} + \frac{b^{\frac{3}{4}} \Gamma\left(- \frac{3}{4}\right)}{4 a^{2} \sqrt[4]{\frac{a}{b x^{4}} + 1} \Gamma\left(\frac{5}{4}\right)}"," ",0,"gamma(-3/4)/(16*a*b**(1/4)*x**4*(a/(b*x**4) + 1)**(1/4)*gamma(5/4)) + b**(3/4)*gamma(-3/4)/(4*a**2*(a/(b*x**4) + 1)**(1/4)*gamma(5/4))","A",0
1159,1,323,0,2.041280," ","integrate(1/x**8/(b*x**4+a)**(5/4),x)","- \frac{3 a^{3} b^{\frac{19}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{64 a^{5} b^{4} x^{4} \Gamma\left(\frac{5}{4}\right) + 128 a^{4} b^{5} x^{8} \Gamma\left(\frac{5}{4}\right) + 64 a^{3} b^{6} x^{12} \Gamma\left(\frac{5}{4}\right)} + \frac{5 a^{2} b^{\frac{23}{4}} x^{4} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{64 a^{5} b^{4} x^{4} \Gamma\left(\frac{5}{4}\right) + 128 a^{4} b^{5} x^{8} \Gamma\left(\frac{5}{4}\right) + 64 a^{3} b^{6} x^{12} \Gamma\left(\frac{5}{4}\right)} + \frac{40 a b^{\frac{27}{4}} x^{8} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{64 a^{5} b^{4} x^{4} \Gamma\left(\frac{5}{4}\right) + 128 a^{4} b^{5} x^{8} \Gamma\left(\frac{5}{4}\right) + 64 a^{3} b^{6} x^{12} \Gamma\left(\frac{5}{4}\right)} + \frac{32 b^{\frac{31}{4}} x^{12} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{64 a^{5} b^{4} x^{4} \Gamma\left(\frac{5}{4}\right) + 128 a^{4} b^{5} x^{8} \Gamma\left(\frac{5}{4}\right) + 64 a^{3} b^{6} x^{12} \Gamma\left(\frac{5}{4}\right)}"," ",0,"-3*a**3*b**(19/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(64*a**5*b**4*x**4*gamma(5/4) + 128*a**4*b**5*x**8*gamma(5/4) + 64*a**3*b**6*x**12*gamma(5/4)) + 5*a**2*b**(23/4)*x**4*(a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(64*a**5*b**4*x**4*gamma(5/4) + 128*a**4*b**5*x**8*gamma(5/4) + 64*a**3*b**6*x**12*gamma(5/4)) + 40*a*b**(27/4)*x**8*(a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(64*a**5*b**4*x**4*gamma(5/4) + 128*a**4*b**5*x**8*gamma(5/4) + 64*a**3*b**6*x**12*gamma(5/4)) + 32*b**(31/4)*x**12*(a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(64*a**5*b**4*x**4*gamma(5/4) + 128*a**4*b**5*x**8*gamma(5/4) + 64*a**3*b**6*x**12*gamma(5/4))","B",0
1160,1,592,0,4.092869," ","integrate(1/x**12/(b*x**4+a)**(5/4),x)","\frac{21 a^{5} b^{\frac{39}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{256 a^{7} b^{9} x^{8} \Gamma\left(\frac{5}{4}\right) + 768 a^{6} b^{10} x^{12} \Gamma\left(\frac{5}{4}\right) + 768 a^{5} b^{11} x^{16} \Gamma\left(\frac{5}{4}\right) + 256 a^{4} b^{12} x^{20} \Gamma\left(\frac{5}{4}\right)} + \frac{6 a^{4} b^{\frac{43}{4}} x^{4} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{256 a^{7} b^{9} x^{8} \Gamma\left(\frac{5}{4}\right) + 768 a^{6} b^{10} x^{12} \Gamma\left(\frac{5}{4}\right) + 768 a^{5} b^{11} x^{16} \Gamma\left(\frac{5}{4}\right) + 256 a^{4} b^{12} x^{20} \Gamma\left(\frac{5}{4}\right)} + \frac{45 a^{3} b^{\frac{47}{4}} x^{8} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{256 a^{7} b^{9} x^{8} \Gamma\left(\frac{5}{4}\right) + 768 a^{6} b^{10} x^{12} \Gamma\left(\frac{5}{4}\right) + 768 a^{5} b^{11} x^{16} \Gamma\left(\frac{5}{4}\right) + 256 a^{4} b^{12} x^{20} \Gamma\left(\frac{5}{4}\right)} + \frac{540 a^{2} b^{\frac{51}{4}} x^{12} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{256 a^{7} b^{9} x^{8} \Gamma\left(\frac{5}{4}\right) + 768 a^{6} b^{10} x^{12} \Gamma\left(\frac{5}{4}\right) + 768 a^{5} b^{11} x^{16} \Gamma\left(\frac{5}{4}\right) + 256 a^{4} b^{12} x^{20} \Gamma\left(\frac{5}{4}\right)} + \frac{864 a b^{\frac{55}{4}} x^{16} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{256 a^{7} b^{9} x^{8} \Gamma\left(\frac{5}{4}\right) + 768 a^{6} b^{10} x^{12} \Gamma\left(\frac{5}{4}\right) + 768 a^{5} b^{11} x^{16} \Gamma\left(\frac{5}{4}\right) + 256 a^{4} b^{12} x^{20} \Gamma\left(\frac{5}{4}\right)} + \frac{384 b^{\frac{59}{4}} x^{20} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{256 a^{7} b^{9} x^{8} \Gamma\left(\frac{5}{4}\right) + 768 a^{6} b^{10} x^{12} \Gamma\left(\frac{5}{4}\right) + 768 a^{5} b^{11} x^{16} \Gamma\left(\frac{5}{4}\right) + 256 a^{4} b^{12} x^{20} \Gamma\left(\frac{5}{4}\right)}"," ",0,"21*a**5*b**(39/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(256*a**7*b**9*x**8*gamma(5/4) + 768*a**6*b**10*x**12*gamma(5/4) + 768*a**5*b**11*x**16*gamma(5/4) + 256*a**4*b**12*x**20*gamma(5/4)) + 6*a**4*b**(43/4)*x**4*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(256*a**7*b**9*x**8*gamma(5/4) + 768*a**6*b**10*x**12*gamma(5/4) + 768*a**5*b**11*x**16*gamma(5/4) + 256*a**4*b**12*x**20*gamma(5/4)) + 45*a**3*b**(47/4)*x**8*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(256*a**7*b**9*x**8*gamma(5/4) + 768*a**6*b**10*x**12*gamma(5/4) + 768*a**5*b**11*x**16*gamma(5/4) + 256*a**4*b**12*x**20*gamma(5/4)) + 540*a**2*b**(51/4)*x**12*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(256*a**7*b**9*x**8*gamma(5/4) + 768*a**6*b**10*x**12*gamma(5/4) + 768*a**5*b**11*x**16*gamma(5/4) + 256*a**4*b**12*x**20*gamma(5/4)) + 864*a*b**(55/4)*x**16*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(256*a**7*b**9*x**8*gamma(5/4) + 768*a**6*b**10*x**12*gamma(5/4) + 768*a**5*b**11*x**16*gamma(5/4) + 256*a**4*b**12*x**20*gamma(5/4)) + 384*b**(59/4)*x**20*(a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(256*a**7*b**9*x**8*gamma(5/4) + 768*a**6*b**10*x**12*gamma(5/4) + 768*a**5*b**11*x**16*gamma(5/4) + 256*a**4*b**12*x**20*gamma(5/4))","B",0
1161,1,928,0,6.406736," ","integrate(1/x**16/(b*x**4+a)**(5/4),x)","- \frac{231 a^{7} b^{\frac{67}{4}} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{1024 a^{9} b^{16} x^{12} \Gamma\left(\frac{5}{4}\right) + 4096 a^{8} b^{17} x^{16} \Gamma\left(\frac{5}{4}\right) + 6144 a^{7} b^{18} x^{20} \Gamma\left(\frac{5}{4}\right) + 4096 a^{6} b^{19} x^{24} \Gamma\left(\frac{5}{4}\right) + 1024 a^{5} b^{20} x^{28} \Gamma\left(\frac{5}{4}\right)} - \frac{357 a^{6} b^{\frac{71}{4}} x^{4} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{1024 a^{9} b^{16} x^{12} \Gamma\left(\frac{5}{4}\right) + 4096 a^{8} b^{17} x^{16} \Gamma\left(\frac{5}{4}\right) + 6144 a^{7} b^{18} x^{20} \Gamma\left(\frac{5}{4}\right) + 4096 a^{6} b^{19} x^{24} \Gamma\left(\frac{5}{4}\right) + 1024 a^{5} b^{20} x^{28} \Gamma\left(\frac{5}{4}\right)} - \frac{261 a^{5} b^{\frac{75}{4}} x^{8} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{1024 a^{9} b^{16} x^{12} \Gamma\left(\frac{5}{4}\right) + 4096 a^{8} b^{17} x^{16} \Gamma\left(\frac{5}{4}\right) + 6144 a^{7} b^{18} x^{20} \Gamma\left(\frac{5}{4}\right) + 4096 a^{6} b^{19} x^{24} \Gamma\left(\frac{5}{4}\right) + 1024 a^{5} b^{20} x^{28} \Gamma\left(\frac{5}{4}\right)} + \frac{585 a^{4} b^{\frac{79}{4}} x^{12} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{1024 a^{9} b^{16} x^{12} \Gamma\left(\frac{5}{4}\right) + 4096 a^{8} b^{17} x^{16} \Gamma\left(\frac{5}{4}\right) + 6144 a^{7} b^{18} x^{20} \Gamma\left(\frac{5}{4}\right) + 4096 a^{6} b^{19} x^{24} \Gamma\left(\frac{5}{4}\right) + 1024 a^{5} b^{20} x^{28} \Gamma\left(\frac{5}{4}\right)} + \frac{9360 a^{3} b^{\frac{83}{4}} x^{16} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{1024 a^{9} b^{16} x^{12} \Gamma\left(\frac{5}{4}\right) + 4096 a^{8} b^{17} x^{16} \Gamma\left(\frac{5}{4}\right) + 6144 a^{7} b^{18} x^{20} \Gamma\left(\frac{5}{4}\right) + 4096 a^{6} b^{19} x^{24} \Gamma\left(\frac{5}{4}\right) + 1024 a^{5} b^{20} x^{28} \Gamma\left(\frac{5}{4}\right)} + \frac{22464 a^{2} b^{\frac{87}{4}} x^{20} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{1024 a^{9} b^{16} x^{12} \Gamma\left(\frac{5}{4}\right) + 4096 a^{8} b^{17} x^{16} \Gamma\left(\frac{5}{4}\right) + 6144 a^{7} b^{18} x^{20} \Gamma\left(\frac{5}{4}\right) + 4096 a^{6} b^{19} x^{24} \Gamma\left(\frac{5}{4}\right) + 1024 a^{5} b^{20} x^{28} \Gamma\left(\frac{5}{4}\right)} + \frac{19968 a b^{\frac{91}{4}} x^{24} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{1024 a^{9} b^{16} x^{12} \Gamma\left(\frac{5}{4}\right) + 4096 a^{8} b^{17} x^{16} \Gamma\left(\frac{5}{4}\right) + 6144 a^{7} b^{18} x^{20} \Gamma\left(\frac{5}{4}\right) + 4096 a^{6} b^{19} x^{24} \Gamma\left(\frac{5}{4}\right) + 1024 a^{5} b^{20} x^{28} \Gamma\left(\frac{5}{4}\right)} + \frac{6144 b^{\frac{95}{4}} x^{28} \left(\frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{1024 a^{9} b^{16} x^{12} \Gamma\left(\frac{5}{4}\right) + 4096 a^{8} b^{17} x^{16} \Gamma\left(\frac{5}{4}\right) + 6144 a^{7} b^{18} x^{20} \Gamma\left(\frac{5}{4}\right) + 4096 a^{6} b^{19} x^{24} \Gamma\left(\frac{5}{4}\right) + 1024 a^{5} b^{20} x^{28} \Gamma\left(\frac{5}{4}\right)}"," ",0,"-231*a**7*b**(67/4)*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(1024*a**9*b**16*x**12*gamma(5/4) + 4096*a**8*b**17*x**16*gamma(5/4) + 6144*a**7*b**18*x**20*gamma(5/4) + 4096*a**6*b**19*x**24*gamma(5/4) + 1024*a**5*b**20*x**28*gamma(5/4)) - 357*a**6*b**(71/4)*x**4*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(1024*a**9*b**16*x**12*gamma(5/4) + 4096*a**8*b**17*x**16*gamma(5/4) + 6144*a**7*b**18*x**20*gamma(5/4) + 4096*a**6*b**19*x**24*gamma(5/4) + 1024*a**5*b**20*x**28*gamma(5/4)) - 261*a**5*b**(75/4)*x**8*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(1024*a**9*b**16*x**12*gamma(5/4) + 4096*a**8*b**17*x**16*gamma(5/4) + 6144*a**7*b**18*x**20*gamma(5/4) + 4096*a**6*b**19*x**24*gamma(5/4) + 1024*a**5*b**20*x**28*gamma(5/4)) + 585*a**4*b**(79/4)*x**12*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(1024*a**9*b**16*x**12*gamma(5/4) + 4096*a**8*b**17*x**16*gamma(5/4) + 6144*a**7*b**18*x**20*gamma(5/4) + 4096*a**6*b**19*x**24*gamma(5/4) + 1024*a**5*b**20*x**28*gamma(5/4)) + 9360*a**3*b**(83/4)*x**16*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(1024*a**9*b**16*x**12*gamma(5/4) + 4096*a**8*b**17*x**16*gamma(5/4) + 6144*a**7*b**18*x**20*gamma(5/4) + 4096*a**6*b**19*x**24*gamma(5/4) + 1024*a**5*b**20*x**28*gamma(5/4)) + 22464*a**2*b**(87/4)*x**20*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(1024*a**9*b**16*x**12*gamma(5/4) + 4096*a**8*b**17*x**16*gamma(5/4) + 6144*a**7*b**18*x**20*gamma(5/4) + 4096*a**6*b**19*x**24*gamma(5/4) + 1024*a**5*b**20*x**28*gamma(5/4)) + 19968*a*b**(91/4)*x**24*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(1024*a**9*b**16*x**12*gamma(5/4) + 4096*a**8*b**17*x**16*gamma(5/4) + 6144*a**7*b**18*x**20*gamma(5/4) + 4096*a**6*b**19*x**24*gamma(5/4) + 1024*a**5*b**20*x**28*gamma(5/4)) + 6144*b**(95/4)*x**28*(a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(1024*a**9*b**16*x**12*gamma(5/4) + 4096*a**8*b**17*x**16*gamma(5/4) + 6144*a**7*b**18*x**20*gamma(5/4) + 4096*a**6*b**19*x**24*gamma(5/4) + 1024*a**5*b**20*x**28*gamma(5/4))","B",0
1162,1,37,0,2.267529," ","integrate(x**14/(b*x**4+a)**(5/4),x)","\frac{x^{15} \Gamma\left(\frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{15}{4} \\ \frac{19}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} \Gamma\left(\frac{19}{4}\right)}"," ",0,"x**15*gamma(15/4)*hyper((5/4, 15/4), (19/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*gamma(19/4))","C",0
1163,1,37,0,1.687161," ","integrate(x**10/(b*x**4+a)**(5/4),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((5/4, 11/4), (15/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*gamma(15/4))","C",0
1164,1,37,0,1.327797," ","integrate(x**6/(b*x**4+a)**(5/4),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((5/4, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*gamma(11/4))","C",0
1165,1,37,0,0.968215," ","integrate(x**2/(b*x**4+a)**(5/4),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((3/4, 5/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*gamma(7/4))","C",0
1166,1,39,0,1.597276," ","integrate(1/x**2/(b*x**4+a)**(5/4),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 5/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*x*gamma(3/4))","C",0
1167,1,44,0,2.057261," ","integrate(1/x**6/(b*x**4+a)**(5/4),x)","\frac{\Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{5}{4} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} x^{5} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"gamma(-5/4)*hyper((-5/4, 5/4), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*x**5*gamma(-1/4))","C",0
1168,1,44,0,3.163398," ","integrate(1/x**10/(b*x**4+a)**(5/4),x)","\frac{\Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, \frac{5}{4} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} x^{9} \Gamma\left(- \frac{5}{4}\right)}"," ",0,"gamma(-9/4)*hyper((-9/4, 5/4), (-5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*x**9*gamma(-5/4))","C",0
1169,1,44,0,3.964397," ","integrate(1/x**14/(b*x**4+a)**(5/4),x)","\frac{\Gamma\left(- \frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{13}{4}, \frac{5}{4} \\ - \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} x^{13} \Gamma\left(- \frac{9}{4}\right)}"," ",0,"gamma(-13/4)*hyper((-13/4, 5/4), (-9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(5/4)*x**13*gamma(-9/4))","C",0
1170,1,36,0,2.119245," ","integrate(1/(b*x**4+a)**(7/4),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{7}{4}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 7/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(7/4)*gamma(5/4))","C",0
1171,1,126,0,2.526766," ","integrate(1/(b*x**4+a)**(9/4),x)","\frac{5 a x \Gamma\left(\frac{1}{4}\right)}{16 a^{\frac{13}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{9}{4}\right) + 16 a^{\frac{9}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{9}{4}\right)} + \frac{4 b x^{5} \Gamma\left(\frac{1}{4}\right)}{16 a^{\frac{13}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{9}{4}\right) + 16 a^{\frac{9}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"5*a*x*gamma(1/4)/(16*a**(13/4)*(1 + b*x**4/a)**(1/4)*gamma(9/4) + 16*a**(9/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(9/4)) + 4*b*x**5*gamma(1/4)/(16*a**(13/4)*(1 + b*x**4/a)**(1/4)*gamma(9/4) + 16*a**(9/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(9/4))","B",0
1172,1,36,0,3.532231," ","integrate(1/(b*x**4+a)**(11/4),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{11}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{11}{4}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 11/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(11/4)*gamma(5/4))","C",0
1173,1,515,0,5.221707," ","integrate(1/(b*x**4+a)**(13/4),x)","\frac{45 a^{5} x \Gamma\left(\frac{1}{4}\right)}{64 a^{\frac{33}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 192 a^{\frac{29}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 192 a^{\frac{25}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 64 a^{\frac{21}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right)} + \frac{117 a^{4} b x^{5} \Gamma\left(\frac{1}{4}\right)}{64 a^{\frac{33}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 192 a^{\frac{29}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 192 a^{\frac{25}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 64 a^{\frac{21}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right)} + \frac{104 a^{3} b^{2} x^{9} \Gamma\left(\frac{1}{4}\right)}{64 a^{\frac{33}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 192 a^{\frac{29}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 192 a^{\frac{25}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 64 a^{\frac{21}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right)} + \frac{32 a^{2} b^{3} x^{13} \Gamma\left(\frac{1}{4}\right)}{64 a^{\frac{33}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 192 a^{\frac{29}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 192 a^{\frac{25}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right) + 64 a^{\frac{21}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"45*a**5*x*gamma(1/4)/(64*a**(33/4)*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 192*a**(29/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 192*a**(25/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 64*a**(21/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(13/4)) + 117*a**4*b*x**5*gamma(1/4)/(64*a**(33/4)*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 192*a**(29/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 192*a**(25/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 64*a**(21/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(13/4)) + 104*a**3*b**2*x**9*gamma(1/4)/(64*a**(33/4)*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 192*a**(29/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 192*a**(25/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 64*a**(21/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(13/4)) + 32*a**2*b**3*x**13*gamma(1/4)/(64*a**(33/4)*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 192*a**(29/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 192*a**(25/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(13/4) + 64*a**(21/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(13/4))","B",0
1174,1,1550,0,7.864227," ","integrate(1/(b*x**4+a)**(17/4),x)","\frac{585 a^{14} x \Gamma\left(\frac{1}{4}\right)}{256 a^{\frac{73}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{69}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{65}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 5120 a^{\frac{61}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{57}{4}} b^{4} x^{16} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{53}{4}} b^{5} x^{20} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 256 a^{\frac{49}{4}} b^{6} x^{24} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right)} + \frac{3159 a^{13} b x^{5} \Gamma\left(\frac{1}{4}\right)}{256 a^{\frac{73}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{69}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{65}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 5120 a^{\frac{61}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{57}{4}} b^{4} x^{16} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{53}{4}} b^{5} x^{20} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 256 a^{\frac{49}{4}} b^{6} x^{24} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right)} + \frac{7215 a^{12} b^{2} x^{9} \Gamma\left(\frac{1}{4}\right)}{256 a^{\frac{73}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{69}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{65}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 5120 a^{\frac{61}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{57}{4}} b^{4} x^{16} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{53}{4}} b^{5} x^{20} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 256 a^{\frac{49}{4}} b^{6} x^{24} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right)} + \frac{8925 a^{11} b^{3} x^{13} \Gamma\left(\frac{1}{4}\right)}{256 a^{\frac{73}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{69}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{65}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 5120 a^{\frac{61}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{57}{4}} b^{4} x^{16} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{53}{4}} b^{5} x^{20} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 256 a^{\frac{49}{4}} b^{6} x^{24} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right)} + \frac{6300 a^{10} b^{4} x^{17} \Gamma\left(\frac{1}{4}\right)}{256 a^{\frac{73}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{69}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{65}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 5120 a^{\frac{61}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{57}{4}} b^{4} x^{16} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{53}{4}} b^{5} x^{20} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 256 a^{\frac{49}{4}} b^{6} x^{24} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right)} + \frac{2400 a^{9} b^{5} x^{21} \Gamma\left(\frac{1}{4}\right)}{256 a^{\frac{73}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{69}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{65}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 5120 a^{\frac{61}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{57}{4}} b^{4} x^{16} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{53}{4}} b^{5} x^{20} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 256 a^{\frac{49}{4}} b^{6} x^{24} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right)} + \frac{384 a^{8} b^{6} x^{25} \Gamma\left(\frac{1}{4}\right)}{256 a^{\frac{73}{4}} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{69}{4}} b x^{4} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{65}{4}} b^{2} x^{8} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 5120 a^{\frac{61}{4}} b^{3} x^{12} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 3840 a^{\frac{57}{4}} b^{4} x^{16} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 1536 a^{\frac{53}{4}} b^{5} x^{20} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right) + 256 a^{\frac{49}{4}} b^{6} x^{24} \sqrt[4]{1 + \frac{b x^{4}}{a}} \Gamma\left(\frac{17}{4}\right)}"," ",0,"585*a**14*x*gamma(1/4)/(256*a**(73/4)*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(69/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(65/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 5120*a**(61/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(57/4)*b**4*x**16*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(53/4)*b**5*x**20*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 256*a**(49/4)*b**6*x**24*(1 + b*x**4/a)**(1/4)*gamma(17/4)) + 3159*a**13*b*x**5*gamma(1/4)/(256*a**(73/4)*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(69/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(65/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 5120*a**(61/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(57/4)*b**4*x**16*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(53/4)*b**5*x**20*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 256*a**(49/4)*b**6*x**24*(1 + b*x**4/a)**(1/4)*gamma(17/4)) + 7215*a**12*b**2*x**9*gamma(1/4)/(256*a**(73/4)*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(69/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(65/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 5120*a**(61/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(57/4)*b**4*x**16*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(53/4)*b**5*x**20*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 256*a**(49/4)*b**6*x**24*(1 + b*x**4/a)**(1/4)*gamma(17/4)) + 8925*a**11*b**3*x**13*gamma(1/4)/(256*a**(73/4)*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(69/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(65/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 5120*a**(61/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(57/4)*b**4*x**16*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(53/4)*b**5*x**20*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 256*a**(49/4)*b**6*x**24*(1 + b*x**4/a)**(1/4)*gamma(17/4)) + 6300*a**10*b**4*x**17*gamma(1/4)/(256*a**(73/4)*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(69/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(65/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 5120*a**(61/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(57/4)*b**4*x**16*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(53/4)*b**5*x**20*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 256*a**(49/4)*b**6*x**24*(1 + b*x**4/a)**(1/4)*gamma(17/4)) + 2400*a**9*b**5*x**21*gamma(1/4)/(256*a**(73/4)*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(69/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(65/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 5120*a**(61/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(57/4)*b**4*x**16*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(53/4)*b**5*x**20*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 256*a**(49/4)*b**6*x**24*(1 + b*x**4/a)**(1/4)*gamma(17/4)) + 384*a**8*b**6*x**25*gamma(1/4)/(256*a**(73/4)*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(69/4)*b*x**4*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(65/4)*b**2*x**8*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 5120*a**(61/4)*b**3*x**12*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 3840*a**(57/4)*b**4*x**16*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 1536*a**(53/4)*b**5*x**20*(1 + b*x**4/a)**(1/4)*gamma(17/4) + 256*a**(49/4)*b**6*x**24*(1 + b*x**4/a)**(1/4)*gamma(17/4))","B",0
1175,1,134,0,31.774584," ","integrate(x**19*(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{2048 a^{5} \sqrt[4]{a - b x^{4}}}{69615 b^{5}} - \frac{512 a^{4} x^{4} \sqrt[4]{a - b x^{4}}}{69615 b^{4}} - \frac{64 a^{3} x^{8} \sqrt[4]{a - b x^{4}}}{13923 b^{3}} - \frac{16 a^{2} x^{12} \sqrt[4]{a - b x^{4}}}{4641 b^{2}} - \frac{a x^{16} \sqrt[4]{a - b x^{4}}}{357 b} + \frac{x^{20} \sqrt[4]{a - b x^{4}}}{21} & \text{for}\: b \neq 0 \\\frac{\sqrt[4]{a} x^{20}}{20} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2048*a**5*(a - b*x**4)**(1/4)/(69615*b**5) - 512*a**4*x**4*(a - b*x**4)**(1/4)/(69615*b**4) - 64*a**3*x**8*(a - b*x**4)**(1/4)/(13923*b**3) - 16*a**2*x**12*(a - b*x**4)**(1/4)/(4641*b**2) - a*x**16*(a - b*x**4)**(1/4)/(357*b) + x**20*(a - b*x**4)**(1/4)/21, Ne(b, 0)), (a**(1/4)*x**20/20, True))","A",0
1176,1,110,0,13.329338," ","integrate(x**15*(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{128 a^{4} \sqrt[4]{a - b x^{4}}}{3315 b^{4}} - \frac{32 a^{3} x^{4} \sqrt[4]{a - b x^{4}}}{3315 b^{3}} - \frac{4 a^{2} x^{8} \sqrt[4]{a - b x^{4}}}{663 b^{2}} - \frac{a x^{12} \sqrt[4]{a - b x^{4}}}{221 b} + \frac{x^{16} \sqrt[4]{a - b x^{4}}}{17} & \text{for}\: b \neq 0 \\\frac{\sqrt[4]{a} x^{16}}{16} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-128*a**4*(a - b*x**4)**(1/4)/(3315*b**4) - 32*a**3*x**4*(a - b*x**4)**(1/4)/(3315*b**3) - 4*a**2*x**8*(a - b*x**4)**(1/4)/(663*b**2) - a*x**12*(a - b*x**4)**(1/4)/(221*b) + x**16*(a - b*x**4)**(1/4)/17, Ne(b, 0)), (a**(1/4)*x**16/16, True))","A",0
1177,1,87,0,6.247947," ","integrate(x**11*(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{32 a^{3} \sqrt[4]{a - b x^{4}}}{585 b^{3}} - \frac{8 a^{2} x^{4} \sqrt[4]{a - b x^{4}}}{585 b^{2}} - \frac{a x^{8} \sqrt[4]{a - b x^{4}}}{117 b} + \frac{x^{12} \sqrt[4]{a - b x^{4}}}{13} & \text{for}\: b \neq 0 \\\frac{\sqrt[4]{a} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*a**3*(a - b*x**4)**(1/4)/(585*b**3) - 8*a**2*x**4*(a - b*x**4)**(1/4)/(585*b**2) - a*x**8*(a - b*x**4)**(1/4)/(117*b) + x**12*(a - b*x**4)**(1/4)/13, Ne(b, 0)), (a**(1/4)*x**12/12, True))","A",0
1178,1,63,0,1.835005," ","integrate(x**7*(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{4 a^{2} \sqrt[4]{a - b x^{4}}}{45 b^{2}} - \frac{a x^{4} \sqrt[4]{a - b x^{4}}}{45 b} + \frac{x^{8} \sqrt[4]{a - b x^{4}}}{9} & \text{for}\: b \neq 0 \\\frac{\sqrt[4]{a} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**2*(a - b*x**4)**(1/4)/(45*b**2) - a*x**4*(a - b*x**4)**(1/4)/(45*b) + x**8*(a - b*x**4)**(1/4)/9, Ne(b, 0)), (a**(1/4)*x**8/8, True))","A",0
1179,1,39,0,0.689096," ","integrate(x**3*(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{a \sqrt[4]{a - b x^{4}}}{5 b} + \frac{x^{4} \sqrt[4]{a - b x^{4}}}{5} & \text{for}\: b \neq 0 \\\frac{\sqrt[4]{a} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*(a - b*x**4)**(1/4)/(5*b) + x**4*(a - b*x**4)**(1/4)/5, Ne(b, 0)), (a**(1/4)*x**4/4, True))","A",0
1180,1,44,0,1.519040," ","integrate((-b*x**4+a)**(1/4)/x,x)","- \frac{\sqrt[4]{b} x e^{\frac{i \pi}{4}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}"," ",0,"-b**(1/4)*x*exp(I*pi/4)*gamma(-1/4)*hyper((-1/4, -1/4), (3/4,), a/(b*x**4))/(4*gamma(3/4))","C",0
1181,1,42,0,1.953681," ","integrate((-b*x**4+a)**(1/4)/x**5,x)","\frac{\sqrt[4]{b} e^{- \frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{4 x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"b**(1/4)*exp(-3*I*pi/4)*gamma(3/4)*hyper((-1/4, 3/4), (7/4,), a/(b*x**4))/(4*x**3*gamma(7/4))","C",0
1182,1,42,0,2.086198," ","integrate((-b*x**4+a)**(1/4)/x**9,x)","- \frac{\sqrt[4]{b} e^{\frac{i \pi}{4}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{4 x^{7} \Gamma\left(\frac{11}{4}\right)}"," ",0,"-b**(1/4)*exp(I*pi/4)*gamma(7/4)*hyper((-1/4, 7/4), (11/4,), a/(b*x**4))/(4*x**7*gamma(11/4))","C",0
1183,1,31,0,1.944265," ","integrate(x**9*(-b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{10} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{10}"," ",0,"a**(1/4)*x**10*hyper((-1/4, 5/2), (7/2,), b*x**4*exp_polar(2*I*pi)/a)/10","C",0
1184,1,31,0,1.903861," ","integrate(x**5*(-b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{6} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{6}"," ",0,"a**(1/4)*x**6*hyper((-1/4, 3/2), (5/2,), b*x**4*exp_polar(2*I*pi)/a)/6","C",0
1185,1,31,0,1.289240," ","integrate(x*(-b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{2}"," ",0,"a**(1/4)*x**2*hyper((-1/4, 1/2), (3/2,), b*x**4*exp_polar(2*I*pi)/a)/2","C",0
1186,1,34,0,1.662326," ","integrate((-b*x**4+a)**(1/4)/x**3,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{2 x^{2}}"," ",0,"-a**(1/4)*hyper((-1/2, -1/4), (1/2,), b*x**4*exp_polar(2*I*pi)/a)/(2*x**2)","C",0
1187,1,36,0,1.848476," ","integrate((-b*x**4+a)**(1/4)/x**7,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{6 x^{6}}"," ",0,"-a**(1/4)*hyper((-3/2, -1/4), (-1/2,), b*x**4*exp_polar(2*I*pi)/a)/(6*x**6)","C",0
1188,1,36,0,2.388108," ","integrate((-b*x**4+a)**(1/4)/x**11,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{10 x^{10}}"," ",0,"-a**(1/4)*hyper((-5/2, -1/4), (-3/2,), b*x**4*exp_polar(2*I*pi)/a)/(10*x**10)","C",0
1189,1,41,0,3.081135," ","integrate(x**6*(-b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**(1/4)*x**7*gamma(7/4)*hyper((-1/4, 7/4), (11/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*gamma(11/4))","C",0
1190,1,41,0,1.853196," ","integrate(x**2*(-b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**(1/4)*x**3*gamma(3/4)*hyper((-1/4, 3/4), (7/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*gamma(7/4))","C",0
1191,1,42,0,1.858823," ","integrate((-b*x**4+a)**(1/4)/x**2,x)","\frac{\sqrt[4]{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"a**(1/4)*gamma(-1/4)*hyper((-1/4, -1/4), (3/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*x*gamma(3/4))","C",0
1192,1,158,0,1.307073," ","integrate((-b*x**4+a)**(1/4)/x**6,x)","\begin{cases} \frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{5}{4}\right)}{4 x^{4} \Gamma\left(- \frac{1}{4}\right)} - \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{5}{4}\right)}{4 a \Gamma\left(- \frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\\frac{\sqrt[4]{b} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{5}{4}\right)}{4 x^{4} \Gamma\left(- \frac{1}{4}\right)} - \frac{b^{\frac{5}{4}} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{5}{4}\right)}{4 a \Gamma\left(- \frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**(1/4)*(a/(b*x**4) - 1)**(1/4)*gamma(-5/4)/(4*x**4*gamma(-1/4)) - b**(5/4)*(a/(b*x**4) - 1)**(1/4)*gamma(-5/4)/(4*a*gamma(-1/4)), Abs(a/(b*x**4)) > 1), (b**(1/4)*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-5/4)/(4*x**4*gamma(-1/4)) - b**(5/4)*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-5/4)/(4*a*gamma(-1/4)), True))","B",0
1193,1,406,0,2.057792," ","integrate((-b*x**4+a)**(1/4)/x**10,x)","\begin{cases} - \frac{5 \sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{9}{4}\right)}{16 x^{8} \Gamma\left(- \frac{1}{4}\right)} + \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{9}{4}\right)}{16 a x^{4} \Gamma\left(- \frac{1}{4}\right)} + \frac{b^{\frac{9}{4}} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{9}{4}\right)}{4 a^{2} \Gamma\left(- \frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\\frac{5 a^{3} b^{\frac{5}{4}} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{x^{4} \left(- 16 a^{3} b x^{4} \Gamma\left(- \frac{1}{4}\right) + 16 a^{2} b^{2} x^{8} \Gamma\left(- \frac{1}{4}\right)\right)} - \frac{6 a^{2} b^{\frac{9}{4}} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{- 16 a^{3} b x^{4} \Gamma\left(- \frac{1}{4}\right) + 16 a^{2} b^{2} x^{8} \Gamma\left(- \frac{1}{4}\right)} - \frac{3 a b^{\frac{13}{4}} x^{4} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{- 16 a^{3} b x^{4} \Gamma\left(- \frac{1}{4}\right) + 16 a^{2} b^{2} x^{8} \Gamma\left(- \frac{1}{4}\right)} + \frac{4 b^{\frac{17}{4}} x^{8} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{- 16 a^{3} b x^{4} \Gamma\left(- \frac{1}{4}\right) + 16 a^{2} b^{2} x^{8} \Gamma\left(- \frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*b**(1/4)*(a/(b*x**4) - 1)**(1/4)*gamma(-9/4)/(16*x**8*gamma(-1/4)) + b**(5/4)*(a/(b*x**4) - 1)**(1/4)*gamma(-9/4)/(16*a*x**4*gamma(-1/4)) + b**(9/4)*(a/(b*x**4) - 1)**(1/4)*gamma(-9/4)/(4*a**2*gamma(-1/4)), Abs(a/(b*x**4)) > 1), (5*a**3*b**(5/4)*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-9/4)/(x**4*(-16*a**3*b*x**4*gamma(-1/4) + 16*a**2*b**2*x**8*gamma(-1/4))) - 6*a**2*b**(9/4)*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-9/4)/(-16*a**3*b*x**4*gamma(-1/4) + 16*a**2*b**2*x**8*gamma(-1/4)) - 3*a*b**(13/4)*x**4*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-9/4)/(-16*a**3*b*x**4*gamma(-1/4) + 16*a**2*b**2*x**8*gamma(-1/4)) + 4*b**(17/4)*x**8*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-9/4)/(-16*a**3*b*x**4*gamma(-1/4) + 16*a**2*b**2*x**8*gamma(-1/4)), True))","B",0
1194,1,1090,0,4.230734," ","integrate((-b*x**4+a)**(1/4)/x**14,x)","\begin{cases} \frac{45 a^{5} b^{\frac{17}{4}} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} - \frac{95 a^{4} b^{\frac{21}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} + \frac{47 a^{3} b^{\frac{25}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} - \frac{21 a^{2} b^{\frac{29}{4}} x^{12} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} + \frac{56 a b^{\frac{33}{4}} x^{16} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} - \frac{32 b^{\frac{37}{4}} x^{20} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\\frac{45 a^{5} b^{\frac{17}{4}} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} - \frac{95 a^{4} b^{\frac{21}{4}} x^{4} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} + \frac{47 a^{3} b^{\frac{25}{4}} x^{8} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} - \frac{21 a^{2} b^{\frac{29}{4}} x^{12} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} + \frac{56 a b^{\frac{33}{4}} x^{16} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} - \frac{32 b^{\frac{37}{4}} x^{20} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{64 a^{5} b^{4} x^{12} \Gamma\left(- \frac{1}{4}\right) - 128 a^{4} b^{5} x^{16} \Gamma\left(- \frac{1}{4}\right) + 64 a^{3} b^{6} x^{20} \Gamma\left(- \frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((45*a**5*b**(17/4)*(a/(b*x**4) - 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) - 95*a**4*b**(21/4)*x**4*(a/(b*x**4) - 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) + 47*a**3*b**(25/4)*x**8*(a/(b*x**4) - 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) - 21*a**2*b**(29/4)*x**12*(a/(b*x**4) - 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) + 56*a*b**(33/4)*x**16*(a/(b*x**4) - 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) - 32*b**(37/4)*x**20*(a/(b*x**4) - 1)**(1/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)), Abs(a/(b*x**4)) > 1), (45*a**5*b**(17/4)*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) - 95*a**4*b**(21/4)*x**4*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) + 47*a**3*b**(25/4)*x**8*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) - 21*a**2*b**(29/4)*x**12*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) + 56*a*b**(33/4)*x**16*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)) - 32*b**(37/4)*x**20*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-13/4)/(64*a**5*b**4*x**12*gamma(-1/4) - 128*a**4*b**5*x**16*gamma(-1/4) + 64*a**3*b**6*x**20*gamma(-1/4)), True))","B",0
1195,1,1756,0,4.921497," ","integrate((-b*x**4+a)**(1/4)/x**18,x)","\begin{cases} \frac{585 a^{7} b^{\frac{37}{4}} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{1800 a^{6} b^{\frac{41}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} + \frac{1830 a^{5} b^{\frac{45}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{636 a^{4} b^{\frac{49}{4}} x^{12} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{231 a^{3} b^{\frac{53}{4}} x^{16} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} + \frac{924 a^{2} b^{\frac{57}{4}} x^{20} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{1056 a b^{\frac{61}{4}} x^{24} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} + \frac{384 b^{\frac{65}{4}} x^{28} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\\frac{585 a^{7} b^{\frac{37}{4}} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{1800 a^{6} b^{\frac{41}{4}} x^{4} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} + \frac{1830 a^{5} b^{\frac{45}{4}} x^{8} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{636 a^{4} b^{\frac{49}{4}} x^{12} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{231 a^{3} b^{\frac{53}{4}} x^{16} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} + \frac{924 a^{2} b^{\frac{57}{4}} x^{20} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} - \frac{1056 a b^{\frac{61}{4}} x^{24} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} + \frac{384 b^{\frac{65}{4}} x^{28} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{17}{4}\right)}{- 256 a^{7} b^{9} x^{16} \Gamma\left(- \frac{1}{4}\right) + 768 a^{6} b^{10} x^{20} \Gamma\left(- \frac{1}{4}\right) - 768 a^{5} b^{11} x^{24} \Gamma\left(- \frac{1}{4}\right) + 256 a^{4} b^{12} x^{28} \Gamma\left(- \frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((585*a**7*b**(37/4)*(a/(b*x**4) - 1)**(1/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 1800*a**6*b**(41/4)*x**4*(a/(b*x**4) - 1)**(1/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) + 1830*a**5*b**(45/4)*x**8*(a/(b*x**4) - 1)**(1/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 636*a**4*b**(49/4)*x**12*(a/(b*x**4) - 1)**(1/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 231*a**3*b**(53/4)*x**16*(a/(b*x**4) - 1)**(1/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) + 924*a**2*b**(57/4)*x**20*(a/(b*x**4) - 1)**(1/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 1056*a*b**(61/4)*x**24*(a/(b*x**4) - 1)**(1/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) + 384*b**(65/4)*x**28*(a/(b*x**4) - 1)**(1/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)), Abs(a/(b*x**4)) > 1), (585*a**7*b**(37/4)*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 1800*a**6*b**(41/4)*x**4*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) + 1830*a**5*b**(45/4)*x**8*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 636*a**4*b**(49/4)*x**12*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 231*a**3*b**(53/4)*x**16*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) + 924*a**2*b**(57/4)*x**20*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) - 1056*a*b**(61/4)*x**24*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)) + 384*b**(65/4)*x**28*(-a/(b*x**4) + 1)**(1/4)*exp(I*pi/4)*gamma(-17/4)/(-256*a**7*b**9*x**16*gamma(-1/4) + 768*a**6*b**10*x**20*gamma(-1/4) - 768*a**5*b**11*x**24*gamma(-1/4) + 256*a**4*b**12*x**28*gamma(-1/4)), True))","B",0
1196,1,41,0,2.250889," ","integrate(x**12*(-b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{13} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{17}{4}\right)}"," ",0,"a**(1/4)*x**13*gamma(13/4)*hyper((-1/4, 13/4), (17/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*gamma(17/4))","C",0
1197,1,41,0,2.045522," ","integrate(x**8*(-b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)}"," ",0,"a**(1/4)*x**9*gamma(9/4)*hyper((-1/4, 9/4), (13/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*gamma(13/4))","C",0
1198,1,41,0,1.368587," ","integrate(x**4*(-b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**(1/4)*x**5*gamma(5/4)*hyper((-1/4, 5/4), (9/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*gamma(9/4))","C",0
1199,1,39,0,0.970339," ","integrate((-b*x**4+a)**(1/4),x)","\frac{\sqrt[4]{a} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**(1/4)*x*gamma(1/4)*hyper((-1/4, 1/4), (5/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*gamma(5/4))","C",0
1200,1,34,0,1.994926," ","integrate((-b*x**4+a)**(1/4)/x**4,x)","- \frac{i \sqrt[4]{b} e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{2 x^{2}}"," ",0,"-I*b**(1/4)*exp(-I*pi/4)*hyper((-1/4, 1/2), (3/2,), a/(b*x**4))/(2*x**2)","C",0
1201,1,34,0,2.391992," ","integrate((-b*x**4+a)**(1/4)/x**8,x)","\frac{i \sqrt[4]{b} e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{6 x^{6}}"," ",0,"I*b**(1/4)*exp(3*I*pi/4)*hyper((-1/4, 3/2), (5/2,), a/(b*x**4))/(6*x**6)","C",0
1202,1,34,0,1.876707," ","integrate((-b*x**4+a)**(1/4)/x**12,x)","- \frac{i \sqrt[4]{b} e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{10 x^{10}}"," ",0,"-I*b**(1/4)*exp(-I*pi/4)*hyper((-1/4, 5/2), (7/2,), a/(b*x**4))/(10*x**10)","C",0
1203,1,34,0,3.132687," ","integrate((-b*x**4+a)**(1/4)/x**16,x)","\frac{i \sqrt[4]{b} e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{14 x^{14}}"," ",0,"I*b**(1/4)*exp(3*I*pi/4)*hyper((-1/4, 7/2), (9/2,), a/(b*x**4))/(14*x**14)","C",0
1204,1,117,0,16.937568," ","integrate(x**19/(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{2048 a^{4} \left(a - b x^{4}\right)^{\frac{3}{4}}}{21945 b^{5}} - \frac{512 a^{3} x^{4} \left(a - b x^{4}\right)^{\frac{3}{4}}}{7315 b^{4}} - \frac{64 a^{2} x^{8} \left(a - b x^{4}\right)^{\frac{3}{4}}}{1045 b^{3}} - \frac{16 a x^{12} \left(a - b x^{4}\right)^{\frac{3}{4}}}{285 b^{2}} - \frac{x^{16} \left(a - b x^{4}\right)^{\frac{3}{4}}}{19 b} & \text{for}\: b \neq 0 \\\frac{x^{20}}{20 \sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2048*a**4*(a - b*x**4)**(3/4)/(21945*b**5) - 512*a**3*x**4*(a - b*x**4)**(3/4)/(7315*b**4) - 64*a**2*x**8*(a - b*x**4)**(3/4)/(1045*b**3) - 16*a*x**12*(a - b*x**4)**(3/4)/(285*b**2) - x**16*(a - b*x**4)**(3/4)/(19*b), Ne(b, 0)), (x**20/(20*a**(1/4)), True))","A",0
1205,1,94,0,9.896510," ","integrate(x**15/(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{128 a^{3} \left(a - b x^{4}\right)^{\frac{3}{4}}}{1155 b^{4}} - \frac{32 a^{2} x^{4} \left(a - b x^{4}\right)^{\frac{3}{4}}}{385 b^{3}} - \frac{4 a x^{8} \left(a - b x^{4}\right)^{\frac{3}{4}}}{55 b^{2}} - \frac{x^{12} \left(a - b x^{4}\right)^{\frac{3}{4}}}{15 b} & \text{for}\: b \neq 0 \\\frac{x^{16}}{16 \sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-128*a**3*(a - b*x**4)**(3/4)/(1155*b**4) - 32*a**2*x**4*(a - b*x**4)**(3/4)/(385*b**3) - 4*a*x**8*(a - b*x**4)**(3/4)/(55*b**2) - x**12*(a - b*x**4)**(3/4)/(15*b), Ne(b, 0)), (x**16/(16*a**(1/4)), True))","A",0
1206,1,70,0,4.229268," ","integrate(x**11/(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{32 a^{2} \left(a - b x^{4}\right)^{\frac{3}{4}}}{231 b^{3}} - \frac{8 a x^{4} \left(a - b x^{4}\right)^{\frac{3}{4}}}{77 b^{2}} - \frac{x^{8} \left(a - b x^{4}\right)^{\frac{3}{4}}}{11 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 \sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*a**2*(a - b*x**4)**(3/4)/(231*b**3) - 8*a*x**4*(a - b*x**4)**(3/4)/(77*b**2) - x**8*(a - b*x**4)**(3/4)/(11*b), Ne(b, 0)), (x**12/(12*a**(1/4)), True))","A",0
1207,1,46,0,1.874761," ","integrate(x**7/(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{4 a \left(a - b x^{4}\right)^{\frac{3}{4}}}{21 b^{2}} - \frac{x^{4} \left(a - b x^{4}\right)^{\frac{3}{4}}}{7 b} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 \sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a*(a - b*x**4)**(3/4)/(21*b**2) - x**4*(a - b*x**4)**(3/4)/(7*b), Ne(b, 0)), (x**8/(8*a**(1/4)), True))","A",0
1208,1,24,0,0.578884," ","integrate(x**3/(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{\left(a - b x^{4}\right)^{\frac{3}{4}}}{3 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(a - b*x**4)**(3/4)/(3*b), Ne(b, 0)), (x**4/(4*a**(1/4)), True))","A",0
1209,1,39,0,1.334044," ","integrate(1/x/(-b*x**4+a)**(1/4),x)","- \frac{e^{- \frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{4 \sqrt[4]{b} x \Gamma\left(\frac{5}{4}\right)}"," ",0,"-exp(-I*pi/4)*gamma(1/4)*hyper((1/4, 1/4), (5/4,), a/(b*x**4))/(4*b**(1/4)*x*gamma(5/4))","C",0
1210,1,41,0,1.723288," ","integrate(1/x**5/(-b*x**4+a)**(1/4),x)","\frac{e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{4 \sqrt[4]{b} x^{5} \Gamma\left(\frac{9}{4}\right)}"," ",0,"exp(3*I*pi/4)*gamma(5/4)*hyper((1/4, 5/4), (9/4,), a/(b*x**4))/(4*b**(1/4)*x**5*gamma(9/4))","C",0
1211,1,41,0,2.118711," ","integrate(1/x**9/(-b*x**4+a)**(1/4),x)","- \frac{e^{- \frac{i \pi}{4}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{4 \sqrt[4]{b} x^{9} \Gamma\left(\frac{13}{4}\right)}"," ",0,"-exp(-I*pi/4)*gamma(9/4)*hyper((1/4, 9/4), (13/4,), a/(b*x**4))/(4*b**(1/4)*x**9*gamma(13/4))","C",0
1212,1,29,0,1.676730," ","integrate(x**13/(-b*x**4+a)**(1/4),x)","\frac{x^{14} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{14 \sqrt[4]{a}}"," ",0,"x**14*hyper((1/4, 7/2), (9/2,), b*x**4*exp_polar(2*I*pi)/a)/(14*a**(1/4))","C",0
1213,1,29,0,1.538019," ","integrate(x**9/(-b*x**4+a)**(1/4),x)","\frac{x^{10} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{10 \sqrt[4]{a}}"," ",0,"x**10*hyper((1/4, 5/2), (7/2,), b*x**4*exp_polar(2*I*pi)/a)/(10*a**(1/4))","C",0
1214,1,29,0,1.700128," ","integrate(x**5/(-b*x**4+a)**(1/4),x)","\frac{x^{6} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{6 \sqrt[4]{a}}"," ",0,"x**6*hyper((1/4, 3/2), (5/2,), b*x**4*exp_polar(2*I*pi)/a)/(6*a**(1/4))","C",0
1215,1,29,0,1.280281," ","integrate(x/(-b*x**4+a)**(1/4),x)","\frac{x^{2} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{2 \sqrt[4]{a}}"," ",0,"x**2*hyper((1/4, 1/2), (3/2,), b*x**4*exp_polar(2*I*pi)/a)/(2*a**(1/4))","C",0
1216,1,32,0,1.412113," ","integrate(1/x**3/(-b*x**4+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{2 \sqrt[4]{a} x^{2}}"," ",0,"-hyper((-1/2, 1/4), (1/2,), b*x**4*exp_polar(2*I*pi)/a)/(2*a**(1/4)*x**2)","C",0
1217,1,34,0,1.905701," ","integrate(1/x**7/(-b*x**4+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{6 \sqrt[4]{a} x^{6}}"," ",0,"-hyper((-3/2, 1/4), (-1/2,), b*x**4*exp_polar(2*I*pi)/a)/(6*a**(1/4)*x**6)","C",0
1218,1,34,0,4.300420," ","integrate(1/x**11/(-b*x**4+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{10 \sqrt[4]{a} x^{10}}"," ",0,"-hyper((-5/2, 1/4), (-3/2,), b*x**4*exp_polar(2*I*pi)/a)/(10*a**(1/4)*x**10)","C",0
1219,1,39,0,2.295831," ","integrate(x**8/(-b*x**4+a)**(1/4),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((1/4, 9/4), (13/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(1/4)*gamma(13/4))","C",0
1220,1,39,0,1.369278," ","integrate(x**4/(-b*x**4+a)**(1/4),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((1/4, 5/4), (9/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(1/4)*gamma(9/4))","C",0
1221,1,37,0,1.577664," ","integrate(1/(-b*x**4+a)**(1/4),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 1/4), (5/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(1/4)*gamma(5/4))","C",0
1222,1,78,0,1.552707," ","integrate(1/x**4/(-b*x**4+a)**(1/4),x)","\begin{cases} \frac{b^{\frac{3}{4}} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{3}{4}\right)}{4 a \Gamma\left(\frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{b^{\frac{3}{4}} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{3}{4}\right)}{4 a \Gamma\left(\frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**(3/4)*(a/(b*x**4) - 1)**(3/4)*gamma(-3/4)/(4*a*gamma(1/4)), Abs(a/(b*x**4)) > 1), (-b**(3/4)*(-a/(b*x**4) + 1)**(3/4)*exp(-I*pi/4)*gamma(-3/4)/(4*a*gamma(1/4)), True))","A",0
1223,1,303,0,1.997102," ","integrate(1/x**8/(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{3 b^{\frac{3}{4}} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{16 a x^{4} \Gamma\left(\frac{1}{4}\right)} - \frac{b^{\frac{7}{4}} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{4 a^{2} \Gamma\left(\frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{3 a^{2} b^{\frac{7}{4}} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{- 16 a^{3} b x^{4} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 16 a^{2} b^{2} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{a b^{\frac{11}{4}} x^{4} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{- 16 a^{3} b x^{4} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 16 a^{2} b^{2} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{4 b^{\frac{15}{4}} x^{8} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{- 16 a^{3} b x^{4} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 16 a^{2} b^{2} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*b**(3/4)*(a/(b*x**4) - 1)**(3/4)*gamma(-7/4)/(16*a*x**4*gamma(1/4)) - b**(7/4)*(a/(b*x**4) - 1)**(3/4)*gamma(-7/4)/(4*a**2*gamma(1/4)), Abs(a/(b*x**4)) > 1), (-3*a**2*b**(7/4)*(-a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(-16*a**3*b*x**4*exp(I*pi/4)*gamma(1/4) + 16*a**2*b**2*x**8*exp(I*pi/4)*gamma(1/4)) - a*b**(11/4)*x**4*(-a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(-16*a**3*b*x**4*exp(I*pi/4)*gamma(1/4) + 16*a**2*b**2*x**8*exp(I*pi/4)*gamma(1/4)) + 4*b**(15/4)*x**8*(-a/(b*x**4) + 1)**(3/4)*gamma(-7/4)/(-16*a**3*b*x**4*exp(I*pi/4)*gamma(1/4) + 16*a**2*b**2*x**8*exp(I*pi/4)*gamma(1/4)), True))","A",0
1224,1,1068,0,3.663514," ","integrate(1/x**12/(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{21 a^{4} b^{\frac{19}{4}} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{18 a^{3} b^{\frac{23}{4}} x^{4} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{5 a^{2} b^{\frac{27}{4}} x^{8} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{40 a b^{\frac{31}{4}} x^{12} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{32 b^{\frac{35}{4}} x^{16} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{21 a^{4} b^{\frac{19}{4}} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{18 a^{3} b^{\frac{23}{4}} x^{4} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{5 a^{2} b^{\frac{27}{4}} x^{8} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{40 a b^{\frac{31}{4}} x^{12} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{32 b^{\frac{35}{4}} x^{16} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{11}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-21*a**4*b**(19/4)*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-11/4)/(64*a**5*b**4*x**8*exp(I*pi/4)*gamma(1/4) - 128*a**4*b**5*x**12*exp(I*pi/4)*gamma(1/4) + 64*a**3*b**6*x**16*exp(I*pi/4)*gamma(1/4)) + 18*a**3*b**(23/4)*x**4*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-11/4)/(64*a**5*b**4*x**8*exp(I*pi/4)*gamma(1/4) - 128*a**4*b**5*x**12*exp(I*pi/4)*gamma(1/4) + 64*a**3*b**6*x**16*exp(I*pi/4)*gamma(1/4)) - 5*a**2*b**(27/4)*x**8*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-11/4)/(64*a**5*b**4*x**8*exp(I*pi/4)*gamma(1/4) - 128*a**4*b**5*x**12*exp(I*pi/4)*gamma(1/4) + 64*a**3*b**6*x**16*exp(I*pi/4)*gamma(1/4)) + 40*a*b**(31/4)*x**12*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-11/4)/(64*a**5*b**4*x**8*exp(I*pi/4)*gamma(1/4) - 128*a**4*b**5*x**12*exp(I*pi/4)*gamma(1/4) + 64*a**3*b**6*x**16*exp(I*pi/4)*gamma(1/4)) - 32*b**(35/4)*x**16*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-11/4)/(64*a**5*b**4*x**8*exp(I*pi/4)*gamma(1/4) - 128*a**4*b**5*x**12*exp(I*pi/4)*gamma(1/4) + 64*a**3*b**6*x**16*exp(I*pi/4)*gamma(1/4)), Abs(a/(b*x**4)) > 1), (-21*a**4*b**(19/4)*(-a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(64*a**5*b**4*x**8*exp(I*pi/4)*gamma(1/4) - 128*a**4*b**5*x**12*exp(I*pi/4)*gamma(1/4) + 64*a**3*b**6*x**16*exp(I*pi/4)*gamma(1/4)) + 18*a**3*b**(23/4)*x**4*(-a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(64*a**5*b**4*x**8*exp(I*pi/4)*gamma(1/4) - 128*a**4*b**5*x**12*exp(I*pi/4)*gamma(1/4) + 64*a**3*b**6*x**16*exp(I*pi/4)*gamma(1/4)) - 5*a**2*b**(27/4)*x**8*(-a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(64*a**5*b**4*x**8*exp(I*pi/4)*gamma(1/4) - 128*a**4*b**5*x**12*exp(I*pi/4)*gamma(1/4) + 64*a**3*b**6*x**16*exp(I*pi/4)*gamma(1/4)) + 40*a*b**(31/4)*x**12*(-a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(64*a**5*b**4*x**8*exp(I*pi/4)*gamma(1/4) - 128*a**4*b**5*x**12*exp(I*pi/4)*gamma(1/4) + 64*a**3*b**6*x**16*exp(I*pi/4)*gamma(1/4)) - 32*b**(35/4)*x**16*(-a/(b*x**4) + 1)**(3/4)*gamma(-11/4)/(64*a**5*b**4*x**8*exp(I*pi/4)*gamma(1/4) - 128*a**4*b**5*x**12*exp(I*pi/4)*gamma(1/4) + 64*a**3*b**6*x**16*exp(I*pi/4)*gamma(1/4)), True))","C",0
1225,1,1821,0,6.840415," ","integrate(1/x**16/(-b*x**4+a)**(1/4),x)","\begin{cases} \frac{231 a^{6} b^{\frac{39}{4}} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{441 a^{5} b^{\frac{43}{4}} x^{4} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{225 a^{4} b^{\frac{47}{4}} x^{8} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{45 a^{3} b^{\frac{51}{4}} x^{12} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{540 a^{2} b^{\frac{55}{4}} x^{16} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{864 a b^{\frac{59}{4}} x^{20} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{384 b^{\frac{63}{4}} x^{24} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{231 a^{6} b^{\frac{39}{4}} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{441 a^{5} b^{\frac{43}{4}} x^{4} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{225 a^{4} b^{\frac{47}{4}} x^{8} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{45 a^{3} b^{\frac{51}{4}} x^{12} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{540 a^{2} b^{\frac{55}{4}} x^{16} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{864 a b^{\frac{59}{4}} x^{20} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{384 b^{\frac{63}{4}} x^{24} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{15}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((231*a**6*b**(39/4)*(a/(b*x**4) - 1)**(3/4)*exp(I*pi/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) - 441*a**5*b**(43/4)*x**4*(a/(b*x**4) - 1)**(3/4)*exp(I*pi/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) + 225*a**4*b**(47/4)*x**8*(a/(b*x**4) - 1)**(3/4)*exp(I*pi/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) + 45*a**3*b**(51/4)*x**12*(a/(b*x**4) - 1)**(3/4)*exp(I*pi/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) - 540*a**2*b**(55/4)*x**16*(a/(b*x**4) - 1)**(3/4)*exp(I*pi/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) + 864*a*b**(59/4)*x**20*(a/(b*x**4) - 1)**(3/4)*exp(I*pi/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) - 384*b**(63/4)*x**24*(a/(b*x**4) - 1)**(3/4)*exp(I*pi/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)), Abs(a/(b*x**4)) > 1), (-231*a**6*b**(39/4)*(-a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) + 441*a**5*b**(43/4)*x**4*(-a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) - 225*a**4*b**(47/4)*x**8*(-a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) - 45*a**3*b**(51/4)*x**12*(-a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) + 540*a**2*b**(55/4)*x**16*(-a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) - 864*a*b**(59/4)*x**20*(-a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)) + 384*b**(63/4)*x**24*(-a/(b*x**4) + 1)**(3/4)*gamma(-15/4)/(-256*a**7*b**9*x**12*exp(I*pi/4)*gamma(1/4) + 768*a**6*b**10*x**16*exp(I*pi/4)*gamma(1/4) - 768*a**5*b**11*x**20*exp(I*pi/4)*gamma(1/4) + 256*a**4*b**12*x**24*exp(I*pi/4)*gamma(1/4)), True))","C",0
1226,1,2788,0,9.876452," ","integrate(1/x**20/(-b*x**4+a)**(1/4),x)","\begin{cases} - \frac{3465 a^{8} b^{\frac{67}{4}} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{10164 a^{7} b^{\frac{71}{4}} x^{4} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{10038 a^{6} b^{\frac{75}{4}} x^{8} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{3204 a^{5} b^{\frac{79}{4}} x^{12} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{585 a^{4} b^{\frac{83}{4}} x^{16} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{9360 a^{3} b^{\frac{87}{4}} x^{20} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{22464 a^{2} b^{\frac{91}{4}} x^{24} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{19968 a b^{\frac{95}{4}} x^{28} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{6144 b^{\frac{99}{4}} x^{32} \left(\frac{a}{b x^{4}} - 1\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{3465 a^{8} b^{\frac{67}{4}} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{10164 a^{7} b^{\frac{71}{4}} x^{4} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{10038 a^{6} b^{\frac{75}{4}} x^{8} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{3204 a^{5} b^{\frac{79}{4}} x^{12} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{585 a^{4} b^{\frac{83}{4}} x^{16} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{9360 a^{3} b^{\frac{87}{4}} x^{20} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{22464 a^{2} b^{\frac{91}{4}} x^{24} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{19968 a b^{\frac{95}{4}} x^{28} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{6144 b^{\frac{99}{4}} x^{32} \left(- \frac{a}{b x^{4}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{19}{4}\right)}{1024 a^{9} b^{16} x^{16} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{8} b^{17} x^{20} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 6144 a^{7} b^{18} x^{24} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) - 4096 a^{6} b^{19} x^{28} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 1024 a^{5} b^{20} x^{32} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3465*a**8*b**(67/4)*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) + 10164*a**7*b**(71/4)*x**4*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) - 10038*a**6*b**(75/4)*x**8*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) + 3204*a**5*b**(79/4)*x**12*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) - 585*a**4*b**(83/4)*x**16*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) + 9360*a**3*b**(87/4)*x**20*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) - 22464*a**2*b**(91/4)*x**24*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) + 19968*a*b**(95/4)*x**28*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) - 6144*b**(99/4)*x**32*(a/(b*x**4) - 1)**(3/4)*exp(-3*I*pi/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)), Abs(a/(b*x**4)) > 1), (-3465*a**8*b**(67/4)*(-a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) + 10164*a**7*b**(71/4)*x**4*(-a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) - 10038*a**6*b**(75/4)*x**8*(-a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) + 3204*a**5*b**(79/4)*x**12*(-a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) - 585*a**4*b**(83/4)*x**16*(-a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) + 9360*a**3*b**(87/4)*x**20*(-a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) - 22464*a**2*b**(91/4)*x**24*(-a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) + 19968*a*b**(95/4)*x**28*(-a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)) - 6144*b**(99/4)*x**32*(-a/(b*x**4) + 1)**(3/4)*gamma(-19/4)/(1024*a**9*b**16*x**16*exp(I*pi/4)*gamma(1/4) - 4096*a**8*b**17*x**20*exp(I*pi/4)*gamma(1/4) + 6144*a**7*b**18*x**24*exp(I*pi/4)*gamma(1/4) - 4096*a**6*b**19*x**28*exp(I*pi/4)*gamma(1/4) + 1024*a**5*b**20*x**32*exp(I*pi/4)*gamma(1/4)), True))","C",0
1227,1,39,0,2.455752," ","integrate(x**10/(-b*x**4+a)**(1/4),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((1/4, 11/4), (15/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(1/4)*gamma(15/4))","C",0
1228,1,39,0,1.855008," ","integrate(x**6/(-b*x**4+a)**(1/4),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((1/4, 7/4), (11/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(1/4)*gamma(11/4))","C",0
1229,1,39,0,1.333466," ","integrate(x**2/(-b*x**4+a)**(1/4),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt[4]{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((1/4, 3/4), (7/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(1/4)*gamma(7/4))","C",0
1230,1,31,0,1.657948," ","integrate(1/x**2/(-b*x**4+a)**(1/4),x)","\frac{i e^{\frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{2 \sqrt[4]{b} x^{2}}"," ",0,"I*exp(I*pi/4)*hyper((1/4, 1/2), (3/2,), a/(b*x**4))/(2*b**(1/4)*x**2)","C",0
1231,1,34,0,2.554554," ","integrate(1/x**6/(-b*x**4+a)**(1/4),x)","- \frac{i e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{6 \sqrt[4]{b} x^{6}}"," ",0,"-I*exp(-3*I*pi/4)*hyper((1/4, 3/2), (5/2,), a/(b*x**4))/(6*b**(1/4)*x**6)","C",0
1232,1,31,0,2.906856," ","integrate(1/x**10/(-b*x**4+a)**(1/4),x)","\frac{i e^{\frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{10 \sqrt[4]{b} x^{10}}"," ",0,"I*exp(I*pi/4)*hyper((1/4, 5/2), (7/2,), a/(b*x**4))/(10*b**(1/4)*x**10)","C",0
1233,1,34,0,5.427951," ","integrate(1/x**14/(-b*x**4+a)**(1/4),x)","- \frac{i e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{14 \sqrt[4]{b} x^{14}}"," ",0,"-I*exp(-3*I*pi/4)*hyper((1/4, 7/2), (9/2,), a/(b*x**4))/(14*b**(1/4)*x**14)","C",0
1234,1,117,0,26.214363," ","integrate(x**19/(-b*x**4+a)**(3/4),x)","\begin{cases} - \frac{2048 a^{4} \sqrt[4]{a - b x^{4}}}{3315 b^{5}} - \frac{512 a^{3} x^{4} \sqrt[4]{a - b x^{4}}}{3315 b^{4}} - \frac{64 a^{2} x^{8} \sqrt[4]{a - b x^{4}}}{663 b^{3}} - \frac{16 a x^{12} \sqrt[4]{a - b x^{4}}}{221 b^{2}} - \frac{x^{16} \sqrt[4]{a - b x^{4}}}{17 b} & \text{for}\: b \neq 0 \\\frac{x^{20}}{20 a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2048*a**4*(a - b*x**4)**(1/4)/(3315*b**5) - 512*a**3*x**4*(a - b*x**4)**(1/4)/(3315*b**4) - 64*a**2*x**8*(a - b*x**4)**(1/4)/(663*b**3) - 16*a*x**12*(a - b*x**4)**(1/4)/(221*b**2) - x**16*(a - b*x**4)**(1/4)/(17*b), Ne(b, 0)), (x**20/(20*a**(3/4)), True))","A",0
1235,1,94,0,12.756697," ","integrate(x**15/(-b*x**4+a)**(3/4),x)","\begin{cases} - \frac{128 a^{3} \sqrt[4]{a - b x^{4}}}{195 b^{4}} - \frac{32 a^{2} x^{4} \sqrt[4]{a - b x^{4}}}{195 b^{3}} - \frac{4 a x^{8} \sqrt[4]{a - b x^{4}}}{39 b^{2}} - \frac{x^{12} \sqrt[4]{a - b x^{4}}}{13 b} & \text{for}\: b \neq 0 \\\frac{x^{16}}{16 a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-128*a**3*(a - b*x**4)**(1/4)/(195*b**4) - 32*a**2*x**4*(a - b*x**4)**(1/4)/(195*b**3) - 4*a*x**8*(a - b*x**4)**(1/4)/(39*b**2) - x**12*(a - b*x**4)**(1/4)/(13*b), Ne(b, 0)), (x**16/(16*a**(3/4)), True))","A",0
1236,1,70,0,5.674124," ","integrate(x**11/(-b*x**4+a)**(3/4),x)","\begin{cases} - \frac{32 a^{2} \sqrt[4]{a - b x^{4}}}{45 b^{3}} - \frac{8 a x^{4} \sqrt[4]{a - b x^{4}}}{45 b^{2}} - \frac{x^{8} \sqrt[4]{a - b x^{4}}}{9 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*a**2*(a - b*x**4)**(1/4)/(45*b**3) - 8*a*x**4*(a - b*x**4)**(1/4)/(45*b**2) - x**8*(a - b*x**4)**(1/4)/(9*b), Ne(b, 0)), (x**12/(12*a**(3/4)), True))","A",0
1237,1,46,0,1.229252," ","integrate(x**7/(-b*x**4+a)**(3/4),x)","\begin{cases} - \frac{4 a \sqrt[4]{a - b x^{4}}}{5 b^{2}} - \frac{x^{4} \sqrt[4]{a - b x^{4}}}{5 b} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a*(a - b*x**4)**(1/4)/(5*b**2) - x**4*(a - b*x**4)**(1/4)/(5*b), Ne(b, 0)), (x**8/(8*a**(3/4)), True))","A",0
1238,1,22,0,0.823661," ","integrate(x**3/(-b*x**4+a)**(3/4),x)","\begin{cases} - \frac{\sqrt[4]{a - b x^{4}}}{b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(a - b*x**4)**(1/4)/b, Ne(b, 0)), (x**4/(4*a**(3/4)), True))","A",0
1239,1,42,0,2.394454," ","integrate(1/x/(-b*x**4+a)**(3/4),x)","- \frac{e^{- \frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{4 b^{\frac{3}{4}} x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-exp(-3*I*pi/4)*gamma(3/4)*hyper((3/4, 3/4), (7/4,), a/(b*x**4))/(4*b**(3/4)*x**3*gamma(7/4))","C",0
1240,1,39,0,2.307009," ","integrate(1/x**5/(-b*x**4+a)**(3/4),x)","\frac{e^{\frac{i \pi}{4}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{4 b^{\frac{3}{4}} x^{7} \Gamma\left(\frac{11}{4}\right)}"," ",0,"exp(I*pi/4)*gamma(7/4)*hyper((3/4, 7/4), (11/4,), a/(b*x**4))/(4*b**(3/4)*x**7*gamma(11/4))","C",0
1241,1,42,0,3.257455," ","integrate(1/x**9/(-b*x**4+a)**(3/4),x)","- \frac{e^{- \frac{3 i \pi}{4}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{4 b^{\frac{3}{4}} x^{11} \Gamma\left(\frac{15}{4}\right)}"," ",0,"-exp(-3*I*pi/4)*gamma(11/4)*hyper((3/4, 11/4), (15/4,), a/(b*x**4))/(4*b**(3/4)*x**11*gamma(15/4))","C",0
1242,1,29,0,1.760847," ","integrate(x**13/(-b*x**4+a)**(3/4),x)","\frac{x^{14} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{14 a^{\frac{3}{4}}}"," ",0,"x**14*hyper((3/4, 7/2), (9/2,), b*x**4*exp_polar(2*I*pi)/a)/(14*a**(3/4))","C",0
1243,1,29,0,1.413530," ","integrate(x**9/(-b*x**4+a)**(3/4),x)","\frac{x^{10} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{10 a^{\frac{3}{4}}}"," ",0,"x**10*hyper((3/4, 5/2), (7/2,), b*x**4*exp_polar(2*I*pi)/a)/(10*a**(3/4))","C",0
1244,1,29,0,1.880453," ","integrate(x**5/(-b*x**4+a)**(3/4),x)","\frac{x^{6} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{6 a^{\frac{3}{4}}}"," ",0,"x**6*hyper((3/4, 3/2), (5/2,), b*x**4*exp_polar(2*I*pi)/a)/(6*a**(3/4))","C",0
1245,1,29,0,1.452172," ","integrate(x/(-b*x**4+a)**(3/4),x)","\frac{x^{2} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}}}"," ",0,"x**2*hyper((1/2, 3/4), (3/2,), b*x**4*exp_polar(2*I*pi)/a)/(2*a**(3/4))","C",0
1246,1,32,0,2.067287," ","integrate(1/x**3/(-b*x**4+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} x^{2}}"," ",0,"-hyper((-1/2, 3/4), (1/2,), b*x**4*exp_polar(2*I*pi)/a)/(2*a**(3/4)*x**2)","C",0
1247,1,34,0,2.770743," ","integrate(1/x**7/(-b*x**4+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{6 a^{\frac{3}{4}} x^{6}}"," ",0,"-hyper((-3/2, 3/4), (-1/2,), b*x**4*exp_polar(2*I*pi)/a)/(6*a**(3/4)*x**6)","C",0
1248,1,34,0,2.177586," ","integrate(1/x**11/(-b*x**4+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{10 a^{\frac{3}{4}} x^{10}}"," ",0,"-hyper((-5/2, 3/4), (-3/2,), b*x**4*exp_polar(2*I*pi)/a)/(10*a**(3/4)*x**10)","C",0
1249,1,39,0,1.771777," ","integrate(x**10/(-b*x**4+a)**(3/4),x)","\frac{x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{15}{4}\right)}"," ",0,"x**11*gamma(11/4)*hyper((3/4, 11/4), (15/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(3/4)*gamma(15/4))","C",0
1250,1,39,0,1.945901," ","integrate(x**6/(-b*x**4+a)**(3/4),x)","\frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**7*gamma(7/4)*hyper((3/4, 7/4), (11/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(3/4)*gamma(11/4))","C",0
1251,1,39,0,1.999712," ","integrate(x**2/(-b*x**4+a)**(3/4),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((3/4, 3/4), (7/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(3/4)*gamma(7/4))","C",0
1252,1,80,0,1.522924," ","integrate(1/x**2/(-b*x**4+a)**(3/4),x)","\begin{cases} \frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{1}{4}\right)}{4 a \Gamma\left(\frac{3}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{\sqrt[4]{b} \sqrt[4]{- \frac{a}{b x^{4}} + 1} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{1}{4}\right)}{4 a \Gamma\left(\frac{3}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**(1/4)*(a/(b*x**4) - 1)**(1/4)*gamma(-1/4)/(4*a*gamma(3/4)), Abs(a/(b*x**4)) > 1), (-b**(1/4)*(-a/(b*x**4) + 1)**(1/4)*exp(-3*I*pi/4)*gamma(-1/4)/(4*a*gamma(3/4)), True))","B",0
1253,1,311,0,2.353741," ","integrate(1/x**6/(-b*x**4+a)**(3/4),x)","\begin{cases} - \frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{5}{4}\right)}{16 a x^{4} \Gamma\left(\frac{3}{4}\right)} - \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{4}} - 1} \Gamma\left(- \frac{5}{4}\right)}{4 a^{2} \Gamma\left(\frac{3}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{a^{2} b^{\frac{5}{4}} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{5}{4}\right)}{- 16 a^{3} b x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 16 a^{2} b^{2} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{3 a b^{\frac{9}{4}} x^{4} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{5}{4}\right)}{- 16 a^{3} b x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 16 a^{2} b^{2} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{4 b^{\frac{13}{4}} x^{8} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{5}{4}\right)}{- 16 a^{3} b x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 16 a^{2} b^{2} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-b**(1/4)*(a/(b*x**4) - 1)**(1/4)*gamma(-5/4)/(16*a*x**4*gamma(3/4)) - b**(5/4)*(a/(b*x**4) - 1)**(1/4)*gamma(-5/4)/(4*a**2*gamma(3/4)), Abs(a/(b*x**4)) > 1), (-a**2*b**(5/4)*(-a/(b*x**4) + 1)**(1/4)*gamma(-5/4)/(-16*a**3*b*x**4*exp(3*I*pi/4)*gamma(3/4) + 16*a**2*b**2*x**8*exp(3*I*pi/4)*gamma(3/4)) - 3*a*b**(9/4)*x**4*(-a/(b*x**4) + 1)**(1/4)*gamma(-5/4)/(-16*a**3*b*x**4*exp(3*I*pi/4)*gamma(3/4) + 16*a**2*b**2*x**8*exp(3*I*pi/4)*gamma(3/4)) + 4*b**(13/4)*x**8*(-a/(b*x**4) + 1)**(1/4)*gamma(-5/4)/(-16*a**3*b*x**4*exp(3*I*pi/4)*gamma(3/4) + 16*a**2*b**2*x**8*exp(3*I*pi/4)*gamma(3/4)), True))","A",0
1254,1,1110,0,2.357004," ","integrate(1/x**10/(-b*x**4+a)**(3/4),x)","\begin{cases} - \frac{5 a^{4} b^{\frac{17}{4}} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{2 a^{3} b^{\frac{21}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{21 a^{2} b^{\frac{25}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{56 a b^{\frac{29}{4}} x^{12} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{32 b^{\frac{33}{4}} x^{16} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{5 a^{4} b^{\frac{17}{4}} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{2 a^{3} b^{\frac{21}{4}} x^{4} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{21 a^{2} b^{\frac{25}{4}} x^{8} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{56 a b^{\frac{29}{4}} x^{12} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{32 b^{\frac{33}{4}} x^{16} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{9}{4}\right)}{64 a^{5} b^{4} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 128 a^{4} b^{5} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 64 a^{3} b^{6} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*a**4*b**(17/4)*(a/(b*x**4) - 1)**(1/4)*exp(-I*pi/4)*gamma(-9/4)/(64*a**5*b**4*x**8*exp(3*I*pi/4)*gamma(3/4) - 128*a**4*b**5*x**12*exp(3*I*pi/4)*gamma(3/4) + 64*a**3*b**6*x**16*exp(3*I*pi/4)*gamma(3/4)) + 2*a**3*b**(21/4)*x**4*(a/(b*x**4) - 1)**(1/4)*exp(-I*pi/4)*gamma(-9/4)/(64*a**5*b**4*x**8*exp(3*I*pi/4)*gamma(3/4) - 128*a**4*b**5*x**12*exp(3*I*pi/4)*gamma(3/4) + 64*a**3*b**6*x**16*exp(3*I*pi/4)*gamma(3/4)) - 21*a**2*b**(25/4)*x**8*(a/(b*x**4) - 1)**(1/4)*exp(-I*pi/4)*gamma(-9/4)/(64*a**5*b**4*x**8*exp(3*I*pi/4)*gamma(3/4) - 128*a**4*b**5*x**12*exp(3*I*pi/4)*gamma(3/4) + 64*a**3*b**6*x**16*exp(3*I*pi/4)*gamma(3/4)) + 56*a*b**(29/4)*x**12*(a/(b*x**4) - 1)**(1/4)*exp(-I*pi/4)*gamma(-9/4)/(64*a**5*b**4*x**8*exp(3*I*pi/4)*gamma(3/4) - 128*a**4*b**5*x**12*exp(3*I*pi/4)*gamma(3/4) + 64*a**3*b**6*x**16*exp(3*I*pi/4)*gamma(3/4)) - 32*b**(33/4)*x**16*(a/(b*x**4) - 1)**(1/4)*exp(-I*pi/4)*gamma(-9/4)/(64*a**5*b**4*x**8*exp(3*I*pi/4)*gamma(3/4) - 128*a**4*b**5*x**12*exp(3*I*pi/4)*gamma(3/4) + 64*a**3*b**6*x**16*exp(3*I*pi/4)*gamma(3/4)), Abs(a/(b*x**4)) > 1), (-5*a**4*b**(17/4)*(-a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(64*a**5*b**4*x**8*exp(3*I*pi/4)*gamma(3/4) - 128*a**4*b**5*x**12*exp(3*I*pi/4)*gamma(3/4) + 64*a**3*b**6*x**16*exp(3*I*pi/4)*gamma(3/4)) + 2*a**3*b**(21/4)*x**4*(-a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(64*a**5*b**4*x**8*exp(3*I*pi/4)*gamma(3/4) - 128*a**4*b**5*x**12*exp(3*I*pi/4)*gamma(3/4) + 64*a**3*b**6*x**16*exp(3*I*pi/4)*gamma(3/4)) - 21*a**2*b**(25/4)*x**8*(-a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(64*a**5*b**4*x**8*exp(3*I*pi/4)*gamma(3/4) - 128*a**4*b**5*x**12*exp(3*I*pi/4)*gamma(3/4) + 64*a**3*b**6*x**16*exp(3*I*pi/4)*gamma(3/4)) + 56*a*b**(29/4)*x**12*(-a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(64*a**5*b**4*x**8*exp(3*I*pi/4)*gamma(3/4) - 128*a**4*b**5*x**12*exp(3*I*pi/4)*gamma(3/4) + 64*a**3*b**6*x**16*exp(3*I*pi/4)*gamma(3/4)) - 32*b**(33/4)*x**16*(-a/(b*x**4) + 1)**(1/4)*gamma(-9/4)/(64*a**5*b**4*x**8*exp(3*I*pi/4)*gamma(3/4) - 128*a**4*b**5*x**12*exp(3*I*pi/4)*gamma(3/4) + 64*a**3*b**6*x**16*exp(3*I*pi/4)*gamma(3/4)), True))","C",0
1255,1,1928,0,5.653979," ","integrate(1/x**14/(-b*x**4+a)**(3/4),x)","\begin{cases} \frac{45 a^{6} b^{\frac{37}{4}} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{\frac{3 i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{75 a^{5} b^{\frac{41}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{\frac{3 i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{51 a^{4} b^{\frac{45}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{\frac{3 i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{231 a^{3} b^{\frac{49}{4}} x^{12} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{\frac{3 i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{924 a^{2} b^{\frac{53}{4}} x^{16} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{\frac{3 i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{1056 a b^{\frac{57}{4}} x^{20} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{\frac{3 i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{384 b^{\frac{61}{4}} x^{24} \sqrt[4]{\frac{a}{b x^{4}} - 1} e^{\frac{3 i \pi}{4}} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{4}}}\right| > 1 \\- \frac{45 a^{6} b^{\frac{37}{4}} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{75 a^{5} b^{\frac{41}{4}} x^{4} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{51 a^{4} b^{\frac{45}{4}} x^{8} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{231 a^{3} b^{\frac{49}{4}} x^{12} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{924 a^{2} b^{\frac{53}{4}} x^{16} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{1056 a b^{\frac{57}{4}} x^{20} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{384 b^{\frac{61}{4}} x^{24} \sqrt[4]{- \frac{a}{b x^{4}} + 1} \Gamma\left(- \frac{13}{4}\right)}{- 256 a^{7} b^{9} x^{12} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 768 a^{6} b^{10} x^{16} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 768 a^{5} b^{11} x^{20} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 256 a^{4} b^{12} x^{24} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((45*a**6*b**(37/4)*(a/(b*x**4) - 1)**(1/4)*exp(3*I*pi/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) - 75*a**5*b**(41/4)*x**4*(a/(b*x**4) - 1)**(1/4)*exp(3*I*pi/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) + 51*a**4*b**(45/4)*x**8*(a/(b*x**4) - 1)**(1/4)*exp(3*I*pi/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) + 231*a**3*b**(49/4)*x**12*(a/(b*x**4) - 1)**(1/4)*exp(3*I*pi/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) - 924*a**2*b**(53/4)*x**16*(a/(b*x**4) - 1)**(1/4)*exp(3*I*pi/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) + 1056*a*b**(57/4)*x**20*(a/(b*x**4) - 1)**(1/4)*exp(3*I*pi/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) - 384*b**(61/4)*x**24*(a/(b*x**4) - 1)**(1/4)*exp(3*I*pi/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)), Abs(a/(b*x**4)) > 1), (-45*a**6*b**(37/4)*(-a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) + 75*a**5*b**(41/4)*x**4*(-a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) - 51*a**4*b**(45/4)*x**8*(-a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) - 231*a**3*b**(49/4)*x**12*(-a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) + 924*a**2*b**(53/4)*x**16*(-a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) - 1056*a*b**(57/4)*x**20*(-a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)) + 384*b**(61/4)*x**24*(-a/(b*x**4) + 1)**(1/4)*gamma(-13/4)/(-256*a**7*b**9*x**12*exp(3*I*pi/4)*gamma(3/4) + 768*a**6*b**10*x**16*exp(3*I*pi/4)*gamma(3/4) - 768*a**5*b**11*x**20*exp(3*I*pi/4)*gamma(3/4) + 256*a**4*b**12*x**24*exp(3*I*pi/4)*gamma(3/4)), True))","C",0
1256,1,39,0,2.673113," ","integrate(x**12/(-b*x**4+a)**(3/4),x)","\frac{x^{13} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{17}{4}\right)}"," ",0,"x**13*gamma(13/4)*hyper((3/4, 13/4), (17/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(3/4)*gamma(17/4))","C",0
1257,1,39,0,1.925184," ","integrate(x**8/(-b*x**4+a)**(3/4),x)","\frac{x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"x**9*gamma(9/4)*hyper((3/4, 9/4), (13/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(3/4)*gamma(13/4))","C",0
1258,1,39,0,1.562750," ","integrate(x**4/(-b*x**4+a)**(3/4),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((3/4, 5/4), (9/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(3/4)*gamma(9/4))","C",0
1259,1,37,0,1.571534," ","integrate(1/(-b*x**4+a)**(3/4),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 a^{\frac{3}{4}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 3/4), (5/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(3/4)*gamma(5/4))","C",0
1260,1,34,0,2.296842," ","integrate(1/x**4/(-b*x**4+a)**(3/4),x)","- \frac{i e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{6 b^{\frac{3}{4}} x^{6}}"," ",0,"-I*exp(3*I*pi/4)*hyper((3/4, 3/2), (5/2,), a/(b*x**4))/(6*b**(3/4)*x**6)","C",0
1261,1,31,0,2.606124," ","integrate(1/x**8/(-b*x**4+a)**(3/4),x)","\frac{i e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{10 b^{\frac{3}{4}} x^{10}}"," ",0,"I*exp(-I*pi/4)*hyper((3/4, 5/2), (7/2,), a/(b*x**4))/(10*b**(3/4)*x**10)","C",0
1262,1,34,0,2.935592," ","integrate(1/x**12/(-b*x**4+a)**(3/4),x)","- \frac{i e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{a}{b x^{4}}} \right)}}{14 b^{\frac{3}{4}} x^{14}}"," ",0,"-I*exp(3*I*pi/4)*hyper((3/4, 7/2), (9/2,), a/(b*x**4))/(14*b**(3/4)*x**14)","C",0
1263,1,39,0,2.273101," ","integrate(x**2/(-b*x**4+a)**(5/4),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 a^{\frac{5}{4}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((3/4, 5/4), (7/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*a**(5/4)*gamma(7/4))","C",0
1264,1,495,0,8.386527," ","integrate(x**7*(b*x**4+a)**p,x)","\begin{cases} \frac{a^{p} x^{8}}{8} & \text{for}\: b = 0 \\\frac{a \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + x \right)}}{4 a b^{2} + 4 b^{3} x^{4}} + \frac{a \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + x \right)}}{4 a b^{2} + 4 b^{3} x^{4}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x^{2} \right)}}{4 a b^{2} + 4 b^{3} x^{4}} + \frac{a}{4 a b^{2} + 4 b^{3} x^{4}} + \frac{b x^{4} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + x \right)}}{4 a b^{2} + 4 b^{3} x^{4}} + \frac{b x^{4} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + x \right)}}{4 a b^{2} + 4 b^{3} x^{4}} + \frac{b x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x^{2} \right)}}{4 a b^{2} + 4 b^{3} x^{4}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + x \right)}}{4 b^{2}} - \frac{a \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + x \right)}}{4 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x^{2} \right)}}{4 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{4}\right)^{p}}{4 b^{2} p^{2} + 12 b^{2} p + 8 b^{2}} + \frac{a b p x^{4} \left(a + b x^{4}\right)^{p}}{4 b^{2} p^{2} + 12 b^{2} p + 8 b^{2}} + \frac{b^{2} p x^{8} \left(a + b x^{4}\right)^{p}}{4 b^{2} p^{2} + 12 b^{2} p + 8 b^{2}} + \frac{b^{2} x^{8} \left(a + b x^{4}\right)^{p}}{4 b^{2} p^{2} + 12 b^{2} p + 8 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**p*x**8/8, Eq(b, 0)), (a*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + x)/(4*a*b**2 + 4*b**3*x**4) + a*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + x)/(4*a*b**2 + 4*b**3*x**4) + a*log(I*sqrt(a)*sqrt(1/b) + x**2)/(4*a*b**2 + 4*b**3*x**4) + a/(4*a*b**2 + 4*b**3*x**4) + b*x**4*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + x)/(4*a*b**2 + 4*b**3*x**4) + b*x**4*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + x)/(4*a*b**2 + 4*b**3*x**4) + b*x**4*log(I*sqrt(a)*sqrt(1/b) + x**2)/(4*a*b**2 + 4*b**3*x**4), Eq(p, -2)), (-a*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + x)/(4*b**2) - a*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + x)/(4*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x**2)/(4*b**2) + x**4/(4*b), Eq(p, -1)), (-a**2*(a + b*x**4)**p/(4*b**2*p**2 + 12*b**2*p + 8*b**2) + a*b*p*x**4*(a + b*x**4)**p/(4*b**2*p**2 + 12*b**2*p + 8*b**2) + b**2*p*x**8*(a + b*x**4)**p/(4*b**2*p**2 + 12*b**2*p + 8*b**2) + b**2*x**8*(a + b*x**4)**p/(4*b**2*p**2 + 12*b**2*p + 8*b**2), True))","A",0
1265,1,129,0,3.363468," ","integrate(x**3*(b*x**4+a)**p,x)","\begin{cases} \frac{x^{4}}{4 a} & \text{for}\: b = 0 \wedge p = -1 \\\frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + x \right)}}{4 b} + \frac{\log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + x \right)}}{4 b} + \frac{\log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x^{2} \right)}}{4 b} & \text{for}\: p = -1 \\\frac{a \left(a + b x^{4}\right)^{p}}{4 b p + 4 b} + \frac{b x^{4} \left(a + b x^{4}\right)^{p}}{4 b p + 4 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**4/(4*a), Eq(b, 0) & Eq(p, -1)), (a**p*x**4/4, Eq(b, 0)), (log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + x)/(4*b) + log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + x)/(4*b) + log(I*sqrt(a)*sqrt(1/b) + x**2)/(4*b), Eq(p, -1)), (a*(a + b*x**4)**p/(4*b*p + 4*b) + b*x**4*(a + b*x**4)**p/(4*b*p + 4*b), True))","A",0
1266,1,39,0,7.824736," ","integrate((b*x**4+a)**p/x,x)","- \frac{b^{p} x^{4 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{4}}} \right)}}{4 \Gamma\left(1 - p\right)}"," ",0,"-b**p*x**(4*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*x**4))/(4*gamma(1 - p))","C",0
1267,1,56,0,0.324408," ","integrate(x**24/(b*x**5+a),x)","\frac{a^{4} \log{\left(a + b x^{5} \right)}}{5 b^{5}} - \frac{a^{3} x^{5}}{5 b^{4}} + \frac{a^{2} x^{10}}{10 b^{3}} - \frac{a x^{15}}{15 b^{2}} + \frac{x^{20}}{20 b}"," ",0,"a**4*log(a + b*x**5)/(5*b**5) - a**3*x**5/(5*b**4) + a**2*x**10/(10*b**3) - a*x**15/(15*b**2) + x**20/(20*b)","A",0
1268,1,44,0,0.669163," ","integrate(x**19/(b*x**5+a),x)","- \frac{a^{3} \log{\left(a + b x^{5} \right)}}{5 b^{4}} + \frac{a^{2} x^{5}}{5 b^{3}} - \frac{a x^{10}}{10 b^{2}} + \frac{x^{15}}{15 b}"," ",0,"-a**3*log(a + b*x**5)/(5*b**4) + a**2*x**5/(5*b**3) - a*x**10/(10*b**2) + x**15/(15*b)","A",0
1269,1,32,0,0.598595," ","integrate(x**14/(b*x**5+a),x)","\frac{a^{2} \log{\left(a + b x^{5} \right)}}{5 b^{3}} - \frac{a x^{5}}{5 b^{2}} + \frac{x^{10}}{10 b}"," ",0,"a**2*log(a + b*x**5)/(5*b**3) - a*x**5/(5*b**2) + x**10/(10*b)","A",0
1270,1,20,0,0.411960," ","integrate(x**9/(b*x**5+a),x)","- \frac{a \log{\left(a + b x^{5} \right)}}{5 b^{2}} + \frac{x^{5}}{5 b}"," ",0,"-a*log(a + b*x**5)/(5*b**2) + x**5/(5*b)","A",0
1271,1,10,0,0.289850," ","integrate(x**4/(b*x**5+a),x)","\frac{\log{\left(a + b x^{5} \right)}}{5 b}"," ",0,"log(a + b*x**5)/(5*b)","A",0
1272,1,15,0,0.531947," ","integrate(1/x/(b*x**5+a),x)","\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{5} \right)}}{5 a}"," ",0,"log(x)/a - log(a/b + x**5)/(5*a)","A",0
1273,1,31,0,0.696511," ","integrate(1/x**6/(b*x**5+a),x)","- \frac{1}{5 a x^{5}} - \frac{b \log{\left(x \right)}}{a^{2}} + \frac{b \log{\left(\frac{a}{b} + x^{5} \right)}}{5 a^{2}}"," ",0,"-1/(5*a*x**5) - b*log(x)/a**2 + b*log(a/b + x**5)/(5*a**2)","A",0
1274,1,42,0,1.258687," ","integrate(1/x**11/(b*x**5+a),x)","\frac{- a + 2 b x^{5}}{10 a^{2} x^{10}} + \frac{b^{2} \log{\left(x \right)}}{a^{3}} - \frac{b^{2} \log{\left(\frac{a}{b} + x^{5} \right)}}{5 a^{3}}"," ",0,"(-a + 2*b*x**5)/(10*a**2*x**10) + b**2*log(x)/a**3 - b**2*log(a/b + x**5)/(5*a**3)","A",0
1275,1,56,0,1.028291," ","integrate(1/x**16/(b*x**5+a),x)","\frac{- 2 a^{2} + 3 a b x^{5} - 6 b^{2} x^{10}}{30 a^{3} x^{15}} - \frac{b^{3} \log{\left(x \right)}}{a^{4}} + \frac{b^{3} \log{\left(\frac{a}{b} + x^{5} \right)}}{5 a^{4}}"," ",0,"(-2*a**2 + 3*a*b*x**5 - 6*b**2*x**10)/(30*a**3*x**15) - b**3*log(x)/a**4 + b**3*log(a/b + x**5)/(5*a**4)","A",0
1276,1,20,0,0.259579," ","integrate(1/(b*x**5+a),x)","\operatorname{RootSum} {\left(3125 t^{5} a^{4} b - 1, \left( t \mapsto t \log{\left(5 t a + x \right)} \right)\right)}"," ",0,"RootSum(3125*_t**5*a**4*b - 1, Lambda(_t, _t*log(5*_t*a + x)))","A",0
1277,1,68,0,1.018885," ","integrate(x**24/(b*x**5+a)**2,x)","- \frac{a^{4}}{5 a b^{5} + 5 b^{6} x^{5}} - \frac{4 a^{3} \log{\left(a + b x^{5} \right)}}{5 b^{5}} + \frac{3 a^{2} x^{5}}{5 b^{4}} - \frac{a x^{10}}{5 b^{3}} + \frac{x^{15}}{15 b^{2}}"," ",0,"-a**4/(5*a*b**5 + 5*b**6*x**5) - 4*a**3*log(a + b*x**5)/(5*b**5) + 3*a**2*x**5/(5*b**4) - a*x**10/(5*b**3) + x**15/(15*b**2)","A",0
1278,1,56,0,0.966434," ","integrate(x**19/(b*x**5+a)**2,x)","\frac{a^{3}}{5 a b^{4} + 5 b^{5} x^{5}} + \frac{3 a^{2} \log{\left(a + b x^{5} \right)}}{5 b^{4}} - \frac{2 a x^{5}}{5 b^{3}} + \frac{x^{10}}{10 b^{2}}"," ",0,"a**3/(5*a*b**4 + 5*b**5*x**5) + 3*a**2*log(a + b*x**5)/(5*b**4) - 2*a*x**5/(5*b**3) + x**10/(10*b**2)","A",0
1279,1,42,0,0.775700," ","integrate(x**14/(b*x**5+a)**2,x)","- \frac{a^{2}}{5 a b^{3} + 5 b^{4} x^{5}} - \frac{2 a \log{\left(a + b x^{5} \right)}}{5 b^{3}} + \frac{x^{5}}{5 b^{2}}"," ",0,"-a**2/(5*a*b**3 + 5*b**4*x**5) - 2*a*log(a + b*x**5)/(5*b**3) + x**5/(5*b**2)","A",0
1280,1,29,0,0.559135," ","integrate(x**9/(b*x**5+a)**2,x)","\frac{a}{5 a b^{2} + 5 b^{3} x^{5}} + \frac{\log{\left(a + b x^{5} \right)}}{5 b^{2}}"," ",0,"a/(5*a*b**2 + 5*b**3*x**5) + log(a + b*x**5)/(5*b**2)","A",0
1281,1,15,0,0.601722," ","integrate(x**4/(b*x**5+a)**2,x)","- \frac{1}{5 a b + 5 b^{2} x^{5}}"," ",0,"-1/(5*a*b + 5*b**2*x**5)","A",0
1282,1,34,0,0.572480," ","integrate(1/x/(b*x**5+a)**2,x)","\frac{1}{5 a^{2} + 5 a b x^{5}} + \frac{\log{\left(x \right)}}{a^{2}} - \frac{\log{\left(\frac{a}{b} + x^{5} \right)}}{5 a^{2}}"," ",0,"1/(5*a**2 + 5*a*b*x**5) + log(x)/a**2 - log(a/b + x**5)/(5*a**2)","A",0
1283,1,54,0,1.270869," ","integrate(1/x**6/(b*x**5+a)**2,x)","\frac{- a - 2 b x^{5}}{5 a^{3} x^{5} + 5 a^{2} b x^{10}} - \frac{2 b \log{\left(x \right)}}{a^{3}} + \frac{2 b \log{\left(\frac{a}{b} + x^{5} \right)}}{5 a^{3}}"," ",0,"(-a - 2*b*x**5)/(5*a**3*x**5 + 5*a**2*b*x**10) - 2*b*log(x)/a**3 + 2*b*log(a/b + x**5)/(5*a**3)","A",0
1284,1,68,0,1.604496," ","integrate(1/x**11/(b*x**5+a)**2,x)","\frac{- a^{2} + 3 a b x^{5} + 6 b^{2} x^{10}}{10 a^{4} x^{10} + 10 a^{3} b x^{15}} + \frac{3 b^{2} \log{\left(x \right)}}{a^{4}} - \frac{3 b^{2} \log{\left(\frac{a}{b} + x^{5} \right)}}{5 a^{4}}"," ",0,"(-a**2 + 3*a*b*x**5 + 6*b**2*x**10)/(10*a**4*x**10 + 10*a**3*b*x**15) + 3*b**2*log(x)/a**4 - 3*b**2*log(a/b + x**5)/(5*a**4)","A",0
1285,1,26,0,0.434176," ","integrate(x**14/(b*x**5+2*b),x)","\frac{x^{10}}{10 b} - \frac{2 x^{5}}{5 b} + \frac{4 \log{\left(x^{5} + 2 \right)}}{5 b}"," ",0,"x**10/(10*b) - 2*x**5/(5*b) + 4*log(x**5 + 2)/(5*b)","A",0
1286,1,17,0,0.280139," ","integrate(x**9/(b*x**5+2*b),x)","\frac{x^{5}}{5 b} - \frac{2 \log{\left(x^{5} + 2 \right)}}{5 b}"," ",0,"x**5/(5*b) - 2*log(x**5 + 2)/(5*b)","A",0
1287,1,8,0,0.366676," ","integrate(x**4/(b*x**5+2*b),x)","\frac{\log{\left(x^{5} + 2 \right)}}{5 b}"," ",0,"log(x**5 + 2)/(5*b)","A",0
1288,1,15,0,0.831640," ","integrate(1/x/(b*x**5+2*b),x)","\frac{\log{\left(x \right)}}{2 b} - \frac{\log{\left(x^{5} + 2 \right)}}{10 b}"," ",0,"log(x)/(2*b) - log(x**5 + 2)/(10*b)","A",0
1289,1,24,0,0.415502," ","integrate(1/x**6/(b*x**5+2*b),x)","- \frac{\log{\left(x \right)}}{4 b} + \frac{\log{\left(x^{5} + 2 \right)}}{20 b} - \frac{1}{10 b x^{5}}"," ",0,"-log(x)/(4*b) + log(x**5 + 2)/(20*b) - 1/(10*b*x**5)","A",0
1290,1,31,0,0.439177," ","integrate(x**14/(b*x**5+3),x)","\frac{x^{10}}{10 b} - \frac{3 x^{5}}{5 b^{2}} + \frac{9 \log{\left(b x^{5} + 3 \right)}}{5 b^{3}}"," ",0,"x**10/(10*b) - 3*x**5/(5*b**2) + 9*log(b*x**5 + 3)/(5*b**3)","A",0
1291,1,20,0,0.254164," ","integrate(x**9/(b*x**5+3),x)","\frac{x^{5}}{5 b} - \frac{3 \log{\left(b x^{5} + 3 \right)}}{5 b^{2}}"," ",0,"x**5/(5*b) - 3*log(b*x**5 + 3)/(5*b**2)","A",0
1292,1,10,0,0.403536," ","integrate(x**4/(b*x**5+3),x)","\frac{\log{\left(b x^{5} + 3 \right)}}{5 b}"," ",0,"log(b*x**5 + 3)/(5*b)","A",0
1293,1,14,0,0.491476," ","integrate(1/x/(b*x**5+3),x)","\frac{\log{\left(x \right)}}{3} - \frac{\log{\left(x^{5} + \frac{3}{b} \right)}}{15}"," ",0,"log(x)/3 - log(x**5 + 3/b)/15","A",0
1294,1,24,0,0.879560," ","integrate(1/x**6/(b*x**5+3),x)","- \frac{b \log{\left(x \right)}}{9} + \frac{b \log{\left(x^{5} + \frac{3}{b} \right)}}{45} - \frac{1}{15 x^{5}}"," ",0,"-b*log(x)/9 + b*log(x**5 + 3/b)/45 - 1/(15*x**5)","A",0
1295,1,17,0,0.192731," ","integrate(x**14/(x**5+1),x)","\frac{x^{10}}{10} - \frac{x^{5}}{5} + \frac{\log{\left(x^{5} + 1 \right)}}{5}"," ",0,"x**10/10 - x**5/5 + log(x**5 + 1)/5","A",0
1296,1,12,0,0.213530," ","integrate(x**9/(x**5+1),x)","\frac{x^{5}}{5} - \frac{\log{\left(x^{5} + 1 \right)}}{5}"," ",0,"x**5/5 - log(x**5 + 1)/5","A",0
1297,1,7,0,0.169188," ","integrate(x**4/(x**5+1),x)","\frac{\log{\left(x^{5} + 1 \right)}}{5}"," ",0,"log(x**5 + 1)/5","A",0
1298,1,10,0,0.173432," ","integrate(1/x/(x**5+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{5} + 1 \right)}}{5}"," ",0,"log(x) - log(x**5 + 1)/5","A",0
1299,1,17,0,0.214829," ","integrate(1/x**6/(x**5+1),x)","- \log{\left(x \right)} + \frac{\log{\left(x^{5} + 1 \right)}}{5} - \frac{1}{5 x^{5}}"," ",0,"-log(x) + log(x**5 + 1)/5 - 1/(5*x**5)","A",0
1300,1,36,0,1.066201," ","integrate(x**5/(x**5+1),x)","x - \frac{\log{\left(x + 1 \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} - 125 t^{3} + 25 t^{2} - 5 t + 1, \left( t \mapsto t \log{\left(- 5 t + x \right)} \right)\right)}"," ",0,"x - log(x + 1)/5 + RootSum(625*_t**4 - 125*_t**3 + 25*_t**2 - 5*_t + 1, Lambda(_t, _t*log(-5*_t + x)))","A",0
1301,1,36,0,1.043690," ","integrate(x**3/(x**5+1),x)","- \frac{\log{\left(x + 1 \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} - 125 t^{3} + 25 t^{2} - 5 t + 1, \left( t \mapsto t \log{\left(625 t^{4} + x \right)} \right)\right)}"," ",0,"-log(x + 1)/5 + RootSum(625*_t**4 - 125*_t**3 + 25*_t**2 - 5*_t + 1, Lambda(_t, _t*log(625*_t**4 + x)))","A",0
1302,1,36,0,2.249437," ","integrate(x**2/(x**5+1),x)","\frac{\log{\left(x + 1 \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(25 t^{2} + x \right)} \right)\right)}"," ",0,"log(x + 1)/5 + RootSum(625*_t**4 + 125*_t**3 + 25*_t**2 + 5*_t + 1, Lambda(_t, _t*log(25*_t**2 + x)))","A",0
1303,1,36,0,2.130870," ","integrate(x/(x**5+1),x)","- \frac{\log{\left(x + 1 \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} - 125 t^{3} + 25 t^{2} - 5 t + 1, \left( t \mapsto t \log{\left(- 125 t^{3} + x \right)} \right)\right)}"," ",0,"-log(x + 1)/5 + RootSum(625*_t**4 - 125*_t**3 + 25*_t**2 - 5*_t + 1, Lambda(_t, _t*log(-125*_t**3 + x)))","A",0
1304,1,34,0,1.925478," ","integrate(1/(x**5+1),x)","\frac{\log{\left(x + 1 \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t + x \right)} \right)\right)}"," ",0,"log(x + 1)/5 + RootSum(625*_t**4 + 125*_t**3 + 25*_t**2 + 5*_t + 1, Lambda(_t, _t*log(5*_t + x)))","A",0
1305,1,39,0,2.825216," ","integrate(1/x**2/(x**5+1),x)","\frac{\log{\left(x + 1 \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(625 t^{4} + x \right)} \right)\right)} - \frac{1}{x}"," ",0,"log(x + 1)/5 + RootSum(625*_t**4 + 125*_t**3 + 25*_t**2 + 5*_t + 1, Lambda(_t, _t*log(625*_t**4 + x))) - 1/x","A",0
1306,1,42,0,1.996170," ","integrate(1/x**3/(x**5+1),x)","- \frac{\log{\left(x + 1 \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} - 125 t^{3} + 25 t^{2} - 5 t + 1, \left( t \mapsto t \log{\left(25 t^{2} + x \right)} \right)\right)} - \frac{1}{2 x^{2}}"," ",0,"-log(x + 1)/5 + RootSum(625*_t**4 - 125*_t**3 + 25*_t**2 - 5*_t + 1, Lambda(_t, _t*log(25*_t**2 + x))) - 1/(2*x**2)","A",0
1307,1,42,0,3.061919," ","integrate(1/x**4/(x**5+1),x)","\frac{\log{\left(x + 1 \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(125 t^{3} + x \right)} \right)\right)} - \frac{1}{3 x^{3}}"," ",0,"log(x + 1)/5 + RootSum(625*_t**4 + 125*_t**3 + 25*_t**2 + 5*_t + 1, Lambda(_t, _t*log(125*_t**3 + x))) - 1/(3*x**3)","A",0
1308,-1,0,0,0.000000," ","integrate(x**(23/2)/(b*x**5+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1309,1,49,0,165.093344," ","integrate(x**(13/2)/(b*x**5+a)**(1/2),x)","\frac{\sqrt{a} x^{\frac{5}{2}} \sqrt{1 + \frac{b x^{5}}{a}}}{5 b} - \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b} x^{\frac{5}{2}}}{\sqrt{a}} \right)}}{5 b^{\frac{3}{2}}}"," ",0,"sqrt(a)*x**(5/2)*sqrt(1 + b*x**5/a)/(5*b) - a*asinh(sqrt(b)*x**(5/2)/sqrt(a))/(5*b**(3/2))","A",0
1310,1,24,0,2.319960," ","integrate(x**(3/2)/(b*x**5+a)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{\sqrt{b} x^{\frac{5}{2}}}{\sqrt{a}} \right)}}{5 \sqrt{b}}"," ",0,"2*asinh(sqrt(b)*x**(5/2)/sqrt(a))/(5*sqrt(b))","A",0
1311,1,22,0,7.206150," ","integrate(1/x**(7/2)/(b*x**5+a)**(1/2),x)","- \frac{2 \sqrt{b} \sqrt{\frac{a}{b x^{5}} + 1}}{5 a}"," ",0,"-2*sqrt(b)*sqrt(a/(b*x**5) + 1)/(5*a)","A",0
1312,-1,0,0,0.000000," ","integrate(1/x**(17/2)/(b*x**5+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1313,-1,0,0,0.000000," ","integrate(x**(23/2)/(x**5+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1314,1,22,0,145.061039," ","integrate(x**(13/2)/(x**5+1)**(1/2),x)","\frac{x^{\frac{5}{2}} \sqrt{x^{5} + 1}}{5} - \frac{\operatorname{asinh}{\left(x^{\frac{5}{2}} \right)}}{5}"," ",0,"x**(5/2)*sqrt(x**5 + 1)/5 - asinh(x**(5/2))/5","A",0
1315,1,8,0,2.375198," ","integrate(x**(3/2)/(x**5+1)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(x^{\frac{5}{2}} \right)}}{5}"," ",0,"2*asinh(x**(5/2))/5","A",0
1316,1,14,0,11.347467," ","integrate(1/x**(7/2)/(x**5+1)**(1/2),x)","- \frac{2 \sqrt{1 + \frac{1}{x^{5}}}}{5}"," ",0,"-2*sqrt(1 + x**(-5))/5","A",0
1317,-1,0,0,0.000000," ","integrate(1/x**(17/2)/(x**5+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1318,1,63,0,0.336805," ","integrate(x**8/(b*x**6+a),x)","\frac{\sqrt{- \frac{a}{b^{3}}} \log{\left(- b \sqrt{- \frac{a}{b^{3}}} + x^{3} \right)}}{6} - \frac{\sqrt{- \frac{a}{b^{3}}} \log{\left(b \sqrt{- \frac{a}{b^{3}}} + x^{3} \right)}}{6} + \frac{x^{3}}{3 b}"," ",0,"sqrt(-a/b**3)*log(-b*sqrt(-a/b**3) + x**3)/6 - sqrt(-a/b**3)*log(b*sqrt(-a/b**3) + x**3)/6 + x**3/(3*b)","A",0
1319,1,27,0,0.431910," ","integrate(x**7/(b*x**6+a),x)","\operatorname{RootSum} {\left(216 t^{3} b^{4} + a, \left( t \mapsto t \log{\left(- 6 t b + x^{2} \right)} \right)\right)} + \frac{x^{2}}{2 b}"," ",0,"RootSum(216*_t**3*b**4 + a, Lambda(_t, _t*log(-6*_t*b + x**2))) + x**2/(2*b)","A",0
1320,1,22,0,0.234772," ","integrate(x**6/(b*x**6+a),x)","\operatorname{RootSum} {\left(46656 t^{6} b^{7} + a, \left( t \mapsto t \log{\left(- 6 t b + x \right)} \right)\right)} + \frac{x}{b}"," ",0,"RootSum(46656*_t**6*b**7 + a, Lambda(_t, _t*log(-6*_t*b + x))) + x/b","A",0
1321,1,10,0,0.236892," ","integrate(x**5/(b*x**6+a),x)","\frac{\log{\left(a + b x^{6} \right)}}{6 b}"," ",0,"log(a + b*x**6)/(6*b)","A",0
1322,1,26,0,0.379513," ","integrate(x**4/(b*x**6+a),x)","\operatorname{RootSum} {\left(46656 t^{6} a b^{5} + 1, \left( t \mapsto t \log{\left(7776 t^{5} a b^{4} + x \right)} \right)\right)}"," ",0,"RootSum(46656*_t**6*a*b**5 + 1, Lambda(_t, _t*log(7776*_t**5*a*b**4 + x)))","A",0
1323,1,26,0,0.216487," ","integrate(x**3/(b*x**6+a),x)","\operatorname{RootSum} {\left(216 t^{3} a b^{2} + 1, \left( t \mapsto t \log{\left(36 t^{2} a b + x^{2} \right)} \right)\right)}"," ",0,"RootSum(216*_t**3*a*b**2 + 1, Lambda(_t, _t*log(36*_t**2*a*b + x**2)))","A",0
1324,1,56,0,0.255115," ","integrate(x**2/(b*x**6+a),x)","- \frac{\sqrt{- \frac{1}{a b}} \log{\left(- a \sqrt{- \frac{1}{a b}} + x^{3} \right)}}{6} + \frac{\sqrt{- \frac{1}{a b}} \log{\left(a \sqrt{- \frac{1}{a b}} + x^{3} \right)}}{6}"," ",0,"-sqrt(-1/(a*b))*log(-a*sqrt(-1/(a*b)) + x**3)/6 + sqrt(-1/(a*b))*log(a*sqrt(-1/(a*b)) + x**3)/6","B",0
1325,1,22,0,0.240480," ","integrate(x/(b*x**6+a),x)","\operatorname{RootSum} {\left(216 t^{3} a^{2} b - 1, \left( t \mapsto t \log{\left(6 t a + x^{2} \right)} \right)\right)}"," ",0,"RootSum(216*_t**3*a**2*b - 1, Lambda(_t, _t*log(6*_t*a + x**2)))","A",0
1326,1,20,0,0.423677," ","integrate(1/(b*x**6+a),x)","\operatorname{RootSum} {\left(46656 t^{6} a^{5} b + 1, \left( t \mapsto t \log{\left(6 t a + x \right)} \right)\right)}"," ",0,"RootSum(46656*_t**6*a**5*b + 1, Lambda(_t, _t*log(6*_t*a + x)))","A",0
1327,1,15,0,0.611074," ","integrate(1/x/(b*x**6+a),x)","\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{6} \right)}}{6 a}"," ",0,"log(x)/a - log(a/b + x**6)/(6*a)","A",0
1328,1,29,0,0.464347," ","integrate(1/x**2/(b*x**6+a),x)","\operatorname{RootSum} {\left(46656 t^{6} a^{7} + b, \left( t \mapsto t \log{\left(- \frac{7776 t^{5} a^{6}}{b} + x \right)} \right)\right)} - \frac{1}{a x}"," ",0,"RootSum(46656*_t**6*a**7 + b, Lambda(_t, _t*log(-7776*_t**5*a**6/b + x))) - 1/(a*x)","A",0
1329,1,34,0,0.326655," ","integrate(1/x**3/(b*x**6+a),x)","\operatorname{RootSum} {\left(216 t^{3} a^{4} - b, \left( t \mapsto t \log{\left(\frac{36 t^{2} a^{3}}{b} + x^{2} \right)} \right)\right)} - \frac{1}{2 a x^{2}}"," ",0,"RootSum(216*_t**3*a**4 - b, Lambda(_t, _t*log(36*_t**2*a**3/b + x**2))) - 1/(2*a*x**2)","A",0
1330,1,71,0,0.560857," ","integrate(1/x**4/(b*x**6+a),x)","\frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(- \frac{a^{2} \sqrt{- \frac{b}{a^{3}}}}{b} + x^{3} \right)}}{6} - \frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(\frac{a^{2} \sqrt{- \frac{b}{a^{3}}}}{b} + x^{3} \right)}}{6} - \frac{1}{3 a x^{3}}"," ",0,"sqrt(-b/a**3)*log(-a**2*sqrt(-b/a**3)/b + x**3)/6 - sqrt(-b/a**3)*log(a**2*sqrt(-b/a**3)/b + x**3)/6 - 1/(3*a*x**3)","A",0
1331,1,83,0,0.611492," ","integrate(x**8/(b*x**6+a)**2,x)","- \frac{x^{3}}{6 a b + 6 b^{2} x^{6}} - \frac{\sqrt{- \frac{1}{a b^{3}}} \log{\left(- a b \sqrt{- \frac{1}{a b^{3}}} + x^{3} \right)}}{12} + \frac{\sqrt{- \frac{1}{a b^{3}}} \log{\left(a b \sqrt{- \frac{1}{a b^{3}}} + x^{3} \right)}}{12}"," ",0,"-x**3/(6*a*b + 6*b**2*x**6) - sqrt(-1/(a*b**3))*log(-a*b*sqrt(-1/(a*b**3)) + x**3)/12 + sqrt(-1/(a*b**3))*log(a*b*sqrt(-1/(a*b**3)) + x**3)/12","B",0
1332,1,42,0,0.778019," ","integrate(x**7/(b*x**6+a)**2,x)","- \frac{x^{2}}{6 a b + 6 b^{2} x^{6}} + \operatorname{RootSum} {\left(5832 t^{3} a^{2} b^{4} - 1, \left( t \mapsto t \log{\left(18 t a b + x^{2} \right)} \right)\right)}"," ",0,"-x**2/(6*a*b + 6*b**2*x**6) + RootSum(5832*_t**3*a**2*b**4 - 1, Lambda(_t, _t*log(18*_t*a*b + x**2)))","A",0
1333,1,39,0,0.724263," ","integrate(x**6/(b*x**6+a)**2,x)","- \frac{x}{6 a b + 6 b^{2} x^{6}} + \operatorname{RootSum} {\left(2176782336 t^{6} a^{5} b^{7} + 1, \left( t \mapsto t \log{\left(36 t a b + x \right)} \right)\right)}"," ",0,"-x/(6*a*b + 6*b**2*x**6) + RootSum(2176782336*_t**6*a**5*b**7 + 1, Lambda(_t, _t*log(36*_t*a*b + x)))","A",0
1334,1,15,0,0.512839," ","integrate(x**5/(b*x**6+a)**2,x)","- \frac{1}{6 a b + 6 b^{2} x^{6}}"," ",0,"-1/(6*a*b + 6*b**2*x**6)","A",0
1335,1,46,0,0.658633," ","integrate(x**4/(b*x**6+a)**2,x)","\frac{x^{5}}{6 a^{2} + 6 a b x^{6}} + \operatorname{RootSum} {\left(2176782336 t^{6} a^{7} b^{5} + 1, \left( t \mapsto t \log{\left(60466176 t^{5} a^{6} b^{4} + x \right)} \right)\right)}"," ",0,"x**5/(6*a**2 + 6*a*b*x**6) + RootSum(2176782336*_t**6*a**7*b**5 + 1, Lambda(_t, _t*log(60466176*_t**5*a**6*b**4 + x)))","A",0
1336,1,46,0,0.668948," ","integrate(x**3/(b*x**6+a)**2,x)","\frac{x^{4}}{6 a^{2} + 6 a b x^{6}} + \operatorname{RootSum} {\left(5832 t^{3} a^{4} b^{2} + 1, \left( t \mapsto t \log{\left(324 t^{2} a^{3} b + x^{2} \right)} \right)\right)}"," ",0,"x**4/(6*a**2 + 6*a*b*x**6) + RootSum(5832*_t**3*a**4*b**2 + 1, Lambda(_t, _t*log(324*_t**2*a**3*b + x**2)))","A",0
1337,1,83,0,0.835063," ","integrate(x**2/(b*x**6+a)**2,x)","\frac{x^{3}}{6 a^{2} + 6 a b x^{6}} - \frac{\sqrt{- \frac{1}{a^{3} b}} \log{\left(- a^{2} \sqrt{- \frac{1}{a^{3} b}} + x^{3} \right)}}{12} + \frac{\sqrt{- \frac{1}{a^{3} b}} \log{\left(a^{2} \sqrt{- \frac{1}{a^{3} b}} + x^{3} \right)}}{12}"," ",0,"x**3/(6*a**2 + 6*a*b*x**6) - sqrt(-1/(a**3*b))*log(-a**2*sqrt(-1/(a**3*b)) + x**3)/12 + sqrt(-1/(a**3*b))*log(a**2*sqrt(-1/(a**3*b)) + x**3)/12","B",0
1338,1,41,0,0.791971," ","integrate(x/(b*x**6+a)**2,x)","\frac{x^{2}}{6 a^{2} + 6 a b x^{6}} + \operatorname{RootSum} {\left(729 t^{3} a^{5} b - 1, \left( t \mapsto t \log{\left(9 t a^{2} + x^{2} \right)} \right)\right)}"," ",0,"x**2/(6*a**2 + 6*a*b*x**6) + RootSum(729*_t**3*a**5*b - 1, Lambda(_t, _t*log(9*_t*a**2 + x**2)))","A",0
1339,1,39,0,0.717670," ","integrate(1/(b*x**6+a)**2,x)","\frac{x}{6 a^{2} + 6 a b x^{6}} + \operatorname{RootSum} {\left(2176782336 t^{6} a^{11} b + 15625, \left( t \mapsto t \log{\left(\frac{36 t a^{2}}{5} + x \right)} \right)\right)}"," ",0,"x/(6*a**2 + 6*a*b*x**6) + RootSum(2176782336*_t**6*a**11*b + 15625, Lambda(_t, _t*log(36*_t*a**2/5 + x)))","A",0
1340,1,34,0,0.604182," ","integrate(1/x/(b*x**6+a)**2,x)","\frac{1}{6 a^{2} + 6 a b x^{6}} + \frac{\log{\left(x \right)}}{a^{2}} - \frac{\log{\left(\frac{a}{b} + x^{6} \right)}}{6 a^{2}}"," ",0,"1/(6*a**2 + 6*a*b*x**6) + log(x)/a**2 - log(a/b + x**6)/(6*a**2)","A",0
1341,1,56,0,0.514720," ","integrate(1/x**2/(b*x**6+a)**2,x)","\frac{- 6 a - 7 b x^{6}}{6 a^{3} x + 6 a^{2} b x^{7}} + \operatorname{RootSum} {\left(2176782336 t^{6} a^{13} + 117649 b, \left( t \mapsto t \log{\left(- \frac{60466176 t^{5} a^{11}}{16807 b} + x \right)} \right)\right)}"," ",0,"(-6*a - 7*b*x**6)/(6*a**3*x + 6*a**2*b*x**7) + RootSum(2176782336*_t**6*a**13 + 117649*b, Lambda(_t, _t*log(-60466176*_t**5*a**11/(16807*b) + x)))","A",0
1342,1,60,0,0.962006," ","integrate(1/x**3/(b*x**6+a)**2,x)","\frac{- 3 a - 4 b x^{6}}{6 a^{3} x^{2} + 6 a^{2} b x^{8}} + \operatorname{RootSum} {\left(729 t^{3} a^{7} - 8 b, \left( t \mapsto t \log{\left(\frac{81 t^{2} a^{5}}{4 b} + x^{2} \right)} \right)\right)}"," ",0,"(-3*a - 4*b*x**6)/(6*a**3*x**2 + 6*a**2*b*x**8) + RootSum(729*_t**3*a**7 - 8*b, Lambda(_t, _t*log(81*_t**2*a**5/(4*b) + x**2)))","A",0
1343,1,94,0,0.973266," ","integrate(1/x**4/(b*x**6+a)**2,x)","\frac{\sqrt{- \frac{b}{a^{5}}} \log{\left(- \frac{a^{3} \sqrt{- \frac{b}{a^{5}}}}{b} + x^{3} \right)}}{4} - \frac{\sqrt{- \frac{b}{a^{5}}} \log{\left(\frac{a^{3} \sqrt{- \frac{b}{a^{5}}}}{b} + x^{3} \right)}}{4} + \frac{- 2 a - 3 b x^{6}}{6 a^{3} x^{3} + 6 a^{2} b x^{9}}"," ",0,"sqrt(-b/a**5)*log(-a**3*sqrt(-b/a**5)/b + x**3)/4 - sqrt(-b/a**5)*log(a**3*sqrt(-b/a**5)/b + x**3)/4 + (-2*a - 3*b*x**6)/(6*a**3*x**3 + 6*a**2*b*x**9)","A",0
1344,1,20,0,0.126736," ","integrate(x**8/(-x**6+1),x)","- \frac{x^{3}}{3} - \frac{\log{\left(x^{3} - 1 \right)}}{6} + \frac{\log{\left(x^{3} + 1 \right)}}{6}"," ",0,"-x**3/3 - log(x**3 - 1)/6 + log(x**3 + 1)/6","A",0
1345,1,51,0,0.176378," ","integrate(x**7/(-x**6+1),x)","- \frac{x^{2}}{2} - \frac{\log{\left(x^{2} - 1 \right)}}{6} + \frac{\log{\left(x^{4} + x^{2} + 1 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"-x**2/2 - log(x**2 - 1)/6 + log(x**4 + x**2 + 1)/12 + sqrt(3)*atan(2*sqrt(3)*x**2/3 + sqrt(3)/3)/6","A",0
1346,1,85,0,0.519166," ","integrate(x**6/(-x**6+1),x)","- x - \frac{\log{\left(x - 1 \right)}}{6} + \frac{\log{\left(x + 1 \right)}}{6} - \frac{\log{\left(x^{2} - x + 1 \right)}}{12} + \frac{\log{\left(x^{2} + x + 1 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"-x - log(x - 1)/6 + log(x + 1)/6 - log(x**2 - x + 1)/12 + log(x**2 + x + 1)/12 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/6","B",0
1347,1,8,0,0.099955," ","integrate(x**5/(-x**6+1),x)","- \frac{\log{\left(x^{6} - 1 \right)}}{6}"," ",0,"-log(x**6 - 1)/6","A",0
1348,1,83,0,0.520810," ","integrate(x**4/(-x**6+1),x)","- \frac{\log{\left(x - 1 \right)}}{6} + \frac{\log{\left(x + 1 \right)}}{6} - \frac{\log{\left(x^{2} - x + 1 \right)}}{12} + \frac{\log{\left(x^{2} + x + 1 \right)}}{12} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"-log(x - 1)/6 + log(x + 1)/6 - log(x**2 - x + 1)/12 + log(x**2 + x + 1)/12 - sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/6 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/6","B",0
1349,1,46,0,0.275454," ","integrate(x**3/(-x**6+1),x)","- \frac{\log{\left(x^{2} - 1 \right)}}{6} + \frac{\log{\left(x^{4} + x^{2} + 1 \right)}}{12} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"-log(x**2 - 1)/6 + log(x**4 + x**2 + 1)/12 - sqrt(3)*atan(2*sqrt(3)*x**2/3 + sqrt(3)/3)/6","A",0
1350,1,15,0,0.115763," ","integrate(x**2/(-x**6+1),x)","- \frac{\log{\left(x^{3} - 1 \right)}}{6} + \frac{\log{\left(x^{3} + 1 \right)}}{6}"," ",0,"-log(x**3 - 1)/6 + log(x**3 + 1)/6","B",0
1351,1,46,0,0.264370," ","integrate(x/(-x**6+1),x)","- \frac{\log{\left(x^{2} - 1 \right)}}{6} + \frac{\log{\left(x^{4} + x^{2} + 1 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"-log(x**2 - 1)/6 + log(x**4 + x**2 + 1)/12 + sqrt(3)*atan(2*sqrt(3)*x**2/3 + sqrt(3)/3)/6","A",0
1352,1,83,0,0.479043," ","integrate(1/(-x**6+1),x)","- \frac{\log{\left(x - 1 \right)}}{6} + \frac{\log{\left(x + 1 \right)}}{6} - \frac{\log{\left(x^{2} - x + 1 \right)}}{12} + \frac{\log{\left(x^{2} + x + 1 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"-log(x - 1)/6 + log(x + 1)/6 - log(x**2 - x + 1)/12 + log(x**2 + x + 1)/12 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/6","B",0
1353,1,10,0,0.176802," ","integrate(1/x/(-x**6+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{6} - 1 \right)}}{6}"," ",0,"log(x) - log(x**6 - 1)/6","A",0
1354,1,87,0,0.552392," ","integrate(1/x**2/(-x**6+1),x)","- \frac{\log{\left(x - 1 \right)}}{6} + \frac{\log{\left(x + 1 \right)}}{6} - \frac{\log{\left(x^{2} - x + 1 \right)}}{12} + \frac{\log{\left(x^{2} + x + 1 \right)}}{12} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6} - \frac{1}{x}"," ",0,"-log(x - 1)/6 + log(x + 1)/6 - log(x**2 - x + 1)/12 + log(x**2 + x + 1)/12 - sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/6 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/6 - 1/x","B",0
1355,1,53,0,0.204638," ","integrate(1/x**3/(-x**6+1),x)","- \frac{\log{\left(x^{2} - 1 \right)}}{6} + \frac{\log{\left(x^{4} + x^{2} + 1 \right)}}{12} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} + \frac{\sqrt{3}}{3} \right)}}{6} - \frac{1}{2 x^{2}}"," ",0,"-log(x**2 - 1)/6 + log(x**4 + x**2 + 1)/12 - sqrt(3)*atan(2*sqrt(3)*x**2/3 + sqrt(3)/3)/6 - 1/(2*x**2)","A",0
1356,1,22,0,0.236610," ","integrate(1/x**4/(-x**6+1),x)","- \frac{\log{\left(x^{3} - 1 \right)}}{6} + \frac{\log{\left(x^{3} + 1 \right)}}{6} - \frac{1}{3 x^{3}}"," ",0,"-log(x**3 - 1)/6 + log(x**3 + 1)/6 - 1/(3*x**3)","A",0
1357,1,53,0,0.211106," ","integrate(1/x**5/(-x**6+1),x)","- \frac{\log{\left(x^{2} - 1 \right)}}{6} + \frac{\log{\left(x^{4} + x^{2} + 1 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} + \frac{\sqrt{3}}{3} \right)}}{6} - \frac{1}{4 x^{4}}"," ",0,"-log(x**2 - 1)/6 + log(x**4 + x**2 + 1)/12 + sqrt(3)*atan(2*sqrt(3)*x**2/3 + sqrt(3)/3)/6 - 1/(4*x**4)","A",0
1358,1,90,0,0.629903," ","integrate(1/x**6/(-x**6+1),x)","- \frac{\log{\left(x - 1 \right)}}{6} + \frac{\log{\left(x + 1 \right)}}{6} - \frac{\log{\left(x^{2} - x + 1 \right)}}{12} + \frac{\log{\left(x^{2} + x + 1 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6} - \frac{1}{5 x^{5}}"," ",0,"-log(x - 1)/6 + log(x + 1)/6 - log(x**2 - x + 1)/12 + log(x**2 + x + 1)/12 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/6 - 1/(5*x**5)","A",0
1359,1,17,0,0.242129," ","integrate(1/x**7/(-x**6+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{6} - 1 \right)}}{6} - \frac{1}{6 x^{6}}"," ",0,"log(x) - log(x**6 - 1)/6 - 1/(6*x**6)","A",0
1360,1,95,0,0.552378," ","integrate(1/x**8/(-x**6+1),x)","- \frac{\log{\left(x - 1 \right)}}{6} + \frac{\log{\left(x + 1 \right)}}{6} - \frac{\log{\left(x^{2} - x + 1 \right)}}{12} + \frac{\log{\left(x^{2} + x + 1 \right)}}{12} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6} - \frac{7 x^{6} + 1}{7 x^{7}}"," ",0,"-log(x - 1)/6 + log(x + 1)/6 - log(x**2 - x + 1)/12 + log(x**2 + x + 1)/12 - sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/6 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/6 - (7*x**6 + 1)/(7*x**7)","A",0
1361,1,10,0,0.209091," ","integrate(x**8/(x**6+1),x)","\frac{x^{3}}{3} - \frac{\operatorname{atan}{\left(x^{3} \right)}}{3}"," ",0,"x**3/3 - atan(x**3)/3","A",0
1362,1,51,0,0.208298," ","integrate(x**7/(x**6+1),x)","\frac{x^{2}}{2} - \frac{\log{\left(x^{2} + 1 \right)}}{6} + \frac{\log{\left(x^{4} - x^{2} + 1 \right)}}{12} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} - \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"x**2/2 - log(x**2 + 1)/6 + log(x**4 - x**2 + 1)/12 - sqrt(3)*atan(2*sqrt(3)*x**2/3 - sqrt(3)/3)/6","A",0
1363,1,70,0,0.423991," ","integrate(x**6/(x**6+1),x)","x + \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{\operatorname{atan}{\left(x \right)}}{3} - \frac{\operatorname{atan}{\left(2 x - \sqrt{3} \right)}}{6} - \frac{\operatorname{atan}{\left(2 x + \sqrt{3} \right)}}{6}"," ",0,"x + sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 - sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12 - atan(x)/3 - atan(2*x - sqrt(3))/6 - atan(2*x + sqrt(3))/6","A",0
1364,1,7,0,0.169082," ","integrate(x**5/(x**6+1),x)","\frac{\log{\left(x^{6} + 1 \right)}}{6}"," ",0,"log(x**6 + 1)/6","A",0
1365,1,68,0,0.371431," ","integrate(x**4/(x**6+1),x)","\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{\operatorname{atan}{\left(x \right)}}{3} + \frac{\operatorname{atan}{\left(2 x - \sqrt{3} \right)}}{6} + \frac{\operatorname{atan}{\left(2 x + \sqrt{3} \right)}}{6}"," ",0,"sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 - sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12 + atan(x)/3 + atan(2*x - sqrt(3))/6 + atan(2*x + sqrt(3))/6","A",0
1366,1,46,0,0.171410," ","integrate(x**3/(x**6+1),x)","- \frac{\log{\left(x^{2} + 1 \right)}}{6} + \frac{\log{\left(x^{4} - x^{2} + 1 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} - \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"-log(x**2 + 1)/6 + log(x**4 - x**2 + 1)/12 + sqrt(3)*atan(2*sqrt(3)*x**2/3 - sqrt(3)/3)/6","A",0
1367,1,5,0,0.146507," ","integrate(x**2/(x**6+1),x)","\frac{\operatorname{atan}{\left(x^{3} \right)}}{3}"," ",0,"atan(x**3)/3","A",0
1368,1,46,0,0.318108," ","integrate(x/(x**6+1),x)","\frac{\log{\left(x^{2} + 1 \right)}}{6} - \frac{\log{\left(x^{4} - x^{2} + 1 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} - \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"log(x**2 + 1)/6 - log(x**4 - x**2 + 1)/12 + sqrt(3)*atan(2*sqrt(3)*x**2/3 - sqrt(3)/3)/6","A",0
1369,1,68,0,0.421081," ","integrate(1/(x**6+1),x)","- \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{\operatorname{atan}{\left(x \right)}}{3} + \frac{\operatorname{atan}{\left(2 x - \sqrt{3} \right)}}{6} + \frac{\operatorname{atan}{\left(2 x + \sqrt{3} \right)}}{6}"," ",0,"-sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 + sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12 + atan(x)/3 + atan(2*x - sqrt(3))/6 + atan(2*x + sqrt(3))/6","A",0
1370,1,10,0,0.158216," ","integrate(1/x/(x**6+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{6} + 1 \right)}}{6}"," ",0,"log(x) - log(x**6 + 1)/6","A",0
1371,1,71,0,0.499446," ","integrate(1/x**2/(x**6+1),x)","- \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{\operatorname{atan}{\left(x \right)}}{3} - \frac{\operatorname{atan}{\left(2 x - \sqrt{3} \right)}}{6} - \frac{\operatorname{atan}{\left(2 x + \sqrt{3} \right)}}{6} - \frac{1}{x}"," ",0,"-sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 + sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12 - atan(x)/3 - atan(2*x - sqrt(3))/6 - atan(2*x + sqrt(3))/6 - 1/x","A",0
1372,1,53,0,0.203364," ","integrate(1/x**3/(x**6+1),x)","\frac{\log{\left(x^{2} + 1 \right)}}{6} - \frac{\log{\left(x^{4} - x^{2} + 1 \right)}}{12} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} - \frac{\sqrt{3}}{3} \right)}}{6} - \frac{1}{2 x^{2}}"," ",0,"log(x**2 + 1)/6 - log(x**4 - x**2 + 1)/12 - sqrt(3)*atan(2*sqrt(3)*x**2/3 - sqrt(3)/3)/6 - 1/(2*x**2)","A",0
1373,1,14,0,0.277766," ","integrate(1/x**4/(x**6+1),x)","- \frac{\operatorname{atan}{\left(x^{3} \right)}}{3} - \frac{1}{3 x^{3}}"," ",0,"-atan(x**3)/3 - 1/(3*x**3)","A",0
1374,1,53,0,0.196133," ","integrate(1/x**5/(x**6+1),x)","- \frac{\log{\left(x^{2} + 1 \right)}}{6} + \frac{\log{\left(x^{4} - x^{2} + 1 \right)}}{12} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} - \frac{\sqrt{3}}{3} \right)}}{6} - \frac{1}{4 x^{4}}"," ",0,"-log(x**2 + 1)/6 + log(x**4 - x**2 + 1)/12 - sqrt(3)*atan(2*sqrt(3)*x**2/3 - sqrt(3)/3)/6 - 1/(4*x**4)","A",0
1375,1,75,0,0.484992," ","integrate(1/x**6/(x**6+1),x)","\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{\operatorname{atan}{\left(x \right)}}{3} - \frac{\operatorname{atan}{\left(2 x - \sqrt{3} \right)}}{6} - \frac{\operatorname{atan}{\left(2 x + \sqrt{3} \right)}}{6} - \frac{1}{5 x^{5}}"," ",0,"sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 - sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12 - atan(x)/3 - atan(2*x - sqrt(3))/6 - atan(2*x + sqrt(3))/6 - 1/(5*x**5)","A",0
1376,1,17,0,0.223915," ","integrate(1/x**7/(x**6+1),x)","- \log{\left(x \right)} + \frac{\log{\left(x^{6} + 1 \right)}}{6} - \frac{1}{6 x^{6}}"," ",0,"-log(x) + log(x**6 + 1)/6 - 1/(6*x**6)","A",0
1377,1,80,0,0.455447," ","integrate(1/x**8/(x**6+1),x)","\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{\operatorname{atan}{\left(x \right)}}{3} + \frac{\operatorname{atan}{\left(2 x - \sqrt{3} \right)}}{6} + \frac{\operatorname{atan}{\left(2 x + \sqrt{3} \right)}}{6} + \frac{7 x^{6} - 1}{7 x^{7}}"," ",0,"sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 - sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12 + atan(x)/3 + atan(2*x - sqrt(3))/6 + atan(2*x + sqrt(3))/6 + (7*x**6 - 1)/(7*x**7)","A",0
1378,1,15,0,0.953725," ","integrate(1/(-3*x**6+2),x)","- \operatorname{RootSum} {\left(4478976 t^{6} - 1, \left( t \mapsto t \log{\left(- 12 t + x \right)} \right)\right)}"," ",0,"-RootSum(4478976*_t**6 - 1, Lambda(_t, _t*log(-12*_t + x)))","A",0
1379,-1,0,0,0.000000," ","integrate(x**(1/3)/(-x**6+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1380,1,119,0,5.614906," ","integrate(x**8*(4*x**6-1)**(1/2),x)","\begin{cases} \frac{x^{15}}{3 \sqrt{4 x^{6} - 1}} - \frac{x^{9}}{8 \sqrt{4 x^{6} - 1}} + \frac{x^{3}}{96 \sqrt{4 x^{6} - 1}} - \frac{\operatorname{acosh}{\left(2 x^{3} \right)}}{192} & \text{for}\: 4 \left|{x^{6}}\right| > 1 \\- \frac{i x^{15}}{3 \sqrt{1 - 4 x^{6}}} + \frac{i x^{9}}{8 \sqrt{1 - 4 x^{6}}} - \frac{i x^{3}}{96 \sqrt{1 - 4 x^{6}}} + \frac{i \operatorname{asin}{\left(2 x^{3} \right)}}{192} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**15/(3*sqrt(4*x**6 - 1)) - x**9/(8*sqrt(4*x**6 - 1)) + x**3/(96*sqrt(4*x**6 - 1)) - acosh(2*x**3)/192, 4*Abs(x**6) > 1), (-I*x**15/(3*sqrt(1 - 4*x**6)) + I*x**9/(8*sqrt(1 - 4*x**6)) - I*x**3/(96*sqrt(1 - 4*x**6)) + I*asin(2*x**3)/192, True))","A",0
1381,1,29,0,0.421835," ","integrate(x**5*(a**6-x**6)**(1/2),x)","- \frac{a^{6} \sqrt{a^{6} - x^{6}}}{9} + \frac{x^{6} \sqrt{a^{6} - x^{6}}}{9}"," ",0,"-a**6*sqrt(a**6 - x**6)/9 + x**6*sqrt(a**6 - x**6)/9","B",0
1382,1,90,0,3.143992," ","integrate(x**2*(x**6-2)**(1/2),x)","\begin{cases} \frac{x^{9}}{6 \sqrt{x^{6} - 2}} - \frac{x^{3}}{3 \sqrt{x^{6} - 2}} - \frac{\operatorname{acosh}{\left(\frac{\sqrt{2} x^{3}}{2} \right)}}{3} & \text{for}\: \frac{\left|{x^{6}}\right|}{2} > 1 \\- \frac{i x^{9}}{6 \sqrt{2 - x^{6}}} + \frac{i x^{3}}{3 \sqrt{2 - x^{6}}} + \frac{i \operatorname{asin}{\left(\frac{\sqrt{2} x^{3}}{2} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**9/(6*sqrt(x**6 - 2)) - x**3/(3*sqrt(x**6 - 2)) - acosh(sqrt(2)*x**3/2)/3, Abs(x**6)/2 > 1), (-I*x**9/(6*sqrt(2 - x**6)) + I*x**3/(3*sqrt(2 - x**6)) + I*asin(sqrt(2)*x**3/2)/3, True))","A",0
1383,1,54,0,24.025156," ","integrate(x**23/(x**6+2)**(1/2),x)","\frac{x^{18} \sqrt{x^{6} + 2}}{21} - \frac{4 x^{12} \sqrt{x^{6} + 2}}{35} + \frac{32 x^{6} \sqrt{x^{6} + 2}}{105} - \frac{128 \sqrt{x^{6} + 2}}{105}"," ",0,"x**18*sqrt(x**6 + 2)/21 - 4*x**12*sqrt(x**6 + 2)/35 + 32*x**6*sqrt(x**6 + 2)/105 - 128*sqrt(x**6 + 2)/105","A",0
1384,1,39,0,9.140619," ","integrate(x**17/(x**6+2)**(1/2),x)","\frac{x^{12} \sqrt{x^{6} + 2}}{15} - \frac{8 x^{6} \sqrt{x^{6} + 2}}{45} + \frac{32 \sqrt{x^{6} + 2}}{45}"," ",0,"x**12*sqrt(x**6 + 2)/15 - 8*x**6*sqrt(x**6 + 2)/45 + 32*sqrt(x**6 + 2)/45","A",0
1385,1,24,0,2.382288," ","integrate(x**11/(x**6+2)**(1/2),x)","\frac{x^{6} \sqrt{x^{6} + 2}}{9} - \frac{4 \sqrt{x^{6} + 2}}{9}"," ",0,"x**6*sqrt(x**6 + 2)/9 - 4*sqrt(x**6 + 2)/9","A",0
1386,1,8,0,0.529110," ","integrate(x**5/(x**6+2)**(1/2),x)","\frac{\sqrt{x^{6} + 2}}{3}"," ",0,"sqrt(x**6 + 2)/3","A",0
1387,1,17,0,1.690700," ","integrate(1/x/(x**6+2)**(1/2),x)","- \frac{\sqrt{2} \operatorname{asinh}{\left(\frac{\sqrt{2}}{x^{3}} \right)}}{6}"," ",0,"-sqrt(2)*asinh(sqrt(2)/x**3)/6","A",0
1388,1,31,0,2.646967," ","integrate(1/x**7/(x**6+2)**(1/2),x)","\frac{\sqrt{2} \operatorname{asinh}{\left(\frac{\sqrt{2}}{x^{3}} \right)}}{24} - \frac{\sqrt{1 + \frac{2}{x^{6}}}}{12 x^{3}}"," ",0,"sqrt(2)*asinh(sqrt(2)/x**3)/24 - sqrt(1 + 2/x**6)/(12*x**3)","A",0
1389,1,66,0,4.148920," ","integrate(1/x**13/(x**6+2)**(1/2),x)","- \frac{\sqrt{2} \operatorname{asinh}{\left(\frac{\sqrt{2}}{x^{3}} \right)}}{64} + \frac{1}{32 x^{3} \sqrt{1 + \frac{2}{x^{6}}}} + \frac{1}{48 x^{9} \sqrt{1 + \frac{2}{x^{6}}}} - \frac{1}{12 x^{15} \sqrt{1 + \frac{2}{x^{6}}}}"," ",0,"-sqrt(2)*asinh(sqrt(2)/x**3)/64 + 1/(32*x**3*sqrt(1 + 2/x**6)) + 1/(48*x**9*sqrt(1 + 2/x**6)) - 1/(12*x**15*sqrt(1 + 2/x**6))","A",0
1390,1,53,0,6.294686," ","integrate(x**14/(x**6+2)**(1/2),x)","\frac{x^{15}}{12 \sqrt{x^{6} + 2}} - \frac{x^{9}}{12 \sqrt{x^{6} + 2}} - \frac{x^{3}}{2 \sqrt{x^{6} + 2}} + \frac{\operatorname{asinh}{\left(\frac{\sqrt{2} x^{3}}{2} \right)}}{2}"," ",0,"x**15/(12*sqrt(x**6 + 2)) - x**9/(12*sqrt(x**6 + 2)) - x**3/(2*sqrt(x**6 + 2)) + asinh(sqrt(2)*x**3/2)/2","A",0
1391,1,39,0,3.324394," ","integrate(x**8/(x**6+2)**(1/2),x)","\frac{x^{9}}{6 \sqrt{x^{6} + 2}} + \frac{x^{3}}{3 \sqrt{x^{6} + 2}} - \frac{\operatorname{asinh}{\left(\frac{\sqrt{2} x^{3}}{2} \right)}}{3}"," ",0,"x**9/(6*sqrt(x**6 + 2)) + x**3/(3*sqrt(x**6 + 2)) - asinh(sqrt(2)*x**3/2)/3","A",0
1392,1,12,0,1.748284," ","integrate(x**2/(x**6+2)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{2} x^{3}}{2} \right)}}{3}"," ",0,"asinh(sqrt(2)*x**3/2)/3","A",0
1393,1,12,0,1.173968," ","integrate(1/x**4/(x**6+2)**(1/2),x)","- \frac{\sqrt{1 + \frac{2}{x^{6}}}}{6}"," ",0,"-sqrt(1 + 2/x**6)/6","A",0
1394,1,26,0,1.981107," ","integrate(1/x**10/(x**6+2)**(1/2),x)","\frac{\sqrt{1 + \frac{2}{x^{6}}}}{18} - \frac{\sqrt{1 + \frac{2}{x^{6}}}}{18 x^{6}}"," ",0,"sqrt(1 + 2/x**6)/18 - sqrt(1 + 2/x**6)/(18*x**6)","A",0
1395,1,41,0,3.709952," ","integrate(1/x**16/(x**6+2)**(1/2),x)","- \frac{\sqrt{1 + \frac{2}{x^{6}}}}{45} + \frac{\sqrt{1 + \frac{2}{x^{6}}}}{45 x^{6}} - \frac{\sqrt{1 + \frac{2}{x^{6}}}}{30 x^{12}}"," ",0,"-sqrt(1 + 2/x**6)/45 + sqrt(1 + 2/x**6)/(45*x**6) - sqrt(1 + 2/x**6)/(30*x**12)","A",0
1396,1,36,0,0.927468," ","integrate(x**7/(x**6+2)**(1/2),x)","\frac{\sqrt{2} x^{8} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 \Gamma\left(\frac{7}{3}\right)}"," ",0,"sqrt(2)*x**8*gamma(4/3)*hyper((1/2, 4/3), (7/3,), x**6*exp_polar(I*pi)/2)/(12*gamma(7/3))","A",0
1397,1,36,0,1.166400," ","integrate(x/(x**6+2)**(1/2),x)","\frac{\sqrt{2} x^{2} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 \Gamma\left(\frac{4}{3}\right)}"," ",0,"sqrt(2)*x**2*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**6*exp_polar(I*pi)/2)/(12*gamma(4/3))","A",0
1398,1,39,0,0.945604," ","integrate(1/x**5/(x**6+2)**(1/2),x)","\frac{\sqrt{2} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 x^{4} \Gamma\left(\frac{1}{3}\right)}"," ",0,"sqrt(2)*gamma(-2/3)*hyper((-2/3, 1/2), (1/3,), x**6*exp_polar(I*pi)/2)/(12*x**4*gamma(1/3))","A",0
1399,1,36,0,1.452154," ","integrate(x**6/(x**6+2)**(1/2),x)","\frac{\sqrt{2} x^{7} \Gamma\left(\frac{7}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{6} \\ \frac{13}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 \Gamma\left(\frac{13}{6}\right)}"," ",0,"sqrt(2)*x**7*gamma(7/6)*hyper((1/2, 7/6), (13/6,), x**6*exp_polar(I*pi)/2)/(12*gamma(13/6))","C",0
1400,1,34,0,1.098191," ","integrate(1/(x**6+2)**(1/2),x)","\frac{\sqrt{2} x \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{1}{2} \\ \frac{7}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 \Gamma\left(\frac{7}{6}\right)}"," ",0,"sqrt(2)*x*gamma(1/6)*hyper((1/6, 1/2), (7/6,), x**6*exp_polar(I*pi)/2)/(12*gamma(7/6))","C",0
1401,1,39,0,1.702149," ","integrate(1/x**6/(x**6+2)**(1/2),x)","\frac{\sqrt{2} \Gamma\left(- \frac{5}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{6}, \frac{1}{2} \\ \frac{1}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 x^{5} \Gamma\left(\frac{1}{6}\right)}"," ",0,"sqrt(2)*gamma(-5/6)*hyper((-5/6, 1/2), (1/6,), x**6*exp_polar(I*pi)/2)/(12*x**5*gamma(1/6))","C",0
1402,1,36,0,1.015939," ","integrate(x**9/(x**6+2)**(1/2),x)","\frac{\sqrt{2} x^{10} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 \Gamma\left(\frac{8}{3}\right)}"," ",0,"sqrt(2)*x**10*gamma(5/3)*hyper((1/2, 5/3), (8/3,), x**6*exp_polar(I*pi)/2)/(12*gamma(8/3))","A",0
1403,1,36,0,0.722663," ","integrate(x**3/(x**6+2)**(1/2),x)","\frac{\sqrt{2} x^{4} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 \Gamma\left(\frac{5}{3}\right)}"," ",0,"sqrt(2)*x**4*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**6*exp_polar(I*pi)/2)/(12*gamma(5/3))","A",0
1404,1,39,0,1.321982," ","integrate(1/x**3/(x**6+2)**(1/2),x)","\frac{\sqrt{2} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{2}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 x^{2} \Gamma\left(\frac{2}{3}\right)}"," ",0,"sqrt(2)*gamma(-1/3)*hyper((-1/3, 1/2), (2/3,), x**6*exp_polar(I*pi)/2)/(12*x**2*gamma(2/3))","A",0
1405,1,36,0,2.147462," ","integrate(x**10/(x**6+2)**(1/2),x)","\frac{\sqrt{2} x^{11} \Gamma\left(\frac{11}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{6} \\ \frac{17}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 \Gamma\left(\frac{17}{6}\right)}"," ",0,"sqrt(2)*x**11*gamma(11/6)*hyper((1/2, 11/6), (17/6,), x**6*exp_polar(I*pi)/2)/(12*gamma(17/6))","C",0
1406,1,36,0,1.171734," ","integrate(x**4/(x**6+2)**(1/2),x)","\frac{\sqrt{2} x^{5} \Gamma\left(\frac{5}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{6} \\ \frac{11}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 \Gamma\left(\frac{11}{6}\right)}"," ",0,"sqrt(2)*x**5*gamma(5/6)*hyper((1/2, 5/6), (11/6,), x**6*exp_polar(I*pi)/2)/(12*gamma(11/6))","C",0
1407,1,37,0,1.317472," ","integrate(1/x**2/(x**6+2)**(1/2),x)","\frac{\sqrt{2} \Gamma\left(- \frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{6}, \frac{1}{2} \\ \frac{5}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{12 x \Gamma\left(\frac{5}{6}\right)}"," ",0,"sqrt(2)*gamma(-1/6)*hyper((-1/6, 1/2), (5/6,), x**6*exp_polar(I*pi)/2)/(12*x*gamma(5/6))","C",0
1408,1,54,0,19.149043," ","integrate(x**23/(x**6+2)**(3/2),x)","\frac{x^{18}}{15 \sqrt{x^{6} + 2}} - \frac{4 x^{12}}{15 \sqrt{x^{6} + 2}} + \frac{32 x^{6}}{15 \sqrt{x^{6} + 2}} + \frac{128}{15 \sqrt{x^{6} + 2}}"," ",0,"x**18/(15*sqrt(x**6 + 2)) - 4*x**12/(15*sqrt(x**6 + 2)) + 32*x**6/(15*sqrt(x**6 + 2)) + 128/(15*sqrt(x**6 + 2))","A",0
1409,1,39,0,8.229964," ","integrate(x**17/(x**6+2)**(3/2),x)","\frac{x^{12}}{9 \sqrt{x^{6} + 2}} - \frac{8 x^{6}}{9 \sqrt{x^{6} + 2}} - \frac{32}{9 \sqrt{x^{6} + 2}}"," ",0,"x**12/(9*sqrt(x**6 + 2)) - 8*x**6/(9*sqrt(x**6 + 2)) - 32/(9*sqrt(x**6 + 2))","A",0
1410,1,24,0,2.823024," ","integrate(x**11/(x**6+2)**(3/2),x)","\frac{x^{6}}{3 \sqrt{x^{6} + 2}} + \frac{4}{3 \sqrt{x^{6} + 2}}"," ",0,"x**6/(3*sqrt(x**6 + 2)) + 4/(3*sqrt(x**6 + 2))","A",0
1411,1,12,0,0.611097," ","integrate(x**5/(x**6+2)**(3/2),x)","- \frac{1}{3 \sqrt{x^{6} + 2}}"," ",0,"-1/(3*sqrt(x**6 + 2))","A",0
1412,1,194,0,1.625495," ","integrate(1/x/(x**6+2)**(3/2),x)","\frac{x^{6} \log{\left(x^{6} \right)}}{12 \sqrt{2} x^{6} + 24 \sqrt{2}} - \frac{2 x^{6} \log{\left(\sqrt{\frac{x^{6}}{2} + 1} + 1 \right)}}{12 \sqrt{2} x^{6} + 24 \sqrt{2}} - \frac{x^{6} \log{\left(2 \right)}}{12 \sqrt{2} x^{6} + 24 \sqrt{2}} + \frac{2 \sqrt{2} \sqrt{x^{6} + 2}}{12 \sqrt{2} x^{6} + 24 \sqrt{2}} + \frac{2 \log{\left(x^{6} \right)}}{12 \sqrt{2} x^{6} + 24 \sqrt{2}} - \frac{4 \log{\left(\sqrt{\frac{x^{6}}{2} + 1} + 1 \right)}}{12 \sqrt{2} x^{6} + 24 \sqrt{2}} - \frac{2 \log{\left(2 \right)}}{12 \sqrt{2} x^{6} + 24 \sqrt{2}}"," ",0,"x**6*log(x**6)/(12*sqrt(2)*x**6 + 24*sqrt(2)) - 2*x**6*log(sqrt(x**6/2 + 1) + 1)/(12*sqrt(2)*x**6 + 24*sqrt(2)) - x**6*log(2)/(12*sqrt(2)*x**6 + 24*sqrt(2)) + 2*sqrt(2)*sqrt(x**6 + 2)/(12*sqrt(2)*x**6 + 24*sqrt(2)) + 2*log(x**6)/(12*sqrt(2)*x**6 + 24*sqrt(2)) - 4*log(sqrt(x**6/2 + 1) + 1)/(12*sqrt(2)*x**6 + 24*sqrt(2)) - 2*log(2)/(12*sqrt(2)*x**6 + 24*sqrt(2))","B",0
1413,1,49,0,2.839440," ","integrate(1/x**7/(x**6+2)**(3/2),x)","\frac{\sqrt{2} \operatorname{asinh}{\left(\frac{\sqrt{2}}{x^{3}} \right)}}{16} - \frac{1}{8 x^{3} \sqrt{1 + \frac{2}{x^{6}}}} - \frac{1}{12 x^{9} \sqrt{1 + \frac{2}{x^{6}}}}"," ",0,"sqrt(2)*asinh(sqrt(2)/x**3)/16 - 1/(8*x**3*sqrt(1 + 2/x**6)) - 1/(12*x**9*sqrt(1 + 2/x**6))","A",0
1414,1,68,0,6.640452," ","integrate(1/x**13/(x**6+2)**(3/2),x)","- \frac{5 \sqrt{2} \operatorname{asinh}{\left(\frac{\sqrt{2}}{x^{3}} \right)}}{128} + \frac{5}{64 x^{3} \sqrt{1 + \frac{2}{x^{6}}}} + \frac{5}{96 x^{9} \sqrt{1 + \frac{2}{x^{6}}}} - \frac{1}{24 x^{15} \sqrt{1 + \frac{2}{x^{6}}}}"," ",0,"-5*sqrt(2)*asinh(sqrt(2)/x**3)/128 + 5/(64*x**3*sqrt(1 + 2/x**6)) + 5/(96*x**9*sqrt(1 + 2/x**6)) - 1/(24*x**15*sqrt(1 + 2/x**6))","A",0
1415,1,36,0,5.510629," ","integrate(x**14/(x**6+2)**(3/2),x)","\frac{x^{9}}{6 \sqrt{x^{6} + 2}} + \frac{x^{3}}{\sqrt{x^{6} + 2}} - \operatorname{asinh}{\left(\frac{\sqrt{2} x^{3}}{2} \right)}"," ",0,"x**9/(6*sqrt(x**6 + 2)) + x**3/sqrt(x**6 + 2) - asinh(sqrt(2)*x**3/2)","A",0
1416,1,26,0,2.825529," ","integrate(x**8/(x**6+2)**(3/2),x)","- \frac{x^{3}}{3 \sqrt{x^{6} + 2}} + \frac{\operatorname{asinh}{\left(\frac{\sqrt{2} x^{3}}{2} \right)}}{3}"," ",0,"-x**3/(3*sqrt(x**6 + 2)) + asinh(sqrt(2)*x**3/2)/3","A",0
1417,1,12,0,1.044978," ","integrate(x**2/(x**6+2)**(3/2),x)","\frac{x^{3}}{6 \sqrt{x^{6} + 2}}"," ",0,"x**3/(6*sqrt(x**6 + 2))","A",0
1418,1,31,0,1.498862," ","integrate(1/x**4/(x**6+2)**(3/2),x)","- \frac{1}{6 \sqrt{1 + \frac{2}{x^{6}}}} - \frac{1}{6 x^{6} \sqrt{1 + \frac{2}{x^{6}}}}"," ",0,"-1/(6*sqrt(1 + 2/x**6)) - 1/(6*x**6*sqrt(1 + 2/x**6))","A",0
1419,1,70,0,2.532162," ","integrate(1/x**10/(x**6+2)**(3/2),x)","\frac{2 x^{12} \sqrt{1 + \frac{2}{x^{6}}}}{18 x^{12} + 36 x^{6}} + \frac{2 x^{6} \sqrt{1 + \frac{2}{x^{6}}}}{18 x^{12} + 36 x^{6}} - \frac{\sqrt{1 + \frac{2}{x^{6}}}}{18 x^{12} + 36 x^{6}}"," ",0,"2*x**12*sqrt(1 + 2/x**6)/(18*x**12 + 36*x**6) + 2*x**6*sqrt(1 + 2/x**6)/(18*x**12 + 36*x**6) - sqrt(1 + 2/x**6)/(18*x**12 + 36*x**6)","A",0
1420,1,36,0,2.411431," ","integrate(x**13/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x^{14} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{10}{3}\right)}"," ",0,"sqrt(2)*x**14*gamma(7/3)*hyper((3/2, 7/3), (10/3,), x**6*exp_polar(I*pi)/2)/(24*gamma(10/3))","A",0
1421,1,36,0,1.609370," ","integrate(x**7/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x^{8} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{3}{2} \\ \frac{7}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{7}{3}\right)}"," ",0,"sqrt(2)*x**8*gamma(4/3)*hyper((4/3, 3/2), (7/3,), x**6*exp_polar(I*pi)/2)/(24*gamma(7/3))","A",0
1422,1,36,0,1.419797," ","integrate(x/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x^{2} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{4}{3}\right)}"," ",0,"sqrt(2)*x**2*gamma(1/3)*hyper((1/3, 3/2), (4/3,), x**6*exp_polar(I*pi)/2)/(24*gamma(4/3))","A",0
1423,1,39,0,1.970649," ","integrate(1/x**5/(x**6+2)**(3/2),x)","\frac{\sqrt{2} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{3}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 x^{4} \Gamma\left(\frac{1}{3}\right)}"," ",0,"sqrt(2)*gamma(-2/3)*hyper((-2/3, 3/2), (1/3,), x**6*exp_polar(I*pi)/2)/(24*x**4*gamma(1/3))","A",0
1424,1,36,0,2.349795," ","integrate(x**12/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x^{13} \Gamma\left(\frac{13}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{13}{6} \\ \frac{19}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{19}{6}\right)}"," ",0,"sqrt(2)*x**13*gamma(13/6)*hyper((3/2, 13/6), (19/6,), x**6*exp_polar(I*pi)/2)/(24*gamma(19/6))","C",0
1425,1,36,0,1.564177," ","integrate(x**6/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x^{7} \Gamma\left(\frac{7}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{6}, \frac{3}{2} \\ \frac{13}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{13}{6}\right)}"," ",0,"sqrt(2)*x**7*gamma(7/6)*hyper((7/6, 3/2), (13/6,), x**6*exp_polar(I*pi)/2)/(24*gamma(13/6))","C",0
1426,1,34,0,0.742435," ","integrate(1/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{3}{2} \\ \frac{7}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{7}{6}\right)}"," ",0,"sqrt(2)*x*gamma(1/6)*hyper((1/6, 3/2), (7/6,), x**6*exp_polar(I*pi)/2)/(24*gamma(7/6))","C",0
1427,1,39,0,2.005376," ","integrate(1/x**6/(x**6+2)**(3/2),x)","\frac{\sqrt{2} \Gamma\left(- \frac{5}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{6}, \frac{3}{2} \\ \frac{1}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 x^{5} \Gamma\left(\frac{1}{6}\right)}"," ",0,"sqrt(2)*gamma(-5/6)*hyper((-5/6, 3/2), (1/6,), x**6*exp_polar(I*pi)/2)/(24*x**5*gamma(1/6))","C",0
1428,1,36,0,2.820475," ","integrate(x**15/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x^{16} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{11}{3}\right)}"," ",0,"sqrt(2)*x**16*gamma(8/3)*hyper((3/2, 8/3), (11/3,), x**6*exp_polar(I*pi)/2)/(24*gamma(11/3))","A",0
1429,1,36,0,1.745722," ","integrate(x**9/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x^{10} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{8}{3}\right)}"," ",0,"sqrt(2)*x**10*gamma(5/3)*hyper((3/2, 5/3), (8/3,), x**6*exp_polar(I*pi)/2)/(24*gamma(8/3))","A",0
1430,1,36,0,1.385658," ","integrate(x**3/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x^{4} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{3}{2} \\ \frac{5}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{5}{3}\right)}"," ",0,"sqrt(2)*x**4*gamma(2/3)*hyper((2/3, 3/2), (5/3,), x**6*exp_polar(I*pi)/2)/(24*gamma(5/3))","A",0
1431,1,39,0,1.684880," ","integrate(1/x**3/(x**6+2)**(3/2),x)","\frac{\sqrt{2} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{3}{2} \\ \frac{2}{3} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 x^{2} \Gamma\left(\frac{2}{3}\right)}"," ",0,"sqrt(2)*gamma(-1/3)*hyper((-1/3, 3/2), (2/3,), x**6*exp_polar(I*pi)/2)/(24*x**2*gamma(2/3))","A",0
1432,1,36,0,1.975104," ","integrate(x**10/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x^{11} \Gamma\left(\frac{11}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{11}{6} \\ \frac{17}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{17}{6}\right)}"," ",0,"sqrt(2)*x**11*gamma(11/6)*hyper((3/2, 11/6), (17/6,), x**6*exp_polar(I*pi)/2)/(24*gamma(17/6))","C",0
1433,1,36,0,1.357908," ","integrate(x**4/(x**6+2)**(3/2),x)","\frac{\sqrt{2} x^{5} \Gamma\left(\frac{5}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{6}, \frac{3}{2} \\ \frac{11}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 \Gamma\left(\frac{11}{6}\right)}"," ",0,"sqrt(2)*x**5*gamma(5/6)*hyper((5/6, 3/2), (11/6,), x**6*exp_polar(I*pi)/2)/(24*gamma(11/6))","C",0
1434,1,37,0,1.540865," ","integrate(1/x**2/(x**6+2)**(3/2),x)","\frac{\sqrt{2} \Gamma\left(- \frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{6}, \frac{3}{2} \\ \frac{5}{6} \end{matrix}\middle| {\frac{x^{6} e^{i \pi}}{2}} \right)}}{24 x \Gamma\left(\frac{5}{6}\right)}"," ",0,"sqrt(2)*gamma(-1/6)*hyper((-1/6, 3/2), (5/6,), x**6*exp_polar(I*pi)/2)/(24*x*gamma(5/6))","C",0
1435,1,94,0,2.972517," ","integrate(x**m*(b*x**7+a),x)","\begin{cases} - \frac{a}{7 x^{7}} + b \log{\left(x \right)} & \text{for}\: m = -8 \\a \log{\left(x \right)} + \frac{b x^{7}}{7} & \text{for}\: m = -1 \\\frac{a m x x^{m}}{m^{2} + 9 m + 8} + \frac{8 a x x^{m}}{m^{2} + 9 m + 8} + \frac{b m x^{8} x^{m}}{m^{2} + 9 m + 8} + \frac{b x^{8} x^{m}}{m^{2} + 9 m + 8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(7*x**7) + b*log(x), Eq(m, -8)), (a*log(x) + b*x**7/7, Eq(m, -1)), (a*m*x*x**m/(m**2 + 9*m + 8) + 8*a*x*x**m/(m**2 + 9*m + 8) + b*m*x**8*x**m/(m**2 + 9*m + 8) + b*x**8*x**m/(m**2 + 9*m + 8), True))","A",0
1436,1,12,0,0.072423," ","integrate(x**8*(b*x**7+a),x)","\frac{a x^{9}}{9} + \frac{b x^{16}}{16}"," ",0,"a*x**9/9 + b*x**16/16","A",0
1437,1,10,0,0.335290," ","integrate((b*x**7+a)/x**8,x)","- \frac{a}{7 x^{7}} + b \log{\left(x \right)}"," ",0,"-a/(7*x**7) + b*log(x)","A",0
1438,1,313,0,13.851287," ","integrate(x**m*(b*x**7+a)**2,x)","\begin{cases} - \frac{a^{2}}{14 x^{14}} - \frac{2 a b}{7 x^{7}} + b^{2} \log{\left(x \right)} & \text{for}\: m = -15 \\- \frac{a^{2}}{7 x^{7}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{7}}{7} & \text{for}\: m = -8 \\a^{2} \log{\left(x \right)} + \frac{2 a b x^{7}}{7} + \frac{b^{2} x^{14}}{14} & \text{for}\: m = -1 \\\frac{a^{2} m^{2} x x^{m}}{m^{3} + 24 m^{2} + 143 m + 120} + \frac{23 a^{2} m x x^{m}}{m^{3} + 24 m^{2} + 143 m + 120} + \frac{120 a^{2} x x^{m}}{m^{3} + 24 m^{2} + 143 m + 120} + \frac{2 a b m^{2} x^{8} x^{m}}{m^{3} + 24 m^{2} + 143 m + 120} + \frac{32 a b m x^{8} x^{m}}{m^{3} + 24 m^{2} + 143 m + 120} + \frac{30 a b x^{8} x^{m}}{m^{3} + 24 m^{2} + 143 m + 120} + \frac{b^{2} m^{2} x^{15} x^{m}}{m^{3} + 24 m^{2} + 143 m + 120} + \frac{9 b^{2} m x^{15} x^{m}}{m^{3} + 24 m^{2} + 143 m + 120} + \frac{8 b^{2} x^{15} x^{m}}{m^{3} + 24 m^{2} + 143 m + 120} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(14*x**14) - 2*a*b/(7*x**7) + b**2*log(x), Eq(m, -15)), (-a**2/(7*x**7) + 2*a*b*log(x) + b**2*x**7/7, Eq(m, -8)), (a**2*log(x) + 2*a*b*x**7/7 + b**2*x**14/14, Eq(m, -1)), (a**2*m**2*x*x**m/(m**3 + 24*m**2 + 143*m + 120) + 23*a**2*m*x*x**m/(m**3 + 24*m**2 + 143*m + 120) + 120*a**2*x*x**m/(m**3 + 24*m**2 + 143*m + 120) + 2*a*b*m**2*x**8*x**m/(m**3 + 24*m**2 + 143*m + 120) + 32*a*b*m*x**8*x**m/(m**3 + 24*m**2 + 143*m + 120) + 30*a*b*x**8*x**m/(m**3 + 24*m**2 + 143*m + 120) + b**2*m**2*x**15*x**m/(m**3 + 24*m**2 + 143*m + 120) + 9*b**2*m*x**15*x**m/(m**3 + 24*m**2 + 143*m + 120) + 8*b**2*x**15*x**m/(m**3 + 24*m**2 + 143*m + 120), True))","A",0
1439,1,24,0,0.070465," ","integrate(x**8*(b*x**7+a)**2,x)","\frac{a^{2} x^{9}}{9} + \frac{a b x^{16}}{8} + \frac{b^{2} x^{23}}{23}"," ",0,"a**2*x**9/9 + a*b*x**16/8 + b**2*x**23/23","A",0
1440,1,24,0,0.279487," ","integrate((b*x**7+a)**2/x**8,x)","- \frac{a^{2}}{7 x^{7}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{7}}{7}"," ",0,"-a**2/(7*x**7) + 2*a*b*log(x) + b**2*x**7/7","A",0
1441,-1,0,0,0.000000," ","integrate(x**m/(b*x**7+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1442,1,10,0,0.329643," ","integrate(x**6/(b*x**7+a),x)","\frac{\log{\left(a + b x^{7} \right)}}{7 b}"," ",0,"log(a + b*x**7)/(7*b)","A",0
1443,1,20,0,0.274561," ","integrate(1/(b*x**7+a),x)","\operatorname{RootSum} {\left(823543 t^{7} a^{6} b - 1, \left( t \mapsto t \log{\left(7 t a + x \right)} \right)\right)}"," ",0,"RootSum(823543*_t**7*a**6*b - 1, Lambda(_t, _t*log(7*_t*a + x)))","A",0
1444,1,15,0,0.521859," ","integrate(1/x/(b*x**7+a),x)","\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{7} \right)}}{7 a}"," ",0,"log(x)/a - log(a/b + x**7)/(7*a)","A",0
1445,-1,0,0,0.000000," ","integrate(x**m/(-b*x**7+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1446,1,12,0,0.380216," ","integrate(x**6/(-b*x**7+a),x)","- \frac{\log{\left(- a + b x^{7} \right)}}{7 b}"," ",0,"-log(-a + b*x**7)/(7*b)","A",0
1447,1,22,0,0.216476," ","integrate(1/(-b*x**7+a),x)","- \operatorname{RootSum} {\left(823543 t^{7} a^{6} b - 1, \left( t \mapsto t \log{\left(- 7 t a + x \right)} \right)\right)}"," ",0,"-RootSum(823543*_t**7*a**6*b - 1, Lambda(_t, _t*log(-7*_t*a + x)))","A",0
1448,1,15,0,0.627624," ","integrate(1/x/(-b*x**7+a),x)","\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(- \frac{a}{b} + x^{7} \right)}}{7 a}"," ",0,"log(x)/a - log(-a/b + x**7)/(7*a)","A",0
1449,1,46,0,0.347493," ","integrate(1/(-x**7+1),x)","- \frac{\log{\left(x - 1 \right)}}{7} - \operatorname{RootSum} {\left(117649 t^{6} + 16807 t^{5} + 2401 t^{4} + 343 t^{3} + 49 t^{2} + 7 t + 1, \left( t \mapsto t \log{\left(- 7 t + x \right)} \right)\right)}"," ",0,"-log(x - 1)/7 - RootSum(117649*_t**6 + 16807*_t**5 + 2401*_t**4 + 343*_t**3 + 49*_t**2 + 7*_t + 1, Lambda(_t, _t*log(-7*_t + x)))","A",0
1450,1,44,0,0.347057," ","integrate(1/(x**7+1),x)","\frac{\log{\left(x + 1 \right)}}{7} + \operatorname{RootSum} {\left(117649 t^{6} + 16807 t^{5} + 2401 t^{4} + 343 t^{3} + 49 t^{2} + 7 t + 1, \left( t \mapsto t \log{\left(7 t + x \right)} \right)\right)}"," ",0,"log(x + 1)/7 + RootSum(117649*_t**6 + 16807*_t**5 + 2401*_t**4 + 343*_t**3 + 49*_t**2 + 7*_t + 1, Lambda(_t, _t*log(7*_t + x)))","A",0
1451,1,27,0,0.379961," ","integrate(x**9/(b*x**8+a),x)","\operatorname{RootSum} {\left(4096 t^{4} b^{5} + a, \left( t \mapsto t \log{\left(- 8 t b + x^{2} \right)} \right)\right)} + \frac{x^{2}}{2 b}"," ",0,"RootSum(4096*_t**4*b**5 + a, Lambda(_t, _t*log(-8*_t*b + x**2))) + x**2/(2*b)","A",0
1452,1,10,0,0.397899," ","integrate(x**7/(b*x**8+a),x)","\frac{\log{\left(a + b x^{8} \right)}}{8 b}"," ",0,"log(a + b*x**8)/(8*b)","A",0
1453,1,27,0,0.278282," ","integrate(x**5/(b*x**8+a),x)","\operatorname{RootSum} {\left(4096 t^{4} a b^{3} + 1, \left( t \mapsto t \log{\left(512 t^{3} a b^{2} + x^{2} \right)} \right)\right)}"," ",0,"RootSum(4096*_t**4*a*b**3 + 1, Lambda(_t, _t*log(512*_t**3*a*b**2 + x**2)))","A",0
1454,1,56,0,0.424736," ","integrate(x**3/(b*x**8+a),x)","- \frac{\sqrt{- \frac{1}{a b}} \log{\left(- a \sqrt{- \frac{1}{a b}} + x^{4} \right)}}{8} + \frac{\sqrt{- \frac{1}{a b}} \log{\left(a \sqrt{- \frac{1}{a b}} + x^{4} \right)}}{8}"," ",0,"-sqrt(-1/(a*b))*log(-a*sqrt(-1/(a*b)) + x**4)/8 + sqrt(-1/(a*b))*log(a*sqrt(-1/(a*b)) + x**4)/8","B",0
1455,1,22,0,0.218680," ","integrate(x/(b*x**8+a),x)","\operatorname{RootSum} {\left(4096 t^{4} a^{3} b + 1, \left( t \mapsto t \log{\left(8 t a + x^{2} \right)} \right)\right)}"," ",0,"RootSum(4096*_t**4*a**3*b + 1, Lambda(_t, _t*log(8*_t*a + x**2)))","A",0
1456,1,15,0,0.649257," ","integrate(1/x/(b*x**8+a),x)","\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{8} \right)}}{8 a}"," ",0,"log(x)/a - log(a/b + x**8)/(8*a)","A",0
1457,1,34,0,0.512345," ","integrate(1/x**3/(b*x**8+a),x)","\operatorname{RootSum} {\left(4096 t^{4} a^{5} + b, \left( t \mapsto t \log{\left(- \frac{512 t^{3} a^{4}}{b} + x^{2} \right)} \right)\right)} - \frac{1}{2 a x^{2}}"," ",0,"RootSum(4096*_t**4*a**5 + b, Lambda(_t, _t*log(-512*_t**3*a**4/b + x**2))) - 1/(2*a*x**2)","A",0
1458,1,71,0,0.693766," ","integrate(1/x**5/(b*x**8+a),x)","\frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(- \frac{a^{2} \sqrt{- \frac{b}{a^{3}}}}{b} + x^{4} \right)}}{8} - \frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(\frac{a^{2} \sqrt{- \frac{b}{a^{3}}}}{b} + x^{4} \right)}}{8} - \frac{1}{4 a x^{4}}"," ",0,"sqrt(-b/a**3)*log(-a**2*sqrt(-b/a**3)/b + x**4)/8 - sqrt(-b/a**3)*log(a**2*sqrt(-b/a**3)/b + x**4)/8 - 1/(4*a*x**4)","A",0
1459,1,34,0,0.391525," ","integrate(1/x**7/(b*x**8+a),x)","\operatorname{RootSum} {\left(4096 t^{4} a^{7} + b^{3}, \left( t \mapsto t \log{\left(- \frac{8 t a^{2}}{b} + x^{2} \right)} \right)\right)} - \frac{1}{6 a x^{6}}"," ",0,"RootSum(4096*_t**4*a**7 + b**3, Lambda(_t, _t*log(-8*_t*a**2/b + x**2))) - 1/(6*a*x**6)","A",0
1460,1,31,0,1.675180," ","integrate(1/x**9/(b*x**8+a),x)","- \frac{1}{8 a x^{8}} - \frac{b \log{\left(x \right)}}{a^{2}} + \frac{b \log{\left(\frac{a}{b} + x^{8} \right)}}{8 a^{2}}"," ",0,"-1/(8*a*x**8) - b*log(x)/a**2 + b*log(a/b + x**8)/(8*a**2)","A",0
1461,1,22,0,0.419420," ","integrate(x**8/(b*x**8+a),x)","\operatorname{RootSum} {\left(16777216 t^{8} b^{9} + a, \left( t \mapsto t \log{\left(- 8 t b + x \right)} \right)\right)} + \frac{x}{b}"," ",0,"RootSum(16777216*_t**8*b**9 + a, Lambda(_t, _t*log(-8*_t*b + x))) + x/b","A",0
1462,1,26,0,0.339200," ","integrate(x**6/(b*x**8+a),x)","\operatorname{RootSum} {\left(16777216 t^{8} a b^{7} + 1, \left( t \mapsto t \log{\left(2097152 t^{7} a b^{6} + x \right)} \right)\right)}"," ",0,"RootSum(16777216*_t**8*a*b**7 + 1, Lambda(_t, _t*log(2097152*_t**7*a*b**6 + x)))","A",0
1463,1,29,0,0.341004," ","integrate(x**4/(b*x**8+a),x)","\operatorname{RootSum} {\left(16777216 t^{8} a^{3} b^{5} + 1, \left( t \mapsto t \log{\left(- 32768 t^{5} a^{2} b^{3} + x \right)} \right)\right)}"," ",0,"RootSum(16777216*_t**8*a**3*b**5 + 1, Lambda(_t, _t*log(-32768*_t**5*a**2*b**3 + x)))","A",0
1464,1,27,0,0.346901," ","integrate(x**2/(b*x**8+a),x)","\operatorname{RootSum} {\left(16777216 t^{8} a^{5} b^{3} + 1, \left( t \mapsto t \log{\left(- 512 t^{3} a^{2} b + x \right)} \right)\right)}"," ",0,"RootSum(16777216*_t**8*a**5*b**3 + 1, Lambda(_t, _t*log(-512*_t**3*a**2*b + x)))","A",0
1465,1,20,0,0.393238," ","integrate(1/(b*x**8+a),x)","\operatorname{RootSum} {\left(16777216 t^{8} a^{7} b + 1, \left( t \mapsto t \log{\left(8 t a + x \right)} \right)\right)}"," ",0,"RootSum(16777216*_t**8*a**7*b + 1, Lambda(_t, _t*log(8*_t*a + x)))","A",0
1466,1,29,0,0.560447," ","integrate(1/x**2/(b*x**8+a),x)","\operatorname{RootSum} {\left(16777216 t^{8} a^{9} + b, \left( t \mapsto t \log{\left(- \frac{2097152 t^{7} a^{8}}{b} + x \right)} \right)\right)} - \frac{1}{a x}"," ",0,"RootSum(16777216*_t**8*a**9 + b, Lambda(_t, _t*log(-2097152*_t**7*a**8/b + x))) - 1/(a*x)","A",0
1467,1,36,0,0.736832," ","integrate(1/x**4/(b*x**8+a),x)","\operatorname{RootSum} {\left(16777216 t^{8} a^{11} + b^{3}, \left( t \mapsto t \log{\left(\frac{32768 t^{5} a^{7}}{b^{2}} + x \right)} \right)\right)} - \frac{1}{3 a x^{3}}"," ",0,"RootSum(16777216*_t**8*a**11 + b**3, Lambda(_t, _t*log(32768*_t**5*a**7/b**2 + x))) - 1/(3*a*x**3)","A",0
1468,1,36,0,0.575126," ","integrate(1/x**6/(b*x**8+a),x)","\operatorname{RootSum} {\left(16777216 t^{8} a^{13} + b^{5}, \left( t \mapsto t \log{\left(\frac{512 t^{3} a^{5}}{b^{2}} + x \right)} \right)\right)} - \frac{1}{5 a x^{5}}"," ",0,"RootSum(16777216*_t**8*a**13 + b**5, Lambda(_t, _t*log(512*_t**3*a**5/b**2 + x))) - 1/(5*a*x**5)","A",0
1469,1,32,0,0.402034," ","integrate(1/x**8/(b*x**8+a),x)","\operatorname{RootSum} {\left(16777216 t^{8} a^{15} + b^{7}, \left( t \mapsto t \log{\left(- \frac{8 t a^{2}}{b} + x \right)} \right)\right)} - \frac{1}{7 a x^{7}}"," ",0,"RootSum(16777216*_t**8*a**15 + b**7, Lambda(_t, _t*log(-8*_t*a**2/b + x))) - 1/(7*a*x**7)","A",0
1470,1,22,0,0.404896," ","integrate(1/(-b*x**8+a),x)","- \operatorname{RootSum} {\left(16777216 t^{8} a^{7} b - 1, \left( t \mapsto t \log{\left(- 8 t a + x \right)} \right)\right)}"," ",0,"-RootSum(16777216*_t**8*a**7*b - 1, Lambda(_t, _t*log(-8*_t*a + x)))","A",0
1471,1,27,0,0.300066," ","integrate(x**9/(-x**8+1),x)","- \frac{x^{2}}{2} - \frac{\log{\left(x^{2} - 1 \right)}}{8} + \frac{\log{\left(x^{2} + 1 \right)}}{8} + \frac{\operatorname{atan}{\left(x^{2} \right)}}{4}"," ",0,"-x**2/2 - log(x**2 - 1)/8 + log(x**2 + 1)/8 + atan(x**2)/4","A",0
1472,1,8,0,0.288183," ","integrate(x**7/(-x**8+1),x)","- \frac{\log{\left(x^{8} - 1 \right)}}{8}"," ",0,"-log(x**8 - 1)/8","A",0
1473,1,22,0,0.418766," ","integrate(x**5/(-x**8+1),x)","- \frac{\log{\left(x^{2} - 1 \right)}}{8} + \frac{\log{\left(x^{2} + 1 \right)}}{8} - \frac{\operatorname{atan}{\left(x^{2} \right)}}{4}"," ",0,"-log(x**2 - 1)/8 + log(x**2 + 1)/8 - atan(x**2)/4","A",0
1474,1,15,0,0.336006," ","integrate(x**3/(-x**8+1),x)","- \frac{\log{\left(x^{4} - 1 \right)}}{8} + \frac{\log{\left(x^{4} + 1 \right)}}{8}"," ",0,"-log(x**4 - 1)/8 + log(x**4 + 1)/8","B",0
1475,1,22,0,0.279494," ","integrate(x/(-x**8+1),x)","- \frac{\log{\left(x^{2} - 1 \right)}}{8} + \frac{\log{\left(x^{2} + 1 \right)}}{8} + \frac{\operatorname{atan}{\left(x^{2} \right)}}{4}"," ",0,"-log(x**2 - 1)/8 + log(x**2 + 1)/8 + atan(x**2)/4","A",0
1476,1,10,0,0.289085," ","integrate(1/x/(-x**8+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{8} - 1 \right)}}{8}"," ",0,"log(x) - log(x**8 - 1)/8","A",0
1477,1,29,0,0.199987," ","integrate(1/x**3/(-x**8+1),x)","- \frac{\log{\left(x^{2} - 1 \right)}}{8} + \frac{\log{\left(x^{2} + 1 \right)}}{8} - \frac{\operatorname{atan}{\left(x^{2} \right)}}{4} - \frac{1}{2 x^{2}}"," ",0,"-log(x**2 - 1)/8 + log(x**2 + 1)/8 - atan(x**2)/4 - 1/(2*x**2)","A",0
1478,1,22,0,0.268569," ","integrate(1/x**5/(-x**8+1),x)","- \frac{\log{\left(x^{4} - 1 \right)}}{8} + \frac{\log{\left(x^{4} + 1 \right)}}{8} - \frac{1}{4 x^{4}}"," ",0,"-log(x**4 - 1)/8 + log(x**4 + 1)/8 - 1/(4*x**4)","A",0
1479,1,29,0,0.211493," ","integrate(1/x**7/(-x**8+1),x)","- \frac{\log{\left(x^{2} - 1 \right)}}{8} + \frac{\log{\left(x^{2} + 1 \right)}}{8} + \frac{\operatorname{atan}{\left(x^{2} \right)}}{4} - \frac{1}{6 x^{6}}"," ",0,"-log(x**2 - 1)/8 + log(x**2 + 1)/8 + atan(x**2)/4 - 1/(6*x**6)","A",0
1480,1,17,0,0.270401," ","integrate(1/x**9/(-x**8+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{8} - 1 \right)}}{8} - \frac{1}{8 x^{8}}"," ",0,"log(x) - log(x**8 - 1)/8 - 1/(8*x**8)","A",0
1481,1,46,0,176.278408," ","integrate(x**8/(-x**8+1),x)","- x - \frac{\log{\left(x - 1 \right)}}{8} + \frac{\log{\left(x + 1 \right)}}{8} - \frac{i \log{\left(x - i \right)}}{8} + \frac{i \log{\left(x + i \right)}}{8} - \operatorname{RootSum} {\left(4096 t^{4} + 1, \left( t \mapsto t \log{\left(- 8 t + x \right)} \right)\right)}"," ",0,"-x - log(x - 1)/8 + log(x + 1)/8 - I*log(x - I)/8 + I*log(x + I)/8 - RootSum(4096*_t**4 + 1, Lambda(_t, _t*log(-8*_t + x)))","C",0
1482,1,46,0,171.713537," ","integrate(x**6/(-x**8+1),x)","- \frac{\log{\left(x - 1 \right)}}{8} + \frac{\log{\left(x + 1 \right)}}{8} + \frac{i \log{\left(x - i \right)}}{8} - \frac{i \log{\left(x + i \right)}}{8} - \operatorname{RootSum} {\left(4096 t^{4} + 1, \left( t \mapsto t \log{\left(- 2097152 t^{7} + x \right)} \right)\right)}"," ",0,"-log(x - 1)/8 + log(x + 1)/8 + I*log(x - I)/8 - I*log(x + I)/8 - RootSum(4096*_t**4 + 1, Lambda(_t, _t*log(-2097152*_t**7 + x)))","C",0
1483,-1,0,0,0.000000," ","integrate(x**4/(-x**8+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1484,-1,0,0,0.000000," ","integrate(x**2/(-x**8+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1485,-1,0,0,0.000000," ","integrate(1/(-x**8+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1486,-1,0,0,0.000000," ","integrate(1/x**2/(-x**8+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1487,-1,0,0,0.000000," ","integrate(1/x**4/(-x**8+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1488,1,53,0,171.553518," ","integrate(1/x**6/(-x**8+1),x)","- \frac{\log{\left(x - 1 \right)}}{8} + \frac{\log{\left(x + 1 \right)}}{8} + \frac{i \log{\left(x - i \right)}}{8} - \frac{i \log{\left(x + i \right)}}{8} - \operatorname{RootSum} {\left(4096 t^{4} + 1, \left( t \mapsto t \log{\left(- 512 t^{3} + x \right)} \right)\right)} - \frac{1}{5 x^{5}}"," ",0,"-log(x - 1)/8 + log(x + 1)/8 + I*log(x - I)/8 - I*log(x + I)/8 - RootSum(4096*_t**4 + 1, Lambda(_t, _t*log(-512*_t**3 + x))) - 1/(5*x**5)","C",0
1489,1,51,0,122.760219," ","integrate(1/x**8/(-x**8+1),x)","- \frac{\log{\left(x - 1 \right)}}{8} + \frac{\log{\left(x + 1 \right)}}{8} - \frac{i \log{\left(x - i \right)}}{8} + \frac{i \log{\left(x + i \right)}}{8} - \operatorname{RootSum} {\left(4096 t^{4} + 1, \left( t \mapsto t \log{\left(- 8 t + x \right)} \right)\right)} - \frac{1}{7 x^{7}}"," ",0,"-log(x - 1)/8 + log(x + 1)/8 - I*log(x - I)/8 + I*log(x + I)/8 - RootSum(4096*_t**4 + 1, Lambda(_t, _t*log(-8*_t + x))) - 1/(7*x**7)","C",0
1490,1,85,0,0.179943," ","integrate(x**9/(x**8+1),x)","\frac{x^{2}}{2} + \frac{\sqrt{2} \log{\left(x^{4} - \sqrt{2} x^{2} + 1 \right)}}{16} - \frac{\sqrt{2} \log{\left(x^{4} + \sqrt{2} x^{2} + 1 \right)}}{16} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} - 1 \right)}}{8} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} + 1 \right)}}{8}"," ",0,"x**2/2 + sqrt(2)*log(x**4 - sqrt(2)*x**2 + 1)/16 - sqrt(2)*log(x**4 + sqrt(2)*x**2 + 1)/16 - sqrt(2)*atan(sqrt(2)*x**2 - 1)/8 - sqrt(2)*atan(sqrt(2)*x**2 + 1)/8","A",0
1491,1,7,0,0.105892," ","integrate(x**7/(x**8+1),x)","\frac{\log{\left(x^{8} + 1 \right)}}{8}"," ",0,"log(x**8 + 1)/8","A",0
1492,1,80,0,0.183956," ","integrate(x**5/(x**8+1),x)","\frac{\sqrt{2} \log{\left(x^{4} - \sqrt{2} x^{2} + 1 \right)}}{16} - \frac{\sqrt{2} \log{\left(x^{4} + \sqrt{2} x^{2} + 1 \right)}}{16} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} - 1 \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} + 1 \right)}}{8}"," ",0,"sqrt(2)*log(x**4 - sqrt(2)*x**2 + 1)/16 - sqrt(2)*log(x**4 + sqrt(2)*x**2 + 1)/16 + sqrt(2)*atan(sqrt(2)*x**2 - 1)/8 + sqrt(2)*atan(sqrt(2)*x**2 + 1)/8","A",0
1493,1,5,0,0.116447," ","integrate(x**3/(x**8+1),x)","\frac{\operatorname{atan}{\left(x^{4} \right)}}{4}"," ",0,"atan(x**4)/4","A",0
1494,1,80,0,0.178370," ","integrate(x/(x**8+1),x)","- \frac{\sqrt{2} \log{\left(x^{4} - \sqrt{2} x^{2} + 1 \right)}}{16} + \frac{\sqrt{2} \log{\left(x^{4} + \sqrt{2} x^{2} + 1 \right)}}{16} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} - 1 \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} + 1 \right)}}{8}"," ",0,"-sqrt(2)*log(x**4 - sqrt(2)*x**2 + 1)/16 + sqrt(2)*log(x**4 + sqrt(2)*x**2 + 1)/16 + sqrt(2)*atan(sqrt(2)*x**2 - 1)/8 + sqrt(2)*atan(sqrt(2)*x**2 + 1)/8","A",0
1495,1,10,0,0.136419," ","integrate(1/x/(x**8+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{8} + 1 \right)}}{8}"," ",0,"log(x) - log(x**8 + 1)/8","A",0
1496,1,87,0,0.221888," ","integrate(1/x**3/(x**8+1),x)","- \frac{\sqrt{2} \log{\left(x^{4} - \sqrt{2} x^{2} + 1 \right)}}{16} + \frac{\sqrt{2} \log{\left(x^{4} + \sqrt{2} x^{2} + 1 \right)}}{16} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} - 1 \right)}}{8} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} + 1 \right)}}{8} - \frac{1}{2 x^{2}}"," ",0,"-sqrt(2)*log(x**4 - sqrt(2)*x**2 + 1)/16 + sqrt(2)*log(x**4 + sqrt(2)*x**2 + 1)/16 - sqrt(2)*atan(sqrt(2)*x**2 - 1)/8 - sqrt(2)*atan(sqrt(2)*x**2 + 1)/8 - 1/(2*x**2)","A",0
1497,1,14,0,0.146772," ","integrate(1/x**5/(x**8+1),x)","- \frac{\operatorname{atan}{\left(x^{4} \right)}}{4} - \frac{1}{4 x^{4}}"," ",0,"-atan(x**4)/4 - 1/(4*x**4)","A",0
1498,1,87,0,0.222051," ","integrate(1/x**7/(x**8+1),x)","\frac{\sqrt{2} \log{\left(x^{4} - \sqrt{2} x^{2} + 1 \right)}}{16} - \frac{\sqrt{2} \log{\left(x^{4} + \sqrt{2} x^{2} + 1 \right)}}{16} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} - 1 \right)}}{8} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} + 1 \right)}}{8} - \frac{1}{6 x^{6}}"," ",0,"sqrt(2)*log(x**4 - sqrt(2)*x**2 + 1)/16 - sqrt(2)*log(x**4 + sqrt(2)*x**2 + 1)/16 - sqrt(2)*atan(sqrt(2)*x**2 - 1)/8 - sqrt(2)*atan(sqrt(2)*x**2 + 1)/8 - 1/(6*x**6)","A",0
1499,1,17,0,0.168727," ","integrate(1/x**9/(x**8+1),x)","- \log{\left(x \right)} + \frac{\log{\left(x^{8} + 1 \right)}}{8} - \frac{1}{8 x^{8}}"," ",0,"-log(x) + log(x**8 + 1)/8 - 1/(8*x**8)","A",0
1500,1,15,0,3.146454," ","integrate(x**8/(x**8+1),x)","x + \operatorname{RootSum} {\left(16777216 t^{8} + 1, \left( t \mapsto t \log{\left(- 8 t + x \right)} \right)\right)}"," ",0,"x + RootSum(16777216*_t**8 + 1, Lambda(_t, _t*log(-8*_t + x)))","A",0
1501,1,15,0,2.960725," ","integrate(x**6/(x**8+1),x)","\operatorname{RootSum} {\left(16777216 t^{8} + 1, \left( t \mapsto t \log{\left(2097152 t^{7} + x \right)} \right)\right)}"," ",0,"RootSum(16777216*_t**8 + 1, Lambda(_t, _t*log(2097152*_t**7 + x)))","A",0
1502,1,15,0,2.988963," ","integrate(x**4/(x**8+1),x)","\operatorname{RootSum} {\left(16777216 t^{8} + 1, \left( t \mapsto t \log{\left(- 32768 t^{5} + x \right)} \right)\right)}"," ",0,"RootSum(16777216*_t**8 + 1, Lambda(_t, _t*log(-32768*_t**5 + x)))","A",0
1503,1,15,0,3.133518," ","integrate(x**2/(x**8+1),x)","\operatorname{RootSum} {\left(16777216 t^{8} + 1, \left( t \mapsto t \log{\left(- 512 t^{3} + x \right)} \right)\right)}"," ",0,"RootSum(16777216*_t**8 + 1, Lambda(_t, _t*log(-512*_t**3 + x)))","A",0
1504,1,14,0,2.972735," ","integrate(1/(x**8+1),x)","\operatorname{RootSum} {\left(16777216 t^{8} + 1, \left( t \mapsto t \log{\left(8 t + x \right)} \right)\right)}"," ",0,"RootSum(16777216*_t**8 + 1, Lambda(_t, _t*log(8*_t + x)))","A",0
1505,1,19,0,3.177843," ","integrate(1/x**2/(x**8+1),x)","\operatorname{RootSum} {\left(16777216 t^{8} + 1, \left( t \mapsto t \log{\left(- 2097152 t^{7} + x \right)} \right)\right)} - \frac{1}{x}"," ",0,"RootSum(16777216*_t**8 + 1, Lambda(_t, _t*log(-2097152*_t**7 + x))) - 1/x","A",0
1506,1,22,0,3.169340," ","integrate(1/x**4/(x**8+1),x)","\operatorname{RootSum} {\left(16777216 t^{8} + 1, \left( t \mapsto t \log{\left(32768 t^{5} + x \right)} \right)\right)} - \frac{1}{3 x^{3}}"," ",0,"RootSum(16777216*_t**8 + 1, Lambda(_t, _t*log(32768*_t**5 + x))) - 1/(3*x**3)","A",0
1507,1,22,0,3.181245," ","integrate(1/x**6/(x**8+1),x)","\operatorname{RootSum} {\left(16777216 t^{8} + 1, \left( t \mapsto t \log{\left(512 t^{3} + x \right)} \right)\right)} - \frac{1}{5 x^{5}}"," ",0,"RootSum(16777216*_t**8 + 1, Lambda(_t, _t*log(512*_t**3 + x))) - 1/(5*x**5)","A",0
1508,1,20,0,3.239923," ","integrate(1/x**8/(x**8+1),x)","\operatorname{RootSum} {\left(16777216 t^{8} + 1, \left( t \mapsto t \log{\left(- 8 t + x \right)} \right)\right)} - \frac{1}{7 x^{7}}"," ",0,"RootSum(16777216*_t**8 + 1, Lambda(_t, _t*log(-8*_t + x))) - 1/(7*x**7)","A",0
1509,1,19,0,1.569078," ","integrate(x**3*(x**8+1)**(1/2),x)","\frac{x^{4} \sqrt{x^{8} + 1}}{8} + \frac{\operatorname{asinh}{\left(x^{4} \right)}}{8}"," ",0,"x**4*sqrt(x**8 + 1)/8 + asinh(x**4)/8","A",0
1510,1,31,0,0.757187," ","integrate(x*(x**8+1)**(1/2),x)","\frac{x^{2} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x**2*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), x**8*exp_polar(I*pi))/(8*gamma(5/4))","C",0
1511,1,39,0,1.302621," ","integrate((x**8+1)**(1/2)/x,x)","\frac{x^{4}}{4 \sqrt{1 + \frac{1}{x^{8}}}} - \frac{\operatorname{asinh}{\left(\frac{1}{x^{4}} \right)}}{4} + \frac{1}{4 x^{4} \sqrt{1 + \frac{1}{x^{8}}}}"," ",0,"x**4/(4*sqrt(1 + x**(-8))) - asinh(x**(-4))/4 + 1/(4*x**4*sqrt(1 + x**(-8)))","A",0
1512,1,34,0,0.761158," ","integrate((x**8+1)**(1/2)/x**3,x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 x^{2} \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), x**8*exp_polar(I*pi))/(8*x**2*gamma(3/4))","C",0
1513,1,90,0,1.769984," ","integrate(x**3*(x**8-2)**(1/2),x)","\begin{cases} \frac{x^{12}}{8 \sqrt{x^{8} - 2}} - \frac{x^{4}}{4 \sqrt{x^{8} - 2}} - \frac{\operatorname{acosh}{\left(\frac{\sqrt{2} x^{4}}{2} \right)}}{4} & \text{for}\: \frac{\left|{x^{8}}\right|}{2} > 1 \\- \frac{i x^{12}}{8 \sqrt{2 - x^{8}}} + \frac{i x^{4}}{4 \sqrt{2 - x^{8}}} + \frac{i \operatorname{asin}{\left(\frac{\sqrt{2} x^{4}}{2} \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**12/(8*sqrt(x**8 - 2)) - x**4/(4*sqrt(x**8 - 2)) - acosh(sqrt(2)*x**4/2)/4, Abs(x**8)/2 > 1), (-I*x**12/(8*sqrt(2 - x**8)) + I*x**4/(4*sqrt(2 - x**8)) + I*asin(sqrt(2)*x**4/2)/4, True))","A",0
1514,1,49,0,4.295653," ","integrate(x**19/(x**8+1)**(1/2),x)","\frac{x^{20}}{16 \sqrt{x^{8} + 1}} - \frac{x^{12}}{32 \sqrt{x^{8} + 1}} - \frac{3 x^{4}}{32 \sqrt{x^{8} + 1}} + \frac{3 \operatorname{asinh}{\left(x^{4} \right)}}{32}"," ",0,"x**20/(16*sqrt(x**8 + 1)) - x**12/(32*sqrt(x**8 + 1)) - 3*x**4/(32*sqrt(x**8 + 1)) + 3*asinh(x**4)/32","A",0
1515,1,22,0,2.829179," ","integrate(x**15/(x**8+1)**(1/2),x)","\frac{x^{8} \sqrt{x^{8} + 1}}{12} - \frac{\sqrt{x^{8} + 1}}{6}"," ",0,"x**8*sqrt(x**8 + 1)/12 - sqrt(x**8 + 1)/6","A",0
1516,1,19,0,2.279330," ","integrate(x**11/(x**8+1)**(1/2),x)","\frac{x^{4} \sqrt{x^{8} + 1}}{8} - \frac{\operatorname{asinh}{\left(x^{4} \right)}}{8}"," ",0,"x**4*sqrt(x**8 + 1)/8 - asinh(x**4)/8","A",0
1517,1,8,0,0.491263," ","integrate(x**7/(x**8+1)**(1/2),x)","\frac{\sqrt{x^{8} + 1}}{4}"," ",0,"sqrt(x**8 + 1)/4","A",0
1518,1,5,0,1.062177," ","integrate(x**3/(x**8+1)**(1/2),x)","\frac{\operatorname{asinh}{\left(x^{4} \right)}}{4}"," ",0,"asinh(x**4)/4","A",0
1519,1,8,0,1.022022," ","integrate(1/x/(x**8+1)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{1}{x^{4}} \right)}}{4}"," ",0,"-asinh(x**(-4))/4","A",0
1520,1,12,0,0.743742," ","integrate(1/x**5/(x**8+1)**(1/2),x)","- \frac{\sqrt{1 + \frac{1}{x^{8}}}}{4}"," ",0,"-sqrt(1 + x**(-8))/4","A",0
1521,1,22,0,2.291666," ","integrate(1/x**9/(x**8+1)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{1}{x^{4}} \right)}}{8} - \frac{\sqrt{1 + \frac{1}{x^{8}}}}{8 x^{4}}"," ",0,"asinh(x**(-4))/8 - sqrt(1 + x**(-8))/(8*x**4)","A",0
1522,1,26,0,1.567335," ","integrate(1/x**13/(x**8+1)**(1/2),x)","\frac{\sqrt{1 + \frac{1}{x^{8}}}}{6} - \frac{\sqrt{1 + \frac{1}{x^{8}}}}{12 x^{8}}"," ",0,"sqrt(1 + x**(-8))/6 - sqrt(1 + x**(-8))/(12*x**8)","A",0
1523,1,60,0,4.663194," ","integrate(1/x**17/(x**8+1)**(1/2),x)","- \frac{3 \operatorname{asinh}{\left(\frac{1}{x^{4}} \right)}}{32} + \frac{3}{32 x^{4} \sqrt{1 + \frac{1}{x^{8}}}} + \frac{1}{32 x^{12} \sqrt{1 + \frac{1}{x^{8}}}} - \frac{1}{16 x^{20} \sqrt{1 + \frac{1}{x^{8}}}}"," ",0,"-3*asinh(x**(-4))/32 + 3/(32*x**4*sqrt(1 + x**(-8))) + 1/(32*x**12*sqrt(1 + x**(-8))) - 1/(16*x**20*sqrt(1 + x**(-8)))","A",0
1524,1,29,0,1.293293," ","integrate(x**13/(x**8+1)**(1/2),x)","\frac{x^{14} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{11}{4}\right)}"," ",0,"x**14*gamma(7/4)*hyper((1/2, 7/4), (11/4,), x**8*exp_polar(I*pi))/(8*gamma(11/4))","C",0
1525,1,29,0,0.967170," ","integrate(x**9/(x**8+1)**(1/2),x)","\frac{x^{10} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**10*gamma(5/4)*hyper((1/2, 5/4), (9/4,), x**8*exp_polar(I*pi))/(8*gamma(9/4))","C",0
1526,1,29,0,0.773710," ","integrate(x**5/(x**8+1)**(1/2),x)","\frac{x^{6} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**6*gamma(3/4)*hyper((1/2, 3/4), (7/4,), x**8*exp_polar(I*pi))/(8*gamma(7/4))","C",0
1527,1,29,0,0.643160," ","integrate(x/(x**8+1)**(1/2),x)","\frac{x^{2} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x**2*gamma(1/4)*hyper((1/4, 1/2), (5/4,), x**8*exp_polar(I*pi))/(8*gamma(5/4))","C",0
1528,1,32,0,0.803226," ","integrate(1/x**3/(x**8+1)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 x^{2} \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), x**8*exp_polar(I*pi))/(8*x**2*gamma(3/4))","C",0
1529,1,32,0,0.989835," ","integrate(1/x**7/(x**8+1)**(1/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 x^{6} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), x**8*exp_polar(I*pi))/(8*x**6*gamma(1/4))","C",0
1530,1,29,0,1.045157," ","integrate(x**10/(x**8+1)**(1/2),x)","\frac{x^{11} \Gamma\left(\frac{11}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{8} \\ \frac{19}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{19}{8}\right)}"," ",0,"x**11*gamma(11/8)*hyper((1/2, 11/8), (19/8,), x**8*exp_polar(I*pi))/(8*gamma(19/8))","C",0
1531,1,29,0,0.869662," ","integrate(x**8/(x**8+1)**(1/2),x)","\frac{x^{9} \Gamma\left(\frac{9}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{8} \\ \frac{17}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{17}{8}\right)}"," ",0,"x**9*gamma(9/8)*hyper((1/2, 9/8), (17/8,), x**8*exp_polar(I*pi))/(8*gamma(17/8))","C",0
1532,1,29,0,0.855897," ","integrate(x**6/(x**8+1)**(1/2),x)","\frac{x^{7} \Gamma\left(\frac{7}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{8} \\ \frac{15}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{15}{8}\right)}"," ",0,"x**7*gamma(7/8)*hyper((1/2, 7/8), (15/8,), x**8*exp_polar(I*pi))/(8*gamma(15/8))","C",0
1533,1,29,0,0.736462," ","integrate(x**4/(x**8+1)**(1/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{8} \\ \frac{13}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{13}{8}\right)}"," ",0,"x**5*gamma(5/8)*hyper((1/2, 5/8), (13/8,), x**8*exp_polar(I*pi))/(8*gamma(13/8))","C",0
1534,1,29,0,0.676922," ","integrate(x**2/(x**8+1)**(1/2),x)","\frac{x^{3} \Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{8}, \frac{1}{2} \\ \frac{11}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{11}{8}\right)}"," ",0,"x**3*gamma(3/8)*hyper((3/8, 1/2), (11/8,), x**8*exp_polar(I*pi))/(8*gamma(11/8))","C",0
1535,1,27,0,0.667991," ","integrate(1/(x**8+1)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{8}, \frac{1}{2} \\ \frac{9}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{9}{8}\right)}"," ",0,"x*gamma(1/8)*hyper((1/8, 1/2), (9/8,), x**8*exp_polar(I*pi))/(8*gamma(9/8))","C",0
1536,1,31,0,0.809920," ","integrate(1/x**2/(x**8+1)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{8}, \frac{1}{2} \\ \frac{7}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 x \Gamma\left(\frac{7}{8}\right)}"," ",0,"gamma(-1/8)*hyper((-1/8, 1/2), (7/8,), x**8*exp_polar(I*pi))/(8*x*gamma(7/8))","C",0
1537,1,32,0,0.841377," ","integrate(1/x**4/(x**8+1)**(1/2),x)","\frac{\Gamma\left(- \frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{8}, \frac{1}{2} \\ \frac{5}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 x^{3} \Gamma\left(\frac{5}{8}\right)}"," ",0,"gamma(-3/8)*hyper((-3/8, 1/2), (5/8,), x**8*exp_polar(I*pi))/(8*x**3*gamma(5/8))","C",0
1538,1,32,0,0.946300," ","integrate(1/x**6/(x**8+1)**(1/2),x)","\frac{\Gamma\left(- \frac{5}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{8}, \frac{1}{2} \\ \frac{3}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 x^{5} \Gamma\left(\frac{3}{8}\right)}"," ",0,"gamma(-5/8)*hyper((-5/8, 1/2), (3/8,), x**8*exp_polar(I*pi))/(8*x**5*gamma(3/8))","C",0
1539,1,32,0,1.046149," ","integrate(1/x**8/(x**8+1)**(1/2),x)","\frac{\Gamma\left(- \frac{7}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{8}, \frac{1}{2} \\ \frac{1}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 x^{7} \Gamma\left(\frac{1}{8}\right)}"," ",0,"gamma(-7/8)*hyper((-7/8, 1/2), (1/8,), x**8*exp_polar(I*pi))/(8*x**7*gamma(1/8))","C",0
1540,1,70,0,7.280377," ","integrate(1/(-x**10+1),x)","- \frac{\log{\left(x - 1 \right)}}{10} + \frac{\log{\left(x + 1 \right)}}{10} - \operatorname{RootSum} {\left(10000 t^{4} - 1000 t^{3} + 100 t^{2} - 10 t + 1, \left( t \mapsto t \log{\left(- 10 t + x \right)} \right)\right)} - \operatorname{RootSum} {\left(10000 t^{4} + 1000 t^{3} + 100 t^{2} + 10 t + 1, \left( t \mapsto t \log{\left(- 10 t + x \right)} \right)\right)}"," ",0,"-log(x - 1)/10 + log(x + 1)/10 - RootSum(10000*_t**4 - 1000*_t**3 + 100*_t**2 - 10*_t + 1, Lambda(_t, _t*log(-10*_t + x))) - RootSum(10000*_t**4 + 1000*_t**3 + 100*_t**2 + 10*_t + 1, Lambda(_t, _t*log(-10*_t + x)))","A",0
1541,1,19,0,1.120367," ","integrate(x**4/(-x**10+1)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(x^{5} \right)}}{5} & \text{for}\: \left|{x^{10}}\right| > 1 \\\frac{\operatorname{asin}{\left(x^{5} \right)}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(x**5)/5, Abs(x**10) > 1), (asin(x**5)/5, True))","A",0
1542,1,34,0,1.174412," ","integrate(x**4/(x**10-2)**(1/2),x)","\begin{cases} \frac{\operatorname{acosh}{\left(\frac{\sqrt{2} x^{5}}{2} \right)}}{5} & \text{for}\: \frac{\left|{x^{10}}\right|}{2} > 1 \\- \frac{i \operatorname{asin}{\left(\frac{\sqrt{2} x^{5}}{2} \right)}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((acosh(sqrt(2)*x**5/2)/5, Abs(x**10)/2 > 1), (-I*asin(sqrt(2)*x**5/2)/5, True))","A",0
1543,1,7,0,0.136301," ","integrate(x**5/(x**12+9),x)","\frac{\operatorname{atan}{\left(\frac{x^{6}}{3} \right)}}{18}"," ",0,"atan(x**6/3)/18","A",0
1544,1,15,0,0.143427," ","integrate(x**5/(-x**12+9),x)","- \frac{\log{\left(x^{6} - 3 \right)}}{36} + \frac{\log{\left(x^{6} + 3 \right)}}{36}"," ",0,"-log(x**6 - 3)/36 + log(x**6 + 3)/36","B",0
1545,1,37,0,1.643286," ","integrate(x**5*(x**12+9)**(1/2),x)","\frac{x^{18}}{12 \sqrt{x^{12} + 9}} + \frac{3 x^{6}}{4 \sqrt{x^{12} + 9}} + \frac{3 \operatorname{asinh}{\left(\frac{x^{6}}{3} \right)}}{4}"," ",0,"x**18/(12*sqrt(x**12 + 9)) + 3*x**6/(4*sqrt(x**12 + 9)) + 3*asinh(x**6/3)/4","A",0
1546,1,12,0,0.062149," ","integrate((a+b/x)*x**6,x)","\frac{a x^{7}}{7} + \frac{b x^{6}}{6}"," ",0,"a*x**7/7 + b*x**6/6","A",0
1547,1,12,0,0.063234," ","integrate((a+b/x)*x**5,x)","\frac{a x^{6}}{6} + \frac{b x^{5}}{5}"," ",0,"a*x**6/6 + b*x**5/5","A",0
1548,1,12,0,0.063338," ","integrate((a+b/x)*x**4,x)","\frac{a x^{5}}{5} + \frac{b x^{4}}{4}"," ",0,"a*x**5/5 + b*x**4/4","A",0
1549,1,12,0,0.064553," ","integrate((a+b/x)*x**3,x)","\frac{a x^{4}}{4} + \frac{b x^{3}}{3}"," ",0,"a*x**4/4 + b*x**3/3","A",0
1550,1,12,0,0.063939," ","integrate((a+b/x)*x**2,x)","\frac{a x^{3}}{3} + \frac{b x^{2}}{2}"," ",0,"a*x**3/3 + b*x**2/2","A",0
1551,1,8,0,0.061190," ","integrate((a+b/x)*x,x)","\frac{a x^{2}}{2} + b x"," ",0,"a*x**2/2 + b*x","A",0
1552,1,7,0,0.086994," ","integrate(a+b/x,x)","a x + b \log{\left(x \right)}"," ",0,"a*x + b*log(x)","A",0
1553,1,7,0,0.106083," ","integrate((a+b/x)/x,x)","a \log{\left(x \right)} - \frac{b}{x}"," ",0,"a*log(x) - b/x","A",0
1554,1,12,0,0.118662," ","integrate((a+b/x)/x**2,x)","\frac{- 2 a x - b}{2 x^{2}}"," ",0,"(-2*a*x - b)/(2*x**2)","A",0
1555,1,14,0,0.121466," ","integrate((a+b/x)/x**3,x)","\frac{- 3 a x - 2 b}{6 x^{3}}"," ",0,"(-3*a*x - 2*b)/(6*x**3)","A",0
1556,1,14,0,0.125840," ","integrate((a+b/x)/x**4,x)","\frac{- 4 a x - 3 b}{12 x^{4}}"," ",0,"(-4*a*x - 3*b)/(12*x**4)","A",0
1557,1,14,0,0.148397," ","integrate((a+b/x)/x**5,x)","\frac{- 5 a x - 4 b}{20 x^{5}}"," ",0,"(-5*a*x - 4*b)/(20*x**5)","A",0
1558,1,14,0,0.146034," ","integrate((a+b/x)/x**6,x)","\frac{- 6 a x - 5 b}{30 x^{6}}"," ",0,"(-6*a*x - 5*b)/(30*x**6)","A",0
1559,1,26,0,0.084150," ","integrate((a+b/x)**2*x**5,x)","\frac{a^{2} x^{6}}{6} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{4}}{4}"," ",0,"a**2*x**6/6 + 2*a*b*x**5/5 + b**2*x**4/4","A",0
1560,1,24,0,0.070063," ","integrate((a+b/x)**2*x**4,x)","\frac{a^{2} x^{5}}{5} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{3}}{3}"," ",0,"a**2*x**5/5 + a*b*x**4/2 + b**2*x**3/3","A",0
1561,1,26,0,0.068307," ","integrate((a+b/x)**2*x**3,x)","\frac{a^{2} x^{4}}{4} + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{2}}{2}"," ",0,"a**2*x**4/4 + 2*a*b*x**3/3 + b**2*x**2/2","A",0
1562,1,19,0,0.070386," ","integrate((a+b/x)**2*x**2,x)","\frac{a^{2} x^{3}}{3} + a b x^{2} + b^{2} x"," ",0,"a**2*x**3/3 + a*b*x**2 + b**2*x","B",0
1563,1,20,0,0.105916," ","integrate((a+b/x)**2*x,x)","\frac{a^{2} x^{2}}{2} + 2 a b x + b^{2} \log{\left(x \right)}"," ",0,"a**2*x**2/2 + 2*a*b*x + b**2*log(x)","A",0
1564,1,17,0,0.118849," ","integrate((a+b/x)**2,x)","a^{2} x + 2 a b \log{\left(x \right)} - \frac{b^{2}}{x}"," ",0,"a**2*x + 2*a*b*log(x) - b**2/x","A",0
1565,1,22,0,0.164956," ","integrate((a+b/x)**2/x,x)","a^{2} \log{\left(x \right)} + \frac{- 4 a b x - b^{2}}{2 x^{2}}"," ",0,"a**2*log(x) + (-4*a*b*x - b**2)/(2*x**2)","A",0
1566,1,24,0,0.171739," ","integrate((a+b/x)**2/x**2,x)","\frac{- 3 a^{2} x^{2} - 3 a b x - b^{2}}{3 x^{3}}"," ",0,"(-3*a**2*x**2 - 3*a*b*x - b**2)/(3*x**3)","B",0
1567,1,26,0,0.182005," ","integrate((a+b/x)**2/x**3,x)","\frac{- 6 a^{2} x^{2} - 8 a b x - 3 b^{2}}{12 x^{4}}"," ",0,"(-6*a**2*x**2 - 8*a*b*x - 3*b**2)/(12*x**4)","A",0
1568,1,26,0,0.188284," ","integrate((a+b/x)**2/x**4,x)","\frac{- 10 a^{2} x^{2} - 15 a b x - 6 b^{2}}{30 x^{5}}"," ",0,"(-10*a**2*x**2 - 15*a*b*x - 6*b**2)/(30*x**5)","A",0
1569,1,26,0,0.218814," ","integrate((a+b/x)**2/x**5,x)","\frac{- 15 a^{2} x^{2} - 24 a b x - 10 b^{2}}{60 x^{6}}"," ",0,"(-15*a**2*x**2 - 24*a*b*x - 10*b**2)/(60*x**6)","A",0
1570,1,37,0,0.075384," ","integrate((a+b/x)**3*x**6,x)","\frac{a^{3} x^{7}}{7} + \frac{a^{2} b x^{6}}{2} + \frac{3 a b^{2} x^{5}}{5} + \frac{b^{3} x^{4}}{4}"," ",0,"a**3*x**7/7 + a**2*b*x**6/2 + 3*a*b**2*x**5/5 + b**3*x**4/4","A",0
1571,1,39,0,0.071411," ","integrate((a+b/x)**3*x**5,x)","\frac{a^{3} x^{6}}{6} + \frac{3 a^{2} b x^{5}}{5} + \frac{3 a b^{2} x^{4}}{4} + \frac{b^{3} x^{3}}{3}"," ",0,"a**3*x**6/6 + 3*a**2*b*x**5/5 + 3*a*b**2*x**4/4 + b**3*x**3/3","A",0
1572,1,36,0,0.079185," ","integrate((a+b/x)**3*x**4,x)","\frac{a^{3} x^{5}}{5} + \frac{3 a^{2} b x^{4}}{4} + a b^{2} x^{3} + \frac{b^{3} x^{2}}{2}"," ",0,"a**3*x**5/5 + 3*a**2*b*x**4/4 + a*b**2*x**3 + b**3*x**2/2","A",0
1573,1,32,0,0.069942," ","integrate((a+b/x)**3*x**3,x)","\frac{a^{3} x^{4}}{4} + a^{2} b x^{3} + \frac{3 a b^{2} x^{2}}{2} + b^{3} x"," ",0,"a**3*x**4/4 + a**2*b*x**3 + 3*a*b**2*x**2/2 + b**3*x","B",0
1574,1,34,0,0.123939," ","integrate((a+b/x)**3*x**2,x)","\frac{a^{3} x^{3}}{3} + \frac{3 a^{2} b x^{2}}{2} + 3 a b^{2} x + b^{3} \log{\left(x \right)}"," ",0,"a**3*x**3/3 + 3*a**2*b*x**2/2 + 3*a*b**2*x + b**3*log(x)","A",0
1575,1,31,0,0.140985," ","integrate((a+b/x)**3*x,x)","\frac{a^{3} x^{2}}{2} + 3 a^{2} b x + 3 a b^{2} \log{\left(x \right)} - \frac{b^{3}}{x}"," ",0,"a**3*x**2/2 + 3*a**2*b*x + 3*a*b**2*log(x) - b**3/x","A",0
1576,1,32,0,0.175463," ","integrate((a+b/x)**3,x)","a^{3} x + 3 a^{2} b \log{\left(x \right)} + \frac{- 6 a b^{2} x - b^{3}}{2 x^{2}}"," ",0,"a**3*x + 3*a**2*b*log(x) + (-6*a*b**2*x - b**3)/(2*x**2)","A",0
1577,1,36,0,0.208234," ","integrate((a+b/x)**3/x,x)","a^{3} \log{\left(x \right)} + \frac{- 18 a^{2} b x^{2} - 9 a b^{2} x - 2 b^{3}}{6 x^{3}}"," ",0,"a**3*log(x) + (-18*a**2*b*x**2 - 9*a*b**2*x - 2*b**3)/(6*x**3)","A",0
1578,1,36,0,0.218943," ","integrate((a+b/x)**3/x**2,x)","\frac{- 4 a^{3} x^{3} - 6 a^{2} b x^{2} - 4 a b^{2} x - b^{3}}{4 x^{4}}"," ",0,"(-4*a**3*x**3 - 6*a**2*b*x**2 - 4*a*b**2*x - b**3)/(4*x**4)","B",0
1579,1,37,0,0.243947," ","integrate((a+b/x)**3/x**3,x)","\frac{- 10 a^{3} x^{3} - 20 a^{2} b x^{2} - 15 a b^{2} x - 4 b^{3}}{20 x^{5}}"," ",0,"(-10*a**3*x**3 - 20*a**2*b*x**2 - 15*a*b**2*x - 4*b**3)/(20*x**5)","A",0
1580,1,37,0,0.258096," ","integrate((a+b/x)**3/x**4,x)","\frac{- 20 a^{3} x^{3} - 45 a^{2} b x^{2} - 36 a b^{2} x - 10 b^{3}}{60 x^{6}}"," ",0,"(-20*a**3*x**3 - 45*a**2*b*x**2 - 36*a*b**2*x - 10*b**3)/(60*x**6)","A",0
1581,1,37,0,0.278740," ","integrate((a+b/x)**3/x**5,x)","\frac{- 35 a^{3} x^{3} - 84 a^{2} b x^{2} - 70 a b^{2} x - 20 b^{3}}{140 x^{7}}"," ",0,"(-35*a**3*x**3 - 84*a**2*b*x**2 - 70*a*b**2*x - 20*b**3)/(140*x**7)","A",0
1582,1,37,0,0.318857," ","integrate((a+b/x)**3/x**6,x)","\frac{- 56 a^{3} x^{3} - 140 a^{2} b x^{2} - 120 a b^{2} x - 35 b^{3}}{280 x^{8}}"," ",0,"(-56*a**3*x**3 - 140*a**2*b*x**2 - 120*a*b**2*x - 35*b**3)/(280*x**8)","A",0
1583,1,104,0,0.091922," ","integrate((a+b/x)**8*x**16,x)","\frac{a^{8} x^{17}}{17} + \frac{a^{7} b x^{16}}{2} + \frac{28 a^{6} b^{2} x^{15}}{15} + 4 a^{5} b^{3} x^{14} + \frac{70 a^{4} b^{4} x^{13}}{13} + \frac{14 a^{3} b^{5} x^{12}}{3} + \frac{28 a^{2} b^{6} x^{11}}{11} + \frac{4 a b^{7} x^{10}}{5} + \frac{b^{8} x^{9}}{9}"," ",0,"a**8*x**17/17 + a**7*b*x**16/2 + 28*a**6*b**2*x**15/15 + 4*a**5*b**3*x**14 + 70*a**4*b**4*x**13/13 + 14*a**3*b**5*x**12/3 + 28*a**2*b**6*x**11/11 + 4*a*b**7*x**10/5 + b**8*x**9/9","A",0
1584,1,105,0,0.093115," ","integrate((a+b/x)**8*x**15,x)","\frac{a^{8} x^{16}}{16} + \frac{8 a^{7} b x^{15}}{15} + 2 a^{6} b^{2} x^{14} + \frac{56 a^{5} b^{3} x^{13}}{13} + \frac{35 a^{4} b^{4} x^{12}}{6} + \frac{56 a^{3} b^{5} x^{11}}{11} + \frac{14 a^{2} b^{6} x^{10}}{5} + \frac{8 a b^{7} x^{9}}{9} + \frac{b^{8} x^{8}}{8}"," ",0,"a**8*x**16/16 + 8*a**7*b*x**15/15 + 2*a**6*b**2*x**14 + 56*a**5*b**3*x**13/13 + 35*a**4*b**4*x**12/6 + 56*a**3*b**5*x**11/11 + 14*a**2*b**6*x**10/5 + 8*a*b**7*x**9/9 + b**8*x**8/8","A",0
1585,1,105,0,0.093785," ","integrate((a+b/x)**8*x**13,x)","\frac{a^{8} x^{14}}{14} + \frac{8 a^{7} b x^{13}}{13} + \frac{7 a^{6} b^{2} x^{12}}{3} + \frac{56 a^{5} b^{3} x^{11}}{11} + 7 a^{4} b^{4} x^{10} + \frac{56 a^{3} b^{5} x^{9}}{9} + \frac{7 a^{2} b^{6} x^{8}}{2} + \frac{8 a b^{7} x^{7}}{7} + \frac{b^{8} x^{6}}{6}"," ",0,"a**8*x**14/14 + 8*a**7*b*x**13/13 + 7*a**6*b**2*x**12/3 + 56*a**5*b**3*x**11/11 + 7*a**4*b**4*x**10 + 56*a**3*b**5*x**9/9 + 7*a**2*b**6*x**8/2 + 8*a*b**7*x**7/7 + b**8*x**6/6","A",0
1586,1,104,0,0.092978," ","integrate((a+b/x)**8*x**12,x)","\frac{a^{8} x^{13}}{13} + \frac{2 a^{7} b x^{12}}{3} + \frac{28 a^{6} b^{2} x^{11}}{11} + \frac{28 a^{5} b^{3} x^{10}}{5} + \frac{70 a^{4} b^{4} x^{9}}{9} + 7 a^{3} b^{5} x^{8} + 4 a^{2} b^{6} x^{7} + \frac{4 a b^{7} x^{6}}{3} + \frac{b^{8} x^{5}}{5}"," ",0,"a**8*x**13/13 + 2*a**7*b*x**12/3 + 28*a**6*b**2*x**11/11 + 28*a**5*b**3*x**10/5 + 70*a**4*b**4*x**9/9 + 7*a**3*b**5*x**8 + 4*a**2*b**6*x**7 + 4*a*b**7*x**6/3 + b**8*x**5/5","A",0
1587,1,105,0,0.095234," ","integrate((a+b/x)**8*x**11,x)","\frac{a^{8} x^{12}}{12} + \frac{8 a^{7} b x^{11}}{11} + \frac{14 a^{6} b^{2} x^{10}}{5} + \frac{56 a^{5} b^{3} x^{9}}{9} + \frac{35 a^{4} b^{4} x^{8}}{4} + 8 a^{3} b^{5} x^{7} + \frac{14 a^{2} b^{6} x^{6}}{3} + \frac{8 a b^{7} x^{5}}{5} + \frac{b^{8} x^{4}}{4}"," ",0,"a**8*x**12/12 + 8*a**7*b*x**11/11 + 14*a**6*b**2*x**10/5 + 56*a**5*b**3*x**9/9 + 35*a**4*b**4*x**8/4 + 8*a**3*b**5*x**7 + 14*a**2*b**6*x**6/3 + 8*a*b**7*x**5/5 + b**8*x**4/4","A",0
1588,1,102,0,0.091307," ","integrate((a+b/x)**8*x**10,x)","\frac{a^{8} x^{11}}{11} + \frac{4 a^{7} b x^{10}}{5} + \frac{28 a^{6} b^{2} x^{9}}{9} + 7 a^{5} b^{3} x^{8} + 10 a^{4} b^{4} x^{7} + \frac{28 a^{3} b^{5} x^{6}}{3} + \frac{28 a^{2} b^{6} x^{5}}{5} + 2 a b^{7} x^{4} + \frac{b^{8} x^{3}}{3}"," ",0,"a**8*x**11/11 + 4*a**7*b*x**10/5 + 28*a**6*b**2*x**9/9 + 7*a**5*b**3*x**8 + 10*a**4*b**4*x**7 + 28*a**3*b**5*x**6/3 + 28*a**2*b**6*x**5/5 + 2*a*b**7*x**4 + b**8*x**3/3","B",0
1589,1,104,0,0.105246," ","integrate((a+b/x)**8*x**9,x)","\frac{a^{8} x^{10}}{10} + \frac{8 a^{7} b x^{9}}{9} + \frac{7 a^{6} b^{2} x^{8}}{2} + 8 a^{5} b^{3} x^{7} + \frac{35 a^{4} b^{4} x^{6}}{3} + \frac{56 a^{3} b^{5} x^{5}}{5} + 7 a^{2} b^{6} x^{4} + \frac{8 a b^{7} x^{3}}{3} + \frac{b^{8} x^{2}}{2}"," ",0,"a**8*x**10/10 + 8*a**7*b*x**9/9 + 7*a**6*b**2*x**8/2 + 8*a**5*b**3*x**7 + 35*a**4*b**4*x**6/3 + 56*a**3*b**5*x**5/5 + 7*a**2*b**6*x**4 + 8*a*b**7*x**3/3 + b**8*x**2/2","B",0
1590,1,94,0,0.094386," ","integrate((a+b/x)**8*x**8,x)","\frac{a^{8} x^{9}}{9} + a^{7} b x^{8} + 4 a^{6} b^{2} x^{7} + \frac{28 a^{5} b^{3} x^{6}}{3} + 14 a^{4} b^{4} x^{5} + 14 a^{3} b^{5} x^{4} + \frac{28 a^{2} b^{6} x^{3}}{3} + 4 a b^{7} x^{2} + b^{8} x"," ",0,"a**8*x**9/9 + a**7*b*x**8 + 4*a**6*b**2*x**7 + 28*a**5*b**3*x**6/3 + 14*a**4*b**4*x**5 + 14*a**3*b**5*x**4 + 28*a**2*b**6*x**3/3 + 4*a*b**7*x**2 + b**8*x","B",0
1591,1,100,0,0.207807," ","integrate((a+b/x)**8*x**7,x)","\frac{a^{8} x^{8}}{8} + \frac{8 a^{7} b x^{7}}{7} + \frac{14 a^{6} b^{2} x^{6}}{3} + \frac{56 a^{5} b^{3} x^{5}}{5} + \frac{35 a^{4} b^{4} x^{4}}{2} + \frac{56 a^{3} b^{5} x^{3}}{3} + 14 a^{2} b^{6} x^{2} + 8 a b^{7} x + b^{8} \log{\left(x \right)}"," ",0,"a**8*x**8/8 + 8*a**7*b*x**7/7 + 14*a**6*b**2*x**6/3 + 56*a**5*b**3*x**5/5 + 35*a**4*b**4*x**4/2 + 56*a**3*b**5*x**3/3 + 14*a**2*b**6*x**2 + 8*a*b**7*x + b**8*log(x)","A",0
1592,1,95,0,0.220976," ","integrate((a+b/x)**8*x**6,x)","\frac{a^{8} x^{7}}{7} + \frac{4 a^{7} b x^{6}}{3} + \frac{28 a^{6} b^{2} x^{5}}{5} + 14 a^{5} b^{3} x^{4} + \frac{70 a^{4} b^{4} x^{3}}{3} + 28 a^{3} b^{5} x^{2} + 28 a^{2} b^{6} x + 8 a b^{7} \log{\left(x \right)} - \frac{b^{8}}{x}"," ",0,"a**8*x**7/7 + 4*a**7*b*x**6/3 + 28*a**6*b**2*x**5/5 + 14*a**5*b**3*x**4 + 70*a**4*b**4*x**3/3 + 28*a**3*b**5*x**2 + 28*a**2*b**6*x + 8*a*b**7*log(x) - b**8/x","A",0
1593,1,97,0,0.263088," ","integrate((a+b/x)**8*x**5,x)","\frac{a^{8} x^{6}}{6} + \frac{8 a^{7} b x^{5}}{5} + 7 a^{6} b^{2} x^{4} + \frac{56 a^{5} b^{3} x^{3}}{3} + 35 a^{4} b^{4} x^{2} + 56 a^{3} b^{5} x + 28 a^{2} b^{6} \log{\left(x \right)} + \frac{- 16 a b^{7} x - b^{8}}{2 x^{2}}"," ",0,"a**8*x**6/6 + 8*a**7*b*x**5/5 + 7*a**6*b**2*x**4 + 56*a**5*b**3*x**3/3 + 35*a**4*b**4*x**2 + 56*a**3*b**5*x + 28*a**2*b**6*log(x) + (-16*a*b**7*x - b**8)/(2*x**2)","A",0
1594,1,95,0,0.320772," ","integrate((a+b/x)**8*x**4,x)","\frac{a^{8} x^{5}}{5} + 2 a^{7} b x^{4} + \frac{28 a^{6} b^{2} x^{3}}{3} + 28 a^{5} b^{3} x^{2} + 70 a^{4} b^{4} x + 56 a^{3} b^{5} \log{\left(x \right)} + \frac{- 84 a^{2} b^{6} x^{2} - 12 a b^{7} x - b^{8}}{3 x^{3}}"," ",0,"a**8*x**5/5 + 2*a**7*b*x**4 + 28*a**6*b**2*x**3/3 + 28*a**5*b**3*x**2 + 70*a**4*b**4*x + 56*a**3*b**5*log(x) + (-84*a**2*b**6*x**2 - 12*a*b**7*x - b**8)/(3*x**3)","A",0
1595,1,97,0,0.369367," ","integrate((a+b/x)**8*x**3,x)","\frac{a^{8} x^{4}}{4} + \frac{8 a^{7} b x^{3}}{3} + 14 a^{6} b^{2} x^{2} + 56 a^{5} b^{3} x + 70 a^{4} b^{4} \log{\left(x \right)} + \frac{- 672 a^{3} b^{5} x^{3} - 168 a^{2} b^{6} x^{2} - 32 a b^{7} x - 3 b^{8}}{12 x^{4}}"," ",0,"a**8*x**4/4 + 8*a**7*b*x**3/3 + 14*a**6*b**2*x**2 + 56*a**5*b**3*x + 70*a**4*b**4*log(x) + (-672*a**3*b**5*x**3 - 168*a**2*b**6*x**2 - 32*a*b**7*x - 3*b**8)/(12*x**4)","A",0
1596,1,95,0,0.454631," ","integrate((a+b/x)**8*x**2,x)","\frac{a^{8} x^{3}}{3} + 4 a^{7} b x^{2} + 28 a^{6} b^{2} x + 56 a^{5} b^{3} \log{\left(x \right)} + \frac{- 1050 a^{4} b^{4} x^{4} - 420 a^{3} b^{5} x^{3} - 140 a^{2} b^{6} x^{2} - 30 a b^{7} x - 3 b^{8}}{15 x^{5}}"," ",0,"a**8*x**3/3 + 4*a**7*b*x**2 + 28*a**6*b**2*x + 56*a**5*b**3*log(x) + (-1050*a**4*b**4*x**4 - 420*a**3*b**5*x**3 - 140*a**2*b**6*x**2 - 30*a*b**7*x - 3*b**8)/(15*x**5)","A",0
1597,1,95,0,0.519189," ","integrate((a+b/x)**8*x,x)","\frac{a^{8} x^{2}}{2} + 8 a^{7} b x + 28 a^{6} b^{2} \log{\left(x \right)} + \frac{- 1680 a^{5} b^{3} x^{5} - 1050 a^{4} b^{4} x^{4} - 560 a^{3} b^{5} x^{3} - 210 a^{2} b^{6} x^{2} - 48 a b^{7} x - 5 b^{8}}{30 x^{6}}"," ",0,"a**8*x**2/2 + 8*a**7*b*x + 28*a**6*b**2*log(x) + (-1680*a**5*b**3*x**5 - 1050*a**4*b**4*x**4 - 560*a**3*b**5*x**3 - 210*a**2*b**6*x**2 - 48*a*b**7*x - 5*b**8)/(30*x**6)","A",0
1598,1,94,0,0.559494," ","integrate((a+b/x)**8,x)","a^{8} x + 8 a^{7} b \log{\left(x \right)} + \frac{- 2940 a^{6} b^{2} x^{6} - 2940 a^{5} b^{3} x^{5} - 2450 a^{4} b^{4} x^{4} - 1470 a^{3} b^{5} x^{3} - 588 a^{2} b^{6} x^{2} - 140 a b^{7} x - 15 b^{8}}{105 x^{7}}"," ",0,"a**8*x + 8*a**7*b*log(x) + (-2940*a**6*b**2*x**6 - 2940*a**5*b**3*x**5 - 2450*a**4*b**4*x**4 - 1470*a**3*b**5*x**3 - 588*a**2*b**6*x**2 - 140*a*b**7*x - 15*b**8)/(105*x**7)","A",0
1599,1,95,0,0.640254," ","integrate((a+b/x)**8/x,x)","a^{8} \log{\left(x \right)} + \frac{- 6720 a^{7} b x^{7} - 11760 a^{6} b^{2} x^{6} - 15680 a^{5} b^{3} x^{5} - 14700 a^{4} b^{4} x^{4} - 9408 a^{3} b^{5} x^{3} - 3920 a^{2} b^{6} x^{2} - 960 a b^{7} x - 105 b^{8}}{840 x^{8}}"," ",0,"a**8*log(x) + (-6720*a**7*b*x**7 - 11760*a**6*b**2*x**6 - 15680*a**5*b**3*x**5 - 14700*a**4*b**4*x**4 - 9408*a**3*b**5*x**3 - 3920*a**2*b**6*x**2 - 960*a*b**7*x - 105*b**8)/(840*x**8)","A",0
1600,1,95,0,0.685163," ","integrate((a+b/x)**8/x**2,x)","\frac{- 9 a^{8} x^{8} - 36 a^{7} b x^{7} - 84 a^{6} b^{2} x^{6} - 126 a^{5} b^{3} x^{5} - 126 a^{4} b^{4} x^{4} - 84 a^{3} b^{5} x^{3} - 36 a^{2} b^{6} x^{2} - 9 a b^{7} x - b^{8}}{9 x^{9}}"," ",0,"(-9*a**8*x**8 - 36*a**7*b*x**7 - 84*a**6*b**2*x**6 - 126*a**5*b**3*x**5 - 126*a**4*b**4*x**4 - 84*a**3*b**5*x**3 - 36*a**2*b**6*x**2 - 9*a*b**7*x - b**8)/(9*x**9)","B",0
1601,1,97,0,0.705434," ","integrate((a+b/x)**8/x**3,x)","\frac{- 45 a^{8} x^{8} - 240 a^{7} b x^{7} - 630 a^{6} b^{2} x^{6} - 1008 a^{5} b^{3} x^{5} - 1050 a^{4} b^{4} x^{4} - 720 a^{3} b^{5} x^{3} - 315 a^{2} b^{6} x^{2} - 80 a b^{7} x - 9 b^{8}}{90 x^{10}}"," ",0,"(-45*a**8*x**8 - 240*a**7*b*x**7 - 630*a**6*b**2*x**6 - 1008*a**5*b**3*x**5 - 1050*a**4*b**4*x**4 - 720*a**3*b**5*x**3 - 315*a**2*b**6*x**2 - 80*a*b**7*x - 9*b**8)/(90*x**10)","B",0
1602,1,97,0,0.764663," ","integrate((a+b/x)**8/x**4,x)","\frac{- 165 a^{8} x^{8} - 990 a^{7} b x^{7} - 2772 a^{6} b^{2} x^{6} - 4620 a^{5} b^{3} x^{5} - 4950 a^{4} b^{4} x^{4} - 3465 a^{3} b^{5} x^{3} - 1540 a^{2} b^{6} x^{2} - 396 a b^{7} x - 45 b^{8}}{495 x^{11}}"," ",0,"(-165*a**8*x**8 - 990*a**7*b*x**7 - 2772*a**6*b**2*x**6 - 4620*a**5*b**3*x**5 - 4950*a**4*b**4*x**4 - 3465*a**3*b**5*x**3 - 1540*a**2*b**6*x**2 - 396*a*b**7*x - 45*b**8)/(495*x**11)","B",0
1603,1,97,0,0.852017," ","integrate((a+b/x)**8/x**5,x)","\frac{- 495 a^{8} x^{8} - 3168 a^{7} b x^{7} - 9240 a^{6} b^{2} x^{6} - 15840 a^{5} b^{3} x^{5} - 17325 a^{4} b^{4} x^{4} - 12320 a^{3} b^{5} x^{3} - 5544 a^{2} b^{6} x^{2} - 1440 a b^{7} x - 165 b^{8}}{1980 x^{12}}"," ",0,"(-495*a**8*x**8 - 3168*a**7*b*x**7 - 9240*a**6*b**2*x**6 - 15840*a**5*b**3*x**5 - 17325*a**4*b**4*x**4 - 12320*a**3*b**5*x**3 - 5544*a**2*b**6*x**2 - 1440*a*b**7*x - 165*b**8)/(1980*x**12)","A",0
1604,1,97,0,0.885863," ","integrate((a+b/x)**8/x**6,x)","\frac{- 1287 a^{8} x^{8} - 8580 a^{7} b x^{7} - 25740 a^{6} b^{2} x^{6} - 45045 a^{5} b^{3} x^{5} - 50050 a^{4} b^{4} x^{4} - 36036 a^{3} b^{5} x^{3} - 16380 a^{2} b^{6} x^{2} - 4290 a b^{7} x - 495 b^{8}}{6435 x^{13}}"," ",0,"(-1287*a**8*x**8 - 8580*a**7*b*x**7 - 25740*a**6*b**2*x**6 - 45045*a**5*b**3*x**5 - 50050*a**4*b**4*x**4 - 36036*a**3*b**5*x**3 - 16380*a**2*b**6*x**2 - 4290*a*b**7*x - 495*b**8)/(6435*x**13)","A",0
1605,1,97,0,0.925475," ","integrate((a+b/x)**8/x**7,x)","\frac{- 3003 a^{8} x^{8} - 20592 a^{7} b x^{7} - 63063 a^{6} b^{2} x^{6} - 112112 a^{5} b^{3} x^{5} - 126126 a^{4} b^{4} x^{4} - 91728 a^{3} b^{5} x^{3} - 42042 a^{2} b^{6} x^{2} - 11088 a b^{7} x - 1287 b^{8}}{18018 x^{14}}"," ",0,"(-3003*a**8*x**8 - 20592*a**7*b*x**7 - 63063*a**6*b**2*x**6 - 112112*a**5*b**3*x**5 - 126126*a**4*b**4*x**4 - 91728*a**3*b**5*x**3 - 42042*a**2*b**6*x**2 - 11088*a*b**7*x - 1287*b**8)/(18018*x**14)","A",0
1606,1,97,0,0.919856," ","integrate((a+b/x)**8/x**8,x)","\frac{- 6435 a^{8} x^{8} - 45045 a^{7} b x^{7} - 140140 a^{6} b^{2} x^{6} - 252252 a^{5} b^{3} x^{5} - 286650 a^{4} b^{4} x^{4} - 210210 a^{3} b^{5} x^{3} - 97020 a^{2} b^{6} x^{2} - 25740 a b^{7} x - 3003 b^{8}}{45045 x^{15}}"," ",0,"(-6435*a**8*x**8 - 45045*a**7*b*x**7 - 140140*a**6*b**2*x**6 - 252252*a**5*b**3*x**5 - 286650*a**4*b**4*x**4 - 210210*a**3*b**5*x**3 - 97020*a**2*b**6*x**2 - 25740*a*b**7*x - 3003*b**8)/(45045*x**15)","A",0
1607,1,61,0,0.154714," ","integrate(x**4/(a+b/x),x)","\frac{x^{5}}{5 a} - \frac{b x^{4}}{4 a^{2}} + \frac{b^{2} x^{3}}{3 a^{3}} - \frac{b^{3} x^{2}}{2 a^{4}} + \frac{b^{4} x}{a^{5}} - \frac{b^{5} \log{\left(a x + b \right)}}{a^{6}}"," ",0,"x**5/(5*a) - b*x**4/(4*a**2) + b**2*x**3/(3*a**3) - b**3*x**2/(2*a**4) + b**4*x/a**5 - b**5*log(a*x + b)/a**6","A",0
1608,1,49,0,0.144847," ","integrate(x**3/(a+b/x),x)","\frac{x^{4}}{4 a} - \frac{b x^{3}}{3 a^{2}} + \frac{b^{2} x^{2}}{2 a^{3}} - \frac{b^{3} x}{a^{4}} + \frac{b^{4} \log{\left(a x + b \right)}}{a^{5}}"," ",0,"x**4/(4*a) - b*x**3/(3*a**2) + b**2*x**2/(2*a**3) - b**3*x/a**4 + b**4*log(a*x + b)/a**5","A",0
1609,1,37,0,0.136238," ","integrate(x**2/(a+b/x),x)","\frac{x^{3}}{3 a} - \frac{b x^{2}}{2 a^{2}} + \frac{b^{2} x}{a^{3}} - \frac{b^{3} \log{\left(a x + b \right)}}{a^{4}}"," ",0,"x**3/(3*a) - b*x**2/(2*a**2) + b**2*x/a**3 - b**3*log(a*x + b)/a**4","A",0
1610,1,26,0,0.119901," ","integrate(x/(a+b/x),x)","\frac{x^{2}}{2 a} - \frac{b x}{a^{2}} + \frac{b^{2} \log{\left(a x + b \right)}}{a^{3}}"," ",0,"x**2/(2*a) - b*x/a**2 + b**2*log(a*x + b)/a**3","A",0
1611,1,14,0,0.115528," ","integrate(1/(a+b/x),x)","\frac{x}{a} - \frac{b \log{\left(a x + b \right)}}{a^{2}}"," ",0,"x/a - b*log(a*x + b)/a**2","A",0
1612,1,7,0,0.071951," ","integrate(1/(a+b/x)/x,x)","\frac{\log{\left(a x + b \right)}}{a}"," ",0,"log(a*x + b)/a","A",0
1613,1,10,0,0.153276," ","integrate(1/(a+b/x)/x**2,x)","\frac{\log{\left(x \right)} - \log{\left(x + \frac{b}{a} \right)}}{b}"," ",0,"(log(x) - log(x + b/a))/b","A",0
1614,1,19,0,0.196925," ","integrate(1/(a+b/x)/x**3,x)","\frac{a \left(- \log{\left(x \right)} + \log{\left(x + \frac{b}{a} \right)}\right)}{b^{2}} - \frac{1}{b x}"," ",0,"a*(-log(x) + log(x + b/a))/b**2 - 1/(b*x)","A",0
1615,1,31,0,0.232169," ","integrate(1/(a+b/x)/x**4,x)","\frac{a^{2} \left(\log{\left(x \right)} - \log{\left(x + \frac{b}{a} \right)}\right)}{b^{3}} + \frac{2 a x - b}{2 b^{2} x^{2}}"," ",0,"a**2*(log(x) - log(x + b/a))/b**3 + (2*a*x - b)/(2*b**2*x**2)","A",0
1616,1,44,0,0.244148," ","integrate(1/(a+b/x)/x**5,x)","\frac{a^{3} \left(- \log{\left(x \right)} + \log{\left(x + \frac{b}{a} \right)}\right)}{b^{4}} + \frac{- 6 a^{2} x^{2} + 3 a b x - 2 b^{2}}{6 b^{3} x^{3}}"," ",0,"a**3*(-log(x) + log(x + b/a))/b**4 + (-6*a**2*x**2 + 3*a*b*x - 2*b**2)/(6*b**3*x**3)","A",0
1617,1,56,0,0.262471," ","integrate(1/(a+b/x)/x**6,x)","\frac{a^{4} \left(\log{\left(x \right)} - \log{\left(x + \frac{b}{a} \right)}\right)}{b^{5}} + \frac{12 a^{3} x^{3} - 6 a^{2} b x^{2} + 4 a b^{2} x - 3 b^{3}}{12 b^{4} x^{4}}"," ",0,"a**4*(log(x) - log(x + b/a))/b**5 + (12*a**3*x**3 - 6*a**2*b*x**2 + 4*a*b**2*x - 3*b**3)/(12*b**4*x**4)","A",0
1618,1,68,0,0.295979," ","integrate(1/(a+b/x)/x**7,x)","\frac{a^{5} \left(- \log{\left(x \right)} + \log{\left(x + \frac{b}{a} \right)}\right)}{b^{6}} + \frac{- 60 a^{4} x^{4} + 30 a^{3} b x^{3} - 20 a^{2} b^{2} x^{2} + 15 a b^{3} x - 12 b^{4}}{60 b^{5} x^{5}}"," ",0,"a**5*(-log(x) + log(x + b/a))/b**6 + (-60*a**4*x**4 + 30*a**3*b*x**3 - 20*a**2*b**2*x**2 + 15*a*b**3*x - 12*b**4)/(60*b**5*x**5)","A",0
1619,1,99,0,0.288631," ","integrate(x**5/(a+b/x)**2,x)","\frac{b^{7}}{a^{9} x + a^{8} b} + \frac{x^{6}}{6 a^{2}} - \frac{2 b x^{5}}{5 a^{3}} + \frac{3 b^{2} x^{4}}{4 a^{4}} - \frac{4 b^{3} x^{3}}{3 a^{5}} + \frac{5 b^{4} x^{2}}{2 a^{6}} - \frac{6 b^{5} x}{a^{7}} + \frac{7 b^{6} \log{\left(a x + b \right)}}{a^{8}}"," ",0,"b**7/(a**9*x + a**8*b) + x**6/(6*a**2) - 2*b*x**5/(5*a**3) + 3*b**2*x**4/(4*a**4) - 4*b**3*x**3/(3*a**5) + 5*b**4*x**2/(2*a**6) - 6*b**5*x/a**7 + 7*b**6*log(a*x + b)/a**8","A",0
1620,1,78,0,0.256943," ","integrate(x**4/(a+b/x)**2,x)","- \frac{b^{6}}{a^{8} x + a^{7} b} + \frac{x^{5}}{5 a^{2}} - \frac{b x^{4}}{2 a^{3}} + \frac{b^{2} x^{3}}{a^{4}} - \frac{2 b^{3} x^{2}}{a^{5}} + \frac{5 b^{4} x}{a^{6}} - \frac{6 b^{5} \log{\left(a x + b \right)}}{a^{7}}"," ",0,"-b**6/(a**8*x + a**7*b) + x**5/(5*a**2) - b*x**4/(2*a**3) + b**2*x**3/a**4 - 2*b**3*x**2/a**5 + 5*b**4*x/a**6 - 6*b**5*log(a*x + b)/a**7","A",0
1621,1,71,0,0.259527," ","integrate(x**3/(a+b/x)**2,x)","\frac{b^{5}}{a^{7} x + a^{6} b} + \frac{x^{4}}{4 a^{2}} - \frac{2 b x^{3}}{3 a^{3}} + \frac{3 b^{2} x^{2}}{2 a^{4}} - \frac{4 b^{3} x}{a^{5}} + \frac{5 b^{4} \log{\left(a x + b \right)}}{a^{6}}"," ",0,"b**5/(a**7*x + a**6*b) + x**4/(4*a**2) - 2*b*x**3/(3*a**3) + 3*b**2*x**2/(2*a**4) - 4*b**3*x/a**5 + 5*b**4*log(a*x + b)/a**6","A",0
1622,1,54,0,0.220709," ","integrate(x**2/(a+b/x)**2,x)","- \frac{b^{4}}{a^{6} x + a^{5} b} + \frac{x^{3}}{3 a^{2}} - \frac{b x^{2}}{a^{3}} + \frac{3 b^{2} x}{a^{4}} - \frac{4 b^{3} \log{\left(a x + b \right)}}{a^{5}}"," ",0,"-b**4/(a**6*x + a**5*b) + x**3/(3*a**2) - b*x**2/a**3 + 3*b**2*x/a**4 - 4*b**3*log(a*x + b)/a**5","A",0
1623,1,44,0,0.198274," ","integrate(x/(a+b/x)**2,x)","\frac{b^{3}}{a^{5} x + a^{4} b} + \frac{x^{2}}{2 a^{2}} - \frac{2 b x}{a^{3}} + \frac{3 b^{2} \log{\left(a x + b \right)}}{a^{4}}"," ",0,"b**3/(a**5*x + a**4*b) + x**2/(2*a**2) - 2*b*x/a**3 + 3*b**2*log(a*x + b)/a**4","A",0
1624,1,31,0,0.173583," ","integrate(1/(a+b/x)**2,x)","- \frac{b^{2}}{a^{4} x + a^{3} b} + \frac{x}{a^{2}} - \frac{2 b \log{\left(a x + b \right)}}{a^{3}}"," ",0,"-b**2/(a**4*x + a**3*b) + x/a**2 - 2*b*log(a*x + b)/a**3","A",0
1625,1,20,0,0.158336," ","integrate(1/(a+b/x)**2/x,x)","\frac{b}{a^{3} x + a^{2} b} + \frac{\log{\left(a x + b \right)}}{a^{2}}"," ",0,"b/(a**3*x + a**2*b) + log(a*x + b)/a**2","A",0
1626,1,10,0,0.141312," ","integrate(1/(a+b/x)**2/x**2,x)","- \frac{1}{a^{2} x + a b}"," ",0,"-1/(a**2*x + a*b)","A",0
1627,1,22,0,0.215402," ","integrate(1/(a+b/x)**2/x**3,x)","\frac{1}{a b x + b^{2}} + \frac{\log{\left(x \right)} - \log{\left(x + \frac{b}{a} \right)}}{b^{2}}"," ",0,"1/(a*b*x + b**2) + (log(x) - log(x + b/a))/b**2","A",0
1628,1,37,0,0.276855," ","integrate(1/(a+b/x)**2/x**4,x)","\frac{2 a \left(- \log{\left(x \right)} + \log{\left(x + \frac{b}{a} \right)}\right)}{b^{3}} + \frac{- 2 a x - b}{a b^{2} x^{2} + b^{3} x}"," ",0,"2*a*(-log(x) + log(x + b/a))/b**3 + (-2*a*x - b)/(a*b**2*x**2 + b**3*x)","A",0
1629,1,54,0,0.322275," ","integrate(1/(a+b/x)**2/x**5,x)","\frac{3 a^{2} \left(\log{\left(x \right)} - \log{\left(x + \frac{b}{a} \right)}\right)}{b^{4}} + \frac{6 a^{2} x^{2} + 3 a b x - b^{2}}{2 a b^{3} x^{3} + 2 b^{4} x^{2}}"," ",0,"3*a**2*(log(x) - log(x + b/a))/b**4 + (6*a**2*x**2 + 3*a*b*x - b**2)/(2*a*b**3*x**3 + 2*b**4*x**2)","A",0
1630,1,66,0,0.389879," ","integrate(1/(a+b/x)**2/x**6,x)","\frac{4 a^{3} \left(- \log{\left(x \right)} + \log{\left(x + \frac{b}{a} \right)}\right)}{b^{5}} + \frac{- 12 a^{3} x^{3} - 6 a^{2} b x^{2} + 2 a b^{2} x - b^{3}}{3 a b^{4} x^{4} + 3 b^{5} x^{3}}"," ",0,"4*a**3*(-log(x) + log(x + b/a))/b**5 + (-12*a**3*x**3 - 6*a**2*b*x**2 + 2*a*b**2*x - b**3)/(3*a*b**4*x**4 + 3*b**5*x**3)","A",0
1631,1,80,0,0.374019," ","integrate(1/(a+b/x)**2/x**7,x)","\frac{5 a^{4} \left(\log{\left(x \right)} - \log{\left(x + \frac{b}{a} \right)}\right)}{b^{6}} + \frac{60 a^{4} x^{4} + 30 a^{3} b x^{3} - 10 a^{2} b^{2} x^{2} + 5 a b^{3} x - 3 b^{4}}{12 a b^{5} x^{5} + 12 b^{6} x^{4}}"," ",0,"5*a**4*(log(x) - log(x + b/a))/b**6 + (60*a**4*x**4 + 30*a**3*b*x**3 - 10*a**2*b**2*x**2 + 5*a*b**3*x - 3*b**4)/(12*a*b**5*x**5 + 12*b**6*x**4)","A",0
1632,1,92,0,0.427181," ","integrate(1/(a+b/x)**2/x**8,x)","\frac{6 a^{5} \left(- \log{\left(x \right)} + \log{\left(x + \frac{b}{a} \right)}\right)}{b^{7}} + \frac{- 60 a^{5} x^{5} - 30 a^{4} b x^{4} + 10 a^{3} b^{2} x^{3} - 5 a^{2} b^{3} x^{2} + 3 a b^{4} x - 2 b^{5}}{10 a b^{6} x^{6} + 10 b^{7} x^{5}}"," ",0,"6*a**5*(-log(x) + log(x + b/a))/b**7 + (-60*a**5*x**5 - 30*a**4*b*x**4 + 10*a**3*b**2*x**3 - 5*a**2*b**3*x**2 + 3*a*b**4*x - 2*b**5)/(10*a*b**6*x**6 + 10*b**7*x**5)","A",0
1633,1,109,0,0.404830," ","integrate(x**4/(a+b/x)**3,x)","\frac{- 14 a b^{6} x - 13 b^{7}}{2 a^{10} x^{2} + 4 a^{9} b x + 2 a^{8} b^{2}} + \frac{x^{5}}{5 a^{3}} - \frac{3 b x^{4}}{4 a^{4}} + \frac{2 b^{2} x^{3}}{a^{5}} - \frac{5 b^{3} x^{2}}{a^{6}} + \frac{15 b^{4} x}{a^{7}} - \frac{21 b^{5} \log{\left(a x + b \right)}}{a^{8}}"," ",0,"(-14*a*b**6*x - 13*b**7)/(2*a**10*x**2 + 4*a**9*b*x + 2*a**8*b**2) + x**5/(5*a**3) - 3*b*x**4/(4*a**4) + 2*b**2*x**3/a**5 - 5*b**3*x**2/a**6 + 15*b**4*x/a**7 - 21*b**5*log(a*x + b)/a**8","A",0
1634,1,92,0,0.354571," ","integrate(x**3/(a+b/x)**3,x)","\frac{12 a b^{5} x + 11 b^{6}}{2 a^{9} x^{2} + 4 a^{8} b x + 2 a^{7} b^{2}} + \frac{x^{4}}{4 a^{3}} - \frac{b x^{3}}{a^{4}} + \frac{3 b^{2} x^{2}}{a^{5}} - \frac{10 b^{3} x}{a^{6}} + \frac{15 b^{4} \log{\left(a x + b \right)}}{a^{7}}"," ",0,"(12*a*b**5*x + 11*b**6)/(2*a**9*x**2 + 4*a**8*b*x + 2*a**7*b**2) + x**4/(4*a**3) - b*x**3/a**4 + 3*b**2*x**2/a**5 - 10*b**3*x/a**6 + 15*b**4*log(a*x + b)/a**7","A",0
1635,1,85,0,0.327868," ","integrate(x**2/(a+b/x)**3,x)","\frac{- 10 a b^{4} x - 9 b^{5}}{2 a^{8} x^{2} + 4 a^{7} b x + 2 a^{6} b^{2}} + \frac{x^{3}}{3 a^{3}} - \frac{3 b x^{2}}{2 a^{4}} + \frac{6 b^{2} x}{a^{5}} - \frac{10 b^{3} \log{\left(a x + b \right)}}{a^{6}}"," ",0,"(-10*a*b**4*x - 9*b**5)/(2*a**8*x**2 + 4*a**7*b*x + 2*a**6*b**2) + x**3/(3*a**3) - 3*b*x**2/(2*a**4) + 6*b**2*x/a**5 - 10*b**3*log(a*x + b)/a**6","A",0
1636,1,70,0,0.299393," ","integrate(x/(a+b/x)**3,x)","\frac{8 a b^{3} x + 7 b^{4}}{2 a^{7} x^{2} + 4 a^{6} b x + 2 a^{5} b^{2}} + \frac{x^{2}}{2 a^{3}} - \frac{3 b x}{a^{4}} + \frac{6 b^{2} \log{\left(a x + b \right)}}{a^{5}}"," ",0,"(8*a*b**3*x + 7*b**4)/(2*a**7*x**2 + 4*a**6*b*x + 2*a**5*b**2) + x**2/(2*a**3) - 3*b*x/a**4 + 6*b**2*log(a*x + b)/a**5","A",0
1637,1,58,0,0.273366," ","integrate(1/(a+b/x)**3,x)","\frac{- 6 a b^{2} x - 5 b^{3}}{2 a^{6} x^{2} + 4 a^{5} b x + 2 a^{4} b^{2}} + \frac{x}{a^{3}} - \frac{3 b \log{\left(a x + b \right)}}{a^{4}}"," ",0,"(-6*a*b**2*x - 5*b**3)/(2*a**6*x**2 + 4*a**5*b*x + 2*a**4*b**2) + x/a**3 - 3*b*log(a*x + b)/a**4","A",0
1638,1,46,0,0.223300," ","integrate(1/(a+b/x)**3/x,x)","\frac{4 a b x + 3 b^{2}}{2 a^{5} x^{2} + 4 a^{4} b x + 2 a^{3} b^{2}} + \frac{\log{\left(a x + b \right)}}{a^{3}}"," ",0,"(4*a*b*x + 3*b**2)/(2*a**5*x**2 + 4*a**4*b*x + 2*a**3*b**2) + log(a*x + b)/a**3","A",0
1639,1,32,0,0.208812," ","integrate(1/(a+b/x)**3/x**2,x)","\frac{- 2 a x - b}{2 a^{4} x^{2} + 4 a^{3} b x + 2 a^{2} b^{2}}"," ",0,"(-2*a*x - b)/(2*a**4*x**2 + 4*a**3*b*x + 2*a**2*b**2)","B",0
1640,1,26,0,0.205593," ","integrate(1/(a+b/x)**3/x**3,x)","- \frac{1}{2 a^{3} x^{2} + 4 a^{2} b x + 2 a b^{2}}"," ",0,"-1/(2*a**3*x**2 + 4*a**2*b*x + 2*a*b**2)","B",0
1641,1,46,0,0.313165," ","integrate(1/(a+b/x)**3/x**4,x)","\frac{2 a x + 3 b}{2 a^{2} b^{2} x^{2} + 4 a b^{3} x + 2 b^{4}} + \frac{\log{\left(x \right)} - \log{\left(x + \frac{b}{a} \right)}}{b^{3}}"," ",0,"(2*a*x + 3*b)/(2*a**2*b**2*x**2 + 4*a*b**3*x + 2*b**4) + (log(x) - log(x + b/a))/b**3","A",0
1642,1,66,0,0.365898," ","integrate(1/(a+b/x)**3/x**5,x)","\frac{3 a \left(- \log{\left(x \right)} + \log{\left(x + \frac{b}{a} \right)}\right)}{b^{4}} + \frac{- 6 a^{2} x^{2} - 9 a b x - 2 b^{2}}{2 a^{2} b^{3} x^{3} + 4 a b^{4} x^{2} + 2 b^{5} x}"," ",0,"3*a*(-log(x) + log(x + b/a))/b**4 + (-6*a**2*x**2 - 9*a*b*x - 2*b**2)/(2*a**2*b**3*x**3 + 4*a*b**4*x**2 + 2*b**5*x)","A",0
1643,1,78,0,0.422320," ","integrate(1/(a+b/x)**3/x**6,x)","\frac{6 a^{2} \left(\log{\left(x \right)} - \log{\left(x + \frac{b}{a} \right)}\right)}{b^{5}} + \frac{12 a^{3} x^{3} + 18 a^{2} b x^{2} + 4 a b^{2} x - b^{3}}{2 a^{2} b^{4} x^{4} + 4 a b^{5} x^{3} + 2 b^{6} x^{2}}"," ",0,"6*a**2*(log(x) - log(x + b/a))/b**5 + (12*a**3*x**3 + 18*a**2*b*x**2 + 4*a*b**2*x - b**3)/(2*a**2*b**4*x**4 + 4*a*b**5*x**3 + 2*b**6*x**2)","A",0
1644,1,92,0,0.444715," ","integrate(1/(a+b/x)**3/x**7,x)","\frac{10 a^{3} \left(- \log{\left(x \right)} + \log{\left(x + \frac{b}{a} \right)}\right)}{b^{6}} + \frac{- 60 a^{4} x^{4} - 90 a^{3} b x^{3} - 20 a^{2} b^{2} x^{2} + 5 a b^{3} x - 2 b^{4}}{6 a^{2} b^{5} x^{5} + 12 a b^{6} x^{4} + 6 b^{7} x^{3}}"," ",0,"10*a**3*(-log(x) + log(x + b/a))/b**6 + (-60*a**4*x**4 - 90*a**3*b*x**3 - 20*a**2*b**2*x**2 + 5*a*b**3*x - 2*b**4)/(6*a**2*b**5*x**5 + 12*a*b**6*x**4 + 6*b**7*x**3)","A",0
1645,1,102,0,0.508866," ","integrate(1/(a+b/x)**3/x**8,x)","\frac{15 a^{4} \left(\log{\left(x \right)} - \log{\left(x + \frac{b}{a} \right)}\right)}{b^{7}} + \frac{60 a^{5} x^{5} + 90 a^{4} b x^{4} + 20 a^{3} b^{2} x^{3} - 5 a^{2} b^{3} x^{2} + 2 a b^{4} x - b^{5}}{4 a^{2} b^{6} x^{6} + 8 a b^{7} x^{5} + 4 b^{8} x^{4}}"," ",0,"15*a**4*(log(x) - log(x + b/a))/b**7 + (60*a**5*x**5 + 90*a**4*b*x**4 + 20*a**3*b**2*x**3 - 5*a**2*b**3*x**2 + 2*a*b**4*x - b**5)/(4*a**2*b**6*x**6 + 8*a*b**7*x**5 + 4*b**8*x**4)","A",0
1646,1,116,0,0.505931," ","integrate(1/(a+b/x)**3/x**9,x)","\frac{21 a^{5} \left(- \log{\left(x \right)} + \log{\left(x + \frac{b}{a} \right)}\right)}{b^{8}} + \frac{- 420 a^{6} x^{6} - 630 a^{5} b x^{5} - 140 a^{4} b^{2} x^{4} + 35 a^{3} b^{3} x^{3} - 14 a^{2} b^{4} x^{2} + 7 a b^{5} x - 4 b^{6}}{20 a^{2} b^{7} x^{7} + 40 a b^{8} x^{6} + 20 b^{9} x^{5}}"," ",0,"21*a**5*(-log(x) + log(x + b/a))/b**8 + (-420*a**6*x**6 - 630*a**5*b*x**5 - 140*a**4*b**2*x**4 + 35*a**3*b**3*x**3 - 14*a**2*b**4*x**2 + 7*a*b**5*x - 4*b**6)/(20*a**2*b**7*x**7 + 40*a*b**8*x**6 + 20*b**9*x**5)","A",0
1647,1,19,0,1.770837," ","integrate((a+b/x)*x**(5/2),x)","\frac{2 a x^{\frac{7}{2}}}{7} + \frac{2 b x^{\frac{5}{2}}}{5}"," ",0,"2*a*x**(7/2)/7 + 2*b*x**(5/2)/5","A",0
1648,1,19,0,0.716962," ","integrate((a+b/x)*x**(3/2),x)","\frac{2 a x^{\frac{5}{2}}}{5} + \frac{2 b x^{\frac{3}{2}}}{3}"," ",0,"2*a*x**(5/2)/5 + 2*b*x**(3/2)/3","A",0
1649,1,17,0,0.221858," ","integrate((a+b/x)*x**(1/2),x)","\frac{2 a x^{\frac{3}{2}}}{3} + 2 b \sqrt{x}"," ",0,"2*a*x**(3/2)/3 + 2*b*sqrt(x)","A",0
1650,1,15,0,0.356120," ","integrate((a+b/x)/x**(1/2),x)","2 a \sqrt{x} - \frac{2 b}{\sqrt{x}}"," ",0,"2*a*sqrt(x) - 2*b/sqrt(x)","A",0
1651,1,19,0,0.503693," ","integrate((a+b/x)/x**(3/2),x)","- \frac{2 a}{\sqrt{x}} - \frac{2 b}{3 x^{\frac{3}{2}}}"," ",0,"-2*a/sqrt(x) - 2*b/(3*x**(3/2))","A",0
1652,1,20,0,0.935450," ","integrate((a+b/x)/x**(5/2),x)","- \frac{2 a}{3 x^{\frac{3}{2}}} - \frac{2 b}{5 x^{\frac{5}{2}}}"," ",0,"-2*a/(3*x**(3/2)) - 2*b/(5*x**(5/2))","A",0
1653,1,34,0,2.561686," ","integrate((a+b/x)**2*x**(5/2),x)","\frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{2 b^{2} x^{\frac{3}{2}}}{3}"," ",0,"2*a**2*x**(7/2)/7 + 4*a*b*x**(5/2)/5 + 2*b**2*x**(3/2)/3","A",0
1654,1,32,0,1.156948," ","integrate((a+b/x)**2*x**(3/2),x)","\frac{2 a^{2} x^{\frac{5}{2}}}{5} + \frac{4 a b x^{\frac{3}{2}}}{3} + 2 b^{2} \sqrt{x}"," ",0,"2*a**2*x**(5/2)/5 + 4*a*b*x**(3/2)/3 + 2*b**2*sqrt(x)","A",0
1655,1,31,0,0.503020," ","integrate((a+b/x)**2*x**(1/2),x)","\frac{2 a^{2} x^{\frac{3}{2}}}{3} + 4 a b \sqrt{x} - \frac{2 b^{2}}{\sqrt{x}}"," ",0,"2*a**2*x**(3/2)/3 + 4*a*b*sqrt(x) - 2*b**2/sqrt(x)","A",0
1656,1,31,0,0.540988," ","integrate((a+b/x)**2/x**(1/2),x)","2 a^{2} \sqrt{x} - \frac{4 a b}{\sqrt{x}} - \frac{2 b^{2}}{3 x^{\frac{3}{2}}}"," ",0,"2*a**2*sqrt(x) - 4*a*b/sqrt(x) - 2*b**2/(3*x**(3/2))","A",0
1657,1,34,0,0.851040," ","integrate((a+b/x)**2/x**(3/2),x)","- \frac{2 a^{2}}{\sqrt{x}} - \frac{4 a b}{3 x^{\frac{3}{2}}} - \frac{2 b^{2}}{5 x^{\frac{5}{2}}}"," ",0,"-2*a**2/sqrt(x) - 4*a*b/(3*x**(3/2)) - 2*b**2/(5*x**(5/2))","A",0
1658,1,36,0,1.480738," ","integrate((a+b/x)**2/x**(5/2),x)","- \frac{2 a^{2}}{3 x^{\frac{3}{2}}} - \frac{4 a b}{5 x^{\frac{5}{2}}} - \frac{2 b^{2}}{7 x^{\frac{7}{2}}}"," ",0,"-2*a**2/(3*x**(3/2)) - 4*a*b/(5*x**(5/2)) - 2*b**2/(7*x**(7/2))","A",0
1659,1,46,0,3.881394," ","integrate((a+b/x)**3*x**(5/2),x)","\frac{2 a^{3} x^{\frac{7}{2}}}{7} + \frac{6 a^{2} b x^{\frac{5}{2}}}{5} + 2 a b^{2} x^{\frac{3}{2}} + 2 b^{3} \sqrt{x}"," ",0,"2*a**3*x**(7/2)/7 + 6*a**2*b*x**(5/2)/5 + 2*a*b**2*x**(3/2) + 2*b**3*sqrt(x)","A",0
1660,1,44,0,1.814386," ","integrate((a+b/x)**3*x**(3/2),x)","\frac{2 a^{3} x^{\frac{5}{2}}}{5} + 2 a^{2} b x^{\frac{3}{2}} + 6 a b^{2} \sqrt{x} - \frac{2 b^{3}}{\sqrt{x}}"," ",0,"2*a**3*x**(5/2)/5 + 2*a**2*b*x**(3/2) + 6*a*b**2*sqrt(x) - 2*b**3/sqrt(x)","A",0
1661,1,46,0,0.798796," ","integrate((a+b/x)**3*x**(1/2),x)","\frac{2 a^{3} x^{\frac{3}{2}}}{3} + 6 a^{2} b \sqrt{x} - \frac{6 a b^{2}}{\sqrt{x}} - \frac{2 b^{3}}{3 x^{\frac{3}{2}}}"," ",0,"2*a**3*x**(3/2)/3 + 6*a**2*b*sqrt(x) - 6*a*b**2/sqrt(x) - 2*b**3/(3*x**(3/2))","A",0
1662,1,44,0,0.853228," ","integrate((a+b/x)**3/x**(1/2),x)","2 a^{3} \sqrt{x} - \frac{6 a^{2} b}{\sqrt{x}} - \frac{2 a b^{2}}{x^{\frac{3}{2}}} - \frac{2 b^{3}}{5 x^{\frac{5}{2}}}"," ",0,"2*a**3*sqrt(x) - 6*a**2*b/sqrt(x) - 2*a*b**2/x**(3/2) - 2*b**3/(5*x**(5/2))","A",0
1663,1,48,0,1.220716," ","integrate((a+b/x)**3/x**(3/2),x)","- \frac{2 a^{3}}{\sqrt{x}} - \frac{2 a^{2} b}{x^{\frac{3}{2}}} - \frac{6 a b^{2}}{5 x^{\frac{5}{2}}} - \frac{2 b^{3}}{7 x^{\frac{7}{2}}}"," ",0,"-2*a**3/sqrt(x) - 2*a**2*b/x**(3/2) - 6*a*b**2/(5*x**(5/2)) - 2*b**3/(7*x**(7/2))","A",0
1664,1,51,0,2.036556," ","integrate((a+b/x)**3/x**(5/2),x)","- \frac{2 a^{3}}{3 x^{\frac{3}{2}}} - \frac{6 a^{2} b}{5 x^{\frac{5}{2}}} - \frac{6 a b^{2}}{7 x^{\frac{7}{2}}} - \frac{2 b^{3}}{9 x^{\frac{9}{2}}}"," ",0,"-2*a**3/(3*x**(3/2)) - 6*a**2*b/(5*x**(5/2)) - 6*a*b**2/(7*x**(7/2)) - 2*b**3/(9*x**(9/2))","A",0
1665,1,136,0,22.576627," ","integrate(x**(5/2)/(a+b/x),x)","\begin{cases} \frac{2 x^{\frac{7}{2}}}{7 a} - \frac{2 b x^{\frac{5}{2}}}{5 a^{2}} + \frac{2 b^{2} x^{\frac{3}{2}}}{3 a^{3}} - \frac{2 b^{3} \sqrt{x}}{a^{4}} - \frac{i b^{\frac{7}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a^{5} \sqrt{\frac{1}{a}}} + \frac{i b^{\frac{7}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a^{5} \sqrt{\frac{1}{a}}} & \text{for}\: a \neq 0 \\\frac{2 x^{\frac{9}{2}}}{9 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x**(7/2)/(7*a) - 2*b*x**(5/2)/(5*a**2) + 2*b**2*x**(3/2)/(3*a**3) - 2*b**3*sqrt(x)/a**4 - I*b**(7/2)*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a**5*sqrt(1/a)) + I*b**(7/2)*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a**5*sqrt(1/a)), Ne(a, 0)), (2*x**(9/2)/(9*b), True))","A",0
1666,1,121,0,5.749228," ","integrate(x**(3/2)/(a+b/x),x)","\begin{cases} \frac{2 x^{\frac{5}{2}}}{5 a} - \frac{2 b x^{\frac{3}{2}}}{3 a^{2}} + \frac{2 b^{2} \sqrt{x}}{a^{3}} + \frac{i b^{\frac{5}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a^{4} \sqrt{\frac{1}{a}}} - \frac{i b^{\frac{5}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a^{4} \sqrt{\frac{1}{a}}} & \text{for}\: a \neq 0 \\\frac{2 x^{\frac{7}{2}}}{7 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x**(5/2)/(5*a) - 2*b*x**(3/2)/(3*a**2) + 2*b**2*sqrt(x)/a**3 + I*b**(5/2)*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a**4*sqrt(1/a)) - I*b**(5/2)*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a**4*sqrt(1/a)), Ne(a, 0)), (2*x**(7/2)/(7*b), True))","A",0
1667,1,105,0,1.367242," ","integrate(x**(1/2)/(a+b/x),x)","\begin{cases} \frac{2 x^{\frac{3}{2}}}{3 a} - \frac{2 b \sqrt{x}}{a^{2}} - \frac{i b^{\frac{3}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a^{3} \sqrt{\frac{1}{a}}} + \frac{i b^{\frac{3}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a^{3} \sqrt{\frac{1}{a}}} & \text{for}\: a \neq 0 \\\frac{2 x^{\frac{5}{2}}}{5 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x**(3/2)/(3*a) - 2*b*sqrt(x)/a**2 - I*b**(3/2)*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a**3*sqrt(1/a)) + I*b**(3/2)*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a**3*sqrt(1/a)), Ne(a, 0)), (2*x**(5/2)/(5*b), True))","A",0
1668,1,92,0,1.352810," ","integrate(1/(a+b/x)/x**(1/2),x)","\begin{cases} \frac{2 \sqrt{x}}{a} + \frac{i \sqrt{b} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a^{2} \sqrt{\frac{1}{a}}} - \frac{i \sqrt{b} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a^{2} \sqrt{\frac{1}{a}}} & \text{for}\: a \neq 0 \\\frac{2 x^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(x)/a + I*sqrt(b)*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a**2*sqrt(1/a)) - I*sqrt(b)*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a**2*sqrt(1/a)), Ne(a, 0)), (2*x**(3/2)/(3*b), True))","A",0
1669,1,94,0,3.292897," ","integrate(1/(a+b/x)/x**(3/2),x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 \sqrt{x}}{b} & \text{for}\: a = 0 \\- \frac{2}{a \sqrt{x}} & \text{for}\: b = 0 \\- \frac{i \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a \sqrt{b} \sqrt{\frac{1}{a}}} + \frac{i \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a \sqrt{b} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*sqrt(x)/b, Eq(a, 0)), (-2/(a*sqrt(x)), Eq(b, 0)), (-I*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a*sqrt(b)*sqrt(1/a)) + I*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a*sqrt(b)*sqrt(1/a)), True))","A",0
1670,1,102,0,12.593121," ","integrate(1/(a+b/x)/x**(5/2),x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{3 a x^{\frac{3}{2}}} & \text{for}\: b = 0 \\- \frac{2}{b \sqrt{x}} & \text{for}\: a = 0 \\- \frac{2}{b \sqrt{x}} + \frac{i \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{i \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (-2/(3*a*x**(3/2)), Eq(b, 0)), (-2/(b*sqrt(x)), Eq(a, 0)), (-2/(b*sqrt(x)) + I*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(b**(3/2)*sqrt(1/a)) - I*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(b**(3/2)*sqrt(1/a)), True))","A",0
1671,1,121,0,57.640221," ","integrate(1/(a+b/x)/x**(7/2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{5 a x^{\frac{5}{2}}} & \text{for}\: b = 0 \\- \frac{2}{3 b x^{\frac{3}{2}}} & \text{for}\: a = 0 \\\frac{2 a}{b^{2} \sqrt{x}} - \frac{i a \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{i a \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{2}{3 b x^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (-2/(5*a*x**(5/2)), Eq(b, 0)), (-2/(3*b*x**(3/2)), Eq(a, 0)), (2*a/(b**2*sqrt(x)) - I*a*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(b**(5/2)*sqrt(1/a)) + I*a*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(b**(5/2)*sqrt(1/a)) - 2/(3*b*x**(3/2)), True))","A",0
1672,1,139,0,149.235865," ","integrate(1/(a+b/x)/x**(9/2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{7 a x^{\frac{7}{2}}} & \text{for}\: b = 0 \\- \frac{2}{5 b x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{2 a^{2}}{b^{3} \sqrt{x}} + \frac{i a^{2} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{b^{\frac{7}{2}} \sqrt{\frac{1}{a}}} - \frac{i a^{2} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{b^{\frac{7}{2}} \sqrt{\frac{1}{a}}} + \frac{2 a}{3 b^{2} x^{\frac{3}{2}}} - \frac{2}{5 b x^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(7*a*x**(7/2)), Eq(b, 0)), (-2/(5*b*x**(5/2)), Eq(a, 0)), (-2*a**2/(b**3*sqrt(x)) + I*a**2*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(b**(7/2)*sqrt(1/a)) - I*a**2*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(b**(7/2)*sqrt(1/a)) + 2*a/(3*b**2*x**(3/2)) - 2/(5*b*x**(5/2)), True))","A",0
1673,-1,0,0,0.000000," ","integrate(x**(5/2)/(a+b/x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1674,1,542,0,57.534673," ","integrate(x**(3/2)/(a+b/x)**2,x)","\begin{cases} \tilde{\infty} x^{\frac{9}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{9}{2}}}{9 b^{2}} & \text{for}\: a = 0 \\\frac{2 x^{\frac{5}{2}}}{5 a^{2}} & \text{for}\: b = 0 \\\frac{12 i a^{4} \sqrt{b} x^{\frac{7}{2}} \sqrt{\frac{1}{a}}}{30 i a^{6} \sqrt{b} x \sqrt{\frac{1}{a}} + 30 i a^{5} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{28 i a^{3} b^{\frac{3}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{a}}}{30 i a^{6} \sqrt{b} x \sqrt{\frac{1}{a}} + 30 i a^{5} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{140 i a^{2} b^{\frac{5}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{a}}}{30 i a^{6} \sqrt{b} x \sqrt{\frac{1}{a}} + 30 i a^{5} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{210 i a b^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{a}}}{30 i a^{6} \sqrt{b} x \sqrt{\frac{1}{a}} + 30 i a^{5} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{105 a b^{3} x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{30 i a^{6} \sqrt{b} x \sqrt{\frac{1}{a}} + 30 i a^{5} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{105 a b^{3} x \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{30 i a^{6} \sqrt{b} x \sqrt{\frac{1}{a}} + 30 i a^{5} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{105 b^{4} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{30 i a^{6} \sqrt{b} x \sqrt{\frac{1}{a}} + 30 i a^{5} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{105 b^{4} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{30 i a^{6} \sqrt{b} x \sqrt{\frac{1}{a}} + 30 i a^{5} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(9/2), Eq(a, 0) & Eq(b, 0)), (2*x**(9/2)/(9*b**2), Eq(a, 0)), (2*x**(5/2)/(5*a**2), Eq(b, 0)), (12*I*a**4*sqrt(b)*x**(7/2)*sqrt(1/a)/(30*I*a**6*sqrt(b)*x*sqrt(1/a) + 30*I*a**5*b**(3/2)*sqrt(1/a)) - 28*I*a**3*b**(3/2)*x**(5/2)*sqrt(1/a)/(30*I*a**6*sqrt(b)*x*sqrt(1/a) + 30*I*a**5*b**(3/2)*sqrt(1/a)) + 140*I*a**2*b**(5/2)*x**(3/2)*sqrt(1/a)/(30*I*a**6*sqrt(b)*x*sqrt(1/a) + 30*I*a**5*b**(3/2)*sqrt(1/a)) + 210*I*a*b**(7/2)*sqrt(x)*sqrt(1/a)/(30*I*a**6*sqrt(b)*x*sqrt(1/a) + 30*I*a**5*b**(3/2)*sqrt(1/a)) - 105*a*b**3*x*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(30*I*a**6*sqrt(b)*x*sqrt(1/a) + 30*I*a**5*b**(3/2)*sqrt(1/a)) + 105*a*b**3*x*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(30*I*a**6*sqrt(b)*x*sqrt(1/a) + 30*I*a**5*b**(3/2)*sqrt(1/a)) - 105*b**4*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(30*I*a**6*sqrt(b)*x*sqrt(1/a) + 30*I*a**5*b**(3/2)*sqrt(1/a)) + 105*b**4*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(30*I*a**6*sqrt(b)*x*sqrt(1/a) + 30*I*a**5*b**(3/2)*sqrt(1/a)), True))","A",0
1675,1,479,0,9.641108," ","integrate(x**(1/2)/(a+b/x)**2,x)","\begin{cases} \tilde{\infty} x^{\frac{7}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{7}{2}}}{7 b^{2}} & \text{for}\: a = 0 \\\frac{2 x^{\frac{3}{2}}}{3 a^{2}} & \text{for}\: b = 0 \\\frac{4 i a^{3} \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{1}{a}}}{6 i a^{5} \sqrt{b} x \sqrt{\frac{1}{a}} + 6 i a^{4} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{20 i a^{2} b^{\frac{3}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{a}}}{6 i a^{5} \sqrt{b} x \sqrt{\frac{1}{a}} + 6 i a^{4} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{30 i a b^{\frac{5}{2}} \sqrt{x} \sqrt{\frac{1}{a}}}{6 i a^{5} \sqrt{b} x \sqrt{\frac{1}{a}} + 6 i a^{4} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{15 a b^{2} x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{6 i a^{5} \sqrt{b} x \sqrt{\frac{1}{a}} + 6 i a^{4} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{15 a b^{2} x \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{6 i a^{5} \sqrt{b} x \sqrt{\frac{1}{a}} + 6 i a^{4} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{15 b^{3} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{6 i a^{5} \sqrt{b} x \sqrt{\frac{1}{a}} + 6 i a^{4} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{15 b^{3} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{6 i a^{5} \sqrt{b} x \sqrt{\frac{1}{a}} + 6 i a^{4} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(7/2), Eq(a, 0) & Eq(b, 0)), (2*x**(7/2)/(7*b**2), Eq(a, 0)), (2*x**(3/2)/(3*a**2), Eq(b, 0)), (4*I*a**3*sqrt(b)*x**(5/2)*sqrt(1/a)/(6*I*a**5*sqrt(b)*x*sqrt(1/a) + 6*I*a**4*b**(3/2)*sqrt(1/a)) - 20*I*a**2*b**(3/2)*x**(3/2)*sqrt(1/a)/(6*I*a**5*sqrt(b)*x*sqrt(1/a) + 6*I*a**4*b**(3/2)*sqrt(1/a)) - 30*I*a*b**(5/2)*sqrt(x)*sqrt(1/a)/(6*I*a**5*sqrt(b)*x*sqrt(1/a) + 6*I*a**4*b**(3/2)*sqrt(1/a)) + 15*a*b**2*x*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(6*I*a**5*sqrt(b)*x*sqrt(1/a) + 6*I*a**4*b**(3/2)*sqrt(1/a)) - 15*a*b**2*x*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(6*I*a**5*sqrt(b)*x*sqrt(1/a) + 6*I*a**4*b**(3/2)*sqrt(1/a)) + 15*b**3*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(6*I*a**5*sqrt(b)*x*sqrt(1/a) + 6*I*a**4*b**(3/2)*sqrt(1/a)) - 15*b**3*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(6*I*a**5*sqrt(b)*x*sqrt(1/a) + 6*I*a**4*b**(3/2)*sqrt(1/a)), True))","A",0
1676,1,411,0,12.338923," ","integrate(1/(a+b/x)**2/x**(1/2),x)","\begin{cases} \tilde{\infty} x^{\frac{5}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 \sqrt{x}}{a^{2}} & \text{for}\: b = 0 \\\frac{2 x^{\frac{5}{2}}}{5 b^{2}} & \text{for}\: a = 0 \\\frac{4 i a^{2} \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{1}{a}}}{2 i a^{4} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{3} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{6 i a b^{\frac{3}{2}} \sqrt{x} \sqrt{\frac{1}{a}}}{2 i a^{4} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{3} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{3 a b x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{4} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{3} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{3 a b x \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{4} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{3} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{3 b^{2} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{4} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{3} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{3 b^{2} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{4} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{3} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(5/2), Eq(a, 0) & Eq(b, 0)), (2*sqrt(x)/a**2, Eq(b, 0)), (2*x**(5/2)/(5*b**2), Eq(a, 0)), (4*I*a**2*sqrt(b)*x**(3/2)*sqrt(1/a)/(2*I*a**4*sqrt(b)*x*sqrt(1/a) + 2*I*a**3*b**(3/2)*sqrt(1/a)) + 6*I*a*b**(3/2)*sqrt(x)*sqrt(1/a)/(2*I*a**4*sqrt(b)*x*sqrt(1/a) + 2*I*a**3*b**(3/2)*sqrt(1/a)) - 3*a*b*x*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**4*sqrt(b)*x*sqrt(1/a) + 2*I*a**3*b**(3/2)*sqrt(1/a)) + 3*a*b*x*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**4*sqrt(b)*x*sqrt(1/a) + 2*I*a**3*b**(3/2)*sqrt(1/a)) - 3*b**2*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**4*sqrt(b)*x*sqrt(1/a) + 2*I*a**3*b**(3/2)*sqrt(1/a)) + 3*b**2*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**4*sqrt(b)*x*sqrt(1/a) + 2*I*a**3*b**(3/2)*sqrt(1/a)), True))","A",0
1677,1,337,0,28.924877," ","integrate(1/(a+b/x)**2/x**(3/2),x)","\begin{cases} \tilde{\infty} x^{\frac{3}{2}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{a^{2} \sqrt{x}} & \text{for}\: b = 0 \\\frac{2 x^{\frac{3}{2}}}{3 b^{2}} & \text{for}\: a = 0 \\- \frac{2 i a \sqrt{b} \sqrt{x} \sqrt{\frac{1}{a}}}{2 i a^{3} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{2} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{a x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{3} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{2} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{a x \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{3} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{2} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{b \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{3} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{2} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{b \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{3} \sqrt{b} x \sqrt{\frac{1}{a}} + 2 i a^{2} b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(3/2), Eq(a, 0) & Eq(b, 0)), (-2/(a**2*sqrt(x)), Eq(b, 0)), (2*x**(3/2)/(3*b**2), Eq(a, 0)), (-2*I*a*sqrt(b)*sqrt(x)*sqrt(1/a)/(2*I*a**3*sqrt(b)*x*sqrt(1/a) + 2*I*a**2*b**(3/2)*sqrt(1/a)) + a*x*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**3*sqrt(b)*x*sqrt(1/a) + 2*I*a**2*b**(3/2)*sqrt(1/a)) - a*x*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**3*sqrt(b)*x*sqrt(1/a) + 2*I*a**2*b**(3/2)*sqrt(1/a)) + b*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**3*sqrt(b)*x*sqrt(1/a) + 2*I*a**2*b**(3/2)*sqrt(1/a)) - b*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**3*sqrt(b)*x*sqrt(1/a) + 2*I*a**2*b**(3/2)*sqrt(1/a)), True))","A",0
1678,1,328,0,102.664913," ","integrate(1/(a+b/x)**2/x**(5/2),x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 \sqrt{x}}{b^{2}} & \text{for}\: a = 0 \\- \frac{2}{3 a^{2} x^{\frac{3}{2}}} & \text{for}\: b = 0 \\\frac{2 i a \sqrt{b} \sqrt{x} \sqrt{\frac{1}{a}}}{2 i a^{2} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 2 i a b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{a x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{2} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 2 i a b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{a x \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{2} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 2 i a b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{b \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{2} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 2 i a b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{b \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{2 i a^{2} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 2 i a b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*sqrt(x)/b**2, Eq(a, 0)), (-2/(3*a**2*x**(3/2)), Eq(b, 0)), (2*I*a*sqrt(b)*sqrt(x)*sqrt(1/a)/(2*I*a**2*b**(3/2)*x*sqrt(1/a) + 2*I*a*b**(5/2)*sqrt(1/a)) + a*x*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**2*b**(3/2)*x*sqrt(1/a) + 2*I*a*b**(5/2)*sqrt(1/a)) - a*x*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**2*b**(3/2)*x*sqrt(1/a) + 2*I*a*b**(5/2)*sqrt(1/a)) + b*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**2*b**(3/2)*x*sqrt(1/a) + 2*I*a*b**(5/2)*sqrt(1/a)) - b*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(2*I*a**2*b**(3/2)*x*sqrt(1/a) + 2*I*a*b**(5/2)*sqrt(1/a)), True))","A",0
1679,-1,0,0,0.000000," ","integrate(1/(a+b/x)**2/x**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1680,-1,0,0,0.000000," ","integrate(1/(a+b/x)**2/x**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1681,-1,0,0,0.000000," ","integrate(1/(a+b/x)**2/x**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1682,-1,0,0,0.000000," ","integrate(x**(3/2)/(a+b/x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1683,1,906,0,43.536763," ","integrate(x**(1/2)/(a+b/x)**3,x)","\begin{cases} \tilde{\infty} x^{\frac{9}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{9}{2}}}{9 b^{3}} & \text{for}\: a = 0 \\\frac{2 x^{\frac{3}{2}}}{3 a^{3}} & \text{for}\: b = 0 \\\frac{16 i a^{4} \sqrt{b} x^{\frac{7}{2}} \sqrt{\frac{1}{a}}}{24 i a^{7} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 48 i a^{6} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 24 i a^{5} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{112 i a^{3} b^{\frac{3}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{a}}}{24 i a^{7} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 48 i a^{6} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 24 i a^{5} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{350 i a^{2} b^{\frac{5}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{a}}}{24 i a^{7} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 48 i a^{6} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 24 i a^{5} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{105 a^{2} b^{2} x^{2} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{24 i a^{7} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 48 i a^{6} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 24 i a^{5} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{105 a^{2} b^{2} x^{2} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{24 i a^{7} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 48 i a^{6} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 24 i a^{5} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{210 i a b^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{a}}}{24 i a^{7} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 48 i a^{6} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 24 i a^{5} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{210 a b^{3} x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{24 i a^{7} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 48 i a^{6} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 24 i a^{5} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{210 a b^{3} x \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{24 i a^{7} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 48 i a^{6} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 24 i a^{5} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{105 b^{4} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{24 i a^{7} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 48 i a^{6} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 24 i a^{5} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{105 b^{4} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{24 i a^{7} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 48 i a^{6} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 24 i a^{5} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(9/2), Eq(a, 0) & Eq(b, 0)), (2*x**(9/2)/(9*b**3), Eq(a, 0)), (2*x**(3/2)/(3*a**3), Eq(b, 0)), (16*I*a**4*sqrt(b)*x**(7/2)*sqrt(1/a)/(24*I*a**7*sqrt(b)*x**2*sqrt(1/a) + 48*I*a**6*b**(3/2)*x*sqrt(1/a) + 24*I*a**5*b**(5/2)*sqrt(1/a)) - 112*I*a**3*b**(3/2)*x**(5/2)*sqrt(1/a)/(24*I*a**7*sqrt(b)*x**2*sqrt(1/a) + 48*I*a**6*b**(3/2)*x*sqrt(1/a) + 24*I*a**5*b**(5/2)*sqrt(1/a)) - 350*I*a**2*b**(5/2)*x**(3/2)*sqrt(1/a)/(24*I*a**7*sqrt(b)*x**2*sqrt(1/a) + 48*I*a**6*b**(3/2)*x*sqrt(1/a) + 24*I*a**5*b**(5/2)*sqrt(1/a)) + 105*a**2*b**2*x**2*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(24*I*a**7*sqrt(b)*x**2*sqrt(1/a) + 48*I*a**6*b**(3/2)*x*sqrt(1/a) + 24*I*a**5*b**(5/2)*sqrt(1/a)) - 105*a**2*b**2*x**2*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(24*I*a**7*sqrt(b)*x**2*sqrt(1/a) + 48*I*a**6*b**(3/2)*x*sqrt(1/a) + 24*I*a**5*b**(5/2)*sqrt(1/a)) - 210*I*a*b**(7/2)*sqrt(x)*sqrt(1/a)/(24*I*a**7*sqrt(b)*x**2*sqrt(1/a) + 48*I*a**6*b**(3/2)*x*sqrt(1/a) + 24*I*a**5*b**(5/2)*sqrt(1/a)) + 210*a*b**3*x*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(24*I*a**7*sqrt(b)*x**2*sqrt(1/a) + 48*I*a**6*b**(3/2)*x*sqrt(1/a) + 24*I*a**5*b**(5/2)*sqrt(1/a)) - 210*a*b**3*x*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(24*I*a**7*sqrt(b)*x**2*sqrt(1/a) + 48*I*a**6*b**(3/2)*x*sqrt(1/a) + 24*I*a**5*b**(5/2)*sqrt(1/a)) + 105*b**4*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(24*I*a**7*sqrt(b)*x**2*sqrt(1/a) + 48*I*a**6*b**(3/2)*x*sqrt(1/a) + 24*I*a**5*b**(5/2)*sqrt(1/a)) - 105*b**4*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(24*I*a**7*sqrt(b)*x**2*sqrt(1/a) + 48*I*a**6*b**(3/2)*x*sqrt(1/a) + 24*I*a**5*b**(5/2)*sqrt(1/a)), True))","A",0
1684,1,816,0,39.807439," ","integrate(1/(a+b/x)**3/x**(1/2),x)","\begin{cases} \tilde{\infty} x^{\frac{7}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 \sqrt{x}}{a^{3}} & \text{for}\: b = 0 \\\frac{2 x^{\frac{7}{2}}}{7 b^{3}} & \text{for}\: a = 0 \\\frac{16 i a^{3} \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{1}{a}}}{8 i a^{6} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{5} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{4} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{50 i a^{2} b^{\frac{3}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{a}}}{8 i a^{6} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{5} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{4} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{15 a^{2} b x^{2} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{6} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{5} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{4} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{15 a^{2} b x^{2} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{6} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{5} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{4} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{30 i a b^{\frac{5}{2}} \sqrt{x} \sqrt{\frac{1}{a}}}{8 i a^{6} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{5} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{4} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{30 a b^{2} x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{6} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{5} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{4} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{30 a b^{2} x \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{6} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{5} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{4} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{15 b^{3} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{6} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{5} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{4} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{15 b^{3} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{6} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{5} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{4} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(7/2), Eq(a, 0) & Eq(b, 0)), (2*sqrt(x)/a**3, Eq(b, 0)), (2*x**(7/2)/(7*b**3), Eq(a, 0)), (16*I*a**3*sqrt(b)*x**(5/2)*sqrt(1/a)/(8*I*a**6*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**5*b**(3/2)*x*sqrt(1/a) + 8*I*a**4*b**(5/2)*sqrt(1/a)) + 50*I*a**2*b**(3/2)*x**(3/2)*sqrt(1/a)/(8*I*a**6*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**5*b**(3/2)*x*sqrt(1/a) + 8*I*a**4*b**(5/2)*sqrt(1/a)) - 15*a**2*b*x**2*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**6*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**5*b**(3/2)*x*sqrt(1/a) + 8*I*a**4*b**(5/2)*sqrt(1/a)) + 15*a**2*b*x**2*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**6*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**5*b**(3/2)*x*sqrt(1/a) + 8*I*a**4*b**(5/2)*sqrt(1/a)) + 30*I*a*b**(5/2)*sqrt(x)*sqrt(1/a)/(8*I*a**6*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**5*b**(3/2)*x*sqrt(1/a) + 8*I*a**4*b**(5/2)*sqrt(1/a)) - 30*a*b**2*x*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**6*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**5*b**(3/2)*x*sqrt(1/a) + 8*I*a**4*b**(5/2)*sqrt(1/a)) + 30*a*b**2*x*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**6*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**5*b**(3/2)*x*sqrt(1/a) + 8*I*a**4*b**(5/2)*sqrt(1/a)) - 15*b**3*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**6*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**5*b**(3/2)*x*sqrt(1/a) + 8*I*a**4*b**(5/2)*sqrt(1/a)) + 15*b**3*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**6*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**5*b**(3/2)*x*sqrt(1/a) + 8*I*a**4*b**(5/2)*sqrt(1/a)), True))","A",0
1685,1,726,0,110.843793," ","integrate(1/(a+b/x)**3/x**(3/2),x)","\begin{cases} \tilde{\infty} x^{\frac{5}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{5}{2}}}{5 b^{3}} & \text{for}\: a = 0 \\- \frac{2}{a^{3} \sqrt{x}} & \text{for}\: b = 0 \\- \frac{10 i a^{2} \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{1}{a}}}{8 i a^{5} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{4} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{3} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{3 a^{2} x^{2} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{5} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{4} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{3} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{3 a^{2} x^{2} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{5} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{4} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{3} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{6 i a b^{\frac{3}{2}} \sqrt{x} \sqrt{\frac{1}{a}}}{8 i a^{5} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{4} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{3} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{6 a b x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{5} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{4} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{3} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{6 a b x \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{5} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{4} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{3} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} + \frac{3 b^{2} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{5} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{4} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{3} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} - \frac{3 b^{2} \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{8 i a^{5} \sqrt{b} x^{2} \sqrt{\frac{1}{a}} + 16 i a^{4} b^{\frac{3}{2}} x \sqrt{\frac{1}{a}} + 8 i a^{3} b^{\frac{5}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(5/2), Eq(a, 0) & Eq(b, 0)), (2*x**(5/2)/(5*b**3), Eq(a, 0)), (-2/(a**3*sqrt(x)), Eq(b, 0)), (-10*I*a**2*sqrt(b)*x**(3/2)*sqrt(1/a)/(8*I*a**5*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**4*b**(3/2)*x*sqrt(1/a) + 8*I*a**3*b**(5/2)*sqrt(1/a)) + 3*a**2*x**2*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**5*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**4*b**(3/2)*x*sqrt(1/a) + 8*I*a**3*b**(5/2)*sqrt(1/a)) - 3*a**2*x**2*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**5*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**4*b**(3/2)*x*sqrt(1/a) + 8*I*a**3*b**(5/2)*sqrt(1/a)) - 6*I*a*b**(3/2)*sqrt(x)*sqrt(1/a)/(8*I*a**5*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**4*b**(3/2)*x*sqrt(1/a) + 8*I*a**3*b**(5/2)*sqrt(1/a)) + 6*a*b*x*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**5*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**4*b**(3/2)*x*sqrt(1/a) + 8*I*a**3*b**(5/2)*sqrt(1/a)) - 6*a*b*x*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**5*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**4*b**(3/2)*x*sqrt(1/a) + 8*I*a**3*b**(5/2)*sqrt(1/a)) + 3*b**2*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**5*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**4*b**(3/2)*x*sqrt(1/a) + 8*I*a**3*b**(5/2)*sqrt(1/a)) - 3*b**2*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(8*I*a**5*sqrt(b)*x**2*sqrt(1/a) + 16*I*a**4*b**(3/2)*x*sqrt(1/a) + 8*I*a**3*b**(5/2)*sqrt(1/a)), True))","A",0
1686,-1,0,0,0.000000," ","integrate(1/(a+b/x)**3/x**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1687,-1,0,0,0.000000," ","integrate(1/(a+b/x)**3/x**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1688,-1,0,0,0.000000," ","integrate(1/(a+b/x)**3/x**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1689,-1,0,0,0.000000," ","integrate(1/(a+b/x)**3/x**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1690,-1,0,0,0.000000," ","integrate(1/(a+b/x)**3/x**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1691,1,153,0,10.571916," ","integrate(x**3*(a+b/x)**(1/2),x)","\frac{a x^{\frac{9}{2}}}{4 \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{7 \sqrt{b} x^{\frac{7}{2}}}{24 \sqrt{\frac{a x}{b} + 1}} - \frac{b^{\frac{3}{2}} x^{\frac{5}{2}}}{96 a \sqrt{\frac{a x}{b} + 1}} + \frac{5 b^{\frac{5}{2}} x^{\frac{3}{2}}}{192 a^{2} \sqrt{\frac{a x}{b} + 1}} + \frac{5 b^{\frac{7}{2}} \sqrt{x}}{64 a^{3} \sqrt{\frac{a x}{b} + 1}} - \frac{5 b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{64 a^{\frac{7}{2}}}"," ",0,"a*x**(9/2)/(4*sqrt(b)*sqrt(a*x/b + 1)) + 7*sqrt(b)*x**(7/2)/(24*sqrt(a*x/b + 1)) - b**(3/2)*x**(5/2)/(96*a*sqrt(a*x/b + 1)) + 5*b**(5/2)*x**(3/2)/(192*a**2*sqrt(a*x/b + 1)) + 5*b**(7/2)*sqrt(x)/(64*a**3*sqrt(a*x/b + 1)) - 5*b**4*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(64*a**(7/2))","A",0
1692,1,122,0,6.166973," ","integrate(x**2*(a+b/x)**(1/2),x)","\frac{a x^{\frac{7}{2}}}{3 \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{5 \sqrt{b} x^{\frac{5}{2}}}{12 \sqrt{\frac{a x}{b} + 1}} - \frac{b^{\frac{3}{2}} x^{\frac{3}{2}}}{24 a \sqrt{\frac{a x}{b} + 1}} - \frac{b^{\frac{5}{2}} \sqrt{x}}{8 a^{2} \sqrt{\frac{a x}{b} + 1}} + \frac{b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{8 a^{\frac{5}{2}}}"," ",0,"a*x**(7/2)/(3*sqrt(b)*sqrt(a*x/b + 1)) + 5*sqrt(b)*x**(5/2)/(12*sqrt(a*x/b + 1)) - b**(3/2)*x**(3/2)/(24*a*sqrt(a*x/b + 1)) - b**(5/2)*sqrt(x)/(8*a**2*sqrt(a*x/b + 1)) + b**3*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(8*a**(5/2))","A",0
1693,1,97,0,4.179482," ","integrate(x*(a+b/x)**(1/2),x)","\frac{a x^{\frac{5}{2}}}{2 \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{3 \sqrt{b} x^{\frac{3}{2}}}{4 \sqrt{\frac{a x}{b} + 1}} + \frac{b^{\frac{3}{2}} \sqrt{x}}{4 a \sqrt{\frac{a x}{b} + 1}} - \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{4 a^{\frac{3}{2}}}"," ",0,"a*x**(5/2)/(2*sqrt(b)*sqrt(a*x/b + 1)) + 3*sqrt(b)*x**(3/2)/(4*sqrt(a*x/b + 1)) + b**(3/2)*sqrt(x)/(4*a*sqrt(a*x/b + 1)) - b**2*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(4*a**(3/2))","A",0
1694,1,42,0,2.012806," ","integrate((a+b/x)**(1/2),x)","\sqrt{b} \sqrt{x} \sqrt{\frac{a x}{b} + 1} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{\sqrt{a}}"," ",0,"sqrt(b)*sqrt(x)*sqrt(a*x/b + 1) + b*asinh(sqrt(a)*sqrt(x)/sqrt(b))/sqrt(a)","A",0
1695,1,68,0,1.822948," ","integrate((a+b/x)**(1/2)/x,x)","2 \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)} - \frac{2 a \sqrt{x}}{\sqrt{b} \sqrt{\frac{a x}{b} + 1}} - \frac{2 \sqrt{b}}{\sqrt{x} \sqrt{\frac{a x}{b} + 1}}"," ",0,"2*sqrt(a)*asinh(sqrt(a)*sqrt(x)/sqrt(b)) - 2*a*sqrt(x)/(sqrt(b)*sqrt(a*x/b + 1)) - 2*sqrt(b)/(sqrt(x)*sqrt(a*x/b + 1))","B",0
1696,1,41,0,0.938890," ","integrate((a+b/x)**(1/2)/x**2,x)","- \frac{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}}{3 b} - \frac{2 \sqrt{a} \sqrt{1 + \frac{b}{a x}}}{3 x}"," ",0,"-2*a**(3/2)*sqrt(1 + b/(a*x))/(3*b) - 2*sqrt(a)*sqrt(1 + b/(a*x))/(3*x)","B",0
1697,1,304,0,1.427086," ","integrate((a+b/x)**(1/2)/x**3,x)","\frac{4 a^{\frac{11}{2}} b^{\frac{3}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} + \frac{2 a^{\frac{9}{2}} b^{\frac{5}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{8 a^{\frac{7}{2}} b^{\frac{7}{2}} x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{6 a^{\frac{5}{2}} b^{\frac{9}{2}} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{4 a^{6} b x^{\frac{7}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}} - \frac{4 a^{5} b^{2} x^{\frac{5}{2}}}{15 a^{\frac{7}{2}} b^{3} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{4} x^{\frac{5}{2}}}"," ",0,"4*a**(11/2)*b**(3/2)*x**3*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) + 2*a**(9/2)*b**(5/2)*x**2*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 8*a**(7/2)*b**(7/2)*x*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 6*a**(5/2)*b**(9/2)*sqrt(a*x/b + 1)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 4*a**6*b*x**(7/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2)) - 4*a**5*b**2*x**(5/2)/(15*a**(7/2)*b**3*x**(7/2) + 15*a**(5/2)*b**4*x**(5/2))","B",0
1698,1,899,0,2.191463," ","integrate((a+b/x)**(1/2)/x**4,x)","- \frac{16 a^{\frac{19}{2}} b^{\frac{9}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{40 a^{\frac{17}{2}} b^{\frac{11}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{30 a^{\frac{15}{2}} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{40 a^{\frac{13}{2}} b^{\frac{15}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{100 a^{\frac{11}{2}} b^{\frac{17}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{96 a^{\frac{9}{2}} b^{\frac{19}{2}} x \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} - \frac{30 a^{\frac{7}{2}} b^{\frac{21}{2}} \sqrt{\frac{a x}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{16 a^{10} b^{4} x^{\frac{13}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{48 a^{9} b^{5} x^{\frac{11}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{48 a^{8} b^{6} x^{\frac{9}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}} + \frac{16 a^{7} b^{7} x^{\frac{7}{2}}}{105 a^{\frac{13}{2}} b^{7} x^{\frac{13}{2}} + 315 a^{\frac{11}{2}} b^{8} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{9} x^{\frac{9}{2}} + 105 a^{\frac{7}{2}} b^{10} x^{\frac{7}{2}}}"," ",0,"-16*a**(19/2)*b**(9/2)*x**6*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 40*a**(17/2)*b**(11/2)*x**5*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 30*a**(15/2)*b**(13/2)*x**4*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 40*a**(13/2)*b**(15/2)*x**3*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 100*a**(11/2)*b**(17/2)*x**2*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 96*a**(9/2)*b**(19/2)*x*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) - 30*a**(7/2)*b**(21/2)*sqrt(a*x/b + 1)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 16*a**10*b**4*x**(13/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 48*a**9*b**5*x**(11/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 48*a**8*b**6*x**(9/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2)) + 16*a**7*b**7*x**(7/2)/(105*a**(13/2)*b**7*x**(13/2) + 315*a**(11/2)*b**8*x**(11/2) + 315*a**(9/2)*b**9*x**(9/2) + 105*a**(7/2)*b**10*x**(7/2))","B",0
1699,1,2297,0,3.005412," ","integrate((a+b/x)**(1/2)/x**5,x)","\frac{32 a^{\frac{29}{2}} b^{\frac{23}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{176 a^{\frac{27}{2}} b^{\frac{25}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{396 a^{\frac{25}{2}} b^{\frac{27}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{462 a^{\frac{23}{2}} b^{\frac{29}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} + \frac{210 a^{\frac{21}{2}} b^{\frac{31}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{378 a^{\frac{19}{2}} b^{\frac{33}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{1134 a^{\frac{17}{2}} b^{\frac{35}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{1494 a^{\frac{15}{2}} b^{\frac{37}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{1098 a^{\frac{13}{2}} b^{\frac{39}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{430 a^{\frac{11}{2}} b^{\frac{41}{2}} x \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{70 a^{\frac{9}{2}} b^{\frac{43}{2}} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{32 a^{15} b^{11} x^{\frac{21}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{192 a^{14} b^{12} x^{\frac{19}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{480 a^{13} b^{13} x^{\frac{17}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{640 a^{12} b^{14} x^{\frac{15}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{480 a^{11} b^{15} x^{\frac{13}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{192 a^{10} b^{16} x^{\frac{11}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}} - \frac{32 a^{9} b^{17} x^{\frac{9}{2}}}{315 a^{\frac{21}{2}} b^{15} x^{\frac{21}{2}} + 1890 a^{\frac{19}{2}} b^{16} x^{\frac{19}{2}} + 4725 a^{\frac{17}{2}} b^{17} x^{\frac{17}{2}} + 6300 a^{\frac{15}{2}} b^{18} x^{\frac{15}{2}} + 4725 a^{\frac{13}{2}} b^{19} x^{\frac{13}{2}} + 1890 a^{\frac{11}{2}} b^{20} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{21} x^{\frac{9}{2}}}"," ",0,"32*a**(29/2)*b**(23/2)*x**10*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 176*a**(27/2)*b**(25/2)*x**9*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 396*a**(25/2)*b**(27/2)*x**8*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 462*a**(23/2)*b**(29/2)*x**7*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) + 210*a**(21/2)*b**(31/2)*x**6*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 378*a**(19/2)*b**(33/2)*x**5*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 1134*a**(17/2)*b**(35/2)*x**4*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 1494*a**(15/2)*b**(37/2)*x**3*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 1098*a**(13/2)*b**(39/2)*x**2*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 430*a**(11/2)*b**(41/2)*x*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 70*a**(9/2)*b**(43/2)*sqrt(a*x/b + 1)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 32*a**15*b**11*x**(21/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 192*a**14*b**12*x**(19/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 480*a**13*b**13*x**(17/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 640*a**12*b**14*x**(15/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 480*a**11*b**15*x**(13/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 192*a**10*b**16*x**(11/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2)) - 32*a**9*b**17*x**(9/2)/(315*a**(21/2)*b**15*x**(21/2) + 1890*a**(19/2)*b**16*x**(19/2) + 4725*a**(17/2)*b**17*x**(17/2) + 6300*a**(15/2)*b**18*x**(15/2) + 4725*a**(13/2)*b**19*x**(13/2) + 1890*a**(11/2)*b**20*x**(11/2) + 315*a**(9/2)*b**21*x**(9/2))","B",0
1700,1,5095,0,5.619473," ","integrate((a+b/x)**(1/2)/x**6,x)","- \frac{256 a^{\frac{41}{2}} b^{\frac{49}{2}} x^{15} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{2432 a^{\frac{39}{2}} b^{\frac{51}{2}} x^{14} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{10336 a^{\frac{37}{2}} b^{\frac{53}{2}} x^{13} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{25840 a^{\frac{35}{2}} b^{\frac{55}{2}} x^{12} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{41990 a^{\frac{33}{2}} b^{\frac{57}{2}} x^{11} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{46882 a^{\frac{31}{2}} b^{\frac{59}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{41514 a^{\frac{29}{2}} b^{\frac{61}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{47982 a^{\frac{27}{2}} b^{\frac{63}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{86460 a^{\frac{25}{2}} b^{\frac{65}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{141460 a^{\frac{23}{2}} b^{\frac{67}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{167156 a^{\frac{21}{2}} b^{\frac{69}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{137932 a^{\frac{19}{2}} b^{\frac{71}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{78046 a^{\frac{17}{2}} b^{\frac{73}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{28970 a^{\frac{15}{2}} b^{\frac{75}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{6370 a^{\frac{13}{2}} b^{\frac{77}{2}} x \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} - \frac{630 a^{\frac{11}{2}} b^{\frac{79}{2}} \sqrt{\frac{a x}{b} + 1}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{256 a^{21} b^{24} x^{\frac{31}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{2560 a^{20} b^{25} x^{\frac{29}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{11520 a^{19} b^{26} x^{\frac{27}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{30720 a^{18} b^{27} x^{\frac{25}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{53760 a^{17} b^{28} x^{\frac{23}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{64512 a^{16} b^{29} x^{\frac{21}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{53760 a^{15} b^{30} x^{\frac{19}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{30720 a^{14} b^{31} x^{\frac{17}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{11520 a^{13} b^{32} x^{\frac{15}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{2560 a^{12} b^{33} x^{\frac{13}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}} + \frac{256 a^{11} b^{34} x^{\frac{11}{2}}}{3465 a^{\frac{31}{2}} b^{29} x^{\frac{31}{2}} + 34650 a^{\frac{29}{2}} b^{30} x^{\frac{29}{2}} + 155925 a^{\frac{27}{2}} b^{31} x^{\frac{27}{2}} + 415800 a^{\frac{25}{2}} b^{32} x^{\frac{25}{2}} + 727650 a^{\frac{23}{2}} b^{33} x^{\frac{23}{2}} + 873180 a^{\frac{21}{2}} b^{34} x^{\frac{21}{2}} + 727650 a^{\frac{19}{2}} b^{35} x^{\frac{19}{2}} + 415800 a^{\frac{17}{2}} b^{36} x^{\frac{17}{2}} + 155925 a^{\frac{15}{2}} b^{37} x^{\frac{15}{2}} + 34650 a^{\frac{13}{2}} b^{38} x^{\frac{13}{2}} + 3465 a^{\frac{11}{2}} b^{39} x^{\frac{11}{2}}}"," ",0,"-256*a**(41/2)*b**(49/2)*x**15*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 2432*a**(39/2)*b**(51/2)*x**14*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 10336*a**(37/2)*b**(53/2)*x**13*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 25840*a**(35/2)*b**(55/2)*x**12*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 41990*a**(33/2)*b**(57/2)*x**11*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 46882*a**(31/2)*b**(59/2)*x**10*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 41514*a**(29/2)*b**(61/2)*x**9*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 47982*a**(27/2)*b**(63/2)*x**8*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 86460*a**(25/2)*b**(65/2)*x**7*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 141460*a**(23/2)*b**(67/2)*x**6*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 167156*a**(21/2)*b**(69/2)*x**5*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 137932*a**(19/2)*b**(71/2)*x**4*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 78046*a**(17/2)*b**(73/2)*x**3*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 28970*a**(15/2)*b**(75/2)*x**2*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 6370*a**(13/2)*b**(77/2)*x*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) - 630*a**(11/2)*b**(79/2)*sqrt(a*x/b + 1)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 256*a**21*b**24*x**(31/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 2560*a**20*b**25*x**(29/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 11520*a**19*b**26*x**(27/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 30720*a**18*b**27*x**(25/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 53760*a**17*b**28*x**(23/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 64512*a**16*b**29*x**(21/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 53760*a**15*b**30*x**(19/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 30720*a**14*b**31*x**(17/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 11520*a**13*b**32*x**(15/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 2560*a**12*b**33*x**(13/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2)) + 256*a**11*b**34*x**(11/2)/(3465*a**(31/2)*b**29*x**(31/2) + 34650*a**(29/2)*b**30*x**(29/2) + 155925*a**(27/2)*b**31*x**(27/2) + 415800*a**(25/2)*b**32*x**(25/2) + 727650*a**(23/2)*b**33*x**(23/2) + 873180*a**(21/2)*b**34*x**(21/2) + 727650*a**(19/2)*b**35*x**(19/2) + 415800*a**(17/2)*b**36*x**(17/2) + 155925*a**(15/2)*b**37*x**(15/2) + 34650*a**(13/2)*b**38*x**(13/2) + 3465*a**(11/2)*b**39*x**(11/2))","B",0
1701,1,153,0,8.937468," ","integrate((a+b/x)**(3/2)*x**3,x)","\frac{a^{2} x^{\frac{9}{2}}}{4 \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{5 a \sqrt{b} x^{\frac{7}{2}}}{8 \sqrt{\frac{a x}{b} + 1}} + \frac{13 b^{\frac{3}{2}} x^{\frac{5}{2}}}{32 \sqrt{\frac{a x}{b} + 1}} - \frac{b^{\frac{5}{2}} x^{\frac{3}{2}}}{64 a \sqrt{\frac{a x}{b} + 1}} - \frac{3 b^{\frac{7}{2}} \sqrt{x}}{64 a^{2} \sqrt{\frac{a x}{b} + 1}} + \frac{3 b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{64 a^{\frac{5}{2}}}"," ",0,"a**2*x**(9/2)/(4*sqrt(b)*sqrt(a*x/b + 1)) + 5*a*sqrt(b)*x**(7/2)/(8*sqrt(a*x/b + 1)) + 13*b**(3/2)*x**(5/2)/(32*sqrt(a*x/b + 1)) - b**(5/2)*x**(3/2)/(64*a*sqrt(a*x/b + 1)) - 3*b**(7/2)*sqrt(x)/(64*a**2*sqrt(a*x/b + 1)) + 3*b**4*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(64*a**(5/2))","A",0
1702,1,124,0,9.201788," ","integrate((a+b/x)**(3/2)*x**2,x)","\frac{a^{2} x^{\frac{7}{2}}}{3 \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{11 a \sqrt{b} x^{\frac{5}{2}}}{12 \sqrt{\frac{a x}{b} + 1}} + \frac{17 b^{\frac{3}{2}} x^{\frac{3}{2}}}{24 \sqrt{\frac{a x}{b} + 1}} + \frac{b^{\frac{5}{2}} \sqrt{x}}{8 a \sqrt{\frac{a x}{b} + 1}} - \frac{b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{8 a^{\frac{3}{2}}}"," ",0,"a**2*x**(7/2)/(3*sqrt(b)*sqrt(a*x/b + 1)) + 11*a*sqrt(b)*x**(5/2)/(12*sqrt(a*x/b + 1)) + 17*b**(3/2)*x**(3/2)/(24*sqrt(a*x/b + 1)) + b**(5/2)*sqrt(x)/(8*a*sqrt(a*x/b + 1)) - b**3*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(8*a**(3/2))","A",0
1703,1,75,0,4.109315," ","integrate((a+b/x)**(3/2)*x,x)","\frac{a \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a x}{b} + 1}}{2} + \frac{5 b^{\frac{3}{2}} \sqrt{x} \sqrt{\frac{a x}{b} + 1}}{4} + \frac{3 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{4 \sqrt{a}}"," ",0,"a*sqrt(b)*x**(3/2)*sqrt(a*x/b + 1)/2 + 5*b**(3/2)*sqrt(x)*sqrt(a*x/b + 1)/4 + 3*b**2*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(4*sqrt(a))","A",0
1704,1,92,0,3.746992," ","integrate((a+b/x)**(3/2),x)","3 \sqrt{a} b \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)} + \frac{a^{2} x^{\frac{3}{2}}}{\sqrt{b} \sqrt{\frac{a x}{b} + 1}} - \frac{a \sqrt{b} \sqrt{x}}{\sqrt{\frac{a x}{b} + 1}} - \frac{2 b^{\frac{3}{2}}}{\sqrt{x} \sqrt{\frac{a x}{b} + 1}}"," ",0,"3*sqrt(a)*b*asinh(sqrt(a)*sqrt(x)/sqrt(b)) + a**2*x**(3/2)/(sqrt(b)*sqrt(a*x/b + 1)) - a*sqrt(b)*sqrt(x)/sqrt(a*x/b + 1) - 2*b**(3/2)/(sqrt(x)*sqrt(a*x/b + 1))","B",0
1705,1,71,0,2.310107," ","integrate((a+b/x)**(3/2)/x,x)","- \frac{8 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}}{3} - a^{\frac{3}{2}} \log{\left(\frac{b}{a x} \right)} + 2 a^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)} - \frac{2 \sqrt{a} b \sqrt{1 + \frac{b}{a x}}}{3 x}"," ",0,"-8*a**(3/2)*sqrt(1 + b/(a*x))/3 - a**(3/2)*log(b/(a*x)) + 2*a**(3/2)*log(sqrt(1 + b/(a*x)) + 1) - 2*sqrt(a)*b*sqrt(1 + b/(a*x))/(3*x)","A",0
1706,1,65,0,1.361982," ","integrate((a+b/x)**(3/2)/x**2,x)","- \frac{2 a^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}}{5 b} - \frac{4 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}}{5 x} - \frac{2 \sqrt{a} b \sqrt{1 + \frac{b}{a x}}}{5 x^{2}}"," ",0,"-2*a**(5/2)*sqrt(1 + b/(a*x))/(5*b) - 4*a**(3/2)*sqrt(1 + b/(a*x))/(5*x) - 2*sqrt(a)*b*sqrt(1 + b/(a*x))/(5*x**2)","B",0
1707,1,360,0,1.471536," ","integrate((a+b/x)**(3/2)/x**3,x)","\frac{4 a^{\frac{15}{2}} b^{\frac{3}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{9}{2}} b^{3} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{4} x^{\frac{7}{2}}} + \frac{2 a^{\frac{13}{2}} b^{\frac{5}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{9}{2}} b^{3} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{4} x^{\frac{7}{2}}} - \frac{18 a^{\frac{11}{2}} b^{\frac{7}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{9}{2}} b^{3} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{4} x^{\frac{7}{2}}} - \frac{26 a^{\frac{9}{2}} b^{\frac{9}{2}} x \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{9}{2}} b^{3} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{4} x^{\frac{7}{2}}} - \frac{10 a^{\frac{7}{2}} b^{\frac{11}{2}} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{9}{2}} b^{3} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{4} x^{\frac{7}{2}}} - \frac{4 a^{8} b x^{\frac{9}{2}}}{35 a^{\frac{9}{2}} b^{3} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{4} x^{\frac{7}{2}}} - \frac{4 a^{7} b^{2} x^{\frac{7}{2}}}{35 a^{\frac{9}{2}} b^{3} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{4} x^{\frac{7}{2}}}"," ",0,"4*a**(15/2)*b**(3/2)*x**4*sqrt(a*x/b + 1)/(35*a**(9/2)*b**3*x**(9/2) + 35*a**(7/2)*b**4*x**(7/2)) + 2*a**(13/2)*b**(5/2)*x**3*sqrt(a*x/b + 1)/(35*a**(9/2)*b**3*x**(9/2) + 35*a**(7/2)*b**4*x**(7/2)) - 18*a**(11/2)*b**(7/2)*x**2*sqrt(a*x/b + 1)/(35*a**(9/2)*b**3*x**(9/2) + 35*a**(7/2)*b**4*x**(7/2)) - 26*a**(9/2)*b**(9/2)*x*sqrt(a*x/b + 1)/(35*a**(9/2)*b**3*x**(9/2) + 35*a**(7/2)*b**4*x**(7/2)) - 10*a**(7/2)*b**(11/2)*sqrt(a*x/b + 1)/(35*a**(9/2)*b**3*x**(9/2) + 35*a**(7/2)*b**4*x**(7/2)) - 4*a**8*b*x**(9/2)/(35*a**(9/2)*b**3*x**(9/2) + 35*a**(7/2)*b**4*x**(7/2)) - 4*a**7*b**2*x**(7/2)/(35*a**(9/2)*b**3*x**(9/2) + 35*a**(7/2)*b**4*x**(7/2))","B",0
1708,1,986,0,2.400674," ","integrate((a+b/x)**(3/2)/x**4,x)","- \frac{16 a^{\frac{23}{2}} b^{\frac{9}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} - \frac{40 a^{\frac{21}{2}} b^{\frac{11}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} - \frac{30 a^{\frac{19}{2}} b^{\frac{13}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} - \frac{110 a^{\frac{17}{2}} b^{\frac{15}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} - \frac{380 a^{\frac{15}{2}} b^{\frac{17}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} - \frac{516 a^{\frac{13}{2}} b^{\frac{19}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} - \frac{310 a^{\frac{11}{2}} b^{\frac{21}{2}} x \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} - \frac{70 a^{\frac{9}{2}} b^{\frac{23}{2}} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} + \frac{16 a^{12} b^{4} x^{\frac{15}{2}}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} + \frac{48 a^{11} b^{5} x^{\frac{13}{2}}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} + \frac{48 a^{10} b^{6} x^{\frac{11}{2}}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}} + \frac{16 a^{9} b^{7} x^{\frac{9}{2}}}{315 a^{\frac{15}{2}} b^{7} x^{\frac{15}{2}} + 945 a^{\frac{13}{2}} b^{8} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{9} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{10} x^{\frac{9}{2}}}"," ",0,"-16*a**(23/2)*b**(9/2)*x**7*sqrt(a*x/b + 1)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) - 40*a**(21/2)*b**(11/2)*x**6*sqrt(a*x/b + 1)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) - 30*a**(19/2)*b**(13/2)*x**5*sqrt(a*x/b + 1)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) - 110*a**(17/2)*b**(15/2)*x**4*sqrt(a*x/b + 1)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) - 380*a**(15/2)*b**(17/2)*x**3*sqrt(a*x/b + 1)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) - 516*a**(13/2)*b**(19/2)*x**2*sqrt(a*x/b + 1)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) - 310*a**(11/2)*b**(21/2)*x*sqrt(a*x/b + 1)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) - 70*a**(9/2)*b**(23/2)*sqrt(a*x/b + 1)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) + 16*a**12*b**4*x**(15/2)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) + 48*a**11*b**5*x**(13/2)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) + 48*a**10*b**6*x**(11/2)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2)) + 16*a**9*b**7*x**(9/2)/(315*a**(15/2)*b**7*x**(15/2) + 945*a**(13/2)*b**8*x**(13/2) + 945*a**(11/2)*b**9*x**(11/2) + 315*a**(9/2)*b**10*x**(9/2))","B",0
1709,1,2297,0,3.506858," ","integrate((a+b/x)**(3/2)/x**5,x)","\frac{32 a^{\frac{33}{2}} b^{\frac{23}{2}} x^{11} \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} + \frac{176 a^{\frac{31}{2}} b^{\frac{25}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} + \frac{396 a^{\frac{29}{2}} b^{\frac{27}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} + \frac{462 a^{\frac{27}{2}} b^{\frac{29}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{1848 a^{\frac{23}{2}} b^{\frac{33}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{5544 a^{\frac{21}{2}} b^{\frac{35}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{8844 a^{\frac{19}{2}} b^{\frac{37}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{8448 a^{\frac{17}{2}} b^{\frac{39}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{4840 a^{\frac{15}{2}} b^{\frac{41}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{1540 a^{\frac{13}{2}} b^{\frac{43}{2}} x \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{210 a^{\frac{11}{2}} b^{\frac{45}{2}} \sqrt{\frac{a x}{b} + 1}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{32 a^{17} b^{11} x^{\frac{23}{2}}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{192 a^{16} b^{12} x^{\frac{21}{2}}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{480 a^{15} b^{13} x^{\frac{19}{2}}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{640 a^{14} b^{14} x^{\frac{17}{2}}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{480 a^{13} b^{15} x^{\frac{15}{2}}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{192 a^{12} b^{16} x^{\frac{13}{2}}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}} - \frac{32 a^{11} b^{17} x^{\frac{11}{2}}}{1155 a^{\frac{23}{2}} b^{15} x^{\frac{23}{2}} + 6930 a^{\frac{21}{2}} b^{16} x^{\frac{21}{2}} + 17325 a^{\frac{19}{2}} b^{17} x^{\frac{19}{2}} + 23100 a^{\frac{17}{2}} b^{18} x^{\frac{17}{2}} + 17325 a^{\frac{15}{2}} b^{19} x^{\frac{15}{2}} + 6930 a^{\frac{13}{2}} b^{20} x^{\frac{13}{2}} + 1155 a^{\frac{11}{2}} b^{21} x^{\frac{11}{2}}}"," ",0,"32*a**(33/2)*b**(23/2)*x**11*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) + 176*a**(31/2)*b**(25/2)*x**10*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) + 396*a**(29/2)*b**(27/2)*x**9*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) + 462*a**(27/2)*b**(29/2)*x**8*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 1848*a**(23/2)*b**(33/2)*x**6*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 5544*a**(21/2)*b**(35/2)*x**5*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 8844*a**(19/2)*b**(37/2)*x**4*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 8448*a**(17/2)*b**(39/2)*x**3*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 4840*a**(15/2)*b**(41/2)*x**2*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 1540*a**(13/2)*b**(43/2)*x*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 210*a**(11/2)*b**(45/2)*sqrt(a*x/b + 1)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 32*a**17*b**11*x**(23/2)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 192*a**16*b**12*x**(21/2)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 480*a**15*b**13*x**(19/2)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 640*a**14*b**14*x**(17/2)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 480*a**13*b**15*x**(15/2)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 192*a**12*b**16*x**(13/2)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2)) - 32*a**11*b**17*x**(11/2)/(1155*a**(23/2)*b**15*x**(23/2) + 6930*a**(21/2)*b**16*x**(21/2) + 17325*a**(19/2)*b**17*x**(19/2) + 23100*a**(17/2)*b**18*x**(17/2) + 17325*a**(15/2)*b**19*x**(15/2) + 6930*a**(13/2)*b**20*x**(13/2) + 1155*a**(11/2)*b**21*x**(11/2))","B",0
1710,1,5289,0,6.154954," ","integrate((a+b/x)**(3/2)/x**6,x)","- \frac{256 a^{\frac{45}{2}} b^{\frac{49}{2}} x^{16} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{2432 a^{\frac{43}{2}} b^{\frac{51}{2}} x^{15} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{10336 a^{\frac{41}{2}} b^{\frac{53}{2}} x^{14} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{25840 a^{\frac{39}{2}} b^{\frac{55}{2}} x^{13} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{41990 a^{\frac{37}{2}} b^{\frac{57}{2}} x^{12} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{49192 a^{\frac{35}{2}} b^{\frac{59}{2}} x^{11} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{66924 a^{\frac{33}{2}} b^{\frac{61}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{175032 a^{\frac{31}{2}} b^{\frac{63}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{467610 a^{\frac{29}{2}} b^{\frac{65}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{903760 a^{\frac{27}{2}} b^{\frac{67}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{1234376 a^{\frac{25}{2}} b^{\frac{69}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{1205152 a^{\frac{23}{2}} b^{\frac{71}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{840346 a^{\frac{21}{2}} b^{\frac{73}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{410120 a^{\frac{19}{2}} b^{\frac{75}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{133420 a^{\frac{17}{2}} b^{\frac{77}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{26040 a^{\frac{15}{2}} b^{\frac{79}{2}} x \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} - \frac{2310 a^{\frac{13}{2}} b^{\frac{81}{2}} \sqrt{\frac{a x}{b} + 1}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{256 a^{23} b^{24} x^{\frac{33}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{2560 a^{22} b^{25} x^{\frac{31}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{11520 a^{21} b^{26} x^{\frac{29}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{30720 a^{20} b^{27} x^{\frac{27}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{53760 a^{19} b^{28} x^{\frac{25}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{64512 a^{18} b^{29} x^{\frac{23}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{53760 a^{17} b^{30} x^{\frac{21}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{30720 a^{16} b^{31} x^{\frac{19}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{11520 a^{15} b^{32} x^{\frac{17}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{2560 a^{14} b^{33} x^{\frac{15}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}} + \frac{256 a^{13} b^{34} x^{\frac{13}{2}}}{15015 a^{\frac{33}{2}} b^{29} x^{\frac{33}{2}} + 150150 a^{\frac{31}{2}} b^{30} x^{\frac{31}{2}} + 675675 a^{\frac{29}{2}} b^{31} x^{\frac{29}{2}} + 1801800 a^{\frac{27}{2}} b^{32} x^{\frac{27}{2}} + 3153150 a^{\frac{25}{2}} b^{33} x^{\frac{25}{2}} + 3783780 a^{\frac{23}{2}} b^{34} x^{\frac{23}{2}} + 3153150 a^{\frac{21}{2}} b^{35} x^{\frac{21}{2}} + 1801800 a^{\frac{19}{2}} b^{36} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{37} x^{\frac{17}{2}} + 150150 a^{\frac{15}{2}} b^{38} x^{\frac{15}{2}} + 15015 a^{\frac{13}{2}} b^{39} x^{\frac{13}{2}}}"," ",0,"-256*a**(45/2)*b**(49/2)*x**16*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 2432*a**(43/2)*b**(51/2)*x**15*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 10336*a**(41/2)*b**(53/2)*x**14*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 25840*a**(39/2)*b**(55/2)*x**13*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 41990*a**(37/2)*b**(57/2)*x**12*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 49192*a**(35/2)*b**(59/2)*x**11*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 66924*a**(33/2)*b**(61/2)*x**10*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 175032*a**(31/2)*b**(63/2)*x**9*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 467610*a**(29/2)*b**(65/2)*x**8*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 903760*a**(27/2)*b**(67/2)*x**7*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 1234376*a**(25/2)*b**(69/2)*x**6*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 1205152*a**(23/2)*b**(71/2)*x**5*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 840346*a**(21/2)*b**(73/2)*x**4*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 410120*a**(19/2)*b**(75/2)*x**3*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 133420*a**(17/2)*b**(77/2)*x**2*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 26040*a**(15/2)*b**(79/2)*x*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 2310*a**(13/2)*b**(81/2)*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 256*a**23*b**24*x**(33/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 2560*a**22*b**25*x**(31/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 11520*a**21*b**26*x**(29/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 30720*a**20*b**27*x**(27/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 53760*a**19*b**28*x**(25/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 64512*a**18*b**29*x**(23/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 53760*a**17*b**30*x**(21/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 30720*a**16*b**31*x**(19/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 11520*a**15*b**32*x**(17/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 2560*a**14*b**33*x**(15/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 256*a**13*b**34*x**(13/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2))","B",0
1711,1,10344,0,11.853233," ","integrate((a+b/x)**(3/2)/x**7,x)","\frac{512 a^{\frac{59}{2}} b^{\frac{91}{2}} x^{22} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} + \frac{7424 a^{\frac{57}{2}} b^{\frac{93}{2}} x^{21} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} + \frac{50112 a^{\frac{55}{2}} b^{\frac{95}{2}} x^{20} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} + \frac{208800 a^{\frac{53}{2}} b^{\frac{97}{2}} x^{19} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} + \frac{600300 a^{\frac{51}{2}} b^{\frac{99}{2}} x^{18} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} + \frac{1260630 a^{\frac{49}{2}} b^{\frac{101}{2}} x^{17} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} + \frac{1988490 a^{\frac{47}{2}} b^{\frac{103}{2}} x^{16} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} + \frac{2305200 a^{\frac{45}{2}} b^{\frac{105}{2}} x^{15} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} + \frac{1395360 a^{\frac{43}{2}} b^{\frac{107}{2}} x^{14} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{2395640 a^{\frac{41}{2}} b^{\frac{109}{2}} x^{13} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{12038312 a^{\frac{39}{2}} b^{\frac{111}{2}} x^{12} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{30264624 a^{\frac{37}{2}} b^{\frac{113}{2}} x^{11} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{55283592 a^{\frac{35}{2}} b^{\frac{115}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{78018780 a^{\frac{33}{2}} b^{\frac{117}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{86576580 a^{\frac{31}{2}} b^{\frac{119}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{75888816 a^{\frac{29}{2}} b^{\frac{121}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{52380672 a^{\frac{27}{2}} b^{\frac{123}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{28170936 a^{\frac{25}{2}} b^{\frac{125}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{11572840 a^{\frac{23}{2}} b^{\frac{127}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{3510640 a^{\frac{21}{2}} b^{\frac{129}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{741636 a^{\frac{19}{2}} b^{\frac{131}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{97482 a^{\frac{17}{2}} b^{\frac{133}{2}} x \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{6006 a^{\frac{15}{2}} b^{\frac{135}{2}} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{512 a^{30} b^{45} x^{\frac{45}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{7680 a^{29} b^{46} x^{\frac{43}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{53760 a^{28} b^{47} x^{\frac{41}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{232960 a^{27} b^{48} x^{\frac{39}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{698880 a^{26} b^{49} x^{\frac{37}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{1537536 a^{25} b^{50} x^{\frac{35}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{2562560 a^{24} b^{51} x^{\frac{33}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{3294720 a^{23} b^{52} x^{\frac{31}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{3294720 a^{22} b^{53} x^{\frac{29}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{2562560 a^{21} b^{54} x^{\frac{27}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{1537536 a^{20} b^{55} x^{\frac{25}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{698880 a^{19} b^{56} x^{\frac{23}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{232960 a^{18} b^{57} x^{\frac{21}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{53760 a^{17} b^{58} x^{\frac{19}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{7680 a^{16} b^{59} x^{\frac{17}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}} - \frac{512 a^{15} b^{60} x^{\frac{15}{2}}}{45045 a^{\frac{45}{2}} b^{51} x^{\frac{45}{2}} + 675675 a^{\frac{43}{2}} b^{52} x^{\frac{43}{2}} + 4729725 a^{\frac{41}{2}} b^{53} x^{\frac{41}{2}} + 20495475 a^{\frac{39}{2}} b^{54} x^{\frac{39}{2}} + 61486425 a^{\frac{37}{2}} b^{55} x^{\frac{37}{2}} + 135270135 a^{\frac{35}{2}} b^{56} x^{\frac{35}{2}} + 225450225 a^{\frac{33}{2}} b^{57} x^{\frac{33}{2}} + 289864575 a^{\frac{31}{2}} b^{58} x^{\frac{31}{2}} + 289864575 a^{\frac{29}{2}} b^{59} x^{\frac{29}{2}} + 225450225 a^{\frac{27}{2}} b^{60} x^{\frac{27}{2}} + 135270135 a^{\frac{25}{2}} b^{61} x^{\frac{25}{2}} + 61486425 a^{\frac{23}{2}} b^{62} x^{\frac{23}{2}} + 20495475 a^{\frac{21}{2}} b^{63} x^{\frac{21}{2}} + 4729725 a^{\frac{19}{2}} b^{64} x^{\frac{19}{2}} + 675675 a^{\frac{17}{2}} b^{65} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{66} x^{\frac{15}{2}}}"," ",0,"512*a**(59/2)*b**(91/2)*x**22*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 7424*a**(57/2)*b**(93/2)*x**21*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 50112*a**(55/2)*b**(95/2)*x**20*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 208800*a**(53/2)*b**(97/2)*x**19*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 600300*a**(51/2)*b**(99/2)*x**18*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 1260630*a**(49/2)*b**(101/2)*x**17*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 1988490*a**(47/2)*b**(103/2)*x**16*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 2305200*a**(45/2)*b**(105/2)*x**15*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 1395360*a**(43/2)*b**(107/2)*x**14*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 2395640*a**(41/2)*b**(109/2)*x**13*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 12038312*a**(39/2)*b**(111/2)*x**12*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 30264624*a**(37/2)*b**(113/2)*x**11*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 55283592*a**(35/2)*b**(115/2)*x**10*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 78018780*a**(33/2)*b**(117/2)*x**9*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 86576580*a**(31/2)*b**(119/2)*x**8*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 75888816*a**(29/2)*b**(121/2)*x**7*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 52380672*a**(27/2)*b**(123/2)*x**6*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 28170936*a**(25/2)*b**(125/2)*x**5*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 11572840*a**(23/2)*b**(127/2)*x**4*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 3510640*a**(21/2)*b**(129/2)*x**3*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 741636*a**(19/2)*b**(131/2)*x**2*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 97482*a**(17/2)*b**(133/2)*x*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 6006*a**(15/2)*b**(135/2)*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 512*a**30*b**45*x**(45/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 7680*a**29*b**46*x**(43/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 53760*a**28*b**47*x**(41/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 232960*a**27*b**48*x**(39/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 698880*a**26*b**49*x**(37/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 1537536*a**25*b**50*x**(35/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 2562560*a**24*b**51*x**(33/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 3294720*a**23*b**52*x**(31/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 3294720*a**22*b**53*x**(29/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 2562560*a**21*b**54*x**(27/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 1537536*a**20*b**55*x**(25/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 698880*a**19*b**56*x**(23/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 232960*a**18*b**57*x**(21/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 53760*a**17*b**58*x**(19/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 7680*a**16*b**59*x**(17/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 512*a**15*b**60*x**(15/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2))","B",0
1712,1,155,0,8.592749," ","integrate((a+b/x)**(5/2)*x**3,x)","\frac{a^{3} x^{\frac{9}{2}}}{4 \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{23 a^{2} \sqrt{b} x^{\frac{7}{2}}}{24 \sqrt{\frac{a x}{b} + 1}} + \frac{127 a b^{\frac{3}{2}} x^{\frac{5}{2}}}{96 \sqrt{\frac{a x}{b} + 1}} + \frac{133 b^{\frac{5}{2}} x^{\frac{3}{2}}}{192 \sqrt{\frac{a x}{b} + 1}} + \frac{5 b^{\frac{7}{2}} \sqrt{x}}{64 a \sqrt{\frac{a x}{b} + 1}} - \frac{5 b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{64 a^{\frac{3}{2}}}"," ",0,"a**3*x**(9/2)/(4*sqrt(b)*sqrt(a*x/b + 1)) + 23*a**2*sqrt(b)*x**(7/2)/(24*sqrt(a*x/b + 1)) + 127*a*b**(3/2)*x**(5/2)/(96*sqrt(a*x/b + 1)) + 133*b**(5/2)*x**(3/2)/(192*sqrt(a*x/b + 1)) + 5*b**(7/2)*sqrt(x)/(64*a*sqrt(a*x/b + 1)) - 5*b**4*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(64*a**(3/2))","A",0
1713,1,102,0,5.577178," ","integrate((a+b/x)**(5/2)*x**2,x)","\frac{a^{2} \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a x}{b} + 1}}{3} + \frac{13 a b^{\frac{3}{2}} x^{\frac{3}{2}} \sqrt{\frac{a x}{b} + 1}}{12} + \frac{11 b^{\frac{5}{2}} \sqrt{x} \sqrt{\frac{a x}{b} + 1}}{8} + \frac{5 b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{8 \sqrt{a}}"," ",0,"a**2*sqrt(b)*x**(5/2)*sqrt(a*x/b + 1)/3 + 13*a*b**(3/2)*x**(3/2)*sqrt(a*x/b + 1)/12 + 11*b**(5/2)*sqrt(x)*sqrt(a*x/b + 1)/8 + 5*b**3*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(8*sqrt(a))","A",0
1714,1,126,0,4.200773," ","integrate((a+b/x)**(5/2)*x,x)","\frac{15 \sqrt{a} b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{4} + \frac{a^{3} x^{\frac{5}{2}}}{2 \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{11 a^{2} \sqrt{b} x^{\frac{3}{2}}}{4 \sqrt{\frac{a x}{b} + 1}} + \frac{a b^{\frac{3}{2}} \sqrt{x}}{4 \sqrt{\frac{a x}{b} + 1}} - \frac{2 b^{\frac{5}{2}}}{\sqrt{x} \sqrt{\frac{a x}{b} + 1}}"," ",0,"15*sqrt(a)*b**2*asinh(sqrt(a)*sqrt(x)/sqrt(b))/4 + a**3*x**(5/2)/(2*sqrt(b)*sqrt(a*x/b + 1)) + 11*a**2*sqrt(b)*x**(3/2)/(4*sqrt(a*x/b + 1)) + a*b**(3/2)*sqrt(x)/(4*sqrt(a*x/b + 1)) - 2*b**(5/2)/(sqrt(x)*sqrt(a*x/b + 1))","A",0
1715,1,99,0,3.902337," ","integrate((a+b/x)**(5/2),x)","a^{\frac{5}{2}} x \sqrt{1 + \frac{b}{a x}} - \frac{14 a^{\frac{3}{2}} b \sqrt{1 + \frac{b}{a x}}}{3} - \frac{5 a^{\frac{3}{2}} b \log{\left(\frac{b}{a x} \right)}}{2} + 5 a^{\frac{3}{2}} b \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)} - \frac{2 \sqrt{a} b^{2} \sqrt{1 + \frac{b}{a x}}}{3 x}"," ",0,"a**(5/2)*x*sqrt(1 + b/(a*x)) - 14*a**(3/2)*b*sqrt(1 + b/(a*x))/3 - 5*a**(3/2)*b*log(b/(a*x))/2 + 5*a**(3/2)*b*log(sqrt(1 + b/(a*x)) + 1) - 2*sqrt(a)*b**2*sqrt(1 + b/(a*x))/(3*x)","A",0
1716,1,97,0,4.423574," ","integrate((a+b/x)**(5/2)/x,x)","- \frac{46 a^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}}{15} - a^{\frac{5}{2}} \log{\left(\frac{b}{a x} \right)} + 2 a^{\frac{5}{2}} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)} - \frac{22 a^{\frac{3}{2}} b \sqrt{1 + \frac{b}{a x}}}{15 x} - \frac{2 \sqrt{a} b^{2} \sqrt{1 + \frac{b}{a x}}}{5 x^{2}}"," ",0,"-46*a**(5/2)*sqrt(1 + b/(a*x))/15 - a**(5/2)*log(b/(a*x)) + 2*a**(5/2)*log(sqrt(1 + b/(a*x)) + 1) - 22*a**(3/2)*b*sqrt(1 + b/(a*x))/(15*x) - 2*sqrt(a)*b**2*sqrt(1 + b/(a*x))/(5*x**2)","A",0
1717,1,80,0,3.526966," ","integrate((a+b/x)**(5/2)/x**2,x)","\begin{cases} - \frac{2 a^{3} \sqrt{a + \frac{b}{x}}}{7 b} - \frac{6 a^{2} \sqrt{a + \frac{b}{x}}}{7 x} - \frac{6 a b \sqrt{a + \frac{b}{x}}}{7 x^{2}} - \frac{2 b^{2} \sqrt{a + \frac{b}{x}}}{7 x^{3}} & \text{for}\: b \neq 0 \\- \frac{a^{\frac{5}{2}}}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*sqrt(a + b/x)/(7*b) - 6*a**2*sqrt(a + b/x)/(7*x) - 6*a*b*sqrt(a + b/x)/(7*x**2) - 2*b**2*sqrt(a + b/x)/(7*x**3), Ne(b, 0)), (-a**(5/2)/x, True))","A",0
1718,1,416,0,1.762309," ","integrate((a+b/x)**(5/2)/x**3,x)","\frac{4 a^{\frac{19}{2}} b^{\frac{3}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{11}{2}} b^{3} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{4} x^{\frac{9}{2}}} + \frac{2 a^{\frac{17}{2}} b^{\frac{5}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{11}{2}} b^{3} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{4} x^{\frac{9}{2}}} - \frac{32 a^{\frac{15}{2}} b^{\frac{7}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{11}{2}} b^{3} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{4} x^{\frac{9}{2}}} - \frac{68 a^{\frac{13}{2}} b^{\frac{9}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{11}{2}} b^{3} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{4} x^{\frac{9}{2}}} - \frac{52 a^{\frac{11}{2}} b^{\frac{11}{2}} x \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{11}{2}} b^{3} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{4} x^{\frac{9}{2}}} - \frac{14 a^{\frac{9}{2}} b^{\frac{13}{2}} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{11}{2}} b^{3} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{4} x^{\frac{9}{2}}} - \frac{4 a^{10} b x^{\frac{11}{2}}}{63 a^{\frac{11}{2}} b^{3} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{4} x^{\frac{9}{2}}} - \frac{4 a^{9} b^{2} x^{\frac{9}{2}}}{63 a^{\frac{11}{2}} b^{3} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{4} x^{\frac{9}{2}}}"," ",0,"4*a**(19/2)*b**(3/2)*x**5*sqrt(a*x/b + 1)/(63*a**(11/2)*b**3*x**(11/2) + 63*a**(9/2)*b**4*x**(9/2)) + 2*a**(17/2)*b**(5/2)*x**4*sqrt(a*x/b + 1)/(63*a**(11/2)*b**3*x**(11/2) + 63*a**(9/2)*b**4*x**(9/2)) - 32*a**(15/2)*b**(7/2)*x**3*sqrt(a*x/b + 1)/(63*a**(11/2)*b**3*x**(11/2) + 63*a**(9/2)*b**4*x**(9/2)) - 68*a**(13/2)*b**(9/2)*x**2*sqrt(a*x/b + 1)/(63*a**(11/2)*b**3*x**(11/2) + 63*a**(9/2)*b**4*x**(9/2)) - 52*a**(11/2)*b**(11/2)*x*sqrt(a*x/b + 1)/(63*a**(11/2)*b**3*x**(11/2) + 63*a**(9/2)*b**4*x**(9/2)) - 14*a**(9/2)*b**(13/2)*sqrt(a*x/b + 1)/(63*a**(11/2)*b**3*x**(11/2) + 63*a**(9/2)*b**4*x**(9/2)) - 4*a**10*b*x**(11/2)/(63*a**(11/2)*b**3*x**(11/2) + 63*a**(9/2)*b**4*x**(9/2)) - 4*a**9*b**2*x**(9/2)/(63*a**(11/2)*b**3*x**(11/2) + 63*a**(9/2)*b**4*x**(9/2))","B",0
1719,1,1073,0,2.763118," ","integrate((a+b/x)**(5/2)/x**4,x)","- \frac{16 a^{\frac{27}{2}} b^{\frac{9}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} - \frac{40 a^{\frac{25}{2}} b^{\frac{11}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} - \frac{30 a^{\frac{23}{2}} b^{\frac{13}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} - \frac{236 a^{\frac{21}{2}} b^{\frac{15}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} - \frac{1010 a^{\frac{19}{2}} b^{\frac{17}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} - \frac{1776 a^{\frac{17}{2}} b^{\frac{19}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} - \frac{1570 a^{\frac{15}{2}} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} - \frac{700 a^{\frac{13}{2}} b^{\frac{23}{2}} x \sqrt{\frac{a x}{b} + 1}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} - \frac{126 a^{\frac{11}{2}} b^{\frac{25}{2}} \sqrt{\frac{a x}{b} + 1}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} + \frac{16 a^{14} b^{4} x^{\frac{17}{2}}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} + \frac{48 a^{13} b^{5} x^{\frac{15}{2}}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} + \frac{48 a^{12} b^{6} x^{\frac{13}{2}}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}} + \frac{16 a^{11} b^{7} x^{\frac{11}{2}}}{693 a^{\frac{17}{2}} b^{7} x^{\frac{17}{2}} + 2079 a^{\frac{15}{2}} b^{8} x^{\frac{15}{2}} + 2079 a^{\frac{13}{2}} b^{9} x^{\frac{13}{2}} + 693 a^{\frac{11}{2}} b^{10} x^{\frac{11}{2}}}"," ",0,"-16*a**(27/2)*b**(9/2)*x**8*sqrt(a*x/b + 1)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) - 40*a**(25/2)*b**(11/2)*x**7*sqrt(a*x/b + 1)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) - 30*a**(23/2)*b**(13/2)*x**6*sqrt(a*x/b + 1)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) - 236*a**(21/2)*b**(15/2)*x**5*sqrt(a*x/b + 1)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) - 1010*a**(19/2)*b**(17/2)*x**4*sqrt(a*x/b + 1)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) - 1776*a**(17/2)*b**(19/2)*x**3*sqrt(a*x/b + 1)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) - 1570*a**(15/2)*b**(21/2)*x**2*sqrt(a*x/b + 1)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) - 700*a**(13/2)*b**(23/2)*x*sqrt(a*x/b + 1)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) - 126*a**(11/2)*b**(25/2)*sqrt(a*x/b + 1)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) + 16*a**14*b**4*x**(17/2)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) + 48*a**13*b**5*x**(15/2)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) + 48*a**12*b**6*x**(13/2)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2)) + 16*a**11*b**7*x**(11/2)/(693*a**(17/2)*b**7*x**(17/2) + 2079*a**(15/2)*b**8*x**(15/2) + 2079*a**(13/2)*b**9*x**(13/2) + 693*a**(11/2)*b**10*x**(11/2))","B",0
1720,1,2562,0,3.355577," ","integrate((a+b/x)**(5/2)/x**5,x)","\frac{32 a^{\frac{37}{2}} b^{\frac{23}{2}} x^{12} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} + \frac{176 a^{\frac{35}{2}} b^{\frac{25}{2}} x^{11} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} + \frac{396 a^{\frac{33}{2}} b^{\frac{27}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} + \frac{462 a^{\frac{31}{2}} b^{\frac{29}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{462 a^{\frac{29}{2}} b^{\frac{31}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{5544 a^{\frac{27}{2}} b^{\frac{33}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{18480 a^{\frac{25}{2}} b^{\frac{35}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{34716 a^{\frac{23}{2}} b^{\frac{37}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{40788 a^{\frac{21}{2}} b^{\frac{39}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{30712 a^{\frac{19}{2}} b^{\frac{41}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{14476 a^{\frac{17}{2}} b^{\frac{43}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{3906 a^{\frac{15}{2}} b^{\frac{45}{2}} x \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{462 a^{\frac{13}{2}} b^{\frac{47}{2}} \sqrt{\frac{a x}{b} + 1}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{32 a^{19} b^{11} x^{\frac{25}{2}}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{192 a^{18} b^{12} x^{\frac{23}{2}}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{480 a^{17} b^{13} x^{\frac{21}{2}}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{640 a^{16} b^{14} x^{\frac{19}{2}}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{480 a^{15} b^{15} x^{\frac{17}{2}}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{192 a^{14} b^{16} x^{\frac{15}{2}}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}} - \frac{32 a^{13} b^{17} x^{\frac{13}{2}}}{3003 a^{\frac{25}{2}} b^{15} x^{\frac{25}{2}} + 18018 a^{\frac{23}{2}} b^{16} x^{\frac{23}{2}} + 45045 a^{\frac{21}{2}} b^{17} x^{\frac{21}{2}} + 60060 a^{\frac{19}{2}} b^{18} x^{\frac{19}{2}} + 45045 a^{\frac{17}{2}} b^{19} x^{\frac{17}{2}} + 18018 a^{\frac{15}{2}} b^{20} x^{\frac{15}{2}} + 3003 a^{\frac{13}{2}} b^{21} x^{\frac{13}{2}}}"," ",0,"32*a**(37/2)*b**(23/2)*x**12*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) + 176*a**(35/2)*b**(25/2)*x**11*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) + 396*a**(33/2)*b**(27/2)*x**10*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) + 462*a**(31/2)*b**(29/2)*x**9*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 462*a**(29/2)*b**(31/2)*x**8*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 5544*a**(27/2)*b**(33/2)*x**7*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 18480*a**(25/2)*b**(35/2)*x**6*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 34716*a**(23/2)*b**(37/2)*x**5*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 40788*a**(21/2)*b**(39/2)*x**4*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 30712*a**(19/2)*b**(41/2)*x**3*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 14476*a**(17/2)*b**(43/2)*x**2*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 3906*a**(15/2)*b**(45/2)*x*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 462*a**(13/2)*b**(47/2)*sqrt(a*x/b + 1)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 32*a**19*b**11*x**(25/2)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 192*a**18*b**12*x**(23/2)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 480*a**17*b**13*x**(21/2)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 640*a**16*b**14*x**(19/2)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 480*a**15*b**15*x**(17/2)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 192*a**14*b**16*x**(15/2)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2)) - 32*a**13*b**17*x**(13/2)/(3003*a**(25/2)*b**15*x**(25/2) + 18018*a**(23/2)*b**16*x**(23/2) + 45045*a**(21/2)*b**17*x**(21/2) + 60060*a**(19/2)*b**18*x**(19/2) + 45045*a**(17/2)*b**19*x**(17/2) + 18018*a**(15/2)*b**20*x**(15/2) + 3003*a**(13/2)*b**21*x**(13/2))","B",0
1721,1,5482,0,5.708886," ","integrate((a+b/x)**(5/2)/x**6,x)","- \frac{256 a^{\frac{49}{2}} b^{\frac{49}{2}} x^{17} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{2432 a^{\frac{47}{2}} b^{\frac{51}{2}} x^{16} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{10336 a^{\frac{45}{2}} b^{\frac{53}{2}} x^{15} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{25840 a^{\frac{43}{2}} b^{\frac{55}{2}} x^{14} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{41990 a^{\frac{41}{2}} b^{\frac{57}{2}} x^{13} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{55198 a^{\frac{39}{2}} b^{\frac{59}{2}} x^{12} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{138996 a^{\frac{37}{2}} b^{\frac{61}{2}} x^{11} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{571428 a^{\frac{35}{2}} b^{\frac{63}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{1788930 a^{\frac{33}{2}} b^{\frac{65}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{3876730 a^{\frac{31}{2}} b^{\frac{67}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{5991128 a^{\frac{29}{2}} b^{\frac{69}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{6754696 a^{\frac{27}{2}} b^{\frac{71}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{5597098 a^{\frac{25}{2}} b^{\frac{73}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{3383090 a^{\frac{23}{2}} b^{\frac{75}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{1454740 a^{\frac{21}{2}} b^{\frac{77}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{422436 a^{\frac{19}{2}} b^{\frac{79}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{74382 a^{\frac{17}{2}} b^{\frac{81}{2}} x \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} - \frac{6006 a^{\frac{15}{2}} b^{\frac{83}{2}} \sqrt{\frac{a x}{b} + 1}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{256 a^{25} b^{24} x^{\frac{35}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{2560 a^{24} b^{25} x^{\frac{33}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{11520 a^{23} b^{26} x^{\frac{31}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{30720 a^{22} b^{27} x^{\frac{29}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{53760 a^{21} b^{28} x^{\frac{27}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{64512 a^{20} b^{29} x^{\frac{25}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{53760 a^{19} b^{30} x^{\frac{23}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{30720 a^{18} b^{31} x^{\frac{21}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{11520 a^{17} b^{32} x^{\frac{19}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{2560 a^{16} b^{33} x^{\frac{17}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}} + \frac{256 a^{15} b^{34} x^{\frac{15}{2}}}{45045 a^{\frac{35}{2}} b^{29} x^{\frac{35}{2}} + 450450 a^{\frac{33}{2}} b^{30} x^{\frac{33}{2}} + 2027025 a^{\frac{31}{2}} b^{31} x^{\frac{31}{2}} + 5405400 a^{\frac{29}{2}} b^{32} x^{\frac{29}{2}} + 9459450 a^{\frac{27}{2}} b^{33} x^{\frac{27}{2}} + 11351340 a^{\frac{25}{2}} b^{34} x^{\frac{25}{2}} + 9459450 a^{\frac{23}{2}} b^{35} x^{\frac{23}{2}} + 5405400 a^{\frac{21}{2}} b^{36} x^{\frac{21}{2}} + 2027025 a^{\frac{19}{2}} b^{37} x^{\frac{19}{2}} + 450450 a^{\frac{17}{2}} b^{38} x^{\frac{17}{2}} + 45045 a^{\frac{15}{2}} b^{39} x^{\frac{15}{2}}}"," ",0,"-256*a**(49/2)*b**(49/2)*x**17*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 2432*a**(47/2)*b**(51/2)*x**16*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 10336*a**(45/2)*b**(53/2)*x**15*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 25840*a**(43/2)*b**(55/2)*x**14*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 41990*a**(41/2)*b**(57/2)*x**13*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 55198*a**(39/2)*b**(59/2)*x**12*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 138996*a**(37/2)*b**(61/2)*x**11*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 571428*a**(35/2)*b**(63/2)*x**10*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 1788930*a**(33/2)*b**(65/2)*x**9*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 3876730*a**(31/2)*b**(67/2)*x**8*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 5991128*a**(29/2)*b**(69/2)*x**7*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 6754696*a**(27/2)*b**(71/2)*x**6*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 5597098*a**(25/2)*b**(73/2)*x**5*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 3383090*a**(23/2)*b**(75/2)*x**4*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 1454740*a**(21/2)*b**(77/2)*x**3*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 422436*a**(19/2)*b**(79/2)*x**2*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 74382*a**(17/2)*b**(81/2)*x*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) - 6006*a**(15/2)*b**(83/2)*sqrt(a*x/b + 1)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 256*a**25*b**24*x**(35/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 2560*a**24*b**25*x**(33/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 11520*a**23*b**26*x**(31/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 30720*a**22*b**27*x**(29/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 53760*a**21*b**28*x**(27/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 64512*a**20*b**29*x**(25/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 53760*a**19*b**30*x**(23/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 30720*a**18*b**31*x**(21/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 11520*a**17*b**32*x**(19/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 2560*a**16*b**33*x**(17/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2)) + 256*a**15*b**34*x**(15/2)/(45045*a**(35/2)*b**29*x**(35/2) + 450450*a**(33/2)*b**30*x**(33/2) + 2027025*a**(31/2)*b**31*x**(31/2) + 5405400*a**(29/2)*b**32*x**(29/2) + 9459450*a**(27/2)*b**33*x**(27/2) + 11351340*a**(25/2)*b**34*x**(25/2) + 9459450*a**(23/2)*b**35*x**(23/2) + 5405400*a**(21/2)*b**36*x**(21/2) + 2027025*a**(19/2)*b**37*x**(19/2) + 450450*a**(17/2)*b**38*x**(17/2) + 45045*a**(15/2)*b**39*x**(15/2))","B",0
1722,1,155,0,11.844270," ","integrate(x**3/(a+b/x)**(1/2),x)","\frac{x^{\frac{9}{2}}}{4 \sqrt{b} \sqrt{\frac{a x}{b} + 1}} - \frac{\sqrt{b} x^{\frac{7}{2}}}{24 a \sqrt{\frac{a x}{b} + 1}} + \frac{7 b^{\frac{3}{2}} x^{\frac{5}{2}}}{96 a^{2} \sqrt{\frac{a x}{b} + 1}} - \frac{35 b^{\frac{5}{2}} x^{\frac{3}{2}}}{192 a^{3} \sqrt{\frac{a x}{b} + 1}} - \frac{35 b^{\frac{7}{2}} \sqrt{x}}{64 a^{4} \sqrt{\frac{a x}{b} + 1}} + \frac{35 b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{64 a^{\frac{9}{2}}}"," ",0,"x**(9/2)/(4*sqrt(b)*sqrt(a*x/b + 1)) - sqrt(b)*x**(7/2)/(24*a*sqrt(a*x/b + 1)) + 7*b**(3/2)*x**(5/2)/(96*a**2*sqrt(a*x/b + 1)) - 35*b**(5/2)*x**(3/2)/(192*a**3*sqrt(a*x/b + 1)) - 35*b**(7/2)*sqrt(x)/(64*a**4*sqrt(a*x/b + 1)) + 35*b**4*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(64*a**(9/2))","A",0
1723,1,128,0,7.921021," ","integrate(x**2/(a+b/x)**(1/2),x)","\frac{x^{\frac{7}{2}}}{3 \sqrt{b} \sqrt{\frac{a x}{b} + 1}} - \frac{\sqrt{b} x^{\frac{5}{2}}}{12 a \sqrt{\frac{a x}{b} + 1}} + \frac{5 b^{\frac{3}{2}} x^{\frac{3}{2}}}{24 a^{2} \sqrt{\frac{a x}{b} + 1}} + \frac{5 b^{\frac{5}{2}} \sqrt{x}}{8 a^{3} \sqrt{\frac{a x}{b} + 1}} - \frac{5 b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{8 a^{\frac{7}{2}}}"," ",0,"x**(7/2)/(3*sqrt(b)*sqrt(a*x/b + 1)) - sqrt(b)*x**(5/2)/(12*a*sqrt(a*x/b + 1)) + 5*b**(3/2)*x**(3/2)/(24*a**2*sqrt(a*x/b + 1)) + 5*b**(5/2)*sqrt(x)/(8*a**3*sqrt(a*x/b + 1)) - 5*b**3*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(8*a**(7/2))","A",0
1724,1,100,0,4.482411," ","integrate(x/(a+b/x)**(1/2),x)","\frac{x^{\frac{5}{2}}}{2 \sqrt{b} \sqrt{\frac{a x}{b} + 1}} - \frac{\sqrt{b} x^{\frac{3}{2}}}{4 a \sqrt{\frac{a x}{b} + 1}} - \frac{3 b^{\frac{3}{2}} \sqrt{x}}{4 a^{2} \sqrt{\frac{a x}{b} + 1}} + \frac{3 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{4 a^{\frac{5}{2}}}"," ",0,"x**(5/2)/(2*sqrt(b)*sqrt(a*x/b + 1)) - sqrt(b)*x**(3/2)/(4*a*sqrt(a*x/b + 1)) - 3*b**(3/2)*sqrt(x)/(4*a**2*sqrt(a*x/b + 1)) + 3*b**2*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(4*a**(5/2))","A",0
1725,1,44,0,2.629970," ","integrate(1/(a+b/x)**(1/2),x)","\frac{\sqrt{b} \sqrt{x} \sqrt{\frac{a x}{b} + 1}}{a} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{a^{\frac{3}{2}}}"," ",0,"sqrt(b)*sqrt(x)*sqrt(a*x/b + 1)/a - b*asinh(sqrt(a)*sqrt(x)/sqrt(b))/a**(3/2)","A",0
1726,1,22,0,1.200335," ","integrate(1/x/(a+b/x)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{\sqrt{a}}"," ",0,"2*asinh(sqrt(a)*sqrt(x)/sqrt(b))/sqrt(a)","A",0
1727,1,22,0,0.958579," ","integrate(1/x**2/(a+b/x)**(1/2),x)","\begin{cases} - \frac{2 \sqrt{a + \frac{b}{x}}}{b} & \text{for}\: b \neq 0 \\- \frac{1}{\sqrt{a} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(a + b/x)/b, Ne(b, 0)), (-1/(sqrt(a)*x), True))","A",0
1728,1,248,0,1.451477," ","integrate(1/x**3/(a+b/x)**(1/2),x)","\frac{4 a^{\frac{7}{2}} b^{\frac{3}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}} + \frac{2 a^{\frac{5}{2}} b^{\frac{5}{2}} x \sqrt{\frac{a x}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}} - \frac{2 a^{\frac{3}{2}} b^{\frac{7}{2}} \sqrt{\frac{a x}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}} - \frac{4 a^{4} b x^{\frac{5}{2}}}{3 a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}} - \frac{4 a^{3} b^{2} x^{\frac{3}{2}}}{3 a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}}"," ",0,"4*a**(7/2)*b**(3/2)*x**2*sqrt(a*x/b + 1)/(3*a**(5/2)*b**3*x**(5/2) + 3*a**(3/2)*b**4*x**(3/2)) + 2*a**(5/2)*b**(5/2)*x*sqrt(a*x/b + 1)/(3*a**(5/2)*b**3*x**(5/2) + 3*a**(3/2)*b**4*x**(3/2)) - 2*a**(3/2)*b**(7/2)*sqrt(a*x/b + 1)/(3*a**(5/2)*b**3*x**(5/2) + 3*a**(3/2)*b**4*x**(3/2)) - 4*a**4*b*x**(5/2)/(3*a**(5/2)*b**3*x**(5/2) + 3*a**(3/2)*b**4*x**(3/2)) - 4*a**3*b**2*x**(3/2)/(3*a**(5/2)*b**3*x**(5/2) + 3*a**(3/2)*b**4*x**(3/2))","B",0
1729,1,813,0,2.252586," ","integrate(1/x**4/(a+b/x)**(1/2),x)","- \frac{16 a^{\frac{15}{2}} b^{\frac{9}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{\frac{11}{2}} + 45 a^{\frac{9}{2}} b^{8} x^{\frac{9}{2}} + 45 a^{\frac{7}{2}} b^{9} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{10} x^{\frac{5}{2}}} - \frac{40 a^{\frac{13}{2}} b^{\frac{11}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{\frac{11}{2}} + 45 a^{\frac{9}{2}} b^{8} x^{\frac{9}{2}} + 45 a^{\frac{7}{2}} b^{9} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{10} x^{\frac{5}{2}}} - \frac{30 a^{\frac{11}{2}} b^{\frac{13}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{\frac{11}{2}} + 45 a^{\frac{9}{2}} b^{8} x^{\frac{9}{2}} + 45 a^{\frac{7}{2}} b^{9} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{10} x^{\frac{5}{2}}} - \frac{10 a^{\frac{9}{2}} b^{\frac{15}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{\frac{11}{2}} + 45 a^{\frac{9}{2}} b^{8} x^{\frac{9}{2}} + 45 a^{\frac{7}{2}} b^{9} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{10} x^{\frac{5}{2}}} - \frac{10 a^{\frac{7}{2}} b^{\frac{17}{2}} x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{\frac{11}{2}} + 45 a^{\frac{9}{2}} b^{8} x^{\frac{9}{2}} + 45 a^{\frac{7}{2}} b^{9} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{10} x^{\frac{5}{2}}} - \frac{6 a^{\frac{5}{2}} b^{\frac{19}{2}} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{\frac{11}{2}} + 45 a^{\frac{9}{2}} b^{8} x^{\frac{9}{2}} + 45 a^{\frac{7}{2}} b^{9} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{10} x^{\frac{5}{2}}} + \frac{16 a^{8} b^{4} x^{\frac{11}{2}}}{15 a^{\frac{11}{2}} b^{7} x^{\frac{11}{2}} + 45 a^{\frac{9}{2}} b^{8} x^{\frac{9}{2}} + 45 a^{\frac{7}{2}} b^{9} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{10} x^{\frac{5}{2}}} + \frac{48 a^{7} b^{5} x^{\frac{9}{2}}}{15 a^{\frac{11}{2}} b^{7} x^{\frac{11}{2}} + 45 a^{\frac{9}{2}} b^{8} x^{\frac{9}{2}} + 45 a^{\frac{7}{2}} b^{9} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{10} x^{\frac{5}{2}}} + \frac{48 a^{6} b^{6} x^{\frac{7}{2}}}{15 a^{\frac{11}{2}} b^{7} x^{\frac{11}{2}} + 45 a^{\frac{9}{2}} b^{8} x^{\frac{9}{2}} + 45 a^{\frac{7}{2}} b^{9} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{10} x^{\frac{5}{2}}} + \frac{16 a^{5} b^{7} x^{\frac{5}{2}}}{15 a^{\frac{11}{2}} b^{7} x^{\frac{11}{2}} + 45 a^{\frac{9}{2}} b^{8} x^{\frac{9}{2}} + 45 a^{\frac{7}{2}} b^{9} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{10} x^{\frac{5}{2}}}"," ",0,"-16*a**(15/2)*b**(9/2)*x**5*sqrt(a*x/b + 1)/(15*a**(11/2)*b**7*x**(11/2) + 45*a**(9/2)*b**8*x**(9/2) + 45*a**(7/2)*b**9*x**(7/2) + 15*a**(5/2)*b**10*x**(5/2)) - 40*a**(13/2)*b**(11/2)*x**4*sqrt(a*x/b + 1)/(15*a**(11/2)*b**7*x**(11/2) + 45*a**(9/2)*b**8*x**(9/2) + 45*a**(7/2)*b**9*x**(7/2) + 15*a**(5/2)*b**10*x**(5/2)) - 30*a**(11/2)*b**(13/2)*x**3*sqrt(a*x/b + 1)/(15*a**(11/2)*b**7*x**(11/2) + 45*a**(9/2)*b**8*x**(9/2) + 45*a**(7/2)*b**9*x**(7/2) + 15*a**(5/2)*b**10*x**(5/2)) - 10*a**(9/2)*b**(15/2)*x**2*sqrt(a*x/b + 1)/(15*a**(11/2)*b**7*x**(11/2) + 45*a**(9/2)*b**8*x**(9/2) + 45*a**(7/2)*b**9*x**(7/2) + 15*a**(5/2)*b**10*x**(5/2)) - 10*a**(7/2)*b**(17/2)*x*sqrt(a*x/b + 1)/(15*a**(11/2)*b**7*x**(11/2) + 45*a**(9/2)*b**8*x**(9/2) + 45*a**(7/2)*b**9*x**(7/2) + 15*a**(5/2)*b**10*x**(5/2)) - 6*a**(5/2)*b**(19/2)*sqrt(a*x/b + 1)/(15*a**(11/2)*b**7*x**(11/2) + 45*a**(9/2)*b**8*x**(9/2) + 45*a**(7/2)*b**9*x**(7/2) + 15*a**(5/2)*b**10*x**(5/2)) + 16*a**8*b**4*x**(11/2)/(15*a**(11/2)*b**7*x**(11/2) + 45*a**(9/2)*b**8*x**(9/2) + 45*a**(7/2)*b**9*x**(7/2) + 15*a**(5/2)*b**10*x**(5/2)) + 48*a**7*b**5*x**(9/2)/(15*a**(11/2)*b**7*x**(11/2) + 45*a**(9/2)*b**8*x**(9/2) + 45*a**(7/2)*b**9*x**(7/2) + 15*a**(5/2)*b**10*x**(5/2)) + 48*a**6*b**6*x**(7/2)/(15*a**(11/2)*b**7*x**(11/2) + 45*a**(9/2)*b**8*x**(9/2) + 45*a**(7/2)*b**9*x**(7/2) + 15*a**(5/2)*b**10*x**(5/2)) + 16*a**5*b**7*x**(5/2)/(15*a**(11/2)*b**7*x**(11/2) + 45*a**(9/2)*b**8*x**(9/2) + 45*a**(7/2)*b**9*x**(7/2) + 15*a**(5/2)*b**10*x**(5/2))","B",0
1730,1,2164,0,3.947957," ","integrate(1/x**5/(a+b/x)**(1/2),x)","\frac{32 a^{\frac{25}{2}} b^{\frac{23}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} + \frac{176 a^{\frac{23}{2}} b^{\frac{25}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} + \frac{396 a^{\frac{21}{2}} b^{\frac{27}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} + \frac{462 a^{\frac{19}{2}} b^{\frac{29}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} + \frac{280 a^{\frac{17}{2}} b^{\frac{31}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} + \frac{42 a^{\frac{15}{2}} b^{\frac{33}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{84 a^{\frac{13}{2}} b^{\frac{35}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{94 a^{\frac{11}{2}} b^{\frac{37}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{48 a^{\frac{9}{2}} b^{\frac{39}{2}} x \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{10 a^{\frac{7}{2}} b^{\frac{41}{2}} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{32 a^{13} b^{11} x^{\frac{19}{2}}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{192 a^{12} b^{12} x^{\frac{17}{2}}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{480 a^{11} b^{13} x^{\frac{15}{2}}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{640 a^{10} b^{14} x^{\frac{13}{2}}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{480 a^{9} b^{15} x^{\frac{11}{2}}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{192 a^{8} b^{16} x^{\frac{9}{2}}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}} - \frac{32 a^{7} b^{17} x^{\frac{7}{2}}}{35 a^{\frac{19}{2}} b^{15} x^{\frac{19}{2}} + 210 a^{\frac{17}{2}} b^{16} x^{\frac{17}{2}} + 525 a^{\frac{15}{2}} b^{17} x^{\frac{15}{2}} + 700 a^{\frac{13}{2}} b^{18} x^{\frac{13}{2}} + 525 a^{\frac{11}{2}} b^{19} x^{\frac{11}{2}} + 210 a^{\frac{9}{2}} b^{20} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{21} x^{\frac{7}{2}}}"," ",0,"32*a**(25/2)*b**(23/2)*x**9*sqrt(a*x/b + 1)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) + 176*a**(23/2)*b**(25/2)*x**8*sqrt(a*x/b + 1)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) + 396*a**(21/2)*b**(27/2)*x**7*sqrt(a*x/b + 1)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) + 462*a**(19/2)*b**(29/2)*x**6*sqrt(a*x/b + 1)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) + 280*a**(17/2)*b**(31/2)*x**5*sqrt(a*x/b + 1)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) + 42*a**(15/2)*b**(33/2)*x**4*sqrt(a*x/b + 1)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 84*a**(13/2)*b**(35/2)*x**3*sqrt(a*x/b + 1)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 94*a**(11/2)*b**(37/2)*x**2*sqrt(a*x/b + 1)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 48*a**(9/2)*b**(39/2)*x*sqrt(a*x/b + 1)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 10*a**(7/2)*b**(41/2)*sqrt(a*x/b + 1)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 32*a**13*b**11*x**(19/2)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 192*a**12*b**12*x**(17/2)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 480*a**11*b**13*x**(15/2)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 640*a**10*b**14*x**(13/2)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 480*a**9*b**15*x**(11/2)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 192*a**8*b**16*x**(9/2)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2)) - 32*a**7*b**17*x**(7/2)/(35*a**(19/2)*b**15*x**(19/2) + 210*a**(17/2)*b**16*x**(17/2) + 525*a**(15/2)*b**17*x**(15/2) + 700*a**(13/2)*b**18*x**(13/2) + 525*a**(11/2)*b**19*x**(11/2) + 210*a**(9/2)*b**20*x**(9/2) + 35*a**(7/2)*b**21*x**(7/2))","B",0
1731,1,4901,0,5.828811," ","integrate(1/x**6/(a+b/x)**(1/2),x)","- \frac{256 a^{\frac{37}{2}} b^{\frac{49}{2}} x^{14} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{2432 a^{\frac{35}{2}} b^{\frac{51}{2}} x^{13} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{10336 a^{\frac{33}{2}} b^{\frac{53}{2}} x^{12} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{25840 a^{\frac{31}{2}} b^{\frac{55}{2}} x^{11} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{41990 a^{\frac{29}{2}} b^{\frac{57}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{46252 a^{\frac{27}{2}} b^{\frac{59}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{35214 a^{\frac{25}{2}} b^{\frac{61}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{19632 a^{\frac{23}{2}} b^{\frac{63}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{10860 a^{\frac{21}{2}} b^{\frac{65}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{9160 a^{\frac{19}{2}} b^{\frac{67}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{8396 a^{\frac{17}{2}} b^{\frac{69}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{5632 a^{\frac{15}{2}} b^{\frac{71}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{2446 a^{\frac{13}{2}} b^{\frac{73}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{620 a^{\frac{11}{2}} b^{\frac{75}{2}} x \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} - \frac{70 a^{\frac{9}{2}} b^{\frac{77}{2}} \sqrt{\frac{a x}{b} + 1}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{256 a^{19} b^{24} x^{\frac{29}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{2560 a^{18} b^{25} x^{\frac{27}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{11520 a^{17} b^{26} x^{\frac{25}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{30720 a^{16} b^{27} x^{\frac{23}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{53760 a^{15} b^{28} x^{\frac{21}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{64512 a^{14} b^{29} x^{\frac{19}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{53760 a^{13} b^{30} x^{\frac{17}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{30720 a^{12} b^{31} x^{\frac{15}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{11520 a^{11} b^{32} x^{\frac{13}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{2560 a^{10} b^{33} x^{\frac{11}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}} + \frac{256 a^{9} b^{34} x^{\frac{9}{2}}}{315 a^{\frac{29}{2}} b^{29} x^{\frac{29}{2}} + 3150 a^{\frac{27}{2}} b^{30} x^{\frac{27}{2}} + 14175 a^{\frac{25}{2}} b^{31} x^{\frac{25}{2}} + 37800 a^{\frac{23}{2}} b^{32} x^{\frac{23}{2}} + 66150 a^{\frac{21}{2}} b^{33} x^{\frac{21}{2}} + 79380 a^{\frac{19}{2}} b^{34} x^{\frac{19}{2}} + 66150 a^{\frac{17}{2}} b^{35} x^{\frac{17}{2}} + 37800 a^{\frac{15}{2}} b^{36} x^{\frac{15}{2}} + 14175 a^{\frac{13}{2}} b^{37} x^{\frac{13}{2}} + 3150 a^{\frac{11}{2}} b^{38} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{39} x^{\frac{9}{2}}}"," ",0,"-256*a**(37/2)*b**(49/2)*x**14*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 2432*a**(35/2)*b**(51/2)*x**13*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 10336*a**(33/2)*b**(53/2)*x**12*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 25840*a**(31/2)*b**(55/2)*x**11*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 41990*a**(29/2)*b**(57/2)*x**10*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 46252*a**(27/2)*b**(59/2)*x**9*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 35214*a**(25/2)*b**(61/2)*x**8*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 19632*a**(23/2)*b**(63/2)*x**7*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 10860*a**(21/2)*b**(65/2)*x**6*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 9160*a**(19/2)*b**(67/2)*x**5*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 8396*a**(17/2)*b**(69/2)*x**4*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 5632*a**(15/2)*b**(71/2)*x**3*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 2446*a**(13/2)*b**(73/2)*x**2*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 620*a**(11/2)*b**(75/2)*x*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) - 70*a**(9/2)*b**(77/2)*sqrt(a*x/b + 1)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 256*a**19*b**24*x**(29/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 2560*a**18*b**25*x**(27/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 11520*a**17*b**26*x**(25/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 30720*a**16*b**27*x**(23/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 53760*a**15*b**28*x**(21/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 64512*a**14*b**29*x**(19/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 53760*a**13*b**30*x**(17/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 30720*a**12*b**31*x**(15/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 11520*a**11*b**32*x**(13/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 2560*a**10*b**33*x**(11/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2)) + 256*a**9*b**34*x**(9/2)/(315*a**(29/2)*b**29*x**(29/2) + 3150*a**(27/2)*b**30*x**(27/2) + 14175*a**(25/2)*b**31*x**(25/2) + 37800*a**(23/2)*b**32*x**(23/2) + 66150*a**(21/2)*b**33*x**(21/2) + 79380*a**(19/2)*b**34*x**(19/2) + 66150*a**(17/2)*b**35*x**(17/2) + 37800*a**(15/2)*b**36*x**(15/2) + 14175*a**(13/2)*b**37*x**(13/2) + 3150*a**(11/2)*b**38*x**(11/2) + 315*a**(9/2)*b**39*x**(9/2))","B",0
1732,1,133,0,9.824723," ","integrate(x**2/(a+b/x)**(3/2),x)","\frac{x^{\frac{7}{2}}}{3 a \sqrt{b} \sqrt{\frac{a x}{b} + 1}} - \frac{7 \sqrt{b} x^{\frac{5}{2}}}{12 a^{2} \sqrt{\frac{a x}{b} + 1}} + \frac{35 b^{\frac{3}{2}} x^{\frac{3}{2}}}{24 a^{3} \sqrt{\frac{a x}{b} + 1}} + \frac{35 b^{\frac{5}{2}} \sqrt{x}}{8 a^{4} \sqrt{\frac{a x}{b} + 1}} - \frac{35 b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{8 a^{\frac{9}{2}}}"," ",0,"x**(7/2)/(3*a*sqrt(b)*sqrt(a*x/b + 1)) - 7*sqrt(b)*x**(5/2)/(12*a**2*sqrt(a*x/b + 1)) + 35*b**(3/2)*x**(3/2)/(24*a**3*sqrt(a*x/b + 1)) + 35*b**(5/2)*sqrt(x)/(8*a**4*sqrt(a*x/b + 1)) - 35*b**3*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(8*a**(9/2))","A",0
1733,1,105,0,5.968010," ","integrate(x/(a+b/x)**(3/2),x)","\frac{x^{\frac{5}{2}}}{2 a \sqrt{b} \sqrt{\frac{a x}{b} + 1}} - \frac{5 \sqrt{b} x^{\frac{3}{2}}}{4 a^{2} \sqrt{\frac{a x}{b} + 1}} - \frac{15 b^{\frac{3}{2}} \sqrt{x}}{4 a^{3} \sqrt{\frac{a x}{b} + 1}} + \frac{15 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{4 a^{\frac{7}{2}}}"," ",0,"x**(5/2)/(2*a*sqrt(b)*sqrt(a*x/b + 1)) - 5*sqrt(b)*x**(3/2)/(4*a**2*sqrt(a*x/b + 1)) - 15*b**(3/2)*sqrt(x)/(4*a**3*sqrt(a*x/b + 1)) + 15*b**2*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(4*a**(7/2))","A",0
1734,1,71,0,5.492861," ","integrate(1/(a+b/x)**(3/2),x)","\frac{x^{\frac{3}{2}}}{a \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{3 \sqrt{b} \sqrt{x}}{a^{2} \sqrt{\frac{a x}{b} + 1}} - \frac{3 b \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{a^{\frac{5}{2}}}"," ",0,"x**(3/2)/(a*sqrt(b)*sqrt(a*x/b + 1)) + 3*sqrt(b)*sqrt(x)/(a**2*sqrt(a*x/b + 1)) - 3*b*asinh(sqrt(a)*sqrt(x)/sqrt(b))/a**(5/2)","A",0
1735,1,148,0,3.818784," ","integrate(1/(a+b/x)**(3/2)/x,x)","- \frac{2 a^{3} x \sqrt{1 + \frac{b}{a x}}}{a^{\frac{9}{2}} x + a^{\frac{7}{2}} b} - \frac{a^{3} x \log{\left(\frac{b}{a x} \right)}}{a^{\frac{9}{2}} x + a^{\frac{7}{2}} b} + \frac{2 a^{3} x \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{a^{\frac{9}{2}} x + a^{\frac{7}{2}} b} - \frac{a^{2} b \log{\left(\frac{b}{a x} \right)}}{a^{\frac{9}{2}} x + a^{\frac{7}{2}} b} + \frac{2 a^{2} b \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{a^{\frac{9}{2}} x + a^{\frac{7}{2}} b}"," ",0,"-2*a**3*x*sqrt(1 + b/(a*x))/(a**(9/2)*x + a**(7/2)*b) - a**3*x*log(b/(a*x))/(a**(9/2)*x + a**(7/2)*b) + 2*a**3*x*log(sqrt(1 + b/(a*x)) + 1)/(a**(9/2)*x + a**(7/2)*b) - a**2*b*log(b/(a*x))/(a**(9/2)*x + a**(7/2)*b) + 2*a**2*b*log(sqrt(1 + b/(a*x)) + 1)/(a**(9/2)*x + a**(7/2)*b)","B",0
1736,1,20,0,1.800864," ","integrate(1/(a+b/x)**(3/2)/x**2,x)","\begin{cases} \frac{2}{b \sqrt{a + \frac{b}{x}}} & \text{for}\: b \neq 0 \\- \frac{1}{a^{\frac{3}{2}} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2/(b*sqrt(a + b/x)), Ne(b, 0)), (-1/(a**(3/2)*x), True))","A",0
1737,1,42,0,3.374691," ","integrate(1/(a+b/x)**(3/2)/x**3,x)","\begin{cases} - \frac{4 a}{b^{2} \sqrt{a + \frac{b}{x}}} - \frac{2}{b x \sqrt{a + \frac{b}{x}}} & \text{for}\: b \neq 0 \\- \frac{1}{2 a^{\frac{3}{2}} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a/(b**2*sqrt(a + b/x)) - 2/(b*x*sqrt(a + b/x)), Ne(b, 0)), (-1/(2*a**(3/2)*x**2), True))","A",0
1738,1,457,0,2.385863," ","integrate(1/(a+b/x)**(3/2)/x**4,x)","\frac{16 a^{\frac{9}{2}} b^{\frac{7}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{3 a^{\frac{7}{2}} b^{6} x^{\frac{7}{2}} + 6 a^{\frac{5}{2}} b^{7} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{8} x^{\frac{3}{2}}} + \frac{24 a^{\frac{7}{2}} b^{\frac{9}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{3 a^{\frac{7}{2}} b^{6} x^{\frac{7}{2}} + 6 a^{\frac{5}{2}} b^{7} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{8} x^{\frac{3}{2}}} + \frac{6 a^{\frac{5}{2}} b^{\frac{11}{2}} x \sqrt{\frac{a x}{b} + 1}}{3 a^{\frac{7}{2}} b^{6} x^{\frac{7}{2}} + 6 a^{\frac{5}{2}} b^{7} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{8} x^{\frac{3}{2}}} - \frac{2 a^{\frac{3}{2}} b^{\frac{13}{2}} \sqrt{\frac{a x}{b} + 1}}{3 a^{\frac{7}{2}} b^{6} x^{\frac{7}{2}} + 6 a^{\frac{5}{2}} b^{7} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{8} x^{\frac{3}{2}}} - \frac{16 a^{5} b^{3} x^{\frac{7}{2}}}{3 a^{\frac{7}{2}} b^{6} x^{\frac{7}{2}} + 6 a^{\frac{5}{2}} b^{7} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{8} x^{\frac{3}{2}}} - \frac{32 a^{4} b^{4} x^{\frac{5}{2}}}{3 a^{\frac{7}{2}} b^{6} x^{\frac{7}{2}} + 6 a^{\frac{5}{2}} b^{7} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{8} x^{\frac{3}{2}}} - \frac{16 a^{3} b^{5} x^{\frac{3}{2}}}{3 a^{\frac{7}{2}} b^{6} x^{\frac{7}{2}} + 6 a^{\frac{5}{2}} b^{7} x^{\frac{5}{2}} + 3 a^{\frac{3}{2}} b^{8} x^{\frac{3}{2}}}"," ",0,"16*a**(9/2)*b**(7/2)*x**3*sqrt(a*x/b + 1)/(3*a**(7/2)*b**6*x**(7/2) + 6*a**(5/2)*b**7*x**(5/2) + 3*a**(3/2)*b**8*x**(3/2)) + 24*a**(7/2)*b**(9/2)*x**2*sqrt(a*x/b + 1)/(3*a**(7/2)*b**6*x**(7/2) + 6*a**(5/2)*b**7*x**(5/2) + 3*a**(3/2)*b**8*x**(3/2)) + 6*a**(5/2)*b**(11/2)*x*sqrt(a*x/b + 1)/(3*a**(7/2)*b**6*x**(7/2) + 6*a**(5/2)*b**7*x**(5/2) + 3*a**(3/2)*b**8*x**(3/2)) - 2*a**(3/2)*b**(13/2)*sqrt(a*x/b + 1)/(3*a**(7/2)*b**6*x**(7/2) + 6*a**(5/2)*b**7*x**(5/2) + 3*a**(3/2)*b**8*x**(3/2)) - 16*a**5*b**3*x**(7/2)/(3*a**(7/2)*b**6*x**(7/2) + 6*a**(5/2)*b**7*x**(5/2) + 3*a**(3/2)*b**8*x**(3/2)) - 32*a**4*b**4*x**(5/2)/(3*a**(7/2)*b**6*x**(7/2) + 6*a**(5/2)*b**7*x**(5/2) + 3*a**(3/2)*b**8*x**(3/2)) - 16*a**3*b**5*x**(3/2)/(3*a**(7/2)*b**6*x**(7/2) + 6*a**(5/2)*b**7*x**(5/2) + 3*a**(3/2)*b**8*x**(3/2))","B",0
1739,1,2032,0,3.605857," ","integrate(1/(a+b/x)**(3/2)/x**5,x)","- \frac{32 a^{\frac{21}{2}} b^{\frac{23}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} - \frac{176 a^{\frac{19}{2}} b^{\frac{25}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} - \frac{396 a^{\frac{17}{2}} b^{\frac{27}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} - \frac{462 a^{\frac{15}{2}} b^{\frac{29}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} - \frac{290 a^{\frac{13}{2}} b^{\frac{31}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} - \frac{92 a^{\frac{11}{2}} b^{\frac{33}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} - \frac{16 a^{\frac{9}{2}} b^{\frac{35}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} - \frac{6 a^{\frac{7}{2}} b^{\frac{37}{2}} x \sqrt{\frac{a x}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} - \frac{2 a^{\frac{5}{2}} b^{\frac{39}{2}} \sqrt{\frac{a x}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} + \frac{32 a^{11} b^{11} x^{\frac{17}{2}}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} + \frac{192 a^{10} b^{12} x^{\frac{15}{2}}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} + \frac{480 a^{9} b^{13} x^{\frac{13}{2}}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} + \frac{640 a^{8} b^{14} x^{\frac{11}{2}}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} + \frac{480 a^{7} b^{15} x^{\frac{9}{2}}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} + \frac{192 a^{6} b^{16} x^{\frac{7}{2}}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}} + \frac{32 a^{5} b^{17} x^{\frac{5}{2}}}{5 a^{\frac{17}{2}} b^{15} x^{\frac{17}{2}} + 30 a^{\frac{15}{2}} b^{16} x^{\frac{15}{2}} + 75 a^{\frac{13}{2}} b^{17} x^{\frac{13}{2}} + 100 a^{\frac{11}{2}} b^{18} x^{\frac{11}{2}} + 75 a^{\frac{9}{2}} b^{19} x^{\frac{9}{2}} + 30 a^{\frac{7}{2}} b^{20} x^{\frac{7}{2}} + 5 a^{\frac{5}{2}} b^{21} x^{\frac{5}{2}}}"," ",0,"-32*a**(21/2)*b**(23/2)*x**8*sqrt(a*x/b + 1)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) - 176*a**(19/2)*b**(25/2)*x**7*sqrt(a*x/b + 1)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) - 396*a**(17/2)*b**(27/2)*x**6*sqrt(a*x/b + 1)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) - 462*a**(15/2)*b**(29/2)*x**5*sqrt(a*x/b + 1)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) - 290*a**(13/2)*b**(31/2)*x**4*sqrt(a*x/b + 1)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) - 92*a**(11/2)*b**(33/2)*x**3*sqrt(a*x/b + 1)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) - 16*a**(9/2)*b**(35/2)*x**2*sqrt(a*x/b + 1)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) - 6*a**(7/2)*b**(37/2)*x*sqrt(a*x/b + 1)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) - 2*a**(5/2)*b**(39/2)*sqrt(a*x/b + 1)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) + 32*a**11*b**11*x**(17/2)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) + 192*a**10*b**12*x**(15/2)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) + 480*a**9*b**13*x**(13/2)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) + 640*a**8*b**14*x**(11/2)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) + 480*a**7*b**15*x**(9/2)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) + 192*a**6*b**16*x**(7/2)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2)) + 32*a**5*b**17*x**(5/2)/(5*a**(17/2)*b**15*x**(17/2) + 30*a**(15/2)*b**16*x**(15/2) + 75*a**(13/2)*b**17*x**(13/2) + 100*a**(11/2)*b**18*x**(11/2) + 75*a**(9/2)*b**19*x**(9/2) + 30*a**(7/2)*b**20*x**(7/2) + 5*a**(5/2)*b**21*x**(5/2))","B",0
1740,1,4707,0,6.287213," ","integrate(1/(a+b/x)**(3/2)/x**6,x)","\frac{256 a^{\frac{33}{2}} b^{\frac{49}{2}} x^{13} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} + \frac{2432 a^{\frac{31}{2}} b^{\frac{51}{2}} x^{12} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} + \frac{10336 a^{\frac{29}{2}} b^{\frac{53}{2}} x^{11} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} + \frac{25840 a^{\frac{27}{2}} b^{\frac{55}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} + \frac{41990 a^{\frac{25}{2}} b^{\frac{57}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} + \frac{46182 a^{\frac{23}{2}} b^{\frac{59}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} + \frac{34584 a^{\frac{21}{2}} b^{\frac{61}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} + \frac{17112 a^{\frac{19}{2}} b^{\frac{63}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} + \frac{4980 a^{\frac{17}{2}} b^{\frac{65}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} + \frac{340 a^{\frac{15}{2}} b^{\frac{67}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{424 a^{\frac{13}{2}} b^{\frac{69}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{248 a^{\frac{11}{2}} b^{\frac{71}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{74 a^{\frac{9}{2}} b^{\frac{73}{2}} x \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{10 a^{\frac{7}{2}} b^{\frac{75}{2}} \sqrt{\frac{a x}{b} + 1}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{256 a^{17} b^{24} x^{\frac{27}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{2560 a^{16} b^{25} x^{\frac{25}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{11520 a^{15} b^{26} x^{\frac{23}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{30720 a^{14} b^{27} x^{\frac{21}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{53760 a^{13} b^{28} x^{\frac{19}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{64512 a^{12} b^{29} x^{\frac{17}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{53760 a^{11} b^{30} x^{\frac{15}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{30720 a^{10} b^{31} x^{\frac{13}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{11520 a^{9} b^{32} x^{\frac{11}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{2560 a^{8} b^{33} x^{\frac{9}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}} - \frac{256 a^{7} b^{34} x^{\frac{7}{2}}}{35 a^{\frac{27}{2}} b^{29} x^{\frac{27}{2}} + 350 a^{\frac{25}{2}} b^{30} x^{\frac{25}{2}} + 1575 a^{\frac{23}{2}} b^{31} x^{\frac{23}{2}} + 4200 a^{\frac{21}{2}} b^{32} x^{\frac{21}{2}} + 7350 a^{\frac{19}{2}} b^{33} x^{\frac{19}{2}} + 8820 a^{\frac{17}{2}} b^{34} x^{\frac{17}{2}} + 7350 a^{\frac{15}{2}} b^{35} x^{\frac{15}{2}} + 4200 a^{\frac{13}{2}} b^{36} x^{\frac{13}{2}} + 1575 a^{\frac{11}{2}} b^{37} x^{\frac{11}{2}} + 350 a^{\frac{9}{2}} b^{38} x^{\frac{9}{2}} + 35 a^{\frac{7}{2}} b^{39} x^{\frac{7}{2}}}"," ",0,"256*a**(33/2)*b**(49/2)*x**13*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 2432*a**(31/2)*b**(51/2)*x**12*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 10336*a**(29/2)*b**(53/2)*x**11*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 25840*a**(27/2)*b**(55/2)*x**10*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 41990*a**(25/2)*b**(57/2)*x**9*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 46182*a**(23/2)*b**(59/2)*x**8*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 34584*a**(21/2)*b**(61/2)*x**7*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 17112*a**(19/2)*b**(63/2)*x**6*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 4980*a**(17/2)*b**(65/2)*x**5*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 340*a**(15/2)*b**(67/2)*x**4*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 424*a**(13/2)*b**(69/2)*x**3*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 248*a**(11/2)*b**(71/2)*x**2*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 74*a**(9/2)*b**(73/2)*x*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 10*a**(7/2)*b**(75/2)*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 256*a**17*b**24*x**(27/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 2560*a**16*b**25*x**(25/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 11520*a**15*b**26*x**(23/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 30720*a**14*b**27*x**(21/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 53760*a**13*b**28*x**(19/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 64512*a**12*b**29*x**(17/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 53760*a**11*b**30*x**(15/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 30720*a**10*b**31*x**(13/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 11520*a**9*b**32*x**(11/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 2560*a**8*b**33*x**(9/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 256*a**7*b**34*x**(7/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2))","B",0
1741,1,9534,0,11.380427," ","integrate(1/(a+b/x)**(3/2)/x**7,x)","- \frac{512 a^{\frac{47}{2}} b^{\frac{91}{2}} x^{19} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{7424 a^{\frac{45}{2}} b^{\frac{93}{2}} x^{18} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{50112 a^{\frac{43}{2}} b^{\frac{95}{2}} x^{17} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{208800 a^{\frac{41}{2}} b^{\frac{97}{2}} x^{16} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{600300 a^{\frac{39}{2}} b^{\frac{99}{2}} x^{15} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{1260630 a^{\frac{37}{2}} b^{\frac{101}{2}} x^{14} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{1996008 a^{\frac{35}{2}} b^{\frac{103}{2}} x^{13} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{2423850 a^{\frac{33}{2}} b^{\frac{105}{2}} x^{12} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{2273076 a^{\frac{31}{2}} b^{\frac{107}{2}} x^{11} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{1644214 a^{\frac{29}{2}} b^{\frac{109}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{910624 a^{\frac{27}{2}} b^{\frac{111}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{383994 a^{\frac{25}{2}} b^{\frac{113}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{127764 a^{\frac{23}{2}} b^{\frac{115}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{41202 a^{\frac{21}{2}} b^{\frac{117}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{17928 a^{\frac{19}{2}} b^{\frac{119}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{9006 a^{\frac{17}{2}} b^{\frac{121}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{3660 a^{\frac{15}{2}} b^{\frac{123}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{1026 a^{\frac{13}{2}} b^{\frac{125}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{176 a^{\frac{11}{2}} b^{\frac{127}{2}} x \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} - \frac{14 a^{\frac{9}{2}} b^{\frac{129}{2}} \sqrt{\frac{a x}{b} + 1}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{512 a^{24} b^{45} x^{\frac{39}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{7680 a^{23} b^{46} x^{\frac{37}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{53760 a^{22} b^{47} x^{\frac{35}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{232960 a^{21} b^{48} x^{\frac{33}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{698880 a^{20} b^{49} x^{\frac{31}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{1537536 a^{19} b^{50} x^{\frac{29}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{2562560 a^{18} b^{51} x^{\frac{27}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{3294720 a^{17} b^{52} x^{\frac{25}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{3294720 a^{16} b^{53} x^{\frac{23}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{2562560 a^{15} b^{54} x^{\frac{21}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{1537536 a^{14} b^{55} x^{\frac{19}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{698880 a^{13} b^{56} x^{\frac{17}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{232960 a^{12} b^{57} x^{\frac{15}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{53760 a^{11} b^{58} x^{\frac{13}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{7680 a^{10} b^{59} x^{\frac{11}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}} + \frac{512 a^{9} b^{60} x^{\frac{9}{2}}}{63 a^{\frac{39}{2}} b^{51} x^{\frac{39}{2}} + 945 a^{\frac{37}{2}} b^{52} x^{\frac{37}{2}} + 6615 a^{\frac{35}{2}} b^{53} x^{\frac{35}{2}} + 28665 a^{\frac{33}{2}} b^{54} x^{\frac{33}{2}} + 85995 a^{\frac{31}{2}} b^{55} x^{\frac{31}{2}} + 189189 a^{\frac{29}{2}} b^{56} x^{\frac{29}{2}} + 315315 a^{\frac{27}{2}} b^{57} x^{\frac{27}{2}} + 405405 a^{\frac{25}{2}} b^{58} x^{\frac{25}{2}} + 405405 a^{\frac{23}{2}} b^{59} x^{\frac{23}{2}} + 315315 a^{\frac{21}{2}} b^{60} x^{\frac{21}{2}} + 189189 a^{\frac{19}{2}} b^{61} x^{\frac{19}{2}} + 85995 a^{\frac{17}{2}} b^{62} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{63} x^{\frac{15}{2}} + 6615 a^{\frac{13}{2}} b^{64} x^{\frac{13}{2}} + 945 a^{\frac{11}{2}} b^{65} x^{\frac{11}{2}} + 63 a^{\frac{9}{2}} b^{66} x^{\frac{9}{2}}}"," ",0,"-512*a**(47/2)*b**(91/2)*x**19*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 7424*a**(45/2)*b**(93/2)*x**18*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 50112*a**(43/2)*b**(95/2)*x**17*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 208800*a**(41/2)*b**(97/2)*x**16*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 600300*a**(39/2)*b**(99/2)*x**15*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 1260630*a**(37/2)*b**(101/2)*x**14*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 1996008*a**(35/2)*b**(103/2)*x**13*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 2423850*a**(33/2)*b**(105/2)*x**12*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 2273076*a**(31/2)*b**(107/2)*x**11*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 1644214*a**(29/2)*b**(109/2)*x**10*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 910624*a**(27/2)*b**(111/2)*x**9*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 383994*a**(25/2)*b**(113/2)*x**8*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 127764*a**(23/2)*b**(115/2)*x**7*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 41202*a**(21/2)*b**(117/2)*x**6*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 17928*a**(19/2)*b**(119/2)*x**5*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 9006*a**(17/2)*b**(121/2)*x**4*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 3660*a**(15/2)*b**(123/2)*x**3*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 1026*a**(13/2)*b**(125/2)*x**2*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 176*a**(11/2)*b**(127/2)*x*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) - 14*a**(9/2)*b**(129/2)*sqrt(a*x/b + 1)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 512*a**24*b**45*x**(39/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 7680*a**23*b**46*x**(37/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 53760*a**22*b**47*x**(35/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 232960*a**21*b**48*x**(33/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 698880*a**20*b**49*x**(31/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 1537536*a**19*b**50*x**(29/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 2562560*a**18*b**51*x**(27/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 3294720*a**17*b**52*x**(25/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 3294720*a**16*b**53*x**(23/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 2562560*a**15*b**54*x**(21/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 1537536*a**14*b**55*x**(19/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 698880*a**13*b**56*x**(17/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 232960*a**12*b**57*x**(15/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 53760*a**11*b**58*x**(13/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 7680*a**10*b**59*x**(11/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2)) + 512*a**9*b**60*x**(9/2)/(63*a**(39/2)*b**51*x**(39/2) + 945*a**(37/2)*b**52*x**(37/2) + 6615*a**(35/2)*b**53*x**(35/2) + 28665*a**(33/2)*b**54*x**(33/2) + 85995*a**(31/2)*b**55*x**(31/2) + 189189*a**(29/2)*b**56*x**(29/2) + 315315*a**(27/2)*b**57*x**(27/2) + 405405*a**(25/2)*b**58*x**(25/2) + 405405*a**(23/2)*b**59*x**(23/2) + 315315*a**(21/2)*b**60*x**(21/2) + 189189*a**(19/2)*b**61*x**(19/2) + 85995*a**(17/2)*b**62*x**(17/2) + 28665*a**(15/2)*b**63*x**(15/2) + 6615*a**(13/2)*b**64*x**(13/2) + 945*a**(11/2)*b**65*x**(11/2) + 63*a**(9/2)*b**66*x**(9/2))","B",0
1742,1,532,0,17.635592," ","integrate(x**2/(a+b/x)**(5/2),x)","\frac{8 a^{\frac{133}{2}} b^{128} x^{72}}{24 a^{\frac{137}{2}} b^{\frac{257}{2}} x^{\frac{137}{2}} \sqrt{\frac{a x}{b} + 1} + 24 a^{\frac{135}{2}} b^{\frac{259}{2}} x^{\frac{135}{2}} \sqrt{\frac{a x}{b} + 1}} - \frac{18 a^{\frac{131}{2}} b^{129} x^{71}}{24 a^{\frac{137}{2}} b^{\frac{257}{2}} x^{\frac{137}{2}} \sqrt{\frac{a x}{b} + 1} + 24 a^{\frac{135}{2}} b^{\frac{259}{2}} x^{\frac{135}{2}} \sqrt{\frac{a x}{b} + 1}} + \frac{63 a^{\frac{129}{2}} b^{130} x^{70}}{24 a^{\frac{137}{2}} b^{\frac{257}{2}} x^{\frac{137}{2}} \sqrt{\frac{a x}{b} + 1} + 24 a^{\frac{135}{2}} b^{\frac{259}{2}} x^{\frac{135}{2}} \sqrt{\frac{a x}{b} + 1}} + \frac{420 a^{\frac{127}{2}} b^{131} x^{69}}{24 a^{\frac{137}{2}} b^{\frac{257}{2}} x^{\frac{137}{2}} \sqrt{\frac{a x}{b} + 1} + 24 a^{\frac{135}{2}} b^{\frac{259}{2}} x^{\frac{135}{2}} \sqrt{\frac{a x}{b} + 1}} + \frac{315 a^{\frac{125}{2}} b^{132} x^{68}}{24 a^{\frac{137}{2}} b^{\frac{257}{2}} x^{\frac{137}{2}} \sqrt{\frac{a x}{b} + 1} + 24 a^{\frac{135}{2}} b^{\frac{259}{2}} x^{\frac{135}{2}} \sqrt{\frac{a x}{b} + 1}} - \frac{315 a^{63} b^{\frac{263}{2}} x^{\frac{137}{2}} \sqrt{\frac{a x}{b} + 1} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{24 a^{\frac{137}{2}} b^{\frac{257}{2}} x^{\frac{137}{2}} \sqrt{\frac{a x}{b} + 1} + 24 a^{\frac{135}{2}} b^{\frac{259}{2}} x^{\frac{135}{2}} \sqrt{\frac{a x}{b} + 1}} - \frac{315 a^{62} b^{\frac{265}{2}} x^{\frac{135}{2}} \sqrt{\frac{a x}{b} + 1} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{24 a^{\frac{137}{2}} b^{\frac{257}{2}} x^{\frac{137}{2}} \sqrt{\frac{a x}{b} + 1} + 24 a^{\frac{135}{2}} b^{\frac{259}{2}} x^{\frac{135}{2}} \sqrt{\frac{a x}{b} + 1}}"," ",0,"8*a**(133/2)*b**128*x**72/(24*a**(137/2)*b**(257/2)*x**(137/2)*sqrt(a*x/b + 1) + 24*a**(135/2)*b**(259/2)*x**(135/2)*sqrt(a*x/b + 1)) - 18*a**(131/2)*b**129*x**71/(24*a**(137/2)*b**(257/2)*x**(137/2)*sqrt(a*x/b + 1) + 24*a**(135/2)*b**(259/2)*x**(135/2)*sqrt(a*x/b + 1)) + 63*a**(129/2)*b**130*x**70/(24*a**(137/2)*b**(257/2)*x**(137/2)*sqrt(a*x/b + 1) + 24*a**(135/2)*b**(259/2)*x**(135/2)*sqrt(a*x/b + 1)) + 420*a**(127/2)*b**131*x**69/(24*a**(137/2)*b**(257/2)*x**(137/2)*sqrt(a*x/b + 1) + 24*a**(135/2)*b**(259/2)*x**(135/2)*sqrt(a*x/b + 1)) + 315*a**(125/2)*b**132*x**68/(24*a**(137/2)*b**(257/2)*x**(137/2)*sqrt(a*x/b + 1) + 24*a**(135/2)*b**(259/2)*x**(135/2)*sqrt(a*x/b + 1)) - 315*a**63*b**(263/2)*x**(137/2)*sqrt(a*x/b + 1)*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(24*a**(137/2)*b**(257/2)*x**(137/2)*sqrt(a*x/b + 1) + 24*a**(135/2)*b**(259/2)*x**(135/2)*sqrt(a*x/b + 1)) - 315*a**62*b**(265/2)*x**(135/2)*sqrt(a*x/b + 1)*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(24*a**(137/2)*b**(257/2)*x**(137/2)*sqrt(a*x/b + 1) + 24*a**(135/2)*b**(259/2)*x**(135/2)*sqrt(a*x/b + 1))","B",0
1743,1,464,0,10.574336," ","integrate(x/(a+b/x)**(5/2),x)","\frac{6 a^{\frac{89}{2}} b^{75} x^{49}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{93}{2}} \sqrt{\frac{a x}{b} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{91}{2}} \sqrt{\frac{a x}{b} + 1}} - \frac{21 a^{\frac{87}{2}} b^{76} x^{48}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{93}{2}} \sqrt{\frac{a x}{b} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{91}{2}} \sqrt{\frac{a x}{b} + 1}} - \frac{140 a^{\frac{85}{2}} b^{77} x^{47}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{93}{2}} \sqrt{\frac{a x}{b} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{91}{2}} \sqrt{\frac{a x}{b} + 1}} - \frac{105 a^{\frac{83}{2}} b^{78} x^{46}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{93}{2}} \sqrt{\frac{a x}{b} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{91}{2}} \sqrt{\frac{a x}{b} + 1}} + \frac{105 a^{42} b^{\frac{155}{2}} x^{\frac{93}{2}} \sqrt{\frac{a x}{b} + 1} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{93}{2}} \sqrt{\frac{a x}{b} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{91}{2}} \sqrt{\frac{a x}{b} + 1}} + \frac{105 a^{41} b^{\frac{157}{2}} x^{\frac{91}{2}} \sqrt{\frac{a x}{b} + 1} \operatorname{asinh}{\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right)}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{93}{2}} \sqrt{\frac{a x}{b} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{91}{2}} \sqrt{\frac{a x}{b} + 1}}"," ",0,"6*a**(89/2)*b**75*x**49/(12*a**(93/2)*b**(151/2)*x**(93/2)*sqrt(a*x/b + 1) + 12*a**(91/2)*b**(153/2)*x**(91/2)*sqrt(a*x/b + 1)) - 21*a**(87/2)*b**76*x**48/(12*a**(93/2)*b**(151/2)*x**(93/2)*sqrt(a*x/b + 1) + 12*a**(91/2)*b**(153/2)*x**(91/2)*sqrt(a*x/b + 1)) - 140*a**(85/2)*b**77*x**47/(12*a**(93/2)*b**(151/2)*x**(93/2)*sqrt(a*x/b + 1) + 12*a**(91/2)*b**(153/2)*x**(91/2)*sqrt(a*x/b + 1)) - 105*a**(83/2)*b**78*x**46/(12*a**(93/2)*b**(151/2)*x**(93/2)*sqrt(a*x/b + 1) + 12*a**(91/2)*b**(153/2)*x**(91/2)*sqrt(a*x/b + 1)) + 105*a**42*b**(155/2)*x**(93/2)*sqrt(a*x/b + 1)*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(12*a**(93/2)*b**(151/2)*x**(93/2)*sqrt(a*x/b + 1) + 12*a**(91/2)*b**(153/2)*x**(91/2)*sqrt(a*x/b + 1)) + 105*a**41*b**(157/2)*x**(91/2)*sqrt(a*x/b + 1)*asinh(sqrt(a)*sqrt(x)/sqrt(b))/(12*a**(93/2)*b**(151/2)*x**(93/2)*sqrt(a*x/b + 1) + 12*a**(91/2)*b**(153/2)*x**(91/2)*sqrt(a*x/b + 1))","B",0
1744,1,774,0,6.572724," ","integrate(1/(a+b/x)**(5/2),x)","\frac{6 a^{17} x^{4} \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{46 a^{16} b x^{3} \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{15 a^{16} b x^{3} \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{30 a^{16} b x^{3} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{70 a^{15} b^{2} x^{2} \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{45 a^{15} b^{2} x^{2} \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{90 a^{15} b^{2} x^{2} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{30 a^{14} b^{3} x \sqrt{1 + \frac{b}{a x}}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{45 a^{14} b^{3} x \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{90 a^{14} b^{3} x \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} + \frac{15 a^{13} b^{4} \log{\left(\frac{b}{a x} \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}} - \frac{30 a^{13} b^{4} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{6 a^{\frac{39}{2}} x^{3} + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x + 6 a^{\frac{33}{2}} b^{3}}"," ",0,"6*a**17*x**4*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 46*a**16*b*x**3*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 15*a**16*b*x**3*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 30*a**16*b*x**3*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 70*a**15*b**2*x**2*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 45*a**15*b**2*x**2*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 90*a**15*b**2*x**2*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 30*a**14*b**3*x*sqrt(1 + b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 45*a**14*b**3*x*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 90*a**14*b**3*x*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) + 15*a**13*b**4*log(b/(a*x))/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3) - 30*a**13*b**4*log(sqrt(1 + b/(a*x)) + 1)/(6*a**(39/2)*x**3 + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x + 6*a**(33/2)*b**3)","B",0
1745,1,700,0,3.559027," ","integrate(1/(a+b/x)**(5/2)/x,x)","- \frac{8 a^{7} x^{3} \sqrt{1 + \frac{b}{a x}}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{3 a^{7} x^{3} \log{\left(\frac{b}{a x} \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} + \frac{6 a^{7} x^{3} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{14 a^{6} b x^{2} \sqrt{1 + \frac{b}{a x}}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{9 a^{6} b x^{2} \log{\left(\frac{b}{a x} \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} + \frac{18 a^{6} b x^{2} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{6 a^{5} b^{2} x \sqrt{1 + \frac{b}{a x}}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{9 a^{5} b^{2} x \log{\left(\frac{b}{a x} \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} + \frac{18 a^{5} b^{2} x \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} - \frac{3 a^{4} b^{3} \log{\left(\frac{b}{a x} \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}} + \frac{6 a^{4} b^{3} \log{\left(\sqrt{1 + \frac{b}{a x}} + 1 \right)}}{3 a^{\frac{19}{2}} x^{3} + 9 a^{\frac{17}{2}} b x^{2} + 9 a^{\frac{15}{2}} b^{2} x + 3 a^{\frac{13}{2}} b^{3}}"," ",0,"-8*a**7*x**3*sqrt(1 + b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 3*a**7*x**3*log(b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) + 6*a**7*x**3*log(sqrt(1 + b/(a*x)) + 1)/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 14*a**6*b*x**2*sqrt(1 + b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 9*a**6*b*x**2*log(b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) + 18*a**6*b*x**2*log(sqrt(1 + b/(a*x)) + 1)/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 6*a**5*b**2*x*sqrt(1 + b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 9*a**5*b**2*x*log(b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) + 18*a**5*b**2*x*log(sqrt(1 + b/(a*x)) + 1)/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) - 3*a**4*b**3*log(b/(a*x))/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3) + 6*a**4*b**3*log(sqrt(1 + b/(a*x)) + 1)/(3*a**(19/2)*x**3 + 9*a**(17/2)*b*x**2 + 9*a**(15/2)*b**2*x + 3*a**(13/2)*b**3)","B",0
1746,1,39,0,2.877710," ","integrate(1/(a+b/x)**(5/2)/x**2,x)","\begin{cases} \frac{2}{3 a b \sqrt{a + \frac{b}{x}} + \frac{3 b^{2} \sqrt{a + \frac{b}{x}}}{x}} & \text{for}\: b \neq 0 \\- \frac{1}{a^{\frac{5}{2}} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2/(3*a*b*sqrt(a + b/x) + 3*b**2*sqrt(a + b/x)/x), Ne(b, 0)), (-1/(a**(5/2)*x), True))","A",0
1747,1,82,0,4.037280," ","integrate(1/(a+b/x)**(5/2)/x**3,x)","\begin{cases} \frac{4 a x}{3 a b^{2} x \sqrt{a + \frac{b}{x}} + 3 b^{3} \sqrt{a + \frac{b}{x}}} + \frac{6 b}{3 a b^{2} x \sqrt{a + \frac{b}{x}} + 3 b^{3} \sqrt{a + \frac{b}{x}}} & \text{for}\: b \neq 0 \\- \frac{1}{2 a^{\frac{5}{2}} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a*x/(3*a*b**2*x*sqrt(a + b/x) + 3*b**3*sqrt(a + b/x)) + 6*b/(3*a*b**2*x*sqrt(a + b/x) + 3*b**3*sqrt(a + b/x)), Ne(b, 0)), (-1/(2*a**(5/2)*x**2), True))","A",0
1748,1,136,0,4.270961," ","integrate(1/(a+b/x)**(5/2)/x**4,x)","\begin{cases} - \frac{16 a^{2} x^{2}}{3 a b^{3} x^{2} \sqrt{a + \frac{b}{x}} + 3 b^{4} x \sqrt{a + \frac{b}{x}}} - \frac{24 a b x}{3 a b^{3} x^{2} \sqrt{a + \frac{b}{x}} + 3 b^{4} x \sqrt{a + \frac{b}{x}}} - \frac{6 b^{2}}{3 a b^{3} x^{2} \sqrt{a + \frac{b}{x}} + 3 b^{4} x \sqrt{a + \frac{b}{x}}} & \text{for}\: b \neq 0 \\- \frac{1}{3 a^{\frac{5}{2}} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*a**2*x**2/(3*a*b**3*x**2*sqrt(a + b/x) + 3*b**4*x*sqrt(a + b/x)) - 24*a*b*x/(3*a*b**3*x**2*sqrt(a + b/x) + 3*b**4*x*sqrt(a + b/x)) - 6*b**2/(3*a*b**3*x**2*sqrt(a + b/x) + 3*b**4*x*sqrt(a + b/x)), Ne(b, 0)), (-1/(3*a**(5/2)*x**3), True))","A",0
1749,1,187,0,5.248634," ","integrate(1/(a+b/x)**(5/2)/x**5,x)","\begin{cases} \frac{32 a^{3} x^{3}}{3 a b^{4} x^{3} \sqrt{a + \frac{b}{x}} + 3 b^{5} x^{2} \sqrt{a + \frac{b}{x}}} + \frac{48 a^{2} b x^{2}}{3 a b^{4} x^{3} \sqrt{a + \frac{b}{x}} + 3 b^{5} x^{2} \sqrt{a + \frac{b}{x}}} + \frac{12 a b^{2} x}{3 a b^{4} x^{3} \sqrt{a + \frac{b}{x}} + 3 b^{5} x^{2} \sqrt{a + \frac{b}{x}}} - \frac{2 b^{3}}{3 a b^{4} x^{3} \sqrt{a + \frac{b}{x}} + 3 b^{5} x^{2} \sqrt{a + \frac{b}{x}}} & \text{for}\: b \neq 0 \\- \frac{1}{4 a^{\frac{5}{2}} x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((32*a**3*x**3/(3*a*b**4*x**3*sqrt(a + b/x) + 3*b**5*x**2*sqrt(a + b/x)) + 48*a**2*b*x**2/(3*a*b**4*x**3*sqrt(a + b/x) + 3*b**5*x**2*sqrt(a + b/x)) + 12*a*b**2*x/(3*a*b**4*x**3*sqrt(a + b/x) + 3*b**5*x**2*sqrt(a + b/x)) - 2*b**3/(3*a*b**4*x**3*sqrt(a + b/x) + 3*b**5*x**2*sqrt(a + b/x)), Ne(b, 0)), (-1/(4*a**(5/2)*x**4), True))","A",0
1750,1,2032,0,6.360464," ","integrate(1/(a+b/x)**(5/2)/x**6,x)","- \frac{256 a^{\frac{21}{2}} b^{\frac{33}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} - \frac{1408 a^{\frac{19}{2}} b^{\frac{35}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} - \frac{3168 a^{\frac{17}{2}} b^{\frac{37}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} - \frac{3696 a^{\frac{15}{2}} b^{\frac{39}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} - \frac{2310 a^{\frac{13}{2}} b^{\frac{41}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} - \frac{696 a^{\frac{11}{2}} b^{\frac{43}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} - \frac{68 a^{\frac{9}{2}} b^{\frac{45}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} - \frac{8 a^{\frac{7}{2}} b^{\frac{47}{2}} x \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} - \frac{6 a^{\frac{5}{2}} b^{\frac{49}{2}} \sqrt{\frac{a x}{b} + 1}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} + \frac{256 a^{11} b^{16} x^{\frac{17}{2}}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} + \frac{1536 a^{10} b^{17} x^{\frac{15}{2}}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} + \frac{3840 a^{9} b^{18} x^{\frac{13}{2}}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} + \frac{5120 a^{8} b^{19} x^{\frac{11}{2}}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} + \frac{3840 a^{7} b^{20} x^{\frac{9}{2}}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} + \frac{1536 a^{6} b^{21} x^{\frac{7}{2}}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}} + \frac{256 a^{5} b^{22} x^{\frac{5}{2}}}{15 a^{\frac{17}{2}} b^{21} x^{\frac{17}{2}} + 90 a^{\frac{15}{2}} b^{22} x^{\frac{15}{2}} + 225 a^{\frac{13}{2}} b^{23} x^{\frac{13}{2}} + 300 a^{\frac{11}{2}} b^{24} x^{\frac{11}{2}} + 225 a^{\frac{9}{2}} b^{25} x^{\frac{9}{2}} + 90 a^{\frac{7}{2}} b^{26} x^{\frac{7}{2}} + 15 a^{\frac{5}{2}} b^{27} x^{\frac{5}{2}}}"," ",0,"-256*a**(21/2)*b**(33/2)*x**8*sqrt(a*x/b + 1)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) - 1408*a**(19/2)*b**(35/2)*x**7*sqrt(a*x/b + 1)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) - 3168*a**(17/2)*b**(37/2)*x**6*sqrt(a*x/b + 1)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) - 3696*a**(15/2)*b**(39/2)*x**5*sqrt(a*x/b + 1)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) - 2310*a**(13/2)*b**(41/2)*x**4*sqrt(a*x/b + 1)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) - 696*a**(11/2)*b**(43/2)*x**3*sqrt(a*x/b + 1)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) - 68*a**(9/2)*b**(45/2)*x**2*sqrt(a*x/b + 1)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) - 8*a**(7/2)*b**(47/2)*x*sqrt(a*x/b + 1)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) - 6*a**(5/2)*b**(49/2)*sqrt(a*x/b + 1)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) + 256*a**11*b**16*x**(17/2)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) + 1536*a**10*b**17*x**(15/2)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) + 3840*a**9*b**18*x**(13/2)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) + 5120*a**8*b**19*x**(11/2)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) + 3840*a**7*b**20*x**(9/2)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) + 1536*a**6*b**21*x**(7/2)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2)) + 256*a**5*b**22*x**(5/2)/(15*a**(17/2)*b**21*x**(17/2) + 90*a**(15/2)*b**22*x**(15/2) + 225*a**(13/2)*b**23*x**(13/2) + 300*a**(11/2)*b**24*x**(11/2) + 225*a**(9/2)*b**25*x**(9/2) + 90*a**(7/2)*b**26*x**(7/2) + 15*a**(5/2)*b**27*x**(5/2))","B",0
1751,1,9263,0,11.993252," ","integrate(1/(a+b/x)**(5/2)/x**7,x)","\frac{512 a^{\frac{43}{2}} b^{\frac{91}{2}} x^{18} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{7424 a^{\frac{41}{2}} b^{\frac{93}{2}} x^{17} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{50112 a^{\frac{39}{2}} b^{\frac{95}{2}} x^{16} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{208800 a^{\frac{37}{2}} b^{\frac{97}{2}} x^{15} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{600300 a^{\frac{35}{2}} b^{\frac{99}{2}} x^{14} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{1260630 a^{\frac{33}{2}} b^{\frac{101}{2}} x^{13} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{1995994 a^{\frac{31}{2}} b^{\frac{103}{2}} x^{12} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{2423668 a^{\frac{29}{2}} b^{\frac{105}{2}} x^{11} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{2271984 a^{\frac{27}{2}} b^{\frac{107}{2}} x^{10} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{1640210 a^{\frac{25}{2}} b^{\frac{109}{2}} x^{9} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{900614 a^{\frac{23}{2}} b^{\frac{111}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{365976 a^{\frac{21}{2}} b^{\frac{113}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{103740 a^{\frac{19}{2}} b^{\frac{115}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} + \frac{17178 a^{\frac{17}{2}} b^{\frac{117}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{90 a^{\frac{15}{2}} b^{\frac{119}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{1004 a^{\frac{13}{2}} b^{\frac{121}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{344 a^{\frac{11}{2}} b^{\frac{123}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{66 a^{\frac{9}{2}} b^{\frac{125}{2}} x \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{6 a^{\frac{7}{2}} b^{\frac{127}{2}} \sqrt{\frac{a x}{b} + 1}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{512 a^{22} b^{45} x^{\frac{37}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{7680 a^{21} b^{46} x^{\frac{35}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{53760 a^{20} b^{47} x^{\frac{33}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{232960 a^{19} b^{48} x^{\frac{31}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{698880 a^{18} b^{49} x^{\frac{29}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{1537536 a^{17} b^{50} x^{\frac{27}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{2562560 a^{16} b^{51} x^{\frac{25}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{3294720 a^{15} b^{52} x^{\frac{23}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{3294720 a^{14} b^{53} x^{\frac{21}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{2562560 a^{13} b^{54} x^{\frac{19}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{1537536 a^{12} b^{55} x^{\frac{17}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{698880 a^{11} b^{56} x^{\frac{15}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{232960 a^{10} b^{57} x^{\frac{13}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{53760 a^{9} b^{58} x^{\frac{11}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{7680 a^{8} b^{59} x^{\frac{9}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}} - \frac{512 a^{7} b^{60} x^{\frac{7}{2}}}{21 a^{\frac{37}{2}} b^{51} x^{\frac{37}{2}} + 315 a^{\frac{35}{2}} b^{52} x^{\frac{35}{2}} + 2205 a^{\frac{33}{2}} b^{53} x^{\frac{33}{2}} + 9555 a^{\frac{31}{2}} b^{54} x^{\frac{31}{2}} + 28665 a^{\frac{29}{2}} b^{55} x^{\frac{29}{2}} + 63063 a^{\frac{27}{2}} b^{56} x^{\frac{27}{2}} + 105105 a^{\frac{25}{2}} b^{57} x^{\frac{25}{2}} + 135135 a^{\frac{23}{2}} b^{58} x^{\frac{23}{2}} + 135135 a^{\frac{21}{2}} b^{59} x^{\frac{21}{2}} + 105105 a^{\frac{19}{2}} b^{60} x^{\frac{19}{2}} + 63063 a^{\frac{17}{2}} b^{61} x^{\frac{17}{2}} + 28665 a^{\frac{15}{2}} b^{62} x^{\frac{15}{2}} + 9555 a^{\frac{13}{2}} b^{63} x^{\frac{13}{2}} + 2205 a^{\frac{11}{2}} b^{64} x^{\frac{11}{2}} + 315 a^{\frac{9}{2}} b^{65} x^{\frac{9}{2}} + 21 a^{\frac{7}{2}} b^{66} x^{\frac{7}{2}}}"," ",0,"512*a**(43/2)*b**(91/2)*x**18*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 7424*a**(41/2)*b**(93/2)*x**17*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 50112*a**(39/2)*b**(95/2)*x**16*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 208800*a**(37/2)*b**(97/2)*x**15*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 600300*a**(35/2)*b**(99/2)*x**14*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 1260630*a**(33/2)*b**(101/2)*x**13*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 1995994*a**(31/2)*b**(103/2)*x**12*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 2423668*a**(29/2)*b**(105/2)*x**11*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 2271984*a**(27/2)*b**(107/2)*x**10*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 1640210*a**(25/2)*b**(109/2)*x**9*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 900614*a**(23/2)*b**(111/2)*x**8*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 365976*a**(21/2)*b**(113/2)*x**7*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 103740*a**(19/2)*b**(115/2)*x**6*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) + 17178*a**(17/2)*b**(117/2)*x**5*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 90*a**(15/2)*b**(119/2)*x**4*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 1004*a**(13/2)*b**(121/2)*x**3*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 344*a**(11/2)*b**(123/2)*x**2*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 66*a**(9/2)*b**(125/2)*x*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 6*a**(7/2)*b**(127/2)*sqrt(a*x/b + 1)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 512*a**22*b**45*x**(37/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 7680*a**21*b**46*x**(35/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 53760*a**20*b**47*x**(33/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 232960*a**19*b**48*x**(31/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 698880*a**18*b**49*x**(29/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 1537536*a**17*b**50*x**(27/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 2562560*a**16*b**51*x**(25/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 3294720*a**15*b**52*x**(23/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 3294720*a**14*b**53*x**(21/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 2562560*a**13*b**54*x**(19/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 1537536*a**12*b**55*x**(17/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 698880*a**11*b**56*x**(15/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 232960*a**10*b**57*x**(13/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 53760*a**9*b**58*x**(11/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 7680*a**8*b**59*x**(9/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2)) - 512*a**7*b**60*x**(7/2)/(21*a**(37/2)*b**51*x**(37/2) + 315*a**(35/2)*b**52*x**(35/2) + 2205*a**(33/2)*b**53*x**(33/2) + 9555*a**(31/2)*b**54*x**(31/2) + 28665*a**(29/2)*b**55*x**(29/2) + 63063*a**(27/2)*b**56*x**(27/2) + 105105*a**(25/2)*b**57*x**(25/2) + 135135*a**(23/2)*b**58*x**(23/2) + 135135*a**(21/2)*b**59*x**(21/2) + 105105*a**(19/2)*b**60*x**(19/2) + 63063*a**(17/2)*b**61*x**(17/2) + 28665*a**(15/2)*b**62*x**(15/2) + 9555*a**(13/2)*b**63*x**(13/2) + 2205*a**(11/2)*b**64*x**(11/2) + 315*a**(9/2)*b**65*x**(9/2) + 21*a**(7/2)*b**66*x**(7/2))","B",0
1752,1,518,0,38.789033," ","integrate((a+b/x)**(1/2)*x**(7/2),x)","\frac{70 a^{7} b^{\frac{19}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{315 a^{7} b^{9} x^{3} + 945 a^{6} b^{10} x^{2} + 945 a^{5} b^{11} x + 315 a^{4} b^{12}} + \frac{220 a^{6} b^{\frac{21}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{315 a^{7} b^{9} x^{3} + 945 a^{6} b^{10} x^{2} + 945 a^{5} b^{11} x + 315 a^{4} b^{12}} + \frac{228 a^{5} b^{\frac{23}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{315 a^{7} b^{9} x^{3} + 945 a^{6} b^{10} x^{2} + 945 a^{5} b^{11} x + 315 a^{4} b^{12}} + \frac{80 a^{4} b^{\frac{25}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{315 a^{7} b^{9} x^{3} + 945 a^{6} b^{10} x^{2} + 945 a^{5} b^{11} x + 315 a^{4} b^{12}} - \frac{10 a^{3} b^{\frac{27}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{315 a^{7} b^{9} x^{3} + 945 a^{6} b^{10} x^{2} + 945 a^{5} b^{11} x + 315 a^{4} b^{12}} - \frac{60 a^{2} b^{\frac{29}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{315 a^{7} b^{9} x^{3} + 945 a^{6} b^{10} x^{2} + 945 a^{5} b^{11} x + 315 a^{4} b^{12}} - \frac{80 a b^{\frac{31}{2}} x \sqrt{\frac{a x}{b} + 1}}{315 a^{7} b^{9} x^{3} + 945 a^{6} b^{10} x^{2} + 945 a^{5} b^{11} x + 315 a^{4} b^{12}} - \frac{32 b^{\frac{33}{2}} \sqrt{\frac{a x}{b} + 1}}{315 a^{7} b^{9} x^{3} + 945 a^{6} b^{10} x^{2} + 945 a^{5} b^{11} x + 315 a^{4} b^{12}}"," ",0,"70*a**7*b**(19/2)*x**7*sqrt(a*x/b + 1)/(315*a**7*b**9*x**3 + 945*a**6*b**10*x**2 + 945*a**5*b**11*x + 315*a**4*b**12) + 220*a**6*b**(21/2)*x**6*sqrt(a*x/b + 1)/(315*a**7*b**9*x**3 + 945*a**6*b**10*x**2 + 945*a**5*b**11*x + 315*a**4*b**12) + 228*a**5*b**(23/2)*x**5*sqrt(a*x/b + 1)/(315*a**7*b**9*x**3 + 945*a**6*b**10*x**2 + 945*a**5*b**11*x + 315*a**4*b**12) + 80*a**4*b**(25/2)*x**4*sqrt(a*x/b + 1)/(315*a**7*b**9*x**3 + 945*a**6*b**10*x**2 + 945*a**5*b**11*x + 315*a**4*b**12) - 10*a**3*b**(27/2)*x**3*sqrt(a*x/b + 1)/(315*a**7*b**9*x**3 + 945*a**6*b**10*x**2 + 945*a**5*b**11*x + 315*a**4*b**12) - 60*a**2*b**(29/2)*x**2*sqrt(a*x/b + 1)/(315*a**7*b**9*x**3 + 945*a**6*b**10*x**2 + 945*a**5*b**11*x + 315*a**4*b**12) - 80*a*b**(31/2)*x*sqrt(a*x/b + 1)/(315*a**7*b**9*x**3 + 945*a**6*b**10*x**2 + 945*a**5*b**11*x + 315*a**4*b**12) - 32*b**(33/2)*sqrt(a*x/b + 1)/(315*a**7*b**9*x**3 + 945*a**6*b**10*x**2 + 945*a**5*b**11*x + 315*a**4*b**12)","B",0
1753,1,314,0,16.439359," ","integrate((a+b/x)**(1/2)*x**(5/2),x)","\frac{30 a^{5} b^{\frac{9}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{105 a^{5} b^{4} x^{2} + 210 a^{4} b^{5} x + 105 a^{3} b^{6}} + \frac{66 a^{4} b^{\frac{11}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{105 a^{5} b^{4} x^{2} + 210 a^{4} b^{5} x + 105 a^{3} b^{6}} + \frac{34 a^{3} b^{\frac{13}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{105 a^{5} b^{4} x^{2} + 210 a^{4} b^{5} x + 105 a^{3} b^{6}} + \frac{6 a^{2} b^{\frac{15}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{105 a^{5} b^{4} x^{2} + 210 a^{4} b^{5} x + 105 a^{3} b^{6}} + \frac{24 a b^{\frac{17}{2}} x \sqrt{\frac{a x}{b} + 1}}{105 a^{5} b^{4} x^{2} + 210 a^{4} b^{5} x + 105 a^{3} b^{6}} + \frac{16 b^{\frac{19}{2}} \sqrt{\frac{a x}{b} + 1}}{105 a^{5} b^{4} x^{2} + 210 a^{4} b^{5} x + 105 a^{3} b^{6}}"," ",0,"30*a**5*b**(9/2)*x**5*sqrt(a*x/b + 1)/(105*a**5*b**4*x**2 + 210*a**4*b**5*x + 105*a**3*b**6) + 66*a**4*b**(11/2)*x**4*sqrt(a*x/b + 1)/(105*a**5*b**4*x**2 + 210*a**4*b**5*x + 105*a**3*b**6) + 34*a**3*b**(13/2)*x**3*sqrt(a*x/b + 1)/(105*a**5*b**4*x**2 + 210*a**4*b**5*x + 105*a**3*b**6) + 6*a**2*b**(15/2)*x**2*sqrt(a*x/b + 1)/(105*a**5*b**4*x**2 + 210*a**4*b**5*x + 105*a**3*b**6) + 24*a*b**(17/2)*x*sqrt(a*x/b + 1)/(105*a**5*b**4*x**2 + 210*a**4*b**5*x + 105*a**3*b**6) + 16*b**(19/2)*sqrt(a*x/b + 1)/(105*a**5*b**4*x**2 + 210*a**4*b**5*x + 105*a**3*b**6)","B",0
1754,1,65,0,5.238363," ","integrate((a+b/x)**(1/2)*x**(3/2),x)","\frac{2 \sqrt{b} x^{2} \sqrt{\frac{a x}{b} + 1}}{5} + \frac{2 b^{\frac{3}{2}} x \sqrt{\frac{a x}{b} + 1}}{15 a} - \frac{4 b^{\frac{5}{2}} \sqrt{\frac{a x}{b} + 1}}{15 a^{2}}"," ",0,"2*sqrt(b)*x**2*sqrt(a*x/b + 1)/5 + 2*b**(3/2)*x*sqrt(a*x/b + 1)/(15*a) - 4*b**(5/2)*sqrt(a*x/b + 1)/(15*a**2)","A",0
1755,1,39,0,2.062697," ","integrate((a+b/x)**(1/2)*x**(1/2),x)","\frac{2 \sqrt{b} x \sqrt{\frac{a x}{b} + 1}}{3} + \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a x}{b} + 1}}{3 a}"," ",0,"2*sqrt(b)*x*sqrt(a*x/b + 1)/3 + 2*b**(3/2)*sqrt(a*x/b + 1)/(3*a)","B",0
1756,1,68,0,2.409303," ","integrate((a+b/x)**(1/2)/x**(1/2),x)","\frac{2 \sqrt{a} \sqrt{x}}{\sqrt{1 + \frac{b}{a x}}} - 2 \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)} + \frac{2 b}{\sqrt{a} \sqrt{x} \sqrt{1 + \frac{b}{a x}}}"," ",0,"2*sqrt(a)*sqrt(x)/sqrt(1 + b/(a*x)) - 2*sqrt(b)*asinh(sqrt(b)/(sqrt(a)*sqrt(x))) + 2*b/(sqrt(a)*sqrt(x)*sqrt(1 + b/(a*x)))","A",0
1757,1,44,0,3.477990," ","integrate((a+b/x)**(1/2)/x**(3/2),x)","- \frac{\sqrt{a} \sqrt{1 + \frac{b}{a x}}}{\sqrt{x}} - \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{\sqrt{b}}"," ",0,"-sqrt(a)*sqrt(1 + b/(a*x))/sqrt(x) - a*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/sqrt(b)","A",0
1758,1,97,0,8.938098," ","integrate((a+b/x)**(1/2)/x**(5/2),x)","- \frac{a^{\frac{3}{2}}}{4 b \sqrt{x} \sqrt{1 + \frac{b}{a x}}} - \frac{3 \sqrt{a}}{4 x^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}} + \frac{a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{4 b^{\frac{3}{2}}} - \frac{b}{2 \sqrt{a} x^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}}"," ",0,"-a**(3/2)/(4*b*sqrt(x)*sqrt(1 + b/(a*x))) - 3*sqrt(a)/(4*x**(3/2)*sqrt(1 + b/(a*x))) + a**2*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/(4*b**(3/2)) - b/(2*sqrt(a)*x**(5/2)*sqrt(1 + b/(a*x)))","A",0
1759,1,122,0,20.965247," ","integrate((a+b/x)**(1/2)/x**(7/2),x)","\frac{a^{\frac{5}{2}}}{8 b^{2} \sqrt{x} \sqrt{1 + \frac{b}{a x}}} + \frac{a^{\frac{3}{2}}}{24 b x^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}} - \frac{5 \sqrt{a}}{12 x^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}} - \frac{a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{8 b^{\frac{5}{2}}} - \frac{b}{3 \sqrt{a} x^{\frac{7}{2}} \sqrt{1 + \frac{b}{a x}}}"," ",0,"a**(5/2)/(8*b**2*sqrt(x)*sqrt(1 + b/(a*x))) + a**(3/2)/(24*b*x**(3/2)*sqrt(1 + b/(a*x))) - 5*sqrt(a)/(12*x**(5/2)*sqrt(1 + b/(a*x))) - a**3*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/(8*b**(5/2)) - b/(3*sqrt(a)*x**(7/2)*sqrt(1 + b/(a*x)))","A",0
1760,1,585,0,171.285767," ","integrate((a+b/x)**(3/2)*x**(9/2),x)","\frac{210 a^{8} b^{\frac{19}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} + \frac{910 a^{7} b^{\frac{21}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} + \frac{1480 a^{6} b^{\frac{23}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} + \frac{1068 a^{5} b^{\frac{25}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} + \frac{290 a^{4} b^{\frac{27}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} - \frac{10 a^{3} b^{\frac{29}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} - \frac{60 a^{2} b^{\frac{31}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} - \frac{80 a b^{\frac{33}{2}} x \sqrt{\frac{a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} - \frac{32 b^{\frac{35}{2}} \sqrt{\frac{a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}}"," ",0,"210*a**8*b**(19/2)*x**8*sqrt(a*x/b + 1)/(1155*a**7*b**9*x**3 + 3465*a**6*b**10*x**2 + 3465*a**5*b**11*x + 1155*a**4*b**12) + 910*a**7*b**(21/2)*x**7*sqrt(a*x/b + 1)/(1155*a**7*b**9*x**3 + 3465*a**6*b**10*x**2 + 3465*a**5*b**11*x + 1155*a**4*b**12) + 1480*a**6*b**(23/2)*x**6*sqrt(a*x/b + 1)/(1155*a**7*b**9*x**3 + 3465*a**6*b**10*x**2 + 3465*a**5*b**11*x + 1155*a**4*b**12) + 1068*a**5*b**(25/2)*x**5*sqrt(a*x/b + 1)/(1155*a**7*b**9*x**3 + 3465*a**6*b**10*x**2 + 3465*a**5*b**11*x + 1155*a**4*b**12) + 290*a**4*b**(27/2)*x**4*sqrt(a*x/b + 1)/(1155*a**7*b**9*x**3 + 3465*a**6*b**10*x**2 + 3465*a**5*b**11*x + 1155*a**4*b**12) - 10*a**3*b**(29/2)*x**3*sqrt(a*x/b + 1)/(1155*a**7*b**9*x**3 + 3465*a**6*b**10*x**2 + 3465*a**5*b**11*x + 1155*a**4*b**12) - 60*a**2*b**(31/2)*x**2*sqrt(a*x/b + 1)/(1155*a**7*b**9*x**3 + 3465*a**6*b**10*x**2 + 3465*a**5*b**11*x + 1155*a**4*b**12) - 80*a*b**(33/2)*x*sqrt(a*x/b + 1)/(1155*a**7*b**9*x**3 + 3465*a**6*b**10*x**2 + 3465*a**5*b**11*x + 1155*a**4*b**12) - 32*b**(35/2)*sqrt(a*x/b + 1)/(1155*a**7*b**9*x**3 + 3465*a**6*b**10*x**2 + 3465*a**5*b**11*x + 1155*a**4*b**12)","B",0
1761,1,369,0,64.429499," ","integrate((a+b/x)**(3/2)*x**(7/2),x)","\frac{70 a^{6} b^{\frac{9}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{315 a^{5} b^{4} x^{2} + 630 a^{4} b^{5} x + 315 a^{3} b^{6}} + \frac{240 a^{5} b^{\frac{11}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{315 a^{5} b^{4} x^{2} + 630 a^{4} b^{5} x + 315 a^{3} b^{6}} + \frac{276 a^{4} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{315 a^{5} b^{4} x^{2} + 630 a^{4} b^{5} x + 315 a^{3} b^{6}} + \frac{104 a^{3} b^{\frac{15}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{315 a^{5} b^{4} x^{2} + 630 a^{4} b^{5} x + 315 a^{3} b^{6}} + \frac{6 a^{2} b^{\frac{17}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{315 a^{5} b^{4} x^{2} + 630 a^{4} b^{5} x + 315 a^{3} b^{6}} + \frac{24 a b^{\frac{19}{2}} x \sqrt{\frac{a x}{b} + 1}}{315 a^{5} b^{4} x^{2} + 630 a^{4} b^{5} x + 315 a^{3} b^{6}} + \frac{16 b^{\frac{21}{2}} \sqrt{\frac{a x}{b} + 1}}{315 a^{5} b^{4} x^{2} + 630 a^{4} b^{5} x + 315 a^{3} b^{6}}"," ",0,"70*a**6*b**(9/2)*x**6*sqrt(a*x/b + 1)/(315*a**5*b**4*x**2 + 630*a**4*b**5*x + 315*a**3*b**6) + 240*a**5*b**(11/2)*x**5*sqrt(a*x/b + 1)/(315*a**5*b**4*x**2 + 630*a**4*b**5*x + 315*a**3*b**6) + 276*a**4*b**(13/2)*x**4*sqrt(a*x/b + 1)/(315*a**5*b**4*x**2 + 630*a**4*b**5*x + 315*a**3*b**6) + 104*a**3*b**(15/2)*x**3*sqrt(a*x/b + 1)/(315*a**5*b**4*x**2 + 630*a**4*b**5*x + 315*a**3*b**6) + 6*a**2*b**(17/2)*x**2*sqrt(a*x/b + 1)/(315*a**5*b**4*x**2 + 630*a**4*b**5*x + 315*a**3*b**6) + 24*a*b**(19/2)*x*sqrt(a*x/b + 1)/(315*a**5*b**4*x**2 + 630*a**4*b**5*x + 315*a**3*b**6) + 16*b**(21/2)*sqrt(a*x/b + 1)/(315*a**5*b**4*x**2 + 630*a**4*b**5*x + 315*a**3*b**6)","B",0
1762,1,88,0,27.921800," ","integrate((a+b/x)**(3/2)*x**(5/2),x)","\frac{2 a \sqrt{b} x^{3} \sqrt{\frac{a x}{b} + 1}}{7} + \frac{16 b^{\frac{3}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{35} + \frac{2 b^{\frac{5}{2}} x \sqrt{\frac{a x}{b} + 1}}{35 a} - \frac{4 b^{\frac{7}{2}} \sqrt{\frac{a x}{b} + 1}}{35 a^{2}}"," ",0,"2*a*sqrt(b)*x**3*sqrt(a*x/b + 1)/7 + 16*b**(3/2)*x**2*sqrt(a*x/b + 1)/35 + 2*b**(5/2)*x*sqrt(a*x/b + 1)/(35*a) - 4*b**(7/2)*sqrt(a*x/b + 1)/(35*a**2)","B",0
1763,1,63,0,9.456560," ","integrate((a+b/x)**(3/2)*x**(3/2),x)","\frac{2 a \sqrt{b} x^{2} \sqrt{\frac{a x}{b} + 1}}{5} + \frac{4 b^{\frac{3}{2}} x \sqrt{\frac{a x}{b} + 1}}{5} + \frac{2 b^{\frac{5}{2}} \sqrt{\frac{a x}{b} + 1}}{5 a}"," ",0,"2*a*sqrt(b)*x**2*sqrt(a*x/b + 1)/5 + 4*b**(3/2)*x*sqrt(a*x/b + 1)/5 + 2*b**(5/2)*sqrt(a*x/b + 1)/(5*a)","B",0
1764,1,71,0,6.738393," ","integrate((a+b/x)**(3/2)*x**(1/2),x)","\frac{2 a \sqrt{b} x \sqrt{\frac{a x}{b} + 1}}{3} + \frac{8 b^{\frac{3}{2}} \sqrt{\frac{a x}{b} + 1}}{3} + b^{\frac{3}{2}} \log{\left(\frac{a x}{b} \right)} - 2 b^{\frac{3}{2}} \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}"," ",0,"2*a*sqrt(b)*x*sqrt(a*x/b + 1)/3 + 8*b**(3/2)*sqrt(a*x/b + 1)/3 + b**(3/2)*log(a*x/b) - 2*b**(3/2)*log(sqrt(a*x/b + 1) + 1)","A",0
1765,1,92,0,9.084222," ","integrate((a+b/x)**(3/2)/x**(1/2),x)","\frac{2 a^{\frac{3}{2}} \sqrt{x}}{\sqrt{1 + \frac{b}{a x}}} + \frac{\sqrt{a} b}{\sqrt{x} \sqrt{1 + \frac{b}{a x}}} - 3 a \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)} - \frac{b^{2}}{\sqrt{a} x^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}}"," ",0,"2*a**(3/2)*sqrt(x)/sqrt(1 + b/(a*x)) + sqrt(a)*b/(sqrt(x)*sqrt(1 + b/(a*x))) - 3*a*sqrt(b)*asinh(sqrt(b)/(sqrt(a)*sqrt(x))) - b**2/(sqrt(a)*x**(3/2)*sqrt(1 + b/(a*x)))","A",0
1766,1,76,0,9.025691," ","integrate((a+b/x)**(3/2)/x**(3/2),x)","- \frac{5 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}}{4 \sqrt{x}} - \frac{\sqrt{a} b \sqrt{1 + \frac{b}{a x}}}{2 x^{\frac{3}{2}}} - \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{4 \sqrt{b}}"," ",0,"-5*a**(3/2)*sqrt(1 + b/(a*x))/(4*sqrt(x)) - sqrt(a)*b*sqrt(1 + b/(a*x))/(2*x**(3/2)) - 3*a**2*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/(4*sqrt(b))","A",0
1767,1,124,0,14.318223," ","integrate((a+b/x)**(3/2)/x**(5/2),x)","- \frac{a^{\frac{5}{2}}}{8 b \sqrt{x} \sqrt{1 + \frac{b}{a x}}} - \frac{17 a^{\frac{3}{2}}}{24 x^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}} - \frac{11 \sqrt{a} b}{12 x^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}} + \frac{a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{8 b^{\frac{3}{2}}} - \frac{b^{2}}{3 \sqrt{a} x^{\frac{7}{2}} \sqrt{1 + \frac{b}{a x}}}"," ",0,"-a**(5/2)/(8*b*sqrt(x)*sqrt(1 + b/(a*x))) - 17*a**(3/2)/(24*x**(3/2)*sqrt(1 + b/(a*x))) - 11*sqrt(a)*b/(12*x**(5/2)*sqrt(1 + b/(a*x))) + a**3*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/(8*b**(3/2)) - b**2/(3*sqrt(a)*x**(7/2)*sqrt(1 + b/(a*x)))","A",0
1768,-1,0,0,0.000000," ","integrate((a+b/x)**(5/2)*x**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1769,-1,0,0,0.000000," ","integrate((a+b/x)**(5/2)*x**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1770,1,114,0,98.842807," ","integrate((a+b/x)**(5/2)*x**(7/2),x)","\frac{2 a^{2} \sqrt{b} x^{4} \sqrt{\frac{a x}{b} + 1}}{9} + \frac{38 a b^{\frac{3}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{63} + \frac{10 b^{\frac{5}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{21} + \frac{2 b^{\frac{7}{2}} x \sqrt{\frac{a x}{b} + 1}}{63 a} - \frac{4 b^{\frac{9}{2}} \sqrt{\frac{a x}{b} + 1}}{63 a^{2}}"," ",0,"2*a**2*sqrt(b)*x**4*sqrt(a*x/b + 1)/9 + 38*a*b**(3/2)*x**3*sqrt(a*x/b + 1)/63 + 10*b**(5/2)*x**2*sqrt(a*x/b + 1)/21 + 2*b**(7/2)*x*sqrt(a*x/b + 1)/(63*a) - 4*b**(9/2)*sqrt(a*x/b + 1)/(63*a**2)","B",0
1771,1,88,0,40.238541," ","integrate((a+b/x)**(5/2)*x**(5/2),x)","\frac{2 a^{2} \sqrt{b} x^{3} \sqrt{\frac{a x}{b} + 1}}{7} + \frac{6 a b^{\frac{3}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{7} + \frac{6 b^{\frac{5}{2}} x \sqrt{\frac{a x}{b} + 1}}{7} + \frac{2 b^{\frac{7}{2}} \sqrt{\frac{a x}{b} + 1}}{7 a}"," ",0,"2*a**2*sqrt(b)*x**3*sqrt(a*x/b + 1)/7 + 6*a*b**(3/2)*x**2*sqrt(a*x/b + 1)/7 + 6*b**(5/2)*x*sqrt(a*x/b + 1)/7 + 2*b**(7/2)*sqrt(a*x/b + 1)/(7*a)","B",0
1772,1,97,0,26.952965," ","integrate((a+b/x)**(5/2)*x**(3/2),x)","\frac{2 a^{2} \sqrt{b} x^{2} \sqrt{\frac{a x}{b} + 1}}{5} + \frac{22 a b^{\frac{3}{2}} x \sqrt{\frac{a x}{b} + 1}}{15} + \frac{46 b^{\frac{5}{2}} \sqrt{\frac{a x}{b} + 1}}{15} + b^{\frac{5}{2}} \log{\left(\frac{a x}{b} \right)} - 2 b^{\frac{5}{2}} \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}"," ",0,"2*a**2*sqrt(b)*x**2*sqrt(a*x/b + 1)/5 + 22*a*b**(3/2)*x*sqrt(a*x/b + 1)/15 + 46*b**(5/2)*sqrt(a*x/b + 1)/15 + b**(5/2)*log(a*x/b) - 2*b**(5/2)*log(sqrt(a*x/b + 1) + 1)","A",0
1773,1,99,0,17.417025," ","integrate((a+b/x)**(5/2)*x**(1/2),x)","\frac{2 a^{2} \sqrt{b} x \sqrt{\frac{a x}{b} + 1}}{3} + \frac{14 a b^{\frac{3}{2}} \sqrt{\frac{a x}{b} + 1}}{3} + \frac{5 a b^{\frac{3}{2}} \log{\left(\frac{a x}{b} \right)}}{2} - 5 a b^{\frac{3}{2}} \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)} - \frac{b^{\frac{5}{2}} \sqrt{\frac{a x}{b} + 1}}{x}"," ",0,"2*a**2*sqrt(b)*x*sqrt(a*x/b + 1)/3 + 14*a*b**(3/2)*sqrt(a*x/b + 1)/3 + 5*a*b**(3/2)*log(a*x/b)/2 - 5*a*b**(3/2)*log(sqrt(a*x/b + 1) + 1) - b**(5/2)*sqrt(a*x/b + 1)/x","A",0
1774,1,126,0,13.985690," ","integrate((a+b/x)**(5/2)/x**(1/2),x)","\frac{2 a^{\frac{5}{2}} \sqrt{x}}{\sqrt{1 + \frac{b}{a x}}} - \frac{a^{\frac{3}{2}} b}{4 \sqrt{x} \sqrt{1 + \frac{b}{a x}}} - \frac{11 \sqrt{a} b^{2}}{4 x^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}} - \frac{15 a^{2} \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{4} - \frac{b^{3}}{2 \sqrt{a} x^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}}"," ",0,"2*a**(5/2)*sqrt(x)/sqrt(1 + b/(a*x)) - a**(3/2)*b/(4*sqrt(x)*sqrt(1 + b/(a*x))) - 11*sqrt(a)*b**2/(4*x**(3/2)*sqrt(1 + b/(a*x))) - 15*a**2*sqrt(b)*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/4 - b**3/(2*sqrt(a)*x**(5/2)*sqrt(1 + b/(a*x)))","A",0
1775,1,104,0,14.402112," ","integrate((a+b/x)**(5/2)/x**(3/2),x)","- \frac{11 a^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}}{8 \sqrt{x}} - \frac{13 a^{\frac{3}{2}} b \sqrt{1 + \frac{b}{a x}}}{12 x^{\frac{3}{2}}} - \frac{\sqrt{a} b^{2} \sqrt{1 + \frac{b}{a x}}}{3 x^{\frac{5}{2}}} - \frac{5 a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{8 \sqrt{b}}"," ",0,"-11*a**(5/2)*sqrt(1 + b/(a*x))/(8*sqrt(x)) - 13*a**(3/2)*b*sqrt(1 + b/(a*x))/(12*x**(3/2)) - sqrt(a)*b**2*sqrt(1 + b/(a*x))/(3*x**(5/2)) - 5*a**3*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/(8*sqrt(b))","A",0
1776,1,155,0,17.396910," ","integrate((a+b/x)**(5/2)/x**(5/2),x)","- \frac{5 a^{\frac{7}{2}}}{64 b \sqrt{x} \sqrt{1 + \frac{b}{a x}}} - \frac{133 a^{\frac{5}{2}}}{192 x^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}} - \frac{127 a^{\frac{3}{2}} b}{96 x^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}} - \frac{23 \sqrt{a} b^{2}}{24 x^{\frac{7}{2}} \sqrt{1 + \frac{b}{a x}}} + \frac{5 a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{64 b^{\frac{3}{2}}} - \frac{b^{3}}{4 \sqrt{a} x^{\frac{9}{2}} \sqrt{1 + \frac{b}{a x}}}"," ",0,"-5*a**(7/2)/(64*b*sqrt(x)*sqrt(1 + b/(a*x))) - 133*a**(5/2)/(192*x**(3/2)*sqrt(1 + b/(a*x))) - 127*a**(3/2)*b/(96*x**(5/2)*sqrt(1 + b/(a*x))) - 23*sqrt(a)*b**2/(24*x**(7/2)*sqrt(1 + b/(a*x))) + 5*a**4*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/(64*b**(3/2)) - b**3/(4*sqrt(a)*x**(9/2)*sqrt(1 + b/(a*x)))","A",0
1777,1,692,0,31.825770," ","integrate(x**(7/2)/(a+b/x)**(1/2),x)","\frac{70 a^{8} b^{\frac{33}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{315 a^{9} b^{16} x^{4} + 1260 a^{8} b^{17} x^{3} + 1890 a^{7} b^{18} x^{2} + 1260 a^{6} b^{19} x + 315 a^{5} b^{20}} + \frac{200 a^{7} b^{\frac{35}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{315 a^{9} b^{16} x^{4} + 1260 a^{8} b^{17} x^{3} + 1890 a^{7} b^{18} x^{2} + 1260 a^{6} b^{19} x + 315 a^{5} b^{20}} + \frac{196 a^{6} b^{\frac{37}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{315 a^{9} b^{16} x^{4} + 1260 a^{8} b^{17} x^{3} + 1890 a^{7} b^{18} x^{2} + 1260 a^{6} b^{19} x + 315 a^{5} b^{20}} + \frac{56 a^{5} b^{\frac{39}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{315 a^{9} b^{16} x^{4} + 1260 a^{8} b^{17} x^{3} + 1890 a^{7} b^{18} x^{2} + 1260 a^{6} b^{19} x + 315 a^{5} b^{20}} + \frac{70 a^{4} b^{\frac{41}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{315 a^{9} b^{16} x^{4} + 1260 a^{8} b^{17} x^{3} + 1890 a^{7} b^{18} x^{2} + 1260 a^{6} b^{19} x + 315 a^{5} b^{20}} + \frac{560 a^{3} b^{\frac{43}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{315 a^{9} b^{16} x^{4} + 1260 a^{8} b^{17} x^{3} + 1890 a^{7} b^{18} x^{2} + 1260 a^{6} b^{19} x + 315 a^{5} b^{20}} + \frac{1120 a^{2} b^{\frac{45}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{315 a^{9} b^{16} x^{4} + 1260 a^{8} b^{17} x^{3} + 1890 a^{7} b^{18} x^{2} + 1260 a^{6} b^{19} x + 315 a^{5} b^{20}} + \frac{896 a b^{\frac{47}{2}} x \sqrt{\frac{a x}{b} + 1}}{315 a^{9} b^{16} x^{4} + 1260 a^{8} b^{17} x^{3} + 1890 a^{7} b^{18} x^{2} + 1260 a^{6} b^{19} x + 315 a^{5} b^{20}} + \frac{256 b^{\frac{49}{2}} \sqrt{\frac{a x}{b} + 1}}{315 a^{9} b^{16} x^{4} + 1260 a^{8} b^{17} x^{3} + 1890 a^{7} b^{18} x^{2} + 1260 a^{6} b^{19} x + 315 a^{5} b^{20}}"," ",0,"70*a**8*b**(33/2)*x**8*sqrt(a*x/b + 1)/(315*a**9*b**16*x**4 + 1260*a**8*b**17*x**3 + 1890*a**7*b**18*x**2 + 1260*a**6*b**19*x + 315*a**5*b**20) + 200*a**7*b**(35/2)*x**7*sqrt(a*x/b + 1)/(315*a**9*b**16*x**4 + 1260*a**8*b**17*x**3 + 1890*a**7*b**18*x**2 + 1260*a**6*b**19*x + 315*a**5*b**20) + 196*a**6*b**(37/2)*x**6*sqrt(a*x/b + 1)/(315*a**9*b**16*x**4 + 1260*a**8*b**17*x**3 + 1890*a**7*b**18*x**2 + 1260*a**6*b**19*x + 315*a**5*b**20) + 56*a**5*b**(39/2)*x**5*sqrt(a*x/b + 1)/(315*a**9*b**16*x**4 + 1260*a**8*b**17*x**3 + 1890*a**7*b**18*x**2 + 1260*a**6*b**19*x + 315*a**5*b**20) + 70*a**4*b**(41/2)*x**4*sqrt(a*x/b + 1)/(315*a**9*b**16*x**4 + 1260*a**8*b**17*x**3 + 1890*a**7*b**18*x**2 + 1260*a**6*b**19*x + 315*a**5*b**20) + 560*a**3*b**(43/2)*x**3*sqrt(a*x/b + 1)/(315*a**9*b**16*x**4 + 1260*a**8*b**17*x**3 + 1890*a**7*b**18*x**2 + 1260*a**6*b**19*x + 315*a**5*b**20) + 1120*a**2*b**(45/2)*x**2*sqrt(a*x/b + 1)/(315*a**9*b**16*x**4 + 1260*a**8*b**17*x**3 + 1890*a**7*b**18*x**2 + 1260*a**6*b**19*x + 315*a**5*b**20) + 896*a*b**(47/2)*x*sqrt(a*x/b + 1)/(315*a**9*b**16*x**4 + 1260*a**8*b**17*x**3 + 1890*a**7*b**18*x**2 + 1260*a**6*b**19*x + 315*a**5*b**20) + 256*b**(49/2)*sqrt(a*x/b + 1)/(315*a**9*b**16*x**4 + 1260*a**8*b**17*x**3 + 1890*a**7*b**18*x**2 + 1260*a**6*b**19*x + 315*a**5*b**20)","B",0
1778,1,452,0,11.926375," ","integrate(x**(5/2)/(a+b/x)**(1/2),x)","\frac{10 a^{6} b^{\frac{19}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{2} + 105 a^{5} b^{11} x + 35 a^{4} b^{12}} + \frac{18 a^{5} b^{\frac{21}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{2} + 105 a^{5} b^{11} x + 35 a^{4} b^{12}} + \frac{10 a^{4} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{2} + 105 a^{5} b^{11} x + 35 a^{4} b^{12}} - \frac{10 a^{3} b^{\frac{25}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{2} + 105 a^{5} b^{11} x + 35 a^{4} b^{12}} - \frac{60 a^{2} b^{\frac{27}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{2} + 105 a^{5} b^{11} x + 35 a^{4} b^{12}} - \frac{80 a b^{\frac{29}{2}} x \sqrt{\frac{a x}{b} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{2} + 105 a^{5} b^{11} x + 35 a^{4} b^{12}} - \frac{32 b^{\frac{31}{2}} \sqrt{\frac{a x}{b} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{2} + 105 a^{5} b^{11} x + 35 a^{4} b^{12}}"," ",0,"10*a**6*b**(19/2)*x**6*sqrt(a*x/b + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**2 + 105*a**5*b**11*x + 35*a**4*b**12) + 18*a**5*b**(21/2)*x**5*sqrt(a*x/b + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**2 + 105*a**5*b**11*x + 35*a**4*b**12) + 10*a**4*b**(23/2)*x**4*sqrt(a*x/b + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**2 + 105*a**5*b**11*x + 35*a**4*b**12) - 10*a**3*b**(25/2)*x**3*sqrt(a*x/b + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**2 + 105*a**5*b**11*x + 35*a**4*b**12) - 60*a**2*b**(27/2)*x**2*sqrt(a*x/b + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**2 + 105*a**5*b**11*x + 35*a**4*b**12) - 80*a*b**(29/2)*x*sqrt(a*x/b + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**2 + 105*a**5*b**11*x + 35*a**4*b**12) - 32*b**(31/2)*sqrt(a*x/b + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**2 + 105*a**5*b**11*x + 35*a**4*b**12)","B",0
1779,1,260,0,3.827797," ","integrate(x**(3/2)/(a+b/x)**(1/2),x)","\frac{6 a^{4} b^{\frac{9}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{15 a^{5} b^{4} x^{2} + 30 a^{4} b^{5} x + 15 a^{3} b^{6}} + \frac{4 a^{3} b^{\frac{11}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{5} b^{4} x^{2} + 30 a^{4} b^{5} x + 15 a^{3} b^{6}} + \frac{6 a^{2} b^{\frac{13}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{5} b^{4} x^{2} + 30 a^{4} b^{5} x + 15 a^{3} b^{6}} + \frac{24 a b^{\frac{15}{2}} x \sqrt{\frac{a x}{b} + 1}}{15 a^{5} b^{4} x^{2} + 30 a^{4} b^{5} x + 15 a^{3} b^{6}} + \frac{16 b^{\frac{17}{2}} \sqrt{\frac{a x}{b} + 1}}{15 a^{5} b^{4} x^{2} + 30 a^{4} b^{5} x + 15 a^{3} b^{6}}"," ",0,"6*a**4*b**(9/2)*x**4*sqrt(a*x/b + 1)/(15*a**5*b**4*x**2 + 30*a**4*b**5*x + 15*a**3*b**6) + 4*a**3*b**(11/2)*x**3*sqrt(a*x/b + 1)/(15*a**5*b**4*x**2 + 30*a**4*b**5*x + 15*a**3*b**6) + 6*a**2*b**(13/2)*x**2*sqrt(a*x/b + 1)/(15*a**5*b**4*x**2 + 30*a**4*b**5*x + 15*a**3*b**6) + 24*a*b**(15/2)*x*sqrt(a*x/b + 1)/(15*a**5*b**4*x**2 + 30*a**4*b**5*x + 15*a**3*b**6) + 16*b**(17/2)*sqrt(a*x/b + 1)/(15*a**5*b**4*x**2 + 30*a**4*b**5*x + 15*a**3*b**6)","B",0
1780,1,42,0,1.407118," ","integrate(x**(1/2)/(a+b/x)**(1/2),x)","\frac{2 \sqrt{b} x \sqrt{\frac{a x}{b} + 1}}{3 a} - \frac{4 b^{\frac{3}{2}} \sqrt{\frac{a x}{b} + 1}}{3 a^{2}}"," ",0,"2*sqrt(b)*x*sqrt(a*x/b + 1)/(3*a) - 4*b**(3/2)*sqrt(a*x/b + 1)/(3*a**2)","A",0
1781,1,17,0,1.722020," ","integrate(1/(a+b/x)**(1/2)/x**(1/2),x)","\frac{2 \sqrt{b} \sqrt{\frac{a x}{b} + 1}}{a}"," ",0,"2*sqrt(b)*sqrt(a*x/b + 1)/a","A",0
1782,1,24,0,3.238104," ","integrate(1/(a+b/x)**(1/2)/x**(3/2),x)","- \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{\sqrt{b}}"," ",0,"-2*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/sqrt(b)","A",0
1783,1,44,0,8.685410," ","integrate(1/(a+b/x)**(1/2)/x**(5/2),x)","- \frac{\sqrt{a} \sqrt{1 + \frac{b}{a x}}}{b \sqrt{x}} + \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{b^{\frac{3}{2}}}"," ",0,"-sqrt(a)*sqrt(1 + b/(a*x))/(b*sqrt(x)) + a*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/b**(3/2)","A",0
1784,1,102,0,22.608831," ","integrate(1/(a+b/x)**(1/2)/x**(7/2),x)","\frac{3 a^{\frac{3}{2}}}{4 b^{2} \sqrt{x} \sqrt{1 + \frac{b}{a x}}} + \frac{\sqrt{a}}{4 b x^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}} - \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{4 b^{\frac{5}{2}}} - \frac{1}{2 \sqrt{a} x^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}}"," ",0,"3*a**(3/2)/(4*b**2*sqrt(x)*sqrt(1 + b/(a*x))) + sqrt(a)/(4*b*x**(3/2)*sqrt(1 + b/(a*x))) - 3*a**2*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/(4*b**(5/2)) - 1/(2*sqrt(a)*x**(5/2)*sqrt(1 + b/(a*x)))","A",0
1785,1,129,0,56.433194," ","integrate(1/(a+b/x)**(1/2)/x**(9/2),x)","- \frac{5 a^{\frac{5}{2}}}{8 b^{3} \sqrt{x} \sqrt{1 + \frac{b}{a x}}} - \frac{5 a^{\frac{3}{2}}}{24 b^{2} x^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}} + \frac{\sqrt{a}}{12 b x^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}} + \frac{5 a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{8 b^{\frac{7}{2}}} - \frac{1}{3 \sqrt{a} x^{\frac{7}{2}} \sqrt{1 + \frac{b}{a x}}}"," ",0,"-5*a**(5/2)/(8*b**3*sqrt(x)*sqrt(1 + b/(a*x))) - 5*a**(3/2)/(24*b**2*x**(3/2)*sqrt(1 + b/(a*x))) + sqrt(a)/(12*b*x**(5/2)*sqrt(1 + b/(a*x))) + 5*a**3*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/(8*b**(7/2)) - 1/(3*sqrt(a)*x**(7/2)*sqrt(1 + b/(a*x)))","A",0
1786,1,614,0,13.997882," ","integrate(x**(5/2)/(a+b/x)**(3/2),x)","\frac{10 a^{7} b^{\frac{33}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{35 a^{9} b^{16} x^{4} + 140 a^{8} b^{17} x^{3} + 210 a^{7} b^{18} x^{2} + 140 a^{6} b^{19} x + 35 a^{5} b^{20}} + \frac{14 a^{6} b^{\frac{35}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{35 a^{9} b^{16} x^{4} + 140 a^{8} b^{17} x^{3} + 210 a^{7} b^{18} x^{2} + 140 a^{6} b^{19} x + 35 a^{5} b^{20}} + \frac{14 a^{5} b^{\frac{37}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{35 a^{9} b^{16} x^{4} + 140 a^{8} b^{17} x^{3} + 210 a^{7} b^{18} x^{2} + 140 a^{6} b^{19} x + 35 a^{5} b^{20}} - \frac{70 a^{4} b^{\frac{39}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{35 a^{9} b^{16} x^{4} + 140 a^{8} b^{17} x^{3} + 210 a^{7} b^{18} x^{2} + 140 a^{6} b^{19} x + 35 a^{5} b^{20}} - \frac{560 a^{3} b^{\frac{41}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{35 a^{9} b^{16} x^{4} + 140 a^{8} b^{17} x^{3} + 210 a^{7} b^{18} x^{2} + 140 a^{6} b^{19} x + 35 a^{5} b^{20}} - \frac{1120 a^{2} b^{\frac{43}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{35 a^{9} b^{16} x^{4} + 140 a^{8} b^{17} x^{3} + 210 a^{7} b^{18} x^{2} + 140 a^{6} b^{19} x + 35 a^{5} b^{20}} - \frac{896 a b^{\frac{45}{2}} x \sqrt{\frac{a x}{b} + 1}}{35 a^{9} b^{16} x^{4} + 140 a^{8} b^{17} x^{3} + 210 a^{7} b^{18} x^{2} + 140 a^{6} b^{19} x + 35 a^{5} b^{20}} - \frac{256 b^{\frac{47}{2}} \sqrt{\frac{a x}{b} + 1}}{35 a^{9} b^{16} x^{4} + 140 a^{8} b^{17} x^{3} + 210 a^{7} b^{18} x^{2} + 140 a^{6} b^{19} x + 35 a^{5} b^{20}}"," ",0,"10*a**7*b**(33/2)*x**7*sqrt(a*x/b + 1)/(35*a**9*b**16*x**4 + 140*a**8*b**17*x**3 + 210*a**7*b**18*x**2 + 140*a**6*b**19*x + 35*a**5*b**20) + 14*a**6*b**(35/2)*x**6*sqrt(a*x/b + 1)/(35*a**9*b**16*x**4 + 140*a**8*b**17*x**3 + 210*a**7*b**18*x**2 + 140*a**6*b**19*x + 35*a**5*b**20) + 14*a**5*b**(37/2)*x**5*sqrt(a*x/b + 1)/(35*a**9*b**16*x**4 + 140*a**8*b**17*x**3 + 210*a**7*b**18*x**2 + 140*a**6*b**19*x + 35*a**5*b**20) - 70*a**4*b**(39/2)*x**4*sqrt(a*x/b + 1)/(35*a**9*b**16*x**4 + 140*a**8*b**17*x**3 + 210*a**7*b**18*x**2 + 140*a**6*b**19*x + 35*a**5*b**20) - 560*a**3*b**(41/2)*x**3*sqrt(a*x/b + 1)/(35*a**9*b**16*x**4 + 140*a**8*b**17*x**3 + 210*a**7*b**18*x**2 + 140*a**6*b**19*x + 35*a**5*b**20) - 1120*a**2*b**(43/2)*x**2*sqrt(a*x/b + 1)/(35*a**9*b**16*x**4 + 140*a**8*b**17*x**3 + 210*a**7*b**18*x**2 + 140*a**6*b**19*x + 35*a**5*b**20) - 896*a*b**(45/2)*x*sqrt(a*x/b + 1)/(35*a**9*b**16*x**4 + 140*a**8*b**17*x**3 + 210*a**7*b**18*x**2 + 140*a**6*b**19*x + 35*a**5*b**20) - 256*b**(47/2)*sqrt(a*x/b + 1)/(35*a**9*b**16*x**4 + 140*a**8*b**17*x**3 + 210*a**7*b**18*x**2 + 140*a**6*b**19*x + 35*a**5*b**20)","B",0
1787,1,320,0,5.101410," ","integrate(x**(3/2)/(a+b/x)**(3/2),x)","\frac{2 a^{5} b^{\frac{19}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{5 a^{7} b^{9} x^{3} + 15 a^{6} b^{10} x^{2} + 15 a^{5} b^{11} x + 5 a^{4} b^{12}} + \frac{10 a^{3} b^{\frac{23}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{5 a^{7} b^{9} x^{3} + 15 a^{6} b^{10} x^{2} + 15 a^{5} b^{11} x + 5 a^{4} b^{12}} + \frac{60 a^{2} b^{\frac{25}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{5 a^{7} b^{9} x^{3} + 15 a^{6} b^{10} x^{2} + 15 a^{5} b^{11} x + 5 a^{4} b^{12}} + \frac{80 a b^{\frac{27}{2}} x \sqrt{\frac{a x}{b} + 1}}{5 a^{7} b^{9} x^{3} + 15 a^{6} b^{10} x^{2} + 15 a^{5} b^{11} x + 5 a^{4} b^{12}} + \frac{32 b^{\frac{29}{2}} \sqrt{\frac{a x}{b} + 1}}{5 a^{7} b^{9} x^{3} + 15 a^{6} b^{10} x^{2} + 15 a^{5} b^{11} x + 5 a^{4} b^{12}}"," ",0,"2*a**5*b**(19/2)*x**5*sqrt(a*x/b + 1)/(5*a**7*b**9*x**3 + 15*a**6*b**10*x**2 + 15*a**5*b**11*x + 5*a**4*b**12) + 10*a**3*b**(23/2)*x**3*sqrt(a*x/b + 1)/(5*a**7*b**9*x**3 + 15*a**6*b**10*x**2 + 15*a**5*b**11*x + 5*a**4*b**12) + 60*a**2*b**(25/2)*x**2*sqrt(a*x/b + 1)/(5*a**7*b**9*x**3 + 15*a**6*b**10*x**2 + 15*a**5*b**11*x + 5*a**4*b**12) + 80*a*b**(27/2)*x*sqrt(a*x/b + 1)/(5*a**7*b**9*x**3 + 15*a**6*b**10*x**2 + 15*a**5*b**11*x + 5*a**4*b**12) + 32*b**(29/2)*sqrt(a*x/b + 1)/(5*a**7*b**9*x**3 + 15*a**6*b**10*x**2 + 15*a**5*b**11*x + 5*a**4*b**12)","B",0
1788,1,206,0,2.680224," ","integrate(x**(1/2)/(a+b/x)**(3/2),x)","\frac{2 a^{3} b^{\frac{9}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x + 3 a^{3} b^{6}} - \frac{6 a^{2} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x + 3 a^{3} b^{6}} - \frac{24 a b^{\frac{13}{2}} x \sqrt{\frac{a x}{b} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x + 3 a^{3} b^{6}} - \frac{16 b^{\frac{15}{2}} \sqrt{\frac{a x}{b} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x + 3 a^{3} b^{6}}"," ",0,"2*a**3*b**(9/2)*x**3*sqrt(a*x/b + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x + 3*a**3*b**6) - 6*a**2*b**(11/2)*x**2*sqrt(a*x/b + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x + 3*a**3*b**6) - 24*a*b**(13/2)*x*sqrt(a*x/b + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x + 3*a**3*b**6) - 16*b**(15/2)*sqrt(a*x/b + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x + 3*a**3*b**6)","B",0
1789,1,39,0,3.818803," ","integrate(1/(a+b/x)**(3/2)/x**(1/2),x)","\frac{2 x}{a \sqrt{b} \sqrt{\frac{a x}{b} + 1}} + \frac{4 \sqrt{b}}{a^{2} \sqrt{\frac{a x}{b} + 1}}"," ",0,"2*x/(a*sqrt(b)*sqrt(a*x/b + 1)) + 4*sqrt(b)/(a**2*sqrt(a*x/b + 1))","A",0
1790,1,19,0,5.401920," ","integrate(1/(a+b/x)**(3/2)/x**(3/2),x)","- \frac{2}{a \sqrt{b} \sqrt{\frac{a x}{b} + 1}}"," ",0,"-2/(a*sqrt(b)*sqrt(a*x/b + 1))","A",0
1791,1,146,0,13.988405," ","integrate(1/(a+b/x)**(3/2)/x**(5/2),x)","\frac{a b^{2} x \log{\left(\frac{a x}{b} \right)}}{a b^{\frac{7}{2}} x + b^{\frac{9}{2}}} - \frac{2 a b^{2} x \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}}{a b^{\frac{7}{2}} x + b^{\frac{9}{2}}} + \frac{2 b^{3} \sqrt{\frac{a x}{b} + 1}}{a b^{\frac{7}{2}} x + b^{\frac{9}{2}}} + \frac{b^{3} \log{\left(\frac{a x}{b} \right)}}{a b^{\frac{7}{2}} x + b^{\frac{9}{2}}} - \frac{2 b^{3} \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}}{a b^{\frac{7}{2}} x + b^{\frac{9}{2}}}"," ",0,"a*b**2*x*log(a*x/b)/(a*b**(7/2)*x + b**(9/2)) - 2*a*b**2*x*log(sqrt(a*x/b + 1) + 1)/(a*b**(7/2)*x + b**(9/2)) + 2*b**3*sqrt(a*x/b + 1)/(a*b**(7/2)*x + b**(9/2)) + b**3*log(a*x/b)/(a*b**(7/2)*x + b**(9/2)) - 2*b**3*log(sqrt(a*x/b + 1) + 1)/(a*b**(7/2)*x + b**(9/2))","B",0
1792,1,73,0,38.022941," ","integrate(1/(a+b/x)**(3/2)/x**(7/2),x)","- \frac{3 \sqrt{a}}{b^{2} \sqrt{x} \sqrt{1 + \frac{b}{a x}}} + \frac{3 a \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{b^{\frac{5}{2}}} - \frac{1}{\sqrt{a} b x^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}}"," ",0,"-3*sqrt(a)/(b**2*sqrt(x)*sqrt(1 + b/(a*x))) + 3*a*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/b**(5/2) - 1/(sqrt(a)*b*x**(3/2)*sqrt(1 + b/(a*x)))","A",0
1793,1,107,0,85.831025," ","integrate(1/(a+b/x)**(3/2)/x**(9/2),x)","\frac{15 a^{\frac{3}{2}}}{4 b^{3} \sqrt{x} \sqrt{1 + \frac{b}{a x}}} + \frac{5 \sqrt{a}}{4 b^{2} x^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}} - \frac{15 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}} \right)}}{4 b^{\frac{7}{2}}} - \frac{1}{2 \sqrt{a} b x^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}}"," ",0,"15*a**(3/2)/(4*b**3*sqrt(x)*sqrt(1 + b/(a*x))) + 5*sqrt(a)/(4*b**2*x**(3/2)*sqrt(1 + b/(a*x))) - 15*a**2*asinh(sqrt(b)/(sqrt(a)*sqrt(x)))/(4*b**(7/2)) - 1/(2*sqrt(a)*b*x**(5/2)*sqrt(1 + b/(a*x)))","A",0
1794,-1,0,0,0.000000," ","integrate(1/(a+b/x)**(3/2)/x**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1795,1,799,0,14.648154," ","integrate(x**(5/2)/(a+b/x)**(5/2),x)","\frac{6 a^{8} b^{\frac{51}{2}} x^{8} \sqrt{\frac{a x}{b} + 1}}{21 a^{11} b^{25} x^{5} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{3} + 210 a^{8} b^{28} x^{2} + 105 a^{7} b^{29} x + 21 a^{6} b^{30}} + \frac{6 a^{7} b^{\frac{53}{2}} x^{7} \sqrt{\frac{a x}{b} + 1}}{21 a^{11} b^{25} x^{5} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{3} + 210 a^{8} b^{28} x^{2} + 105 a^{7} b^{29} x + 21 a^{6} b^{30}} + \frac{14 a^{6} b^{\frac{55}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{21 a^{11} b^{25} x^{5} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{3} + 210 a^{8} b^{28} x^{2} + 105 a^{7} b^{29} x + 21 a^{6} b^{30}} - \frac{126 a^{5} b^{\frac{57}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{21 a^{11} b^{25} x^{5} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{3} + 210 a^{8} b^{28} x^{2} + 105 a^{7} b^{29} x + 21 a^{6} b^{30}} - \frac{1260 a^{4} b^{\frac{59}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{21 a^{11} b^{25} x^{5} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{3} + 210 a^{8} b^{28} x^{2} + 105 a^{7} b^{29} x + 21 a^{6} b^{30}} - \frac{3360 a^{3} b^{\frac{61}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{21 a^{11} b^{25} x^{5} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{3} + 210 a^{8} b^{28} x^{2} + 105 a^{7} b^{29} x + 21 a^{6} b^{30}} - \frac{4032 a^{2} b^{\frac{63}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{21 a^{11} b^{25} x^{5} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{3} + 210 a^{8} b^{28} x^{2} + 105 a^{7} b^{29} x + 21 a^{6} b^{30}} - \frac{2304 a b^{\frac{65}{2}} x \sqrt{\frac{a x}{b} + 1}}{21 a^{11} b^{25} x^{5} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{3} + 210 a^{8} b^{28} x^{2} + 105 a^{7} b^{29} x + 21 a^{6} b^{30}} - \frac{512 b^{\frac{67}{2}} \sqrt{\frac{a x}{b} + 1}}{21 a^{11} b^{25} x^{5} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{3} + 210 a^{8} b^{28} x^{2} + 105 a^{7} b^{29} x + 21 a^{6} b^{30}}"," ",0,"6*a**8*b**(51/2)*x**8*sqrt(a*x/b + 1)/(21*a**11*b**25*x**5 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**3 + 210*a**8*b**28*x**2 + 105*a**7*b**29*x + 21*a**6*b**30) + 6*a**7*b**(53/2)*x**7*sqrt(a*x/b + 1)/(21*a**11*b**25*x**5 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**3 + 210*a**8*b**28*x**2 + 105*a**7*b**29*x + 21*a**6*b**30) + 14*a**6*b**(55/2)*x**6*sqrt(a*x/b + 1)/(21*a**11*b**25*x**5 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**3 + 210*a**8*b**28*x**2 + 105*a**7*b**29*x + 21*a**6*b**30) - 126*a**5*b**(57/2)*x**5*sqrt(a*x/b + 1)/(21*a**11*b**25*x**5 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**3 + 210*a**8*b**28*x**2 + 105*a**7*b**29*x + 21*a**6*b**30) - 1260*a**4*b**(59/2)*x**4*sqrt(a*x/b + 1)/(21*a**11*b**25*x**5 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**3 + 210*a**8*b**28*x**2 + 105*a**7*b**29*x + 21*a**6*b**30) - 3360*a**3*b**(61/2)*x**3*sqrt(a*x/b + 1)/(21*a**11*b**25*x**5 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**3 + 210*a**8*b**28*x**2 + 105*a**7*b**29*x + 21*a**6*b**30) - 4032*a**2*b**(63/2)*x**2*sqrt(a*x/b + 1)/(21*a**11*b**25*x**5 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**3 + 210*a**8*b**28*x**2 + 105*a**7*b**29*x + 21*a**6*b**30) - 2304*a*b**(65/2)*x*sqrt(a*x/b + 1)/(21*a**11*b**25*x**5 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**3 + 210*a**8*b**28*x**2 + 105*a**7*b**29*x + 21*a**6*b**30) - 512*b**(67/2)*sqrt(a*x/b + 1)/(21*a**11*b**25*x**5 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**3 + 210*a**8*b**28*x**2 + 105*a**7*b**29*x + 21*a**6*b**30)","B",0
1796,1,536,0,8.804893," ","integrate(x**(3/2)/(a+b/x)**(5/2),x)","\frac{6 a^{6} b^{\frac{33}{2}} x^{6} \sqrt{\frac{a x}{b} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{3} + 90 a^{7} b^{18} x^{2} + 60 a^{6} b^{19} x + 15 a^{5} b^{20}} - \frac{4 a^{5} b^{\frac{35}{2}} x^{5} \sqrt{\frac{a x}{b} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{3} + 90 a^{7} b^{18} x^{2} + 60 a^{6} b^{19} x + 15 a^{5} b^{20}} + \frac{70 a^{4} b^{\frac{37}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{3} + 90 a^{7} b^{18} x^{2} + 60 a^{6} b^{19} x + 15 a^{5} b^{20}} + \frac{560 a^{3} b^{\frac{39}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{3} + 90 a^{7} b^{18} x^{2} + 60 a^{6} b^{19} x + 15 a^{5} b^{20}} + \frac{1120 a^{2} b^{\frac{41}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{3} + 90 a^{7} b^{18} x^{2} + 60 a^{6} b^{19} x + 15 a^{5} b^{20}} + \frac{896 a b^{\frac{43}{2}} x \sqrt{\frac{a x}{b} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{3} + 90 a^{7} b^{18} x^{2} + 60 a^{6} b^{19} x + 15 a^{5} b^{20}} + \frac{256 b^{\frac{45}{2}} \sqrt{\frac{a x}{b} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{3} + 90 a^{7} b^{18} x^{2} + 60 a^{6} b^{19} x + 15 a^{5} b^{20}}"," ",0,"6*a**6*b**(33/2)*x**6*sqrt(a*x/b + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**3 + 90*a**7*b**18*x**2 + 60*a**6*b**19*x + 15*a**5*b**20) - 4*a**5*b**(35/2)*x**5*sqrt(a*x/b + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**3 + 90*a**7*b**18*x**2 + 60*a**6*b**19*x + 15*a**5*b**20) + 70*a**4*b**(37/2)*x**4*sqrt(a*x/b + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**3 + 90*a**7*b**18*x**2 + 60*a**6*b**19*x + 15*a**5*b**20) + 560*a**3*b**(39/2)*x**3*sqrt(a*x/b + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**3 + 90*a**7*b**18*x**2 + 60*a**6*b**19*x + 15*a**5*b**20) + 1120*a**2*b**(41/2)*x**2*sqrt(a*x/b + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**3 + 90*a**7*b**18*x**2 + 60*a**6*b**19*x + 15*a**5*b**20) + 896*a*b**(43/2)*x*sqrt(a*x/b + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**3 + 90*a**7*b**18*x**2 + 60*a**6*b**19*x + 15*a**5*b**20) + 256*b**(45/2)*sqrt(a*x/b + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**3 + 90*a**7*b**18*x**2 + 60*a**6*b**19*x + 15*a**5*b**20)","B",0
1797,1,320,0,6.453707," ","integrate(x**(1/2)/(a+b/x)**(5/2),x)","\frac{2 a^{4} b^{\frac{19}{2}} x^{4} \sqrt{\frac{a x}{b} + 1}}{3 a^{7} b^{9} x^{3} + 9 a^{6} b^{10} x^{2} + 9 a^{5} b^{11} x + 3 a^{4} b^{12}} - \frac{10 a^{3} b^{\frac{21}{2}} x^{3} \sqrt{\frac{a x}{b} + 1}}{3 a^{7} b^{9} x^{3} + 9 a^{6} b^{10} x^{2} + 9 a^{5} b^{11} x + 3 a^{4} b^{12}} - \frac{60 a^{2} b^{\frac{23}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{3 a^{7} b^{9} x^{3} + 9 a^{6} b^{10} x^{2} + 9 a^{5} b^{11} x + 3 a^{4} b^{12}} - \frac{80 a b^{\frac{25}{2}} x \sqrt{\frac{a x}{b} + 1}}{3 a^{7} b^{9} x^{3} + 9 a^{6} b^{10} x^{2} + 9 a^{5} b^{11} x + 3 a^{4} b^{12}} - \frac{32 b^{\frac{27}{2}} \sqrt{\frac{a x}{b} + 1}}{3 a^{7} b^{9} x^{3} + 9 a^{6} b^{10} x^{2} + 9 a^{5} b^{11} x + 3 a^{4} b^{12}}"," ",0,"2*a**4*b**(19/2)*x**4*sqrt(a*x/b + 1)/(3*a**7*b**9*x**3 + 9*a**6*b**10*x**2 + 9*a**5*b**11*x + 3*a**4*b**12) - 10*a**3*b**(21/2)*x**3*sqrt(a*x/b + 1)/(3*a**7*b**9*x**3 + 9*a**6*b**10*x**2 + 9*a**5*b**11*x + 3*a**4*b**12) - 60*a**2*b**(23/2)*x**2*sqrt(a*x/b + 1)/(3*a**7*b**9*x**3 + 9*a**6*b**10*x**2 + 9*a**5*b**11*x + 3*a**4*b**12) - 80*a*b**(25/2)*x*sqrt(a*x/b + 1)/(3*a**7*b**9*x**3 + 9*a**6*b**10*x**2 + 9*a**5*b**11*x + 3*a**4*b**12) - 32*b**(27/2)*sqrt(a*x/b + 1)/(3*a**7*b**9*x**3 + 9*a**6*b**10*x**2 + 9*a**5*b**11*x + 3*a**4*b**12)","B",0
1798,1,151,0,7.542720," ","integrate(1/(a+b/x)**(5/2)/x**(1/2),x)","\frac{6 a^{2} b^{\frac{9}{2}} x^{2} \sqrt{\frac{a x}{b} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x + 3 a^{3} b^{6}} + \frac{24 a b^{\frac{11}{2}} x \sqrt{\frac{a x}{b} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x + 3 a^{3} b^{6}} + \frac{16 b^{\frac{13}{2}} \sqrt{\frac{a x}{b} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x + 3 a^{3} b^{6}}"," ",0,"6*a**2*b**(9/2)*x**2*sqrt(a*x/b + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x + 3*a**3*b**6) + 24*a*b**(11/2)*x*sqrt(a*x/b + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x + 3*a**3*b**6) + 16*b**(13/2)*sqrt(a*x/b + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x + 3*a**3*b**6)","B",0
1799,1,94,0,14.289472," ","integrate(1/(a+b/x)**(5/2)/x**(3/2),x)","- \frac{6 a x}{3 a^{3} \sqrt{b} x \sqrt{\frac{a x}{b} + 1} + 3 a^{2} b^{\frac{3}{2}} \sqrt{\frac{a x}{b} + 1}} - \frac{4 b}{3 a^{3} \sqrt{b} x \sqrt{\frac{a x}{b} + 1} + 3 a^{2} b^{\frac{3}{2}} \sqrt{\frac{a x}{b} + 1}}"," ",0,"-6*a*x/(3*a**3*sqrt(b)*x*sqrt(a*x/b + 1) + 3*a**2*b**(3/2)*sqrt(a*x/b + 1)) - 4*b/(3*a**3*sqrt(b)*x*sqrt(a*x/b + 1) + 3*a**2*b**(3/2)*sqrt(a*x/b + 1))","B",0
1800,1,42,0,20.020158," ","integrate(1/(a+b/x)**(5/2)/x**(5/2),x)","- \frac{2}{3 a^{2} \sqrt{b} x \sqrt{\frac{a x}{b} + 1} + 3 a b^{\frac{3}{2}} \sqrt{\frac{a x}{b} + 1}}"," ",0,"-2/(3*a**2*sqrt(b)*x*sqrt(a*x/b + 1) + 3*a*b**(3/2)*sqrt(a*x/b + 1))","B",0
1801,1,697,0,51.155703," ","integrate(1/(a+b/x)**(5/2)/x**(7/2),x)","\frac{3 a^{3} b^{4} x^{3} \log{\left(\frac{a x}{b} \right)}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}} - \frac{6 a^{3} b^{4} x^{3} \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}} + \frac{6 a^{2} b^{5} x^{2} \sqrt{\frac{a x}{b} + 1}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}} + \frac{9 a^{2} b^{5} x^{2} \log{\left(\frac{a x}{b} \right)}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}} - \frac{18 a^{2} b^{5} x^{2} \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}} + \frac{14 a b^{6} x \sqrt{\frac{a x}{b} + 1}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}} + \frac{9 a b^{6} x \log{\left(\frac{a x}{b} \right)}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}} - \frac{18 a b^{6} x \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}} + \frac{8 b^{7} \sqrt{\frac{a x}{b} + 1}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}} + \frac{3 b^{7} \log{\left(\frac{a x}{b} \right)}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}} - \frac{6 b^{7} \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}}{3 a^{3} b^{\frac{13}{2}} x^{3} + 9 a^{2} b^{\frac{15}{2}} x^{2} + 9 a b^{\frac{17}{2}} x + 3 b^{\frac{19}{2}}}"," ",0,"3*a**3*b**4*x**3*log(a*x/b)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2)) - 6*a**3*b**4*x**3*log(sqrt(a*x/b + 1) + 1)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2)) + 6*a**2*b**5*x**2*sqrt(a*x/b + 1)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2)) + 9*a**2*b**5*x**2*log(a*x/b)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2)) - 18*a**2*b**5*x**2*log(sqrt(a*x/b + 1) + 1)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2)) + 14*a*b**6*x*sqrt(a*x/b + 1)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2)) + 9*a*b**6*x*log(a*x/b)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2)) - 18*a*b**6*x*log(sqrt(a*x/b + 1) + 1)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2)) + 8*b**7*sqrt(a*x/b + 1)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2)) + 3*b**7*log(a*x/b)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2)) - 6*b**7*log(sqrt(a*x/b + 1) + 1)/(3*a**3*b**(13/2)*x**3 + 9*a**2*b**(15/2)*x**2 + 9*a*b**(17/2)*x + 3*b**(19/2))","B",0
1802,1,818,0,133.442246," ","integrate(1/(a+b/x)**(5/2)/x**(9/2),x)","- \frac{15 a^{4} b^{13} x^{4} \log{\left(\frac{a x}{b} \right)}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} + \frac{30 a^{4} b^{13} x^{4} \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} - \frac{30 a^{3} b^{14} x^{3} \sqrt{\frac{a x}{b} + 1}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} - \frac{45 a^{3} b^{14} x^{3} \log{\left(\frac{a x}{b} \right)}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} + \frac{90 a^{3} b^{14} x^{3} \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} - \frac{70 a^{2} b^{15} x^{2} \sqrt{\frac{a x}{b} + 1}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} - \frac{45 a^{2} b^{15} x^{2} \log{\left(\frac{a x}{b} \right)}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} + \frac{90 a^{2} b^{15} x^{2} \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} - \frac{46 a b^{16} x \sqrt{\frac{a x}{b} + 1}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} - \frac{15 a b^{16} x \log{\left(\frac{a x}{b} \right)}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} + \frac{30 a b^{16} x \log{\left(\sqrt{\frac{a x}{b} + 1} + 1 \right)}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x} - \frac{6 b^{17} \sqrt{\frac{a x}{b} + 1}}{6 a^{3} b^{\frac{33}{2}} x^{4} + 18 a^{2} b^{\frac{35}{2}} x^{3} + 18 a b^{\frac{37}{2}} x^{2} + 6 b^{\frac{39}{2}} x}"," ",0,"-15*a**4*b**13*x**4*log(a*x/b)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) + 30*a**4*b**13*x**4*log(sqrt(a*x/b + 1) + 1)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) - 30*a**3*b**14*x**3*sqrt(a*x/b + 1)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) - 45*a**3*b**14*x**3*log(a*x/b)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) + 90*a**3*b**14*x**3*log(sqrt(a*x/b + 1) + 1)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) - 70*a**2*b**15*x**2*sqrt(a*x/b + 1)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) - 45*a**2*b**15*x**2*log(a*x/b)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) + 90*a**2*b**15*x**2*log(sqrt(a*x/b + 1) + 1)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) - 46*a*b**16*x*sqrt(a*x/b + 1)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) - 15*a*b**16*x*log(a*x/b)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) + 30*a*b**16*x*log(sqrt(a*x/b + 1) + 1)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x) - 6*b**17*sqrt(a*x/b + 1)/(6*a**3*b**(33/2)*x**4 + 18*a**2*b**(35/2)*x**3 + 18*a*b**(37/2)*x**2 + 6*b**(39/2)*x)","B",0
1803,-1,0,0,0.000000," ","integrate(1/(a+b/x)**(5/2)/x**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1804,1,12,0,0.063565," ","integrate((a+b/x**2)*x**6,x)","\frac{a x^{7}}{7} + \frac{b x^{5}}{5}"," ",0,"a*x**7/7 + b*x**5/5","A",0
1805,1,12,0,0.064037," ","integrate((a+b/x**2)*x**5,x)","\frac{a x^{6}}{6} + \frac{b x^{4}}{4}"," ",0,"a*x**6/6 + b*x**4/4","A",0
1806,1,12,0,0.062627," ","integrate((a+b/x**2)*x**4,x)","\frac{a x^{5}}{5} + \frac{b x^{3}}{3}"," ",0,"a*x**5/5 + b*x**3/3","A",0
1807,1,12,0,0.062518," ","integrate((a+b/x**2)*x**3,x)","\frac{a x^{4}}{4} + \frac{b x^{2}}{2}"," ",0,"a*x**4/4 + b*x**2/2","A",0
1808,1,8,0,0.062485," ","integrate((a+b/x**2)*x**2,x)","\frac{a x^{3}}{3} + b x"," ",0,"a*x**3/3 + b*x","A",0
1809,1,10,0,0.090512," ","integrate((a+b/x**2)*x,x)","\frac{a x^{2}}{2} + b \log{\left(x \right)}"," ",0,"a*x**2/2 + b*log(x)","A",0
1810,1,5,0,0.084117," ","integrate(a+b/x**2,x)","a x - \frac{b}{x}"," ",0,"a*x - b/x","A",0
1811,1,10,0,0.111814," ","integrate((a+b/x**2)/x,x)","a \log{\left(x \right)} - \frac{b}{2 x^{2}}"," ",0,"a*log(x) - b/(2*x**2)","A",0
1812,1,14,0,0.121736," ","integrate((a+b/x**2)/x**2,x)","\frac{- 3 a x^{2} - b}{3 x^{3}}"," ",0,"(-3*a*x**2 - b)/(3*x**3)","A",0
1813,1,14,0,0.124050," ","integrate((a+b/x**2)/x**3,x)","\frac{- 2 a x^{2} - b}{4 x^{4}}"," ",0,"(-2*a*x**2 - b)/(4*x**4)","A",0
1814,1,15,0,0.142468," ","integrate((a+b/x**2)/x**4,x)","\frac{- 5 a x^{2} - 3 b}{15 x^{5}}"," ",0,"(-5*a*x**2 - 3*b)/(15*x**5)","A",0
1815,1,15,0,0.141237," ","integrate((a+b/x**2)/x**5,x)","\frac{- 3 a x^{2} - 2 b}{12 x^{6}}"," ",0,"(-3*a*x**2 - 2*b)/(12*x**6)","A",0
1816,1,15,0,0.157447," ","integrate((a+b/x**2)/x**6,x)","\frac{- 7 a x^{2} - 5 b}{35 x^{7}}"," ",0,"(-7*a*x**2 - 5*b)/(35*x**7)","A",0
1817,1,26,0,0.069115," ","integrate((a+b/x**2)**2*x**6,x)","\frac{a^{2} x^{7}}{7} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{3}}{3}"," ",0,"a**2*x**7/7 + 2*a*b*x**5/5 + b**2*x**3/3","A",0
1818,1,24,0,0.067903," ","integrate((a+b/x**2)**2*x**5,x)","\frac{a^{2} x^{6}}{6} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{2}}{2}"," ",0,"a**2*x**6/6 + a*b*x**4/2 + b**2*x**2/2","B",0
1819,1,22,0,0.066489," ","integrate((a+b/x**2)**2*x**4,x)","\frac{a^{2} x^{5}}{5} + \frac{2 a b x^{3}}{3} + b^{2} x"," ",0,"a**2*x**5/5 + 2*a*b*x**3/3 + b**2*x","A",0
1820,1,20,0,0.108229," ","integrate((a+b/x**2)**2*x**3,x)","\frac{a^{2} x^{4}}{4} + a b x^{2} + b^{2} \log{\left(x \right)}"," ",0,"a**2*x**4/4 + a*b*x**2 + b**2*log(x)","A",0
1821,1,19,0,0.103451," ","integrate((a+b/x**2)**2*x**2,x)","\frac{a^{2} x^{3}}{3} + 2 a b x - \frac{b^{2}}{x}"," ",0,"a**2*x**3/3 + 2*a*b*x - b**2/x","A",0
1822,1,24,0,0.138221," ","integrate((a+b/x**2)**2*x,x)","\frac{a^{2} x^{2}}{2} + 2 a b \log{\left(x \right)} - \frac{b^{2}}{2 x^{2}}"," ",0,"a**2*x**2/2 + 2*a*b*log(x) - b**2/(2*x**2)","A",0
1823,1,22,0,0.143626," ","integrate((a+b/x**2)**2,x)","a^{2} x + \frac{- 6 a b x^{2} - b^{2}}{3 x^{3}}"," ",0,"a**2*x + (-6*a*b*x**2 - b**2)/(3*x**3)","A",0
1824,1,24,0,0.179761," ","integrate((a+b/x**2)**2/x,x)","a^{2} \log{\left(x \right)} + \frac{- 4 a b x^{2} - b^{2}}{4 x^{4}}"," ",0,"a**2*log(x) + (-4*a*b*x**2 - b**2)/(4*x**4)","A",0
1825,1,27,0,0.186829," ","integrate((a+b/x**2)**2/x**2,x)","\frac{- 15 a^{2} x^{4} - 10 a b x^{2} - 3 b^{2}}{15 x^{5}}"," ",0,"(-15*a**2*x**4 - 10*a*b*x**2 - 3*b**2)/(15*x**5)","A",0
1826,1,26,0,0.194412," ","integrate((a+b/x**2)**2/x**3,x)","\frac{- 3 a^{2} x^{4} - 3 a b x^{2} - b^{2}}{6 x^{6}}"," ",0,"(-3*a**2*x**4 - 3*a*b*x**2 - b**2)/(6*x**6)","B",0
1827,1,27,0,0.206862," ","integrate((a+b/x**2)**2/x**4,x)","\frac{- 35 a^{2} x^{4} - 42 a b x^{2} - 15 b^{2}}{105 x^{7}}"," ",0,"(-35*a**2*x**4 - 42*a*b*x**2 - 15*b**2)/(105*x**7)","A",0
1828,1,27,0,0.223424," ","integrate((a+b/x**2)**2/x**5,x)","\frac{- 6 a^{2} x^{4} - 8 a b x^{2} - 3 b^{2}}{24 x^{8}}"," ",0,"(-6*a**2*x**4 - 8*a*b*x**2 - 3*b**2)/(24*x**8)","A",0
1829,1,27,0,0.233152," ","integrate((a+b/x**2)**2/x**6,x)","\frac{- 63 a^{2} x^{4} - 90 a b x^{2} - 35 b^{2}}{315 x^{9}}"," ",0,"(-63*a**2*x**4 - 90*a*b*x**2 - 35*b**2)/(315*x**9)","A",0
1830,1,32,0,0.070786," ","integrate((a+b/x**2)**3*x**6,x)","\frac{a^{3} x^{7}}{7} + \frac{3 a^{2} b x^{5}}{5} + a b^{2} x^{3} + b^{3} x"," ",0,"a**3*x**7/7 + 3*a**2*b*x**5/5 + a*b**2*x**3 + b**3*x","A",0
1831,1,37,0,0.120926," ","integrate((a+b/x**2)**3*x**5,x)","\frac{a^{3} x^{6}}{6} + \frac{3 a^{2} b x^{4}}{4} + \frac{3 a b^{2} x^{2}}{2} + b^{3} \log{\left(x \right)}"," ",0,"a**3*x**6/6 + 3*a**2*b*x**4/4 + 3*a*b**2*x**2/2 + b**3*log(x)","A",0
1832,1,29,0,0.117149," ","integrate((a+b/x**2)**3*x**4,x)","\frac{a^{3} x^{5}}{5} + a^{2} b x^{3} + 3 a b^{2} x - \frac{b^{3}}{x}"," ",0,"a**3*x**5/5 + a**2*b*x**3 + 3*a*b**2*x - b**3/x","A",0
1833,1,37,0,0.154470," ","integrate((a+b/x**2)**3*x**3,x)","\frac{a^{3} x^{4}}{4} + \frac{3 a^{2} b x^{2}}{2} + 3 a b^{2} \log{\left(x \right)} - \frac{b^{3}}{2 x^{2}}"," ",0,"a**3*x**4/4 + 3*a**2*b*x**2/2 + 3*a*b**2*log(x) - b**3/(2*x**2)","A",0
1834,1,36,0,0.159972," ","integrate((a+b/x**2)**3*x**2,x)","\frac{a^{3} x^{3}}{3} + 3 a^{2} b x + \frac{- 9 a b^{2} x^{2} - b^{3}}{3 x^{3}}"," ",0,"a**3*x**3/3 + 3*a**2*b*x + (-9*a*b**2*x**2 - b**3)/(3*x**3)","A",0
1835,1,37,0,0.203654," ","integrate((a+b/x**2)**3*x,x)","\frac{a^{3} x^{2}}{2} + 3 a^{2} b \log{\left(x \right)} + \frac{- 6 a b^{2} x^{2} - b^{3}}{4 x^{4}}"," ",0,"a**3*x**2/2 + 3*a**2*b*log(x) + (-6*a*b**2*x**2 - b**3)/(4*x**4)","A",0
1836,1,34,0,0.205678," ","integrate((a+b/x**2)**3,x)","a^{3} x + \frac{- 15 a^{2} b x^{4} - 5 a b^{2} x^{2} - b^{3}}{5 x^{5}}"," ",0,"a**3*x + (-15*a**2*b*x**4 - 5*a*b**2*x**2 - b**3)/(5*x**5)","A",0
1837,1,37,0,0.262572," ","integrate((a+b/x**2)**3/x,x)","a^{3} \log{\left(x \right)} + \frac{- 18 a^{2} b x^{4} - 9 a b^{2} x^{2} - 2 b^{3}}{12 x^{6}}"," ",0,"a**3*log(x) + (-18*a**2*b*x**4 - 9*a*b**2*x**2 - 2*b**3)/(12*x**6)","A",0
1838,1,39,0,0.264234," ","integrate((a+b/x**2)**3/x**2,x)","\frac{- 35 a^{3} x^{6} - 35 a^{2} b x^{4} - 21 a b^{2} x^{2} - 5 b^{3}}{35 x^{7}}"," ",0,"(-35*a**3*x**6 - 35*a**2*b*x**4 - 21*a*b**2*x**2 - 5*b**3)/(35*x**7)","A",0
1839,1,37,0,0.295144," ","integrate((a+b/x**2)**3/x**3,x)","\frac{- 4 a^{3} x^{6} - 6 a^{2} b x^{4} - 4 a b^{2} x^{2} - b^{3}}{8 x^{8}}"," ",0,"(-4*a**3*x**6 - 6*a**2*b*x**4 - 4*a*b**2*x**2 - b**3)/(8*x**8)","B",0
1840,1,39,0,0.292068," ","integrate((a+b/x**2)**3/x**4,x)","\frac{- 105 a^{3} x^{6} - 189 a^{2} b x^{4} - 135 a b^{2} x^{2} - 35 b^{3}}{315 x^{9}}"," ",0,"(-105*a**3*x**6 - 189*a**2*b*x**4 - 135*a*b**2*x**2 - 35*b**3)/(315*x**9)","A",0
1841,1,39,0,0.314357," ","integrate((a+b/x**2)**3/x**5,x)","\frac{- 10 a^{3} x^{6} - 20 a^{2} b x^{4} - 15 a b^{2} x^{2} - 4 b^{3}}{40 x^{10}}"," ",0,"(-10*a**3*x**6 - 20*a**2*b*x**4 - 15*a*b**2*x**2 - 4*b**3)/(40*x**10)","A",0
1842,1,39,0,0.315612," ","integrate((a+b/x**2)**3/x**6,x)","\frac{- 231 a^{3} x^{6} - 495 a^{2} b x^{4} - 385 a b^{2} x^{2} - 105 b^{3}}{1155 x^{11}}"," ",0,"(-231*a**3*x**6 - 495*a**2*b*x**4 - 385*a*b**2*x**2 - 105*b**3)/(1155*x**11)","A",0
1843,1,107,0,0.205829," ","integrate(x**6/(a+b/x**2),x)","- \frac{\sqrt{- \frac{b^{7}}{a^{9}}} \log{\left(- \frac{a^{4} \sqrt{- \frac{b^{7}}{a^{9}}}}{b^{3}} + x \right)}}{2} + \frac{\sqrt{- \frac{b^{7}}{a^{9}}} \log{\left(\frac{a^{4} \sqrt{- \frac{b^{7}}{a^{9}}}}{b^{3}} + x \right)}}{2} + \frac{x^{7}}{7 a} - \frac{b x^{5}}{5 a^{2}} + \frac{b^{2} x^{3}}{3 a^{3}} - \frac{b^{3} x}{a^{4}}"," ",0,"-sqrt(-b**7/a**9)*log(-a**4*sqrt(-b**7/a**9)/b**3 + x)/2 + sqrt(-b**7/a**9)*log(a**4*sqrt(-b**7/a**9)/b**3 + x)/2 + x**7/(7*a) - b*x**5/(5*a**2) + b**2*x**3/(3*a**3) - b**3*x/a**4","A",0
1844,1,44,0,0.166768," ","integrate(x**5/(a+b/x**2),x)","\frac{x^{6}}{6 a} - \frac{b x^{4}}{4 a^{2}} + \frac{b^{2} x^{2}}{2 a^{3}} - \frac{b^{3} \log{\left(a x^{2} + b \right)}}{2 a^{4}}"," ",0,"x**6/(6*a) - b*x**4/(4*a**2) + b**2*x**2/(2*a**3) - b**3*log(a*x**2 + b)/(2*a**4)","A",0
1845,1,95,0,0.191797," ","integrate(x**4/(a+b/x**2),x)","\frac{\sqrt{- \frac{b^{5}}{a^{7}}} \log{\left(- \frac{a^{3} \sqrt{- \frac{b^{5}}{a^{7}}}}{b^{2}} + x \right)}}{2} - \frac{\sqrt{- \frac{b^{5}}{a^{7}}} \log{\left(\frac{a^{3} \sqrt{- \frac{b^{5}}{a^{7}}}}{b^{2}} + x \right)}}{2} + \frac{x^{5}}{5 a} - \frac{b x^{3}}{3 a^{2}} + \frac{b^{2} x}{a^{3}}"," ",0,"sqrt(-b**5/a**7)*log(-a**3*sqrt(-b**5/a**7)/b**2 + x)/2 - sqrt(-b**5/a**7)*log(a**3*sqrt(-b**5/a**7)/b**2 + x)/2 + x**5/(5*a) - b*x**3/(3*a**2) + b**2*x/a**3","A",0
1846,1,32,0,0.159745," ","integrate(x**3/(a+b/x**2),x)","\frac{x^{4}}{4 a} - \frac{b x^{2}}{2 a^{2}} + \frac{b^{2} \log{\left(a x^{2} + b \right)}}{2 a^{3}}"," ",0,"x**4/(4*a) - b*x**2/(2*a**2) + b**2*log(a*x**2 + b)/(2*a**3)","A",0
1847,1,80,0,0.178514," ","integrate(x**2/(a+b/x**2),x)","- \frac{\sqrt{- \frac{b^{3}}{a^{5}}} \log{\left(- \frac{a^{2} \sqrt{- \frac{b^{3}}{a^{5}}}}{b} + x \right)}}{2} + \frac{\sqrt{- \frac{b^{3}}{a^{5}}} \log{\left(\frac{a^{2} \sqrt{- \frac{b^{3}}{a^{5}}}}{b} + x \right)}}{2} + \frac{x^{3}}{3 a} - \frac{b x}{a^{2}}"," ",0,"-sqrt(-b**3/a**5)*log(-a**2*sqrt(-b**3/a**5)/b + x)/2 + sqrt(-b**3/a**5)*log(a**2*sqrt(-b**3/a**5)/b + x)/2 + x**3/(3*a) - b*x/a**2","B",0
1848,1,20,0,0.145710," ","integrate(x/(a+b/x**2),x)","\frac{x^{2}}{2 a} - \frac{b \log{\left(a x^{2} + b \right)}}{2 a^{2}}"," ",0,"x**2/(2*a) - b*log(a*x**2 + b)/(2*a**2)","A",0
1849,1,56,0,0.159527," ","integrate(1/(a+b/x**2),x)","\frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(- a \sqrt{- \frac{b}{a^{3}}} + x \right)}}{2} - \frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(a \sqrt{- \frac{b}{a^{3}}} + x \right)}}{2} + \frac{x}{a}"," ",0,"sqrt(-b/a**3)*log(-a*sqrt(-b/a**3) + x)/2 - sqrt(-b/a**3)*log(a*sqrt(-b/a**3) + x)/2 + x/a","B",0
1850,1,10,0,0.118536," ","integrate(1/(a+b/x**2)/x,x)","\frac{\log{\left(a x^{2} + b \right)}}{2 a}"," ",0,"log(a*x**2 + b)/(2*a)","A",0
1851,1,53,0,0.144909," ","integrate(1/(a+b/x**2)/x**2,x)","- \frac{\sqrt{- \frac{1}{a b}} \log{\left(- b \sqrt{- \frac{1}{a b}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a b}} \log{\left(b \sqrt{- \frac{1}{a b}} + x \right)}}{2}"," ",0,"-sqrt(-1/(a*b))*log(-b*sqrt(-1/(a*b)) + x)/2 + sqrt(-1/(a*b))*log(b*sqrt(-1/(a*b)) + x)/2","B",0
1852,1,15,0,0.218317," ","integrate(1/(a+b/x**2)/x**3,x)","\frac{\log{\left(x \right)}}{b} - \frac{\log{\left(x^{2} + \frac{b}{a} \right)}}{2 b}"," ",0,"log(x)/b - log(x**2 + b/a)/(2*b)","A",0
1853,1,65,0,0.188332," ","integrate(1/(a+b/x**2)/x**4,x)","\frac{\sqrt{- \frac{a}{b^{3}}} \log{\left(x - \frac{b^{2} \sqrt{- \frac{a}{b^{3}}}}{a} \right)}}{2} - \frac{\sqrt{- \frac{a}{b^{3}}} \log{\left(x + \frac{b^{2} \sqrt{- \frac{a}{b^{3}}}}{a} \right)}}{2} - \frac{1}{b x}"," ",0,"sqrt(-a/b**3)*log(x - b**2*sqrt(-a/b**3)/a)/2 - sqrt(-a/b**3)*log(x + b**2*sqrt(-a/b**3)/a)/2 - 1/(b*x)","B",0
1854,1,31,0,0.277650," ","integrate(1/(a+b/x**2)/x**5,x)","- \frac{a \log{\left(x \right)}}{b^{2}} + \frac{a \log{\left(x^{2} + \frac{b}{a} \right)}}{2 b^{2}} - \frac{1}{2 b x^{2}}"," ",0,"-a*log(x)/b**2 + a*log(x**2 + b/a)/(2*b**2) - 1/(2*b*x**2)","A",0
1855,1,87,0,0.233241," ","integrate(1/(a+b/x**2)/x**6,x)","- \frac{\sqrt{- \frac{a^{3}}{b^{5}}} \log{\left(x - \frac{b^{3} \sqrt{- \frac{a^{3}}{b^{5}}}}{a^{2}} \right)}}{2} + \frac{\sqrt{- \frac{a^{3}}{b^{5}}} \log{\left(x + \frac{b^{3} \sqrt{- \frac{a^{3}}{b^{5}}}}{a^{2}} \right)}}{2} + \frac{3 a x^{2} - b}{3 b^{2} x^{3}}"," ",0,"-sqrt(-a**3/b**5)*log(x - b**3*sqrt(-a**3/b**5)/a**2)/2 + sqrt(-a**3/b**5)*log(x + b**3*sqrt(-a**3/b**5)/a**2)/2 + (3*a*x**2 - b)/(3*b**2*x**3)","B",0
1856,1,42,0,0.324473," ","integrate(1/(a+b/x**2)/x**7,x)","\frac{a^{2} \log{\left(x \right)}}{b^{3}} - \frac{a^{2} \log{\left(x^{2} + \frac{b}{a} \right)}}{2 b^{3}} + \frac{2 a x^{2} - b}{4 b^{2} x^{4}}"," ",0,"a**2*log(x)/b**3 - a**2*log(x**2 + b/a)/(2*b**3) + (2*a*x**2 - b)/(4*b**2*x**4)","A",0
1857,1,100,0,0.279360," ","integrate(1/(a+b/x**2)/x**8,x)","\frac{\sqrt{- \frac{a^{5}}{b^{7}}} \log{\left(x - \frac{b^{4} \sqrt{- \frac{a^{5}}{b^{7}}}}{a^{3}} \right)}}{2} - \frac{\sqrt{- \frac{a^{5}}{b^{7}}} \log{\left(x + \frac{b^{4} \sqrt{- \frac{a^{5}}{b^{7}}}}{a^{3}} \right)}}{2} + \frac{- 15 a^{2} x^{4} + 5 a b x^{2} - 3 b^{2}}{15 b^{3} x^{5}}"," ",0,"sqrt(-a**5/b**7)*log(x - b**4*sqrt(-a**5/b**7)/a**3)/2 - sqrt(-a**5/b**7)*log(x + b**4*sqrt(-a**5/b**7)/a**3)/2 + (-15*a**2*x**4 + 5*a*b*x**2 - 3*b**2)/(15*b**3*x**5)","B",0
1858,1,134,0,0.346390," ","integrate(x**6/(a+b/x**2)**2,x)","- \frac{b^{4} x}{2 a^{6} x^{2} + 2 a^{5} b} - \frac{9 \sqrt{- \frac{b^{7}}{a^{11}}} \log{\left(- \frac{a^{5} \sqrt{- \frac{b^{7}}{a^{11}}}}{b^{3}} + x \right)}}{4} + \frac{9 \sqrt{- \frac{b^{7}}{a^{11}}} \log{\left(\frac{a^{5} \sqrt{- \frac{b^{7}}{a^{11}}}}{b^{3}} + x \right)}}{4} + \frac{x^{7}}{7 a^{2}} - \frac{2 b x^{5}}{5 a^{3}} + \frac{b^{2} x^{3}}{a^{4}} - \frac{4 b^{3} x}{a^{5}}"," ",0,"-b**4*x/(2*a**6*x**2 + 2*a**5*b) - 9*sqrt(-b**7/a**11)*log(-a**5*sqrt(-b**7/a**11)/b**3 + x)/4 + 9*sqrt(-b**7/a**11)*log(a**5*sqrt(-b**7/a**11)/b**3 + x)/4 + x**7/(7*a**2) - 2*b*x**5/(5*a**3) + b**2*x**3/a**4 - 4*b**3*x/a**5","A",0
1859,1,66,0,0.292274," ","integrate(x**5/(a+b/x**2)**2,x)","- \frac{b^{4}}{2 a^{6} x^{2} + 2 a^{5} b} + \frac{x^{6}}{6 a^{2}} - \frac{b x^{4}}{2 a^{3}} + \frac{3 b^{2} x^{2}}{2 a^{4}} - \frac{2 b^{3} \log{\left(a x^{2} + b \right)}}{a^{5}}"," ",0,"-b**4/(2*a**6*x**2 + 2*a**5*b) + x**6/(6*a**2) - b*x**4/(2*a**3) + 3*b**2*x**2/(2*a**4) - 2*b**3*log(a*x**2 + b)/a**5","A",0
1860,1,124,0,0.324096," ","integrate(x**4/(a+b/x**2)**2,x)","\frac{b^{3} x}{2 a^{5} x^{2} + 2 a^{4} b} + \frac{7 \sqrt{- \frac{b^{5}}{a^{9}}} \log{\left(- \frac{a^{4} \sqrt{- \frac{b^{5}}{a^{9}}}}{b^{2}} + x \right)}}{4} - \frac{7 \sqrt{- \frac{b^{5}}{a^{9}}} \log{\left(\frac{a^{4} \sqrt{- \frac{b^{5}}{a^{9}}}}{b^{2}} + x \right)}}{4} + \frac{x^{5}}{5 a^{2}} - \frac{2 b x^{3}}{3 a^{3}} + \frac{3 b^{2} x}{a^{4}}"," ",0,"b**3*x/(2*a**5*x**2 + 2*a**4*b) + 7*sqrt(-b**5/a**9)*log(-a**4*sqrt(-b**5/a**9)/b**2 + x)/4 - 7*sqrt(-b**5/a**9)*log(a**4*sqrt(-b**5/a**9)/b**2 + x)/4 + x**5/(5*a**2) - 2*b*x**3/(3*a**3) + 3*b**2*x/a**4","A",0
1861,1,53,0,0.270686," ","integrate(x**3/(a+b/x**2)**2,x)","\frac{b^{3}}{2 a^{5} x^{2} + 2 a^{4} b} + \frac{x^{4}}{4 a^{2}} - \frac{b x^{2}}{a^{3}} + \frac{3 b^{2} \log{\left(a x^{2} + b \right)}}{2 a^{4}}"," ",0,"b**3/(2*a**5*x**2 + 2*a**4*b) + x**4/(4*a**2) - b*x**2/a**3 + 3*b**2*log(a*x**2 + b)/(2*a**4)","A",0
1862,1,107,0,0.300681," ","integrate(x**2/(a+b/x**2)**2,x)","- \frac{b^{2} x}{2 a^{4} x^{2} + 2 a^{3} b} - \frac{5 \sqrt{- \frac{b^{3}}{a^{7}}} \log{\left(- \frac{a^{3} \sqrt{- \frac{b^{3}}{a^{7}}}}{b} + x \right)}}{4} + \frac{5 \sqrt{- \frac{b^{3}}{a^{7}}} \log{\left(\frac{a^{3} \sqrt{- \frac{b^{3}}{a^{7}}}}{b} + x \right)}}{4} + \frac{x^{3}}{3 a^{2}} - \frac{2 b x}{a^{3}}"," ",0,"-b**2*x/(2*a**4*x**2 + 2*a**3*b) - 5*sqrt(-b**3/a**7)*log(-a**3*sqrt(-b**3/a**7)/b + x)/4 + 5*sqrt(-b**3/a**7)*log(a**3*sqrt(-b**3/a**7)/b + x)/4 + x**3/(3*a**2) - 2*b*x/a**3","A",0
1863,1,39,0,0.250953," ","integrate(x/(a+b/x**2)**2,x)","- \frac{b^{2}}{2 a^{4} x^{2} + 2 a^{3} b} + \frac{x^{2}}{2 a^{2}} - \frac{b \log{\left(a x^{2} + b \right)}}{a^{3}}"," ",0,"-b**2/(2*a**4*x**2 + 2*a**3*b) + x**2/(2*a**2) - b*log(a*x**2 + b)/a**3","A",0
1864,1,83,0,0.275784," ","integrate(1/(a+b/x**2)**2,x)","\frac{b x}{2 a^{3} x^{2} + 2 a^{2} b} + \frac{3 \sqrt{- \frac{b}{a^{5}}} \log{\left(- a^{2} \sqrt{- \frac{b}{a^{5}}} + x \right)}}{4} - \frac{3 \sqrt{- \frac{b}{a^{5}}} \log{\left(a^{2} \sqrt{- \frac{b}{a^{5}}} + x \right)}}{4} + \frac{x}{a^{2}}"," ",0,"b*x/(2*a**3*x**2 + 2*a**2*b) + 3*sqrt(-b/a**5)*log(-a**2*sqrt(-b/a**5) + x)/4 - 3*sqrt(-b/a**5)*log(a**2*sqrt(-b/a**5) + x)/4 + x/a**2","A",0
1865,1,29,0,0.206358," ","integrate(1/(a+b/x**2)**2/x,x)","\frac{b}{2 a^{3} x^{2} + 2 a^{2} b} + \frac{\log{\left(a x^{2} + b \right)}}{2 a^{2}}"," ",0,"b/(2*a**3*x**2 + 2*a**2*b) + log(a*x**2 + b)/(2*a**2)","A",0
1866,1,78,0,0.221939," ","integrate(1/(a+b/x**2)**2/x**2,x)","- \frac{x}{2 a^{2} x^{2} + 2 a b} - \frac{\sqrt{- \frac{1}{a^{3} b}} \log{\left(- a b \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b}} \log{\left(a b \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{4}"," ",0,"-x/(2*a**2*x**2 + 2*a*b) - sqrt(-1/(a**3*b))*log(-a*b*sqrt(-1/(a**3*b)) + x)/4 + sqrt(-1/(a**3*b))*log(a*b*sqrt(-1/(a**3*b)) + x)/4","B",0
1867,1,15,0,0.169156," ","integrate(1/(a+b/x**2)**2/x**3,x)","- \frac{1}{2 a^{2} x^{2} + 2 a b}"," ",0,"-1/(2*a**2*x**2 + 2*a*b)","A",0
1868,1,78,0,0.227480," ","integrate(1/(a+b/x**2)**2/x**4,x)","\frac{x}{2 a b x^{2} + 2 b^{2}} - \frac{\sqrt{- \frac{1}{a b^{3}}} \log{\left(- b^{2} \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a b^{3}}} \log{\left(b^{2} \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{4}"," ",0,"x/(2*a*b*x**2 + 2*b**2) - sqrt(-1/(a*b**3))*log(-b**2*sqrt(-1/(a*b**3)) + x)/4 + sqrt(-1/(a*b**3))*log(b**2*sqrt(-1/(a*b**3)) + x)/4","B",0
1869,1,34,0,0.305944," ","integrate(1/(a+b/x**2)**2/x**5,x)","\frac{1}{2 a b x^{2} + 2 b^{2}} + \frac{\log{\left(x \right)}}{b^{2}} - \frac{\log{\left(x^{2} + \frac{b}{a} \right)}}{2 b^{2}}"," ",0,"1/(2*a*b*x**2 + 2*b**2) + log(x)/b**2 - log(x**2 + b/a)/(2*b**2)","A",0
1870,1,92,0,0.312100," ","integrate(1/(a+b/x**2)**2/x**6,x)","\frac{3 \sqrt{- \frac{a}{b^{5}}} \log{\left(x - \frac{b^{3} \sqrt{- \frac{a}{b^{5}}}}{a} \right)}}{4} - \frac{3 \sqrt{- \frac{a}{b^{5}}} \log{\left(x + \frac{b^{3} \sqrt{- \frac{a}{b^{5}}}}{a} \right)}}{4} + \frac{- 3 a x^{2} - 2 b}{2 a b^{2} x^{3} + 2 b^{3} x}"," ",0,"3*sqrt(-a/b**5)*log(x - b**3*sqrt(-a/b**5)/a)/4 - 3*sqrt(-a/b**5)*log(x + b**3*sqrt(-a/b**5)/a)/4 + (-3*a*x**2 - 2*b)/(2*a*b**2*x**3 + 2*b**3*x)","A",0
1871,1,51,0,0.390693," ","integrate(1/(a+b/x**2)**2/x**7,x)","- \frac{2 a \log{\left(x \right)}}{b^{3}} + \frac{a \log{\left(x^{2} + \frac{b}{a} \right)}}{b^{3}} + \frac{- 2 a x^{2} - b}{2 a b^{2} x^{4} + 2 b^{3} x^{2}}"," ",0,"-2*a*log(x)/b**3 + a*log(x**2 + b/a)/b**3 + (-2*a*x**2 - b)/(2*a*b**2*x**4 + 2*b**3*x**2)","A",0
1872,1,114,0,0.371376," ","integrate(1/(a+b/x**2)**2/x**8,x)","- \frac{5 \sqrt{- \frac{a^{3}}{b^{7}}} \log{\left(x - \frac{b^{4} \sqrt{- \frac{a^{3}}{b^{7}}}}{a^{2}} \right)}}{4} + \frac{5 \sqrt{- \frac{a^{3}}{b^{7}}} \log{\left(x + \frac{b^{4} \sqrt{- \frac{a^{3}}{b^{7}}}}{a^{2}} \right)}}{4} + \frac{15 a^{2} x^{4} + 10 a b x^{2} - 2 b^{2}}{6 a b^{3} x^{5} + 6 b^{4} x^{3}}"," ",0,"-5*sqrt(-a**3/b**7)*log(x - b**4*sqrt(-a**3/b**7)/a**2)/4 + 5*sqrt(-a**3/b**7)*log(x + b**4*sqrt(-a**3/b**7)/a**2)/4 + (15*a**2*x**4 + 10*a*b*x**2 - 2*b**2)/(6*a*b**3*x**5 + 6*b**4*x**3)","A",0
1873,1,68,0,0.458842," ","integrate(1/(a+b/x**2)**2/x**9,x)","\frac{3 a^{2} \log{\left(x \right)}}{b^{4}} - \frac{3 a^{2} \log{\left(x^{2} + \frac{b}{a} \right)}}{2 b^{4}} + \frac{6 a^{2} x^{4} + 3 a b x^{2} - b^{2}}{4 a b^{3} x^{6} + 4 b^{4} x^{4}}"," ",0,"3*a**2*log(x)/b**4 - 3*a**2*log(x**2 + b/a)/(2*b**4) + (6*a**2*x**4 + 3*a*b*x**2 - b**2)/(4*a*b**3*x**6 + 4*b**4*x**4)","A",0
1874,1,92,0,0.465892," ","integrate(x**5/(a+b/x**2)**3,x)","\frac{- 10 a b^{4} x^{2} - 9 b^{5}}{4 a^{8} x^{4} + 8 a^{7} b x^{2} + 4 a^{6} b^{2}} + \frac{x^{6}}{6 a^{3}} - \frac{3 b x^{4}}{4 a^{4}} + \frac{3 b^{2} x^{2}}{a^{5}} - \frac{5 b^{3} \log{\left(a x^{2} + b \right)}}{a^{6}}"," ",0,"(-10*a*b**4*x**2 - 9*b**5)/(4*a**8*x**4 + 8*a**7*b*x**2 + 4*a**6*b**2) + x**6/(6*a**3) - 3*b*x**4/(4*a**4) + 3*b**2*x**2/a**5 - 5*b**3*log(a*x**2 + b)/a**6","A",0
1875,1,144,0,0.485417," ","integrate(x**4/(a+b/x**2)**3,x)","\frac{63 \sqrt{- \frac{b^{5}}{a^{11}}} \log{\left(- \frac{a^{5} \sqrt{- \frac{b^{5}}{a^{11}}}}{b^{2}} + x \right)}}{16} - \frac{63 \sqrt{- \frac{b^{5}}{a^{11}}} \log{\left(\frac{a^{5} \sqrt{- \frac{b^{5}}{a^{11}}}}{b^{2}} + x \right)}}{16} + \frac{17 a b^{3} x^{3} + 15 b^{4} x}{8 a^{7} x^{4} + 16 a^{6} b x^{2} + 8 a^{5} b^{2}} + \frac{x^{5}}{5 a^{3}} - \frac{b x^{3}}{a^{4}} + \frac{6 b^{2} x}{a^{5}}"," ",0,"63*sqrt(-b**5/a**11)*log(-a**5*sqrt(-b**5/a**11)/b**2 + x)/16 - 63*sqrt(-b**5/a**11)*log(a**5*sqrt(-b**5/a**11)/b**2 + x)/16 + (17*a*b**3*x**3 + 15*b**4*x)/(8*a**7*x**4 + 16*a**6*b*x**2 + 8*a**5*b**2) + x**5/(5*a**3) - b*x**3/a**4 + 6*b**2*x/a**5","A",0
1876,1,78,0,0.440693," ","integrate(x**3/(a+b/x**2)**3,x)","\frac{8 a b^{3} x^{2} + 7 b^{4}}{4 a^{7} x^{4} + 8 a^{6} b x^{2} + 4 a^{5} b^{2}} + \frac{x^{4}}{4 a^{3}} - \frac{3 b x^{2}}{2 a^{4}} + \frac{3 b^{2} \log{\left(a x^{2} + b \right)}}{a^{5}}"," ",0,"(8*a*b**3*x**2 + 7*b**4)/(4*a**7*x**4 + 8*a**6*b*x**2 + 4*a**5*b**2) + x**4/(4*a**3) - 3*b*x**2/(2*a**4) + 3*b**2*log(a*x**2 + b)/a**5","A",0
1877,1,133,0,0.476796," ","integrate(x**2/(a+b/x**2)**3,x)","- \frac{35 \sqrt{- \frac{b^{3}}{a^{9}}} \log{\left(- \frac{a^{4} \sqrt{- \frac{b^{3}}{a^{9}}}}{b} + x \right)}}{16} + \frac{35 \sqrt{- \frac{b^{3}}{a^{9}}} \log{\left(\frac{a^{4} \sqrt{- \frac{b^{3}}{a^{9}}}}{b} + x \right)}}{16} + \frac{- 13 a b^{2} x^{3} - 11 b^{3} x}{8 a^{6} x^{4} + 16 a^{5} b x^{2} + 8 a^{4} b^{2}} + \frac{x^{3}}{3 a^{3}} - \frac{3 b x}{a^{4}}"," ",0,"-35*sqrt(-b**3/a**9)*log(-a**4*sqrt(-b**3/a**9)/b + x)/16 + 35*sqrt(-b**3/a**9)*log(a**4*sqrt(-b**3/a**9)/b + x)/16 + (-13*a*b**2*x**3 - 11*b**3*x)/(8*a**6*x**4 + 16*a**5*b*x**2 + 8*a**4*b**2) + x**3/(3*a**3) - 3*b*x/a**4","A",0
1878,1,68,0,0.403708," ","integrate(x/(a+b/x**2)**3,x)","\frac{- 6 a b^{2} x^{2} - 5 b^{3}}{4 a^{6} x^{4} + 8 a^{5} b x^{2} + 4 a^{4} b^{2}} + \frac{x^{2}}{2 a^{3}} - \frac{3 b \log{\left(a x^{2} + b \right)}}{2 a^{4}}"," ",0,"(-6*a*b**2*x**2 - 5*b**3)/(4*a**6*x**4 + 8*a**5*b*x**2 + 4*a**4*b**2) + x**2/(2*a**3) - 3*b*log(a*x**2 + b)/(2*a**4)","A",0
1879,1,107,0,0.425330," ","integrate(1/(a+b/x**2)**3,x)","\frac{15 \sqrt{- \frac{b}{a^{7}}} \log{\left(- a^{3} \sqrt{- \frac{b}{a^{7}}} + x \right)}}{16} - \frac{15 \sqrt{- \frac{b}{a^{7}}} \log{\left(a^{3} \sqrt{- \frac{b}{a^{7}}} + x \right)}}{16} + \frac{9 a b x^{3} + 7 b^{2} x}{8 a^{5} x^{4} + 16 a^{4} b x^{2} + 8 a^{3} b^{2}} + \frac{x}{a^{3}}"," ",0,"15*sqrt(-b/a**7)*log(-a**3*sqrt(-b/a**7) + x)/16 - 15*sqrt(-b/a**7)*log(a**3*sqrt(-b/a**7) + x)/16 + (9*a*b*x**3 + 7*b**2*x)/(8*a**5*x**4 + 16*a**4*b*x**2 + 8*a**3*b**2) + x/a**3","A",0
1880,1,53,0,0.346199," ","integrate(1/(a+b/x**2)**3/x,x)","\frac{4 a b x^{2} + 3 b^{2}}{4 a^{5} x^{4} + 8 a^{4} b x^{2} + 4 a^{3} b^{2}} + \frac{\log{\left(a x^{2} + b \right)}}{2 a^{3}}"," ",0,"(4*a*b*x**2 + 3*b**2)/(4*a**5*x**4 + 8*a**4*b*x**2 + 4*a**3*b**2) + log(a*x**2 + b)/(2*a**3)","A",0
1881,1,110,0,0.366709," ","integrate(1/(a+b/x**2)**3/x**2,x)","- \frac{3 \sqrt{- \frac{1}{a^{5} b}} \log{\left(- a^{2} b \sqrt{- \frac{1}{a^{5} b}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{a^{5} b}} \log{\left(a^{2} b \sqrt{- \frac{1}{a^{5} b}} + x \right)}}{16} + \frac{- 5 a x^{3} - 3 b x}{8 a^{4} x^{4} + 16 a^{3} b x^{2} + 8 a^{2} b^{2}}"," ",0,"-3*sqrt(-1/(a**5*b))*log(-a**2*b*sqrt(-1/(a**5*b)) + x)/16 + 3*sqrt(-1/(a**5*b))*log(a**2*b*sqrt(-1/(a**5*b)) + x)/16 + (-5*a*x**3 - 3*b*x)/(8*a**4*x**4 + 16*a**3*b*x**2 + 8*a**2*b**2)","A",0
1882,1,36,0,0.287840," ","integrate(1/(a+b/x**2)**3/x**3,x)","\frac{- 2 a x^{2} - b}{4 a^{4} x^{4} + 8 a^{3} b x^{2} + 4 a^{2} b^{2}}"," ",0,"(-2*a*x**2 - b)/(4*a**4*x**4 + 8*a**3*b*x**2 + 4*a**2*b**2)","B",0
1883,1,110,0,0.333882," ","integrate(1/(a+b/x**2)**3/x**4,x)","- \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \log{\left(- a b^{2} \sqrt{- \frac{1}{a^{3} b^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \log{\left(a b^{2} \sqrt{- \frac{1}{a^{3} b^{3}}} + x \right)}}{16} + \frac{a x^{3} - b x}{8 a^{3} b x^{4} + 16 a^{2} b^{2} x^{2} + 8 a b^{3}}"," ",0,"-sqrt(-1/(a**3*b**3))*log(-a*b**2*sqrt(-1/(a**3*b**3)) + x)/16 + sqrt(-1/(a**3*b**3))*log(a*b**2*sqrt(-1/(a**3*b**3)) + x)/16 + (a*x**3 - b*x)/(8*a**3*b*x**4 + 16*a**2*b**2*x**2 + 8*a*b**3)","B",0
1884,1,27,0,0.259656," ","integrate(1/(a+b/x**2)**3/x**5,x)","- \frac{1}{4 a^{3} x^{4} + 8 a^{2} b x^{2} + 4 a b^{2}}"," ",0,"-1/(4*a**3*x**4 + 8*a**2*b*x**2 + 4*a*b**2)","A",0
1885,1,105,0,0.335859," ","integrate(1/(a+b/x**2)**3/x**6,x)","- \frac{3 \sqrt{- \frac{1}{a b^{5}}} \log{\left(- b^{3} \sqrt{- \frac{1}{a b^{5}}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{a b^{5}}} \log{\left(b^{3} \sqrt{- \frac{1}{a b^{5}}} + x \right)}}{16} + \frac{3 a x^{3} + 5 b x}{8 a^{2} b^{2} x^{4} + 16 a b^{3} x^{2} + 8 b^{4}}"," ",0,"-3*sqrt(-1/(a*b**5))*log(-b**3*sqrt(-1/(a*b**5)) + x)/16 + 3*sqrt(-1/(a*b**5))*log(b**3*sqrt(-1/(a*b**5)) + x)/16 + (3*a*x**3 + 5*b*x)/(8*a**2*b**2*x**4 + 16*a*b**3*x**2 + 8*b**4)","A",0
1886,1,56,0,0.434243," ","integrate(1/(a+b/x**2)**3/x**7,x)","\frac{2 a x^{2} + 3 b}{4 a^{2} b^{2} x^{4} + 8 a b^{3} x^{2} + 4 b^{4}} + \frac{\log{\left(x \right)}}{b^{3}} - \frac{\log{\left(x^{2} + \frac{b}{a} \right)}}{2 b^{3}}"," ",0,"(2*a*x**2 + 3*b)/(4*a**2*b**2*x**4 + 8*a*b**3*x**2 + 4*b**4) + log(x)/b**3 - log(x**2 + b/a)/(2*b**3)","A",0
1887,1,116,0,0.432438," ","integrate(1/(a+b/x**2)**3/x**8,x)","\frac{15 \sqrt{- \frac{a}{b^{7}}} \log{\left(x - \frac{b^{4} \sqrt{- \frac{a}{b^{7}}}}{a} \right)}}{16} - \frac{15 \sqrt{- \frac{a}{b^{7}}} \log{\left(x + \frac{b^{4} \sqrt{- \frac{a}{b^{7}}}}{a} \right)}}{16} + \frac{- 15 a^{2} x^{4} - 25 a b x^{2} - 8 b^{2}}{8 a^{2} b^{3} x^{5} + 16 a b^{4} x^{3} + 8 b^{5} x}"," ",0,"15*sqrt(-a/b**7)*log(x - b**4*sqrt(-a/b**7)/a)/16 - 15*sqrt(-a/b**7)*log(x + b**4*sqrt(-a/b**7)/a)/16 + (-15*a**2*x**4 - 25*a*b*x**2 - 8*b**2)/(8*a**2*b**3*x**5 + 16*a*b**4*x**3 + 8*b**5*x)","A",0
1888,1,80,0,0.530416," ","integrate(1/(a+b/x**2)**3/x**9,x)","- \frac{3 a \log{\left(x \right)}}{b^{4}} + \frac{3 a \log{\left(x^{2} + \frac{b}{a} \right)}}{2 b^{4}} + \frac{- 6 a^{2} x^{4} - 9 a b x^{2} - 2 b^{2}}{4 a^{2} b^{3} x^{6} + 8 a b^{4} x^{4} + 4 b^{5} x^{2}}"," ",0,"-3*a*log(x)/b**4 + 3*a*log(x**2 + b/a)/(2*b**4) + (-6*a**2*x**4 - 9*a*b*x**2 - 2*b**2)/(4*a**2*b**3*x**6 + 8*a*b**4*x**4 + 4*b**5*x**2)","A",0
1889,1,138,0,0.485585," ","integrate(1/(a+b/x**2)**3/x**10,x)","- \frac{35 \sqrt{- \frac{a^{3}}{b^{9}}} \log{\left(x - \frac{b^{5} \sqrt{- \frac{a^{3}}{b^{9}}}}{a^{2}} \right)}}{16} + \frac{35 \sqrt{- \frac{a^{3}}{b^{9}}} \log{\left(x + \frac{b^{5} \sqrt{- \frac{a^{3}}{b^{9}}}}{a^{2}} \right)}}{16} + \frac{105 a^{3} x^{6} + 175 a^{2} b x^{4} + 56 a b^{2} x^{2} - 8 b^{3}}{24 a^{2} b^{4} x^{7} + 48 a b^{5} x^{5} + 24 b^{6} x^{3}}"," ",0,"-35*sqrt(-a**3/b**9)*log(x - b**5*sqrt(-a**3/b**9)/a**2)/16 + 35*sqrt(-a**3/b**9)*log(x + b**5*sqrt(-a**3/b**9)/a**2)/16 + (105*a**3*x**6 + 175*a**2*b*x**4 + 56*a*b**2*x**2 - 8*b**3)/(24*a**2*b**4*x**7 + 48*a*b**5*x**5 + 24*b**6*x**3)","A",0
1890,1,90,0,0.571793," ","integrate(1/(a+b/x**2)**3/x**11,x)","\frac{6 a^{2} \log{\left(x \right)}}{b^{5}} - \frac{3 a^{2} \log{\left(x^{2} + \frac{b}{a} \right)}}{b^{5}} + \frac{12 a^{3} x^{6} + 18 a^{2} b x^{4} + 4 a b^{2} x^{2} - b^{3}}{4 a^{2} b^{4} x^{8} + 8 a b^{5} x^{6} + 4 b^{6} x^{4}}"," ",0,"6*a**2*log(x)/b**5 - 3*a**2*log(x**2 + b/a)/b**5 + (12*a**3*x**6 + 18*a**2*b*x**4 + 4*a*b**2*x**2 - b**3)/(4*a**2*b**4*x**8 + 8*a*b**5*x**6 + 4*b**6*x**4)","A",0
1891,1,92,0,3.929328," ","integrate((a+b/x**2)**(1/2)*x**3,x)","\frac{a x^{5}}{4 \sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}} + \frac{3 \sqrt{b} x^{3}}{8 \sqrt{\frac{a x^{2}}{b} + 1}} + \frac{b^{\frac{3}{2}} x}{8 a \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{8 a^{\frac{3}{2}}}"," ",0,"a*x**5/(4*sqrt(b)*sqrt(a*x**2/b + 1)) + 3*sqrt(b)*x**3/(8*sqrt(a*x**2/b + 1)) + b**(3/2)*x/(8*a*sqrt(a*x**2/b + 1)) - b**2*asinh(sqrt(a)*x/sqrt(b))/(8*a**(3/2))","A",0
1892,1,41,0,0.850935," ","integrate((a+b/x**2)**(1/2)*x**2,x)","\frac{\sqrt{b} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{3} + \frac{b^{\frac{3}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a}"," ",0,"sqrt(b)*x**2*sqrt(a*x**2/b + 1)/3 + b**(3/2)*sqrt(a*x**2/b + 1)/(3*a)","B",0
1893,1,41,0,2.056033," ","integrate((a+b/x**2)**(1/2)*x,x)","\frac{\sqrt{b} x \sqrt{\frac{a x^{2}}{b} + 1}}{2} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{2 \sqrt{a}}"," ",0,"sqrt(b)*x*sqrt(a*x**2/b + 1)/2 + b*asinh(sqrt(a)*x/sqrt(b))/(2*sqrt(a))","A",0
1894,1,56,0,1.583176," ","integrate((a+b/x**2)**(1/2),x)","\frac{\sqrt{a} x}{\sqrt{1 + \frac{b}{a x^{2}}}} - \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)} + \frac{b}{\sqrt{a} x \sqrt{1 + \frac{b}{a x^{2}}}}"," ",0,"sqrt(a)*x/sqrt(1 + b/(a*x**2)) - sqrt(b)*asinh(sqrt(b)/(sqrt(a)*x)) + b/(sqrt(a)*x*sqrt(1 + b/(a*x**2)))","A",0
1895,1,56,0,1.585246," ","integrate((a+b/x**2)**(1/2)/x,x)","\sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)} - \frac{a x}{\sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{\sqrt{b}}{x \sqrt{\frac{a x^{2}}{b} + 1}}"," ",0,"sqrt(a)*asinh(sqrt(a)*x/sqrt(b)) - a*x/(sqrt(b)*sqrt(a*x**2/b + 1)) - sqrt(b)/(x*sqrt(a*x**2/b + 1))","A",0
1896,1,42,0,2.245343," ","integrate((a+b/x**2)**(1/2)/x**2,x)","- \frac{\sqrt{a} \sqrt{1 + \frac{b}{a x^{2}}}}{2 x} - \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{2 \sqrt{b}}"," ",0,"-sqrt(a)*sqrt(1 + b/(a*x**2))/(2*x) - a*asinh(sqrt(b)/(sqrt(a)*x))/(2*sqrt(b))","A",0
1897,1,42,0,1.096534," ","integrate((a+b/x**2)**(1/2)/x**3,x)","- \frac{a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{2}}}}{3 b} - \frac{\sqrt{a} \sqrt{1 + \frac{b}{a x^{2}}}}{3 x^{2}}"," ",0,"-a**(3/2)*sqrt(1 + b/(a*x**2))/(3*b) - sqrt(a)*sqrt(1 + b/(a*x**2))/(3*x**2)","B",0
1898,1,92,0,4.078717," ","integrate((a+b/x**2)**(1/2)/x**4,x)","- \frac{a^{\frac{3}{2}}}{8 b x \sqrt{1 + \frac{b}{a x^{2}}}} - \frac{3 \sqrt{a}}{8 x^{3} \sqrt{1 + \frac{b}{a x^{2}}}} + \frac{a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{8 b^{\frac{3}{2}}} - \frac{b}{4 \sqrt{a} x^{5} \sqrt{1 + \frac{b}{a x^{2}}}}"," ",0,"-a**(3/2)/(8*b*x*sqrt(1 + b/(a*x**2))) - 3*sqrt(a)/(8*x**3*sqrt(1 + b/(a*x**2))) + a**2*asinh(sqrt(b)/(sqrt(a)*x))/(8*b**(3/2)) - b/(4*sqrt(a)*x**5*sqrt(1 + b/(a*x**2)))","A",0
1899,1,70,0,3.526058," ","integrate((a+b/x**2)**(3/2)*x**3,x)","\frac{a \sqrt{b} x^{3} \sqrt{\frac{a x^{2}}{b} + 1}}{4} + \frac{5 b^{\frac{3}{2}} x \sqrt{\frac{a x^{2}}{b} + 1}}{8} + \frac{3 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{8 \sqrt{a}}"," ",0,"a*sqrt(b)*x**3*sqrt(a*x**2/b + 1)/4 + 5*b**(3/2)*x*sqrt(a*x**2/b + 1)/8 + 3*b**2*asinh(sqrt(a)*x/sqrt(b))/(8*sqrt(a))","A",0
1900,1,78,0,2.423005," ","integrate((a+b/x**2)**(3/2)*x**2,x)","\frac{a \sqrt{b} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{3} + \frac{4 b^{\frac{3}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{3} + \frac{b^{\frac{3}{2}} \log{\left(\frac{a x^{2}}{b} \right)}}{2} - b^{\frac{3}{2}} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}"," ",0,"a*sqrt(b)*x**2*sqrt(a*x**2/b + 1)/3 + 4*b**(3/2)*sqrt(a*x**2/b + 1)/3 + b**(3/2)*log(a*x**2/b)/2 - b**(3/2)*log(sqrt(a*x**2/b + 1) + 1)","A",0
1901,1,88,0,2.718374," ","integrate((a+b/x**2)**(3/2)*x,x)","\frac{3 \sqrt{a} b \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{2} + \frac{a^{2} x^{3}}{2 \sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{a \sqrt{b} x}{2 \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{b^{\frac{3}{2}}}{x \sqrt{\frac{a x^{2}}{b} + 1}}"," ",0,"3*sqrt(a)*b*asinh(sqrt(a)*x/sqrt(b))/2 + a**2*x**3/(2*sqrt(b)*sqrt(a*x**2/b + 1)) - a*sqrt(b)*x/(2*sqrt(a*x**2/b + 1)) - b**(3/2)/(x*sqrt(a*x**2/b + 1))","A",0
1902,1,88,0,2.806720," ","integrate((a+b/x**2)**(3/2),x)","\frac{a^{\frac{3}{2}} x}{\sqrt{1 + \frac{b}{a x^{2}}}} + \frac{\sqrt{a} b}{2 x \sqrt{1 + \frac{b}{a x^{2}}}} - \frac{3 a \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{2} - \frac{b^{2}}{2 \sqrt{a} x^{3} \sqrt{1 + \frac{b}{a x^{2}}}}"," ",0,"a**(3/2)*x/sqrt(1 + b/(a*x**2)) + sqrt(a)*b/(2*x*sqrt(1 + b/(a*x**2))) - 3*a*sqrt(b)*asinh(sqrt(b)/(sqrt(a)*x))/2 - b**2/(2*sqrt(a)*x**3*sqrt(1 + b/(a*x**2)))","A",0
1903,1,78,0,2.340881," ","integrate((a+b/x**2)**(3/2)/x,x)","- \frac{4 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{2}}}}{3} - \frac{a^{\frac{3}{2}} \log{\left(\frac{b}{a x^{2}} \right)}}{2} + a^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)} - \frac{\sqrt{a} b \sqrt{1 + \frac{b}{a x^{2}}}}{3 x^{2}}"," ",0,"-4*a**(3/2)*sqrt(1 + b/(a*x**2))/3 - a**(3/2)*log(b/(a*x**2))/2 + a**(3/2)*log(sqrt(1 + b/(a*x**2)) + 1) - sqrt(a)*b*sqrt(1 + b/(a*x**2))/(3*x**2)","A",0
1904,1,71,0,3.645439," ","integrate((a+b/x**2)**(3/2)/x**2,x)","- \frac{5 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{2}}}}{8 x} - \frac{\sqrt{a} b \sqrt{1 + \frac{b}{a x^{2}}}}{4 x^{3}} - \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{8 \sqrt{b}}"," ",0,"-5*a**(3/2)*sqrt(1 + b/(a*x**2))/(8*x) - sqrt(a)*b*sqrt(1 + b/(a*x**2))/(4*x**3) - 3*a**2*asinh(sqrt(b)/(sqrt(a)*x))/(8*sqrt(b))","A",0
1905,1,68,0,1.175828," ","integrate((a+b/x**2)**(3/2)/x**3,x)","- \frac{a^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x^{2}}}}{5 b} - \frac{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{2}}}}{5 x^{2}} - \frac{\sqrt{a} b \sqrt{1 + \frac{b}{a x^{2}}}}{5 x^{4}}"," ",0,"-a**(5/2)*sqrt(1 + b/(a*x**2))/(5*b) - 2*a**(3/2)*sqrt(1 + b/(a*x**2))/(5*x**2) - sqrt(a)*b*sqrt(1 + b/(a*x**2))/(5*x**4)","B",0
1906,1,119,0,5.973997," ","integrate((a+b/x**2)**(3/2)/x**4,x)","- \frac{a^{\frac{5}{2}}}{16 b x \sqrt{1 + \frac{b}{a x^{2}}}} - \frac{17 a^{\frac{3}{2}}}{48 x^{3} \sqrt{1 + \frac{b}{a x^{2}}}} - \frac{11 \sqrt{a} b}{24 x^{5} \sqrt{1 + \frac{b}{a x^{2}}}} + \frac{a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{16 b^{\frac{3}{2}}} - \frac{b^{2}}{6 \sqrt{a} x^{7} \sqrt{1 + \frac{b}{a x^{2}}}}"," ",0,"-a**(5/2)/(16*b*x*sqrt(1 + b/(a*x**2))) - 17*a**(3/2)/(48*x**3*sqrt(1 + b/(a*x**2))) - 11*sqrt(a)*b/(24*x**5*sqrt(1 + b/(a*x**2))) + a**3*asinh(sqrt(b)/(sqrt(a)*x))/(16*b**(3/2)) - b**2/(6*sqrt(a)*x**7*sqrt(1 + b/(a*x**2)))","A",0
1907,1,117,0,4.666552," ","integrate((a+b/x**2)**(5/2)*x**3,x)","\frac{15 \sqrt{a} b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{8} + \frac{a^{3} x^{5}}{4 \sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}} + \frac{11 a^{2} \sqrt{b} x^{3}}{8 \sqrt{\frac{a x^{2}}{b} + 1}} + \frac{a b^{\frac{3}{2}} x}{8 \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{b^{\frac{5}{2}}}{x \sqrt{\frac{a x^{2}}{b} + 1}}"," ",0,"15*sqrt(a)*b**2*asinh(sqrt(a)*x/sqrt(b))/8 + a**3*x**5/(4*sqrt(b)*sqrt(a*x**2/b + 1)) + 11*a**2*sqrt(b)*x**3/(8*sqrt(a*x**2/b + 1)) + a*b**(3/2)*x/(8*sqrt(a*x**2/b + 1)) - b**(5/2)/(x*sqrt(a*x**2/b + 1))","A",0
1908,1,112,0,3.995932," ","integrate((a+b/x**2)**(5/2)*x**2,x)","\frac{a^{2} \sqrt{b} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{3} + \frac{7 a b^{\frac{3}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{3} + \frac{5 a b^{\frac{3}{2}} \log{\left(\frac{a x^{2}}{b} \right)}}{4} - \frac{5 a b^{\frac{3}{2}} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{2} - \frac{b^{\frac{5}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{2 x^{2}}"," ",0,"a**2*sqrt(b)*x**2*sqrt(a*x**2/b + 1)/3 + 7*a*b**(3/2)*sqrt(a*x**2/b + 1)/3 + 5*a*b**(3/2)*log(a*x**2/b)/4 - 5*a*b**(3/2)*log(sqrt(a*x**2/b + 1) + 1)/2 - b**(5/2)*sqrt(a*x**2/b + 1)/(2*x**2)","A",0
1909,1,112,0,4.004741," ","integrate((a+b/x**2)**(5/2)*x,x)","\frac{a^{\frac{5}{2}} x^{2} \sqrt{1 + \frac{b}{a x^{2}}}}{2} - \frac{7 a^{\frac{3}{2}} b \sqrt{1 + \frac{b}{a x^{2}}}}{3} - \frac{5 a^{\frac{3}{2}} b \log{\left(\frac{b}{a x^{2}} \right)}}{4} + \frac{5 a^{\frac{3}{2}} b \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{2} - \frac{\sqrt{a} b^{2} \sqrt{1 + \frac{b}{a x^{2}}}}{3 x^{2}}"," ",0,"a**(5/2)*x**2*sqrt(1 + b/(a*x**2))/2 - 7*a**(3/2)*b*sqrt(1 + b/(a*x**2))/3 - 5*a**(3/2)*b*log(b/(a*x**2))/4 + 5*a**(3/2)*b*log(sqrt(1 + b/(a*x**2)) + 1)/2 - sqrt(a)*b**2*sqrt(1 + b/(a*x**2))/(3*x**2)","A",0
1910,1,117,0,4.435012," ","integrate((a+b/x**2)**(5/2),x)","\frac{a^{\frac{5}{2}} x}{\sqrt{1 + \frac{b}{a x^{2}}}} - \frac{a^{\frac{3}{2}} b}{8 x \sqrt{1 + \frac{b}{a x^{2}}}} - \frac{11 \sqrt{a} b^{2}}{8 x^{3} \sqrt{1 + \frac{b}{a x^{2}}}} - \frac{15 a^{2} \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{8} - \frac{b^{3}}{4 \sqrt{a} x^{5} \sqrt{1 + \frac{b}{a x^{2}}}}"," ",0,"a**(5/2)*x/sqrt(1 + b/(a*x**2)) - a**(3/2)*b/(8*x*sqrt(1 + b/(a*x**2))) - 11*sqrt(a)*b**2/(8*x**3*sqrt(1 + b/(a*x**2))) - 15*a**2*sqrt(b)*asinh(sqrt(b)/(sqrt(a)*x))/8 - b**3/(4*sqrt(a)*x**5*sqrt(1 + b/(a*x**2)))","A",0
1911,1,105,0,4.103238," ","integrate((a+b/x**2)**(5/2)/x,x)","- \frac{23 a^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x^{2}}}}{15} - \frac{a^{\frac{5}{2}} \log{\left(\frac{b}{a x^{2}} \right)}}{2} + a^{\frac{5}{2}} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)} - \frac{11 a^{\frac{3}{2}} b \sqrt{1 + \frac{b}{a x^{2}}}}{15 x^{2}} - \frac{\sqrt{a} b^{2} \sqrt{1 + \frac{b}{a x^{2}}}}{5 x^{4}}"," ",0,"-23*a**(5/2)*sqrt(1 + b/(a*x**2))/15 - a**(5/2)*log(b/(a*x**2))/2 + a**(5/2)*log(sqrt(1 + b/(a*x**2)) + 1) - 11*a**(3/2)*b*sqrt(1 + b/(a*x**2))/(15*x**2) - sqrt(a)*b**2*sqrt(1 + b/(a*x**2))/(5*x**4)","A",0
1912,1,99,0,4.822353," ","integrate((a+b/x**2)**(5/2)/x**2,x)","- \frac{11 a^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x^{2}}}}{16 x} - \frac{13 a^{\frac{3}{2}} b \sqrt{1 + \frac{b}{a x^{2}}}}{24 x^{3}} - \frac{\sqrt{a} b^{2} \sqrt{1 + \frac{b}{a x^{2}}}}{6 x^{5}} - \frac{5 a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{16 \sqrt{b}}"," ",0,"-11*a**(5/2)*sqrt(1 + b/(a*x**2))/(16*x) - 13*a**(3/2)*b*sqrt(1 + b/(a*x**2))/(24*x**3) - sqrt(a)*b**2*sqrt(1 + b/(a*x**2))/(6*x**5) - 5*a**3*asinh(sqrt(b)/(sqrt(a)*x))/(16*sqrt(b))","A",0
1913,1,88,0,3.632057," ","integrate((a+b/x**2)**(5/2)/x**3,x)","\begin{cases} - \frac{a^{3} \sqrt{a + \frac{b}{x^{2}}}}{7 b} - \frac{3 a^{2} \sqrt{a + \frac{b}{x^{2}}}}{7 x^{2}} - \frac{3 a b \sqrt{a + \frac{b}{x^{2}}}}{7 x^{4}} - \frac{b^{2} \sqrt{a + \frac{b}{x^{2}}}}{7 x^{6}} & \text{for}\: b \neq 0 \\- \frac{a^{\frac{5}{2}}}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*sqrt(a + b/x**2)/(7*b) - 3*a**2*sqrt(a + b/x**2)/(7*x**2) - 3*a*b*sqrt(a + b/x**2)/(7*x**4) - b**2*sqrt(a + b/x**2)/(7*x**6), Ne(b, 0)), (-a**(5/2)/(2*x**2), True))","A",0
1914,1,150,0,8.186339," ","integrate((a+b/x**2)**(5/2)/x**4,x)","- \frac{5 a^{\frac{7}{2}}}{128 b x \sqrt{1 + \frac{b}{a x^{2}}}} - \frac{133 a^{\frac{5}{2}}}{384 x^{3} \sqrt{1 + \frac{b}{a x^{2}}}} - \frac{127 a^{\frac{3}{2}} b}{192 x^{5} \sqrt{1 + \frac{b}{a x^{2}}}} - \frac{23 \sqrt{a} b^{2}}{48 x^{7} \sqrt{1 + \frac{b}{a x^{2}}}} + \frac{5 a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{128 b^{\frac{3}{2}}} - \frac{b^{3}}{8 \sqrt{a} x^{9} \sqrt{1 + \frac{b}{a x^{2}}}}"," ",0,"-5*a**(7/2)/(128*b*x*sqrt(1 + b/(a*x**2))) - 133*a**(5/2)/(384*x**3*sqrt(1 + b/(a*x**2))) - 127*a**(3/2)*b/(192*x**5*sqrt(1 + b/(a*x**2))) - 23*sqrt(a)*b**2/(48*x**7*sqrt(1 + b/(a*x**2))) + 5*a**4*asinh(sqrt(b)/(sqrt(a)*x))/(128*b**(3/2)) - b**3/(8*sqrt(a)*x**9*sqrt(1 + b/(a*x**2)))","A",0
1915,1,95,0,4.866407," ","integrate(x**3/(a+b/x**2)**(1/2),x)","\frac{x^{5}}{4 \sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{\sqrt{b} x^{3}}{8 a \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{3 b^{\frac{3}{2}} x}{8 a^{2} \sqrt{\frac{a x^{2}}{b} + 1}} + \frac{3 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{8 a^{\frac{5}{2}}}"," ",0,"x**5/(4*sqrt(b)*sqrt(a*x**2/b + 1)) - sqrt(b)*x**3/(8*a*sqrt(a*x**2/b + 1)) - 3*b**(3/2)*x/(8*a**2*sqrt(a*x**2/b + 1)) + 3*b**2*asinh(sqrt(a)*x/sqrt(b))/(8*a**(5/2))","A",0
1916,1,42,0,2.739397," ","integrate(x/(a+b/x**2)**(1/2),x)","\frac{\sqrt{b} x \sqrt{\frac{a x^{2}}{b} + 1}}{2 a} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{2 a^{\frac{3}{2}}}"," ",0,"sqrt(b)*x*sqrt(a*x**2/b + 1)/(2*a) - b*asinh(sqrt(a)*x/sqrt(b))/(2*a**(3/2))","A",0
1917,1,17,0,1.286503," ","integrate(1/(a+b/x**2)**(1/2)/x,x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{\sqrt{a}}"," ",0,"asinh(sqrt(a)*x/sqrt(b))/sqrt(a)","A",0
1918,1,26,0,1.391320," ","integrate(1/(a+b/x**2)**(1/2)/x**3,x)","\begin{cases} - \frac{\sqrt{a + \frac{b}{x^{2}}}}{b} & \text{for}\: b \neq 0 \\- \frac{1}{2 \sqrt{a} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(a + b/x**2)/b, Ne(b, 0)), (-1/(2*sqrt(a)*x**2), True))","A",0
1919,1,231,0,1.619465," ","integrate(1/(a+b/x**2)**(1/2)/x**5,x)","\frac{2 a^{\frac{7}{2}} b^{\frac{3}{2}} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} x^{5} + 3 a^{\frac{3}{2}} b^{4} x^{3}} + \frac{a^{\frac{5}{2}} b^{\frac{5}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} x^{5} + 3 a^{\frac{3}{2}} b^{4} x^{3}} - \frac{a^{\frac{3}{2}} b^{\frac{7}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} x^{5} + 3 a^{\frac{3}{2}} b^{4} x^{3}} - \frac{2 a^{4} b x^{5}}{3 a^{\frac{5}{2}} b^{3} x^{5} + 3 a^{\frac{3}{2}} b^{4} x^{3}} - \frac{2 a^{3} b^{2} x^{3}}{3 a^{\frac{5}{2}} b^{3} x^{5} + 3 a^{\frac{3}{2}} b^{4} x^{3}}"," ",0,"2*a**(7/2)*b**(3/2)*x**4*sqrt(a*x**2/b + 1)/(3*a**(5/2)*b**3*x**5 + 3*a**(3/2)*b**4*x**3) + a**(5/2)*b**(5/2)*x**2*sqrt(a*x**2/b + 1)/(3*a**(5/2)*b**3*x**5 + 3*a**(3/2)*b**4*x**3) - a**(3/2)*b**(7/2)*sqrt(a*x**2/b + 1)/(3*a**(5/2)*b**3*x**5 + 3*a**(3/2)*b**4*x**3) - 2*a**4*b*x**5/(3*a**(5/2)*b**3*x**5 + 3*a**(3/2)*b**4*x**3) - 2*a**3*b**2*x**3/(3*a**(5/2)*b**3*x**5 + 3*a**(3/2)*b**4*x**3)","B",0
1920,1,750,0,2.312091," ","integrate(1/(a+b/x**2)**(1/2)/x**7,x)","- \frac{8 a^{\frac{15}{2}} b^{\frac{9}{2}} x^{10} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{11} + 45 a^{\frac{9}{2}} b^{8} x^{9} + 45 a^{\frac{7}{2}} b^{9} x^{7} + 15 a^{\frac{5}{2}} b^{10} x^{5}} - \frac{20 a^{\frac{13}{2}} b^{\frac{11}{2}} x^{8} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{11} + 45 a^{\frac{9}{2}} b^{8} x^{9} + 45 a^{\frac{7}{2}} b^{9} x^{7} + 15 a^{\frac{5}{2}} b^{10} x^{5}} - \frac{15 a^{\frac{11}{2}} b^{\frac{13}{2}} x^{6} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{11} + 45 a^{\frac{9}{2}} b^{8} x^{9} + 45 a^{\frac{7}{2}} b^{9} x^{7} + 15 a^{\frac{5}{2}} b^{10} x^{5}} - \frac{5 a^{\frac{9}{2}} b^{\frac{15}{2}} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{11} + 45 a^{\frac{9}{2}} b^{8} x^{9} + 45 a^{\frac{7}{2}} b^{9} x^{7} + 15 a^{\frac{5}{2}} b^{10} x^{5}} - \frac{5 a^{\frac{7}{2}} b^{\frac{17}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{11} + 45 a^{\frac{9}{2}} b^{8} x^{9} + 45 a^{\frac{7}{2}} b^{9} x^{7} + 15 a^{\frac{5}{2}} b^{10} x^{5}} - \frac{3 a^{\frac{5}{2}} b^{\frac{19}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} x^{11} + 45 a^{\frac{9}{2}} b^{8} x^{9} + 45 a^{\frac{7}{2}} b^{9} x^{7} + 15 a^{\frac{5}{2}} b^{10} x^{5}} + \frac{8 a^{8} b^{4} x^{11}}{15 a^{\frac{11}{2}} b^{7} x^{11} + 45 a^{\frac{9}{2}} b^{8} x^{9} + 45 a^{\frac{7}{2}} b^{9} x^{7} + 15 a^{\frac{5}{2}} b^{10} x^{5}} + \frac{24 a^{7} b^{5} x^{9}}{15 a^{\frac{11}{2}} b^{7} x^{11} + 45 a^{\frac{9}{2}} b^{8} x^{9} + 45 a^{\frac{7}{2}} b^{9} x^{7} + 15 a^{\frac{5}{2}} b^{10} x^{5}} + \frac{24 a^{6} b^{6} x^{7}}{15 a^{\frac{11}{2}} b^{7} x^{11} + 45 a^{\frac{9}{2}} b^{8} x^{9} + 45 a^{\frac{7}{2}} b^{9} x^{7} + 15 a^{\frac{5}{2}} b^{10} x^{5}} + \frac{8 a^{5} b^{7} x^{5}}{15 a^{\frac{11}{2}} b^{7} x^{11} + 45 a^{\frac{9}{2}} b^{8} x^{9} + 45 a^{\frac{7}{2}} b^{9} x^{7} + 15 a^{\frac{5}{2}} b^{10} x^{5}}"," ",0,"-8*a**(15/2)*b**(9/2)*x**10*sqrt(a*x**2/b + 1)/(15*a**(11/2)*b**7*x**11 + 45*a**(9/2)*b**8*x**9 + 45*a**(7/2)*b**9*x**7 + 15*a**(5/2)*b**10*x**5) - 20*a**(13/2)*b**(11/2)*x**8*sqrt(a*x**2/b + 1)/(15*a**(11/2)*b**7*x**11 + 45*a**(9/2)*b**8*x**9 + 45*a**(7/2)*b**9*x**7 + 15*a**(5/2)*b**10*x**5) - 15*a**(11/2)*b**(13/2)*x**6*sqrt(a*x**2/b + 1)/(15*a**(11/2)*b**7*x**11 + 45*a**(9/2)*b**8*x**9 + 45*a**(7/2)*b**9*x**7 + 15*a**(5/2)*b**10*x**5) - 5*a**(9/2)*b**(15/2)*x**4*sqrt(a*x**2/b + 1)/(15*a**(11/2)*b**7*x**11 + 45*a**(9/2)*b**8*x**9 + 45*a**(7/2)*b**9*x**7 + 15*a**(5/2)*b**10*x**5) - 5*a**(7/2)*b**(17/2)*x**2*sqrt(a*x**2/b + 1)/(15*a**(11/2)*b**7*x**11 + 45*a**(9/2)*b**8*x**9 + 45*a**(7/2)*b**9*x**7 + 15*a**(5/2)*b**10*x**5) - 3*a**(5/2)*b**(19/2)*sqrt(a*x**2/b + 1)/(15*a**(11/2)*b**7*x**11 + 45*a**(9/2)*b**8*x**9 + 45*a**(7/2)*b**9*x**7 + 15*a**(5/2)*b**10*x**5) + 8*a**8*b**4*x**11/(15*a**(11/2)*b**7*x**11 + 45*a**(9/2)*b**8*x**9 + 45*a**(7/2)*b**9*x**7 + 15*a**(5/2)*b**10*x**5) + 24*a**7*b**5*x**9/(15*a**(11/2)*b**7*x**11 + 45*a**(9/2)*b**8*x**9 + 45*a**(7/2)*b**9*x**7 + 15*a**(5/2)*b**10*x**5) + 24*a**6*b**6*x**7/(15*a**(11/2)*b**7*x**11 + 45*a**(9/2)*b**8*x**9 + 45*a**(7/2)*b**9*x**7 + 15*a**(5/2)*b**10*x**5) + 8*a**5*b**7*x**5/(15*a**(11/2)*b**7*x**11 + 45*a**(9/2)*b**8*x**9 + 45*a**(7/2)*b**9*x**7 + 15*a**(5/2)*b**10*x**5)","B",0
1921,1,1969,0,3.555201," ","integrate(1/(a+b/x**2)**(1/2)/x**9,x)","\frac{16 a^{\frac{25}{2}} b^{\frac{23}{2}} x^{18} \sqrt{\frac{a x^{2}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} + \frac{88 a^{\frac{23}{2}} b^{\frac{25}{2}} x^{16} \sqrt{\frac{a x^{2}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} + \frac{198 a^{\frac{21}{2}} b^{\frac{27}{2}} x^{14} \sqrt{\frac{a x^{2}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} + \frac{231 a^{\frac{19}{2}} b^{\frac{29}{2}} x^{12} \sqrt{\frac{a x^{2}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} + \frac{140 a^{\frac{17}{2}} b^{\frac{31}{2}} x^{10} \sqrt{\frac{a x^{2}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} + \frac{21 a^{\frac{15}{2}} b^{\frac{33}{2}} x^{8} \sqrt{\frac{a x^{2}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{42 a^{\frac{13}{2}} b^{\frac{35}{2}} x^{6} \sqrt{\frac{a x^{2}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{47 a^{\frac{11}{2}} b^{\frac{37}{2}} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{24 a^{\frac{9}{2}} b^{\frac{39}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{5 a^{\frac{7}{2}} b^{\frac{41}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{16 a^{13} b^{11} x^{19}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{96 a^{12} b^{12} x^{17}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{240 a^{11} b^{13} x^{15}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{320 a^{10} b^{14} x^{13}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{240 a^{9} b^{15} x^{11}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{96 a^{8} b^{16} x^{9}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}} - \frac{16 a^{7} b^{17} x^{7}}{35 a^{\frac{19}{2}} b^{15} x^{19} + 210 a^{\frac{17}{2}} b^{16} x^{17} + 525 a^{\frac{15}{2}} b^{17} x^{15} + 700 a^{\frac{13}{2}} b^{18} x^{13} + 525 a^{\frac{11}{2}} b^{19} x^{11} + 210 a^{\frac{9}{2}} b^{20} x^{9} + 35 a^{\frac{7}{2}} b^{21} x^{7}}"," ",0,"16*a**(25/2)*b**(23/2)*x**18*sqrt(a*x**2/b + 1)/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) + 88*a**(23/2)*b**(25/2)*x**16*sqrt(a*x**2/b + 1)/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) + 198*a**(21/2)*b**(27/2)*x**14*sqrt(a*x**2/b + 1)/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) + 231*a**(19/2)*b**(29/2)*x**12*sqrt(a*x**2/b + 1)/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) + 140*a**(17/2)*b**(31/2)*x**10*sqrt(a*x**2/b + 1)/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) + 21*a**(15/2)*b**(33/2)*x**8*sqrt(a*x**2/b + 1)/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 42*a**(13/2)*b**(35/2)*x**6*sqrt(a*x**2/b + 1)/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 47*a**(11/2)*b**(37/2)*x**4*sqrt(a*x**2/b + 1)/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 24*a**(9/2)*b**(39/2)*x**2*sqrt(a*x**2/b + 1)/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 5*a**(7/2)*b**(41/2)*sqrt(a*x**2/b + 1)/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 16*a**13*b**11*x**19/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 96*a**12*b**12*x**17/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 240*a**11*b**13*x**15/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 320*a**10*b**14*x**13/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 240*a**9*b**15*x**11/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 96*a**8*b**16*x**9/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7) - 16*a**7*b**17*x**7/(35*a**(19/2)*b**15*x**19 + 210*a**(17/2)*b**16*x**17 + 525*a**(15/2)*b**17*x**15 + 700*a**(13/2)*b**18*x**13 + 525*a**(11/2)*b**19*x**11 + 210*a**(9/2)*b**20*x**9 + 35*a**(7/2)*b**21*x**7)","B",0
1922,1,279,0,1.252836," ","integrate(x**4/(a+b/x**2)**(1/2),x)","\frac{3 a^{4} b^{\frac{9}{2}} x^{8} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{2} + 15 a^{3} b^{6}} + \frac{2 a^{3} b^{\frac{11}{2}} x^{6} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{2} + 15 a^{3} b^{6}} + \frac{3 a^{2} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{2} + 15 a^{3} b^{6}} + \frac{12 a b^{\frac{15}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{2} + 15 a^{3} b^{6}} + \frac{8 b^{\frac{17}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{2} + 15 a^{3} b^{6}}"," ",0,"3*a**4*b**(9/2)*x**8*sqrt(a*x**2/b + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**2 + 15*a**3*b**6) + 2*a**3*b**(11/2)*x**6*sqrt(a*x**2/b + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**2 + 15*a**3*b**6) + 3*a**2*b**(13/2)*x**4*sqrt(a*x**2/b + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**2 + 15*a**3*b**6) + 12*a*b**(15/2)*x**2*sqrt(a*x**2/b + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**2 + 15*a**3*b**6) + 8*b**(17/2)*sqrt(a*x**2/b + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**2 + 15*a**3*b**6)","B",0
1923,1,46,0,0.863991," ","integrate(x**2/(a+b/x**2)**(1/2),x)","\frac{\sqrt{b} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a} - \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{2}}"," ",0,"sqrt(b)*x**2*sqrt(a*x**2/b + 1)/(3*a) - 2*b**(3/2)*sqrt(a*x**2/b + 1)/(3*a**2)","A",0
1924,1,17,0,0.783311," ","integrate(1/(a+b/x**2)**(1/2),x)","\frac{\sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}}{a}"," ",0,"sqrt(b)*sqrt(a*x**2/b + 1)/a","A",0
1925,1,19,0,1.465259," ","integrate(1/(a+b/x**2)**(1/2)/x**2,x)","- \frac{\operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{\sqrt{b}}"," ",0,"-asinh(sqrt(b)/(sqrt(a)*x))/sqrt(b)","A",0
1926,1,42,0,2.678131," ","integrate(1/(a+b/x**2)**(1/2)/x**4,x)","- \frac{\sqrt{a} \sqrt{1 + \frac{b}{a x^{2}}}}{2 b x} + \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{2 b^{\frac{3}{2}}}"," ",0,"-sqrt(a)*sqrt(1 + b/(a*x**2))/(2*b*x) + a*asinh(sqrt(b)/(sqrt(a)*x))/(2*b**(3/2))","A",0
1927,1,46,0,1.305954," ","integrate(1/x/(-a+b/x**2)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{\sqrt{a}} & \text{for}\: \left|{\frac{a x^{2}}{b}}\right| > 1 \\\frac{\operatorname{asin}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(sqrt(a)*x/sqrt(b))/sqrt(a), Abs(a*x**2/b) > 1), (asin(sqrt(a)*x/sqrt(b))/sqrt(a), True))","A",0
1928,1,20,0,1.317538," ","integrate(1/x**2/(2+b/x**2)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b}}{2 x} \right)}}{\sqrt{b}}"," ",0,"-asinh(sqrt(2)*sqrt(b)/(2*x))/sqrt(b)","A",0
1929,1,49,0,1.325832," ","integrate(1/x**2/(2-b/x**2)**(1/2),x)","\begin{cases} \frac{i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b}}{2 x} \right)}}{\sqrt{b}} & \text{for}\: \frac{\left|{\frac{b}{x^{2}}}\right|}{2} > 1 \\- \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b}}{2 x} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*acosh(sqrt(2)*sqrt(b)/(2*x))/sqrt(b), Abs(b/x**2)/2 > 1), (-asin(sqrt(2)*sqrt(b)/(2*x))/sqrt(b), True))","A",0
1930,1,100,0,6.327164," ","integrate(x**3/(a+b/x**2)**(3/2),x)","\frac{x^{5}}{4 a \sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{5 \sqrt{b} x^{3}}{8 a^{2} \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{15 b^{\frac{3}{2}} x}{8 a^{3} \sqrt{\frac{a x^{2}}{b} + 1}} + \frac{15 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{8 a^{\frac{7}{2}}}"," ",0,"x**5/(4*a*sqrt(b)*sqrt(a*x**2/b + 1)) - 5*sqrt(b)*x**3/(8*a**2*sqrt(a*x**2/b + 1)) - 15*b**(3/2)*x/(8*a**3*sqrt(a*x**2/b + 1)) + 15*b**2*asinh(sqrt(a)*x/sqrt(b))/(8*a**(7/2))","A",0
1931,1,71,0,3.574886," ","integrate(x/(a+b/x**2)**(3/2),x)","\frac{x^{3}}{2 a \sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}} + \frac{3 \sqrt{b} x}{2 a^{2} \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{3 b \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{2 a^{\frac{5}{2}}}"," ",0,"x**3/(2*a*sqrt(b)*sqrt(a*x**2/b + 1)) + 3*sqrt(b)*x/(2*a**2*sqrt(a*x**2/b + 1)) - 3*b*asinh(sqrt(a)*x/sqrt(b))/(2*a**(5/2))","A",0
1932,1,187,0,2.179890," ","integrate(1/(a+b/x**2)**(3/2)/x,x)","- \frac{2 a^{3} x^{2} \sqrt{1 + \frac{b}{a x^{2}}}}{2 a^{\frac{9}{2}} x^{2} + 2 a^{\frac{7}{2}} b} - \frac{a^{3} x^{2} \log{\left(\frac{b}{a x^{2}} \right)}}{2 a^{\frac{9}{2}} x^{2} + 2 a^{\frac{7}{2}} b} + \frac{2 a^{3} x^{2} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{2 a^{\frac{9}{2}} x^{2} + 2 a^{\frac{7}{2}} b} - \frac{a^{2} b \log{\left(\frac{b}{a x^{2}} \right)}}{2 a^{\frac{9}{2}} x^{2} + 2 a^{\frac{7}{2}} b} + \frac{2 a^{2} b \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{2 a^{\frac{9}{2}} x^{2} + 2 a^{\frac{7}{2}} b}"," ",0,"-2*a**3*x**2*sqrt(1 + b/(a*x**2))/(2*a**(9/2)*x**2 + 2*a**(7/2)*b) - a**3*x**2*log(b/(a*x**2))/(2*a**(9/2)*x**2 + 2*a**(7/2)*b) + 2*a**3*x**2*log(sqrt(1 + b/(a*x**2)) + 1)/(2*a**(9/2)*x**2 + 2*a**(7/2)*b) - a**2*b*log(b/(a*x**2))/(2*a**(9/2)*x**2 + 2*a**(7/2)*b) + 2*a**2*b*log(sqrt(1 + b/(a*x**2)) + 1)/(2*a**(9/2)*x**2 + 2*a**(7/2)*b)","B",0
1933,1,26,0,2.368409," ","integrate(1/(a+b/x**2)**(3/2)/x**3,x)","\begin{cases} \frac{1}{b \sqrt{a + \frac{b}{x^{2}}}} & \text{for}\: b \neq 0 \\- \frac{1}{2 a^{\frac{3}{2}} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1/(b*sqrt(a + b/x**2)), Ne(b, 0)), (-1/(2*a**(3/2)*x**2), True))","A",0
1934,1,48,0,3.383071," ","integrate(1/(a+b/x**2)**(3/2)/x**5,x)","\begin{cases} - \frac{2 a}{b^{2} \sqrt{a + \frac{b}{x^{2}}}} - \frac{1}{b x^{2} \sqrt{a + \frac{b}{x^{2}}}} & \text{for}\: b \neq 0 \\- \frac{1}{4 a^{\frac{3}{2}} x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a/(b**2*sqrt(a + b/x**2)) - 1/(b*x**2*sqrt(a + b/x**2)), Ne(b, 0)), (-1/(4*a**(3/2)*x**4), True))","A",0
1935,1,423,0,2.603718," ","integrate(1/(a+b/x**2)**(3/2)/x**7,x)","\frac{8 a^{\frac{9}{2}} b^{\frac{7}{2}} x^{6} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{\frac{7}{2}} b^{6} x^{7} + 6 a^{\frac{5}{2}} b^{7} x^{5} + 3 a^{\frac{3}{2}} b^{8} x^{3}} + \frac{12 a^{\frac{7}{2}} b^{\frac{9}{2}} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{\frac{7}{2}} b^{6} x^{7} + 6 a^{\frac{5}{2}} b^{7} x^{5} + 3 a^{\frac{3}{2}} b^{8} x^{3}} + \frac{3 a^{\frac{5}{2}} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{\frac{7}{2}} b^{6} x^{7} + 6 a^{\frac{5}{2}} b^{7} x^{5} + 3 a^{\frac{3}{2}} b^{8} x^{3}} - \frac{a^{\frac{3}{2}} b^{\frac{13}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{\frac{7}{2}} b^{6} x^{7} + 6 a^{\frac{5}{2}} b^{7} x^{5} + 3 a^{\frac{3}{2}} b^{8} x^{3}} - \frac{8 a^{5} b^{3} x^{7}}{3 a^{\frac{7}{2}} b^{6} x^{7} + 6 a^{\frac{5}{2}} b^{7} x^{5} + 3 a^{\frac{3}{2}} b^{8} x^{3}} - \frac{16 a^{4} b^{4} x^{5}}{3 a^{\frac{7}{2}} b^{6} x^{7} + 6 a^{\frac{5}{2}} b^{7} x^{5} + 3 a^{\frac{3}{2}} b^{8} x^{3}} - \frac{8 a^{3} b^{5} x^{3}}{3 a^{\frac{7}{2}} b^{6} x^{7} + 6 a^{\frac{5}{2}} b^{7} x^{5} + 3 a^{\frac{3}{2}} b^{8} x^{3}}"," ",0,"8*a**(9/2)*b**(7/2)*x**6*sqrt(a*x**2/b + 1)/(3*a**(7/2)*b**6*x**7 + 6*a**(5/2)*b**7*x**5 + 3*a**(3/2)*b**8*x**3) + 12*a**(7/2)*b**(9/2)*x**4*sqrt(a*x**2/b + 1)/(3*a**(7/2)*b**6*x**7 + 6*a**(5/2)*b**7*x**5 + 3*a**(3/2)*b**8*x**3) + 3*a**(5/2)*b**(11/2)*x**2*sqrt(a*x**2/b + 1)/(3*a**(7/2)*b**6*x**7 + 6*a**(5/2)*b**7*x**5 + 3*a**(3/2)*b**8*x**3) - a**(3/2)*b**(13/2)*sqrt(a*x**2/b + 1)/(3*a**(7/2)*b**6*x**7 + 6*a**(5/2)*b**7*x**5 + 3*a**(3/2)*b**8*x**3) - 8*a**5*b**3*x**7/(3*a**(7/2)*b**6*x**7 + 6*a**(5/2)*b**7*x**5 + 3*a**(3/2)*b**8*x**3) - 16*a**4*b**4*x**5/(3*a**(7/2)*b**6*x**7 + 6*a**(5/2)*b**7*x**5 + 3*a**(3/2)*b**8*x**3) - 8*a**3*b**5*x**3/(3*a**(7/2)*b**6*x**7 + 6*a**(5/2)*b**7*x**5 + 3*a**(3/2)*b**8*x**3)","B",0
1936,1,1844,0,4.251364," ","integrate(1/(a+b/x**2)**(3/2)/x**9,x)","- \frac{16 a^{\frac{21}{2}} b^{\frac{23}{2}} x^{16} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} - \frac{88 a^{\frac{19}{2}} b^{\frac{25}{2}} x^{14} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} - \frac{198 a^{\frac{17}{2}} b^{\frac{27}{2}} x^{12} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} - \frac{231 a^{\frac{15}{2}} b^{\frac{29}{2}} x^{10} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} - \frac{145 a^{\frac{13}{2}} b^{\frac{31}{2}} x^{8} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} - \frac{46 a^{\frac{11}{2}} b^{\frac{33}{2}} x^{6} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} - \frac{8 a^{\frac{9}{2}} b^{\frac{35}{2}} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} - \frac{3 a^{\frac{7}{2}} b^{\frac{37}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} - \frac{a^{\frac{5}{2}} b^{\frac{39}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} + \frac{16 a^{11} b^{11} x^{17}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} + \frac{96 a^{10} b^{12} x^{15}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} + \frac{240 a^{9} b^{13} x^{13}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} + \frac{320 a^{8} b^{14} x^{11}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} + \frac{240 a^{7} b^{15} x^{9}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} + \frac{96 a^{6} b^{16} x^{7}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}} + \frac{16 a^{5} b^{17} x^{5}}{5 a^{\frac{17}{2}} b^{15} x^{17} + 30 a^{\frac{15}{2}} b^{16} x^{15} + 75 a^{\frac{13}{2}} b^{17} x^{13} + 100 a^{\frac{11}{2}} b^{18} x^{11} + 75 a^{\frac{9}{2}} b^{19} x^{9} + 30 a^{\frac{7}{2}} b^{20} x^{7} + 5 a^{\frac{5}{2}} b^{21} x^{5}}"," ",0,"-16*a**(21/2)*b**(23/2)*x**16*sqrt(a*x**2/b + 1)/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) - 88*a**(19/2)*b**(25/2)*x**14*sqrt(a*x**2/b + 1)/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) - 198*a**(17/2)*b**(27/2)*x**12*sqrt(a*x**2/b + 1)/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) - 231*a**(15/2)*b**(29/2)*x**10*sqrt(a*x**2/b + 1)/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) - 145*a**(13/2)*b**(31/2)*x**8*sqrt(a*x**2/b + 1)/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) - 46*a**(11/2)*b**(33/2)*x**6*sqrt(a*x**2/b + 1)/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) - 8*a**(9/2)*b**(35/2)*x**4*sqrt(a*x**2/b + 1)/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) - 3*a**(7/2)*b**(37/2)*x**2*sqrt(a*x**2/b + 1)/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) - a**(5/2)*b**(39/2)*sqrt(a*x**2/b + 1)/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) + 16*a**11*b**11*x**17/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) + 96*a**10*b**12*x**15/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) + 240*a**9*b**13*x**13/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) + 320*a**8*b**14*x**11/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) + 240*a**7*b**15*x**9/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) + 96*a**6*b**16*x**7/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5) + 16*a**5*b**17*x**5/(5*a**(17/2)*b**15*x**17 + 30*a**(15/2)*b**16*x**15 + 75*a**(13/2)*b**17*x**13 + 100*a**(11/2)*b**18*x**11 + 75*a**(9/2)*b**19*x**9 + 30*a**(7/2)*b**20*x**7 + 5*a**(5/2)*b**21*x**5)","B",0
1937,1,337,0,1.643683," ","integrate(x**4/(a+b/x**2)**(3/2),x)","\frac{a^{5} b^{\frac{19}{2}} x^{10} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{7} b^{9} x^{6} + 15 a^{6} b^{10} x^{4} + 15 a^{5} b^{11} x^{2} + 5 a^{4} b^{12}} + \frac{5 a^{3} b^{\frac{23}{2}} x^{6} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{7} b^{9} x^{6} + 15 a^{6} b^{10} x^{4} + 15 a^{5} b^{11} x^{2} + 5 a^{4} b^{12}} + \frac{30 a^{2} b^{\frac{25}{2}} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{7} b^{9} x^{6} + 15 a^{6} b^{10} x^{4} + 15 a^{5} b^{11} x^{2} + 5 a^{4} b^{12}} + \frac{40 a b^{\frac{27}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{7} b^{9} x^{6} + 15 a^{6} b^{10} x^{4} + 15 a^{5} b^{11} x^{2} + 5 a^{4} b^{12}} + \frac{16 b^{\frac{29}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{5 a^{7} b^{9} x^{6} + 15 a^{6} b^{10} x^{4} + 15 a^{5} b^{11} x^{2} + 5 a^{4} b^{12}}"," ",0,"a**5*b**(19/2)*x**10*sqrt(a*x**2/b + 1)/(5*a**7*b**9*x**6 + 15*a**6*b**10*x**4 + 15*a**5*b**11*x**2 + 5*a**4*b**12) + 5*a**3*b**(23/2)*x**6*sqrt(a*x**2/b + 1)/(5*a**7*b**9*x**6 + 15*a**6*b**10*x**4 + 15*a**5*b**11*x**2 + 5*a**4*b**12) + 30*a**2*b**(25/2)*x**4*sqrt(a*x**2/b + 1)/(5*a**7*b**9*x**6 + 15*a**6*b**10*x**4 + 15*a**5*b**11*x**2 + 5*a**4*b**12) + 40*a*b**(27/2)*x**2*sqrt(a*x**2/b + 1)/(5*a**7*b**9*x**6 + 15*a**6*b**10*x**4 + 15*a**5*b**11*x**2 + 5*a**4*b**12) + 16*b**(29/2)*sqrt(a*x**2/b + 1)/(5*a**7*b**9*x**6 + 15*a**6*b**10*x**4 + 15*a**5*b**11*x**2 + 5*a**4*b**12)","B",0
1938,1,219,0,1.278993," ","integrate(x**2/(a+b/x**2)**(3/2),x)","\frac{a^{3} b^{\frac{9}{2}} x^{6} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{5} b^{4} x^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6}} - \frac{3 a^{2} b^{\frac{11}{2}} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{5} b^{4} x^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6}} - \frac{12 a b^{\frac{13}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{5} b^{4} x^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6}} - \frac{8 b^{\frac{15}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{5} b^{4} x^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6}}"," ",0,"a**3*b**(9/2)*x**6*sqrt(a*x**2/b + 1)/(3*a**5*b**4*x**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6) - 3*a**2*b**(11/2)*x**4*sqrt(a*x**2/b + 1)/(3*a**5*b**4*x**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6) - 12*a*b**(13/2)*x**2*sqrt(a*x**2/b + 1)/(3*a**5*b**4*x**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6) - 8*b**(15/2)*sqrt(a*x**2/b + 1)/(3*a**5*b**4*x**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6)","B",0
1939,1,42,0,0.987577," ","integrate(1/(a+b/x**2)**(3/2),x)","\frac{x^{2}}{a \sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}} + \frac{2 \sqrt{b}}{a^{2} \sqrt{\frac{a x^{2}}{b} + 1}}"," ",0,"x**2/(a*sqrt(b)*sqrt(a*x**2/b + 1)) + 2*sqrt(b)/(a**2*sqrt(a*x**2/b + 1))","A",0
1940,1,20,0,1.015015," ","integrate(1/(a+b/x**2)**(3/2)/x**2,x)","- \frac{1}{a \sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}}"," ",0,"-1/(a*sqrt(b)*sqrt(a*x**2/b + 1))","A",0
1941,1,184,0,2.370577," ","integrate(1/(a+b/x**2)**(3/2)/x**4,x)","\frac{a b^{2} x^{2} \log{\left(\frac{a x^{2}}{b} \right)}}{2 a b^{\frac{7}{2}} x^{2} + 2 b^{\frac{9}{2}}} - \frac{2 a b^{2} x^{2} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{2 a b^{\frac{7}{2}} x^{2} + 2 b^{\frac{9}{2}}} + \frac{2 b^{3} \sqrt{\frac{a x^{2}}{b} + 1}}{2 a b^{\frac{7}{2}} x^{2} + 2 b^{\frac{9}{2}}} + \frac{b^{3} \log{\left(\frac{a x^{2}}{b} \right)}}{2 a b^{\frac{7}{2}} x^{2} + 2 b^{\frac{9}{2}}} - \frac{2 b^{3} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{2 a b^{\frac{7}{2}} x^{2} + 2 b^{\frac{9}{2}}}"," ",0,"a*b**2*x**2*log(a*x**2/b)/(2*a*b**(7/2)*x**2 + 2*b**(9/2)) - 2*a*b**2*x**2*log(sqrt(a*x**2/b + 1) + 1)/(2*a*b**(7/2)*x**2 + 2*b**(9/2)) + 2*b**3*sqrt(a*x**2/b + 1)/(2*a*b**(7/2)*x**2 + 2*b**(9/2)) + b**3*log(a*x**2/b)/(2*a*b**(7/2)*x**2 + 2*b**(9/2)) - 2*b**3*log(sqrt(a*x**2/b + 1) + 1)/(2*a*b**(7/2)*x**2 + 2*b**(9/2))","B",0
1942,1,73,0,4.141255," ","integrate(1/(a+b/x**2)**(3/2)/x**6,x)","- \frac{3 \sqrt{a}}{2 b^{2} x \sqrt{1 + \frac{b}{a x^{2}}}} + \frac{3 a \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{2 b^{\frac{5}{2}}} - \frac{1}{2 \sqrt{a} b x^{3} \sqrt{1 + \frac{b}{a x^{2}}}}"," ",0,"-3*sqrt(a)/(2*b**2*x*sqrt(1 + b/(a*x**2))) + 3*a*asinh(sqrt(b)/(sqrt(a)*x))/(2*b**(5/2)) - 1/(2*sqrt(a)*b*x**3*sqrt(1 + b/(a*x**2)))","A",0
1943,1,102,0,6.998316," ","integrate(1/(a+b/x**2)**(3/2)/x**8,x)","\frac{15 a^{\frac{3}{2}}}{8 b^{3} x \sqrt{1 + \frac{b}{a x^{2}}}} + \frac{5 \sqrt{a}}{8 b^{2} x^{3} \sqrt{1 + \frac{b}{a x^{2}}}} - \frac{15 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x} \right)}}{8 b^{\frac{7}{2}}} - \frac{1}{4 \sqrt{a} b x^{5} \sqrt{1 + \frac{b}{a x^{2}}}}"," ",0,"15*a**(3/2)/(8*b**3*x*sqrt(1 + b/(a*x**2))) + 5*sqrt(a)/(8*b**2*x**3*sqrt(1 + b/(a*x**2))) - 15*a**2*asinh(sqrt(b)/(sqrt(a)*x))/(8*b**(7/2)) - 1/(4*sqrt(a)*b*x**5*sqrt(1 + b/(a*x**2)))","A",0
1944,1,432,0,8.921604," ","integrate(x**3/(a+b/x**2)**(5/2),x)","\frac{6 a^{\frac{89}{2}} b^{75} x^{7}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{21 a^{\frac{87}{2}} b^{76} x^{5}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{140 a^{\frac{85}{2}} b^{77} x^{3}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{105 a^{\frac{83}{2}} b^{78} x}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} \sqrt{\frac{a x^{2}}{b} + 1}} + \frac{105 a^{42} b^{\frac{155}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1} \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} \sqrt{\frac{a x^{2}}{b} + 1}} + \frac{105 a^{41} b^{\frac{157}{2}} \sqrt{\frac{a x^{2}}{b} + 1} \operatorname{asinh}{\left(\frac{\sqrt{a} x}{\sqrt{b}} \right)}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}"," ",0,"6*a**(89/2)*b**75*x**7/(24*a**(93/2)*b**(151/2)*x**2*sqrt(a*x**2/b + 1) + 24*a**(91/2)*b**(153/2)*sqrt(a*x**2/b + 1)) - 21*a**(87/2)*b**76*x**5/(24*a**(93/2)*b**(151/2)*x**2*sqrt(a*x**2/b + 1) + 24*a**(91/2)*b**(153/2)*sqrt(a*x**2/b + 1)) - 140*a**(85/2)*b**77*x**3/(24*a**(93/2)*b**(151/2)*x**2*sqrt(a*x**2/b + 1) + 24*a**(91/2)*b**(153/2)*sqrt(a*x**2/b + 1)) - 105*a**(83/2)*b**78*x/(24*a**(93/2)*b**(151/2)*x**2*sqrt(a*x**2/b + 1) + 24*a**(91/2)*b**(153/2)*sqrt(a*x**2/b + 1)) + 105*a**42*b**(155/2)*x**2*sqrt(a*x**2/b + 1)*asinh(sqrt(a)*x/sqrt(b))/(24*a**(93/2)*b**(151/2)*x**2*sqrt(a*x**2/b + 1) + 24*a**(91/2)*b**(153/2)*sqrt(a*x**2/b + 1)) + 105*a**41*b**(157/2)*sqrt(a*x**2/b + 1)*asinh(sqrt(a)*x/sqrt(b))/(24*a**(93/2)*b**(151/2)*x**2*sqrt(a*x**2/b + 1) + 24*a**(91/2)*b**(153/2)*sqrt(a*x**2/b + 1))","B",0
1945,1,819,0,5.724066," ","integrate(x/(a+b/x**2)**(5/2),x)","\frac{6 a^{17} x^{8} \sqrt{1 + \frac{b}{a x^{2}}}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} + \frac{46 a^{16} b x^{6} \sqrt{1 + \frac{b}{a x^{2}}}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} + \frac{15 a^{16} b x^{6} \log{\left(\frac{b}{a x^{2}} \right)}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} - \frac{30 a^{16} b x^{6} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} + \frac{70 a^{15} b^{2} x^{4} \sqrt{1 + \frac{b}{a x^{2}}}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} + \frac{45 a^{15} b^{2} x^{4} \log{\left(\frac{b}{a x^{2}} \right)}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} - \frac{90 a^{15} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} + \frac{30 a^{14} b^{3} x^{2} \sqrt{1 + \frac{b}{a x^{2}}}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} + \frac{45 a^{14} b^{3} x^{2} \log{\left(\frac{b}{a x^{2}} \right)}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} - \frac{90 a^{14} b^{3} x^{2} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} + \frac{15 a^{13} b^{4} \log{\left(\frac{b}{a x^{2}} \right)}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}} - \frac{30 a^{13} b^{4} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{6} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{2} + 12 a^{\frac{33}{2}} b^{3}}"," ",0,"6*a**17*x**8*sqrt(1 + b/(a*x**2))/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) + 46*a**16*b*x**6*sqrt(1 + b/(a*x**2))/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) + 15*a**16*b*x**6*log(b/(a*x**2))/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) - 30*a**16*b*x**6*log(sqrt(1 + b/(a*x**2)) + 1)/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) + 70*a**15*b**2*x**4*sqrt(1 + b/(a*x**2))/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) + 45*a**15*b**2*x**4*log(b/(a*x**2))/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) - 90*a**15*b**2*x**4*log(sqrt(1 + b/(a*x**2)) + 1)/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) + 30*a**14*b**3*x**2*sqrt(1 + b/(a*x**2))/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) + 45*a**14*b**3*x**2*log(b/(a*x**2))/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) - 90*a**14*b**3*x**2*log(sqrt(1 + b/(a*x**2)) + 1)/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) + 15*a**13*b**4*log(b/(a*x**2))/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3) - 30*a**13*b**4*log(sqrt(1 + b/(a*x**2)) + 1)/(12*a**(39/2)*x**6 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**2 + 12*a**(33/2)*b**3)","B",0
1946,1,743,0,3.500179," ","integrate(1/(a+b/x**2)**(5/2)/x,x)","- \frac{8 a^{7} x^{6} \sqrt{1 + \frac{b}{a x^{2}}}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}} - \frac{3 a^{7} x^{6} \log{\left(\frac{b}{a x^{2}} \right)}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}} + \frac{6 a^{7} x^{6} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}} - \frac{14 a^{6} b x^{4} \sqrt{1 + \frac{b}{a x^{2}}}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}} - \frac{9 a^{6} b x^{4} \log{\left(\frac{b}{a x^{2}} \right)}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}} + \frac{18 a^{6} b x^{4} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}} - \frac{6 a^{5} b^{2} x^{2} \sqrt{1 + \frac{b}{a x^{2}}}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}} - \frac{9 a^{5} b^{2} x^{2} \log{\left(\frac{b}{a x^{2}} \right)}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}} + \frac{18 a^{5} b^{2} x^{2} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}} - \frac{3 a^{4} b^{3} \log{\left(\frac{b}{a x^{2}} \right)}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}} + \frac{6 a^{4} b^{3} \log{\left(\sqrt{1 + \frac{b}{a x^{2}}} + 1 \right)}}{6 a^{\frac{19}{2}} x^{6} + 18 a^{\frac{17}{2}} b x^{4} + 18 a^{\frac{15}{2}} b^{2} x^{2} + 6 a^{\frac{13}{2}} b^{3}}"," ",0,"-8*a**7*x**6*sqrt(1 + b/(a*x**2))/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3) - 3*a**7*x**6*log(b/(a*x**2))/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3) + 6*a**7*x**6*log(sqrt(1 + b/(a*x**2)) + 1)/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3) - 14*a**6*b*x**4*sqrt(1 + b/(a*x**2))/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3) - 9*a**6*b*x**4*log(b/(a*x**2))/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3) + 18*a**6*b*x**4*log(sqrt(1 + b/(a*x**2)) + 1)/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3) - 6*a**5*b**2*x**2*sqrt(1 + b/(a*x**2))/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3) - 9*a**5*b**2*x**2*log(b/(a*x**2))/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3) + 18*a**5*b**2*x**2*log(sqrt(1 + b/(a*x**2)) + 1)/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3) - 3*a**4*b**3*log(b/(a*x**2))/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3) + 6*a**4*b**3*log(sqrt(1 + b/(a*x**2)) + 1)/(6*a**(19/2)*x**6 + 18*a**(17/2)*b*x**4 + 18*a**(15/2)*b**2*x**2 + 6*a**(13/2)*b**3)","B",0
1947,1,48,0,3.779184," ","integrate(1/(a+b/x**2)**(5/2)/x**3,x)","\begin{cases} \frac{1}{3 a b \sqrt{a + \frac{b}{x^{2}}} + \frac{3 b^{2} \sqrt{a + \frac{b}{x^{2}}}}{x^{2}}} & \text{for}\: b \neq 0 \\- \frac{1}{2 a^{\frac{5}{2}} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1/(3*a*b*sqrt(a + b/x**2) + 3*b**2*sqrt(a + b/x**2)/x**2), Ne(b, 0)), (-1/(2*a**(5/2)*x**2), True))","A",0
1948,1,94,0,5.696542," ","integrate(1/(a+b/x**2)**(5/2)/x**5,x)","\begin{cases} \frac{2 a x^{2}}{3 a b^{2} x^{2} \sqrt{a + \frac{b}{x^{2}}} + 3 b^{3} \sqrt{a + \frac{b}{x^{2}}}} + \frac{3 b}{3 a b^{2} x^{2} \sqrt{a + \frac{b}{x^{2}}} + 3 b^{3} \sqrt{a + \frac{b}{x^{2}}}} & \text{for}\: b \neq 0 \\- \frac{1}{4 a^{\frac{5}{2}} x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*x**2/(3*a*b**2*x**2*sqrt(a + b/x**2) + 3*b**3*sqrt(a + b/x**2)) + 3*b/(3*a*b**2*x**2*sqrt(a + b/x**2) + 3*b**3*sqrt(a + b/x**2)), Ne(b, 0)), (-1/(4*a**(5/2)*x**4), True))","A",0
1949,1,153,0,8.359088," ","integrate(1/(a+b/x**2)**(5/2)/x**7,x)","\begin{cases} - \frac{8 a^{2} x^{4}}{3 a b^{3} x^{4} \sqrt{a + \frac{b}{x^{2}}} + 3 b^{4} x^{2} \sqrt{a + \frac{b}{x^{2}}}} - \frac{12 a b x^{2}}{3 a b^{3} x^{4} \sqrt{a + \frac{b}{x^{2}}} + 3 b^{4} x^{2} \sqrt{a + \frac{b}{x^{2}}}} - \frac{3 b^{2}}{3 a b^{3} x^{4} \sqrt{a + \frac{b}{x^{2}}} + 3 b^{4} x^{2} \sqrt{a + \frac{b}{x^{2}}}} & \text{for}\: b \neq 0 \\- \frac{1}{6 a^{\frac{5}{2}} x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*a**2*x**4/(3*a*b**3*x**4*sqrt(a + b/x**2) + 3*b**4*x**2*sqrt(a + b/x**2)) - 12*a*b*x**2/(3*a*b**3*x**4*sqrt(a + b/x**2) + 3*b**4*x**2*sqrt(a + b/x**2)) - 3*b**2/(3*a*b**3*x**4*sqrt(a + b/x**2) + 3*b**4*x**2*sqrt(a + b/x**2)), Ne(b, 0)), (-1/(6*a**(5/2)*x**6), True))","A",0
1950,1,201,0,12.147860," ","integrate(1/(a+b/x**2)**(5/2)/x**9,x)","\begin{cases} \frac{16 a^{3} x^{6}}{3 a b^{4} x^{6} \sqrt{a + \frac{b}{x^{2}}} + 3 b^{5} x^{4} \sqrt{a + \frac{b}{x^{2}}}} + \frac{24 a^{2} b x^{4}}{3 a b^{4} x^{6} \sqrt{a + \frac{b}{x^{2}}} + 3 b^{5} x^{4} \sqrt{a + \frac{b}{x^{2}}}} + \frac{6 a b^{2} x^{2}}{3 a b^{4} x^{6} \sqrt{a + \frac{b}{x^{2}}} + 3 b^{5} x^{4} \sqrt{a + \frac{b}{x^{2}}}} - \frac{b^{3}}{3 a b^{4} x^{6} \sqrt{a + \frac{b}{x^{2}}} + 3 b^{5} x^{4} \sqrt{a + \frac{b}{x^{2}}}} & \text{for}\: b \neq 0 \\- \frac{1}{8 a^{\frac{5}{2}} x^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**3*x**6/(3*a*b**4*x**6*sqrt(a + b/x**2) + 3*b**5*x**4*sqrt(a + b/x**2)) + 24*a**2*b*x**4/(3*a*b**4*x**6*sqrt(a + b/x**2) + 3*b**5*x**4*sqrt(a + b/x**2)) + 6*a*b**2*x**2/(3*a*b**4*x**6*sqrt(a + b/x**2) + 3*b**5*x**4*sqrt(a + b/x**2)) - b**3/(3*a*b**4*x**6*sqrt(a + b/x**2) + 3*b**5*x**4*sqrt(a + b/x**2)), Ne(b, 0)), (-1/(8*a**(5/2)*x**8), True))","A",0
1951,1,337,0,1.875744," ","integrate(x**2/(a+b/x**2)**(5/2),x)","\frac{a^{4} b^{\frac{19}{2}} x^{8} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{7} b^{9} x^{6} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{2} + 3 a^{4} b^{12}} - \frac{5 a^{3} b^{\frac{21}{2}} x^{6} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{7} b^{9} x^{6} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{2} + 3 a^{4} b^{12}} - \frac{30 a^{2} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{7} b^{9} x^{6} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{2} + 3 a^{4} b^{12}} - \frac{40 a b^{\frac{25}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{7} b^{9} x^{6} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{2} + 3 a^{4} b^{12}} - \frac{16 b^{\frac{27}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{7} b^{9} x^{6} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{2} + 3 a^{4} b^{12}}"," ",0,"a**4*b**(19/2)*x**8*sqrt(a*x**2/b + 1)/(3*a**7*b**9*x**6 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**2 + 3*a**4*b**12) - 5*a**3*b**(21/2)*x**6*sqrt(a*x**2/b + 1)/(3*a**7*b**9*x**6 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**2 + 3*a**4*b**12) - 30*a**2*b**(23/2)*x**4*sqrt(a*x**2/b + 1)/(3*a**7*b**9*x**6 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**2 + 3*a**4*b**12) - 40*a*b**(25/2)*x**2*sqrt(a*x**2/b + 1)/(3*a**7*b**9*x**6 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**2 + 3*a**4*b**12) - 16*b**(27/2)*sqrt(a*x**2/b + 1)/(3*a**7*b**9*x**6 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**2 + 3*a**4*b**12)","B",0
1952,1,163,0,1.744815," ","integrate(1/(a+b/x**2)**(5/2),x)","\frac{3 a^{2} b^{\frac{9}{2}} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{5} b^{4} x^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6}} + \frac{12 a b^{\frac{11}{2}} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{5} b^{4} x^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6}} + \frac{8 b^{\frac{13}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}{3 a^{5} b^{4} x^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6}}"," ",0,"3*a**2*b**(9/2)*x**4*sqrt(a*x**2/b + 1)/(3*a**5*b**4*x**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6) + 12*a*b**(11/2)*x**2*sqrt(a*x**2/b + 1)/(3*a**5*b**4*x**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6) + 8*b**(13/2)*sqrt(a*x**2/b + 1)/(3*a**5*b**4*x**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6)","B",0
1953,1,105,0,1.855878," ","integrate(1/(a+b/x**2)**(5/2)/x**2,x)","- \frac{3 a x^{2}}{3 a^{3} \sqrt{b} x^{2} \sqrt{\frac{a x^{2}}{b} + 1} + 3 a^{2} b^{\frac{3}{2}} \sqrt{\frac{a x^{2}}{b} + 1}} - \frac{2 b}{3 a^{3} \sqrt{b} x^{2} \sqrt{\frac{a x^{2}}{b} + 1} + 3 a^{2} b^{\frac{3}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}"," ",0,"-3*a*x**2/(3*a**3*sqrt(b)*x**2*sqrt(a*x**2/b + 1) + 3*a**2*b**(3/2)*sqrt(a*x**2/b + 1)) - 2*b/(3*a**3*sqrt(b)*x**2*sqrt(a*x**2/b + 1) + 3*a**2*b**(3/2)*sqrt(a*x**2/b + 1))","B",0
1954,1,48,0,1.957147," ","integrate(1/(a+b/x**2)**(5/2)/x**4,x)","- \frac{1}{3 a^{2} \sqrt{b} x^{2} \sqrt{\frac{a x^{2}}{b} + 1} + 3 a b^{\frac{3}{2}} \sqrt{\frac{a x^{2}}{b} + 1}}"," ",0,"-1/(3*a**2*sqrt(b)*x**2*sqrt(a*x**2/b + 1) + 3*a*b**(3/2)*sqrt(a*x**2/b + 1))","B",0
1955,1,740,0,4.589244," ","integrate(1/(a+b/x**2)**(5/2)/x**6,x)","\frac{3 a^{3} b^{4} x^{6} \log{\left(\frac{a x^{2}}{b} \right)}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}} - \frac{6 a^{3} b^{4} x^{6} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}} + \frac{6 a^{2} b^{5} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}} + \frac{9 a^{2} b^{5} x^{4} \log{\left(\frac{a x^{2}}{b} \right)}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}} - \frac{18 a^{2} b^{5} x^{4} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}} + \frac{14 a b^{6} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}} + \frac{9 a b^{6} x^{2} \log{\left(\frac{a x^{2}}{b} \right)}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}} - \frac{18 a b^{6} x^{2} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}} + \frac{8 b^{7} \sqrt{\frac{a x^{2}}{b} + 1}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}} + \frac{3 b^{7} \log{\left(\frac{a x^{2}}{b} \right)}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}} - \frac{6 b^{7} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{6 a^{3} b^{\frac{13}{2}} x^{6} + 18 a^{2} b^{\frac{15}{2}} x^{4} + 18 a b^{\frac{17}{2}} x^{2} + 6 b^{\frac{19}{2}}}"," ",0,"3*a**3*b**4*x**6*log(a*x**2/b)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2)) - 6*a**3*b**4*x**6*log(sqrt(a*x**2/b + 1) + 1)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2)) + 6*a**2*b**5*x**4*sqrt(a*x**2/b + 1)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2)) + 9*a**2*b**5*x**4*log(a*x**2/b)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2)) - 18*a**2*b**5*x**4*log(sqrt(a*x**2/b + 1) + 1)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2)) + 14*a*b**6*x**2*sqrt(a*x**2/b + 1)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2)) + 9*a*b**6*x**2*log(a*x**2/b)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2)) - 18*a*b**6*x**2*log(sqrt(a*x**2/b + 1) + 1)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2)) + 8*b**7*sqrt(a*x**2/b + 1)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2)) + 3*b**7*log(a*x**2/b)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2)) - 6*b**7*log(sqrt(a*x**2/b + 1) + 1)/(6*a**3*b**(13/2)*x**6 + 18*a**2*b**(15/2)*x**4 + 18*a*b**(17/2)*x**2 + 6*b**(19/2))","B",0
1956,1,864,0,7.012854," ","integrate(1/(a+b/x**2)**(5/2)/x**8,x)","- \frac{15 a^{4} b^{13} x^{8} \log{\left(\frac{a x^{2}}{b} \right)}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} + \frac{30 a^{4} b^{13} x^{8} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} - \frac{30 a^{3} b^{14} x^{6} \sqrt{\frac{a x^{2}}{b} + 1}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} - \frac{45 a^{3} b^{14} x^{6} \log{\left(\frac{a x^{2}}{b} \right)}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} + \frac{90 a^{3} b^{14} x^{6} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} - \frac{70 a^{2} b^{15} x^{4} \sqrt{\frac{a x^{2}}{b} + 1}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} - \frac{45 a^{2} b^{15} x^{4} \log{\left(\frac{a x^{2}}{b} \right)}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} + \frac{90 a^{2} b^{15} x^{4} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} - \frac{46 a b^{16} x^{2} \sqrt{\frac{a x^{2}}{b} + 1}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} - \frac{15 a b^{16} x^{2} \log{\left(\frac{a x^{2}}{b} \right)}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} + \frac{30 a b^{16} x^{2} \log{\left(\sqrt{\frac{a x^{2}}{b} + 1} + 1 \right)}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}} - \frac{6 b^{17} \sqrt{\frac{a x^{2}}{b} + 1}}{12 a^{3} b^{\frac{33}{2}} x^{8} + 36 a^{2} b^{\frac{35}{2}} x^{6} + 36 a b^{\frac{37}{2}} x^{4} + 12 b^{\frac{39}{2}} x^{2}}"," ",0,"-15*a**4*b**13*x**8*log(a*x**2/b)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) + 30*a**4*b**13*x**8*log(sqrt(a*x**2/b + 1) + 1)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) - 30*a**3*b**14*x**6*sqrt(a*x**2/b + 1)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) - 45*a**3*b**14*x**6*log(a*x**2/b)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) + 90*a**3*b**14*x**6*log(sqrt(a*x**2/b + 1) + 1)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) - 70*a**2*b**15*x**4*sqrt(a*x**2/b + 1)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) - 45*a**2*b**15*x**4*log(a*x**2/b)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) + 90*a**2*b**15*x**4*log(sqrt(a*x**2/b + 1) + 1)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) - 46*a*b**16*x**2*sqrt(a*x**2/b + 1)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) - 15*a*b**16*x**2*log(a*x**2/b)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) + 30*a*b**16*x**2*log(sqrt(a*x**2/b + 1) + 1)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2) - 6*b**17*sqrt(a*x**2/b + 1)/(12*a**3*b**(33/2)*x**8 + 36*a**2*b**(35/2)*x**6 + 36*a*b**(37/2)*x**4 + 12*b**(39/2)*x**2)","B",0
1957,1,31,0,1.096242," ","integrate((1+1/x**2)**(1/3)/x**3,x)","- \frac{3 \sqrt[3]{1 + \frac{1}{x^{2}}}}{8} - \frac{3 \sqrt[3]{1 + \frac{1}{x^{2}}}}{8 x^{2}}"," ",0,"-3*(1 + x**(-2))**(1/3)/8 - 3*(1 + x**(-2))**(1/3)/(8*x**2)","B",0
1958,1,48,0,2.288305," ","integrate((1+1/x**2)**(5/3)/x**3,x)","- \frac{3 \left(1 + \frac{1}{x^{2}}\right)^{\frac{2}{3}}}{16} - \frac{3 \left(1 + \frac{1}{x^{2}}\right)^{\frac{2}{3}}}{8 x^{2}} - \frac{3 \left(1 + \frac{1}{x^{2}}\right)^{\frac{2}{3}}}{16 x^{4}}"," ",0,"-3*(1 + x**(-2))**(2/3)/16 - 3*(1 + x**(-2))**(2/3)/(8*x**2) - 3*(1 + x**(-2))**(2/3)/(16*x**4)","B",0
1959,1,56,0,5.294085," ","integrate((1+b/x**2)**(3/2)*(c*x)**m,x)","- \frac{c^{m} x x^{m} \Gamma\left(- \frac{m}{2} - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{m}{2} - \frac{1}{2} \\ \frac{1}{2} - \frac{m}{2} \end{matrix}\middle| {\frac{b e^{i \pi}}{x^{2}}} \right)}}{2 \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}"," ",0,"-c**m*x*x**m*gamma(-m/2 - 1/2)*hyper((-3/2, -m/2 - 1/2), (1/2 - m/2,), b*exp_polar(I*pi)/x**2)/(2*gamma(1/2 - m/2))","C",0
1960,1,48,0,2.040499," ","integrate((1+b/x**2)**(1/2)*(c*x)**m,x)","- \frac{\sqrt{b} c^{m} x^{m} \Gamma\left(- \frac{m}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} \\ \frac{m}{2} + 1 \end{matrix}\middle| {\frac{x^{2} e^{i \pi}}{b}} \right)}}{2 \Gamma\left(1 - \frac{m}{2}\right)}"," ",0,"-sqrt(b)*c**m*x**m*gamma(-m/2)*hyper((-1/2, m/2), (m/2 + 1,), x**2*exp_polar(I*pi)/b)/(2*gamma(1 - m/2))","C",0
1961,1,54,0,1.406404," ","integrate((c*x)**m/(1+b/x**2)**(1/2),x)","- \frac{c^{m} x x^{m} \Gamma\left(- \frac{m}{2} - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - \frac{m}{2} - \frac{1}{2} \\ \frac{1}{2} - \frac{m}{2} \end{matrix}\middle| {\frac{b e^{i \pi}}{x^{2}}} \right)}}{2 \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}"," ",0,"-c**m*x*x**m*gamma(-m/2 - 1/2)*hyper((1/2, -m/2 - 1/2), (1/2 - m/2,), b*exp_polar(I*pi)/x**2)/(2*gamma(1/2 - m/2))","C",0
1962,1,54,0,2.475286," ","integrate((c*x)**m/(1+b/x**2)**(3/2),x)","- \frac{c^{m} x x^{m} \Gamma\left(- \frac{m}{2} - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - \frac{m}{2} - \frac{1}{2} \\ \frac{1}{2} - \frac{m}{2} \end{matrix}\middle| {\frac{b e^{i \pi}}{x^{2}}} \right)}}{2 \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}"," ",0,"-c**m*x*x**m*gamma(-m/2 - 1/2)*hyper((3/2, -m/2 - 1/2), (1/2 - m/2,), b*exp_polar(I*pi)/x**2)/(2*gamma(1/2 - m/2))","C",0
1963,1,54,0,17.754285," ","integrate((1+b/x**2)**p*(c*x)**m,x)","- \frac{c^{m} x x^{m} \Gamma\left(- \frac{m}{2} - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - \frac{m}{2} - \frac{1}{2} \\ \frac{1}{2} - \frac{m}{2} \end{matrix}\middle| {\frac{b e^{i \pi}}{x^{2}}} \right)}}{2 \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}"," ",0,"-c**m*x*x**m*gamma(-m/2 - 1/2)*hyper((-p, -m/2 - 1/2), (1/2 - m/2,), b*exp_polar(I*pi)/x**2)/(2*gamma(1/2 - m/2))","C",0
1964,1,60,0,22.269999," ","integrate((a+b/x**2)**p*(c*x)**m,x)","- \frac{a^{p} c^{m} x x^{m} \Gamma\left(- \frac{m}{2} - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - \frac{m}{2} - \frac{1}{2} \\ \frac{1}{2} - \frac{m}{2} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{2}}} \right)}}{2 \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}"," ",0,"-a**p*c**m*x*x**m*gamma(-m/2 - 1/2)*hyper((-p, -m/2 - 1/2), (1/2 - m/2,), b*exp_polar(I*pi)/(a*x**2))/(2*gamma(1/2 - m/2))","C",0
1965,1,32,0,0.230103," ","integrate(x**5/(a+b/x**3),x)","\frac{x^{6}}{6 a} - \frac{b x^{3}}{3 a^{2}} + \frac{b^{2} \log{\left(a x^{3} + b \right)}}{3 a^{3}}"," ",0,"x**6/(6*a) - b*x**3/(3*a**2) + b**2*log(a*x**3 + b)/(3*a**3)","A",0
1966,1,44,0,0.263870," ","integrate(x**4/(a+b/x**3),x)","\operatorname{RootSum} {\left(27 t^{3} a^{8} + b^{5}, \left( t \mapsto t \log{\left(\frac{9 t^{2} a^{5}}{b^{3}} + x \right)} \right)\right)} + \frac{x^{5}}{5 a} - \frac{b x^{2}}{2 a^{2}}"," ",0,"RootSum(27*_t**3*a**8 + b**5, Lambda(_t, _t*log(9*_t**2*a**5/b**3 + x))) + x**5/(5*a) - b*x**2/(2*a**2)","A",0
1967,1,37,0,0.212461," ","integrate(x**3/(a+b/x**3),x)","\operatorname{RootSum} {\left(27 t^{3} a^{7} - b^{4}, \left( t \mapsto t \log{\left(\frac{3 t a^{2}}{b} + x \right)} \right)\right)} + \frac{x^{4}}{4 a} - \frac{b x}{a^{2}}"," ",0,"RootSum(27*_t**3*a**7 - b**4, Lambda(_t, _t*log(3*_t*a**2/b + x))) + x**4/(4*a) - b*x/a**2","A",0
1968,1,20,0,0.236126," ","integrate(x**2/(a+b/x**3),x)","\frac{x^{3}}{3 a} - \frac{b \log{\left(a x^{3} + b \right)}}{3 a^{2}}"," ",0,"x**3/(3*a) - b*log(a*x**3 + b)/(3*a**2)","A",0
1969,1,32,0,0.189438," ","integrate(x/(a+b/x**3),x)","\operatorname{RootSum} {\left(27 t^{3} a^{5} - b^{2}, \left( t \mapsto t \log{\left(\frac{9 t^{2} a^{3}}{b} + x \right)} \right)\right)} + \frac{x^{2}}{2 a}"," ",0,"RootSum(27*_t**3*a**5 - b**2, Lambda(_t, _t*log(9*_t**2*a**3/b + x))) + x**2/(2*a)","A",0
1970,1,22,0,0.176568," ","integrate(1/(a+b/x**3),x)","\operatorname{RootSum} {\left(27 t^{3} a^{4} + b, \left( t \mapsto t \log{\left(- 3 t a + x \right)} \right)\right)} + \frac{x}{a}"," ",0,"RootSum(27*_t**3*a**4 + b, Lambda(_t, _t*log(-3*_t*a + x))) + x/a","A",0
1971,1,10,0,0.160312," ","integrate(1/(a+b/x**3)/x,x)","\frac{\log{\left(a x^{3} + b \right)}}{3 a}"," ",0,"log(a*x**3 + b)/(3*a)","A",0
1972,1,24,0,0.163750," ","integrate(1/(a+b/x**3)/x**2,x)","\operatorname{RootSum} {\left(27 t^{3} a^{2} b + 1, \left( t \mapsto t \log{\left(9 t^{2} a b + x \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*a**2*b + 1, Lambda(_t, _t*log(9*_t**2*a*b + x)))","A",0
1973,1,20,0,0.189083," ","integrate(1/(a+b/x**3)/x**3,x)","\operatorname{RootSum} {\left(27 t^{3} a b^{2} - 1, \left( t \mapsto t \log{\left(3 t b + x \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*a*b**2 - 1, Lambda(_t, _t*log(3*_t*b + x)))","A",0
1974,1,15,0,0.316115," ","integrate(1/(a+b/x**3)/x**4,x)","\frac{\log{\left(x \right)}}{b} - \frac{\log{\left(x^{3} + \frac{b}{a} \right)}}{3 b}"," ",0,"log(x)/b - log(x**3 + b/a)/(3*b)","A",0
1975,1,29,0,0.227936," ","integrate(1/(a+b/x**3)/x**5,x)","\operatorname{RootSum} {\left(27 t^{3} b^{4} - a, \left( t \mapsto t \log{\left(\frac{9 t^{2} b^{3}}{a} + x \right)} \right)\right)} - \frac{1}{b x}"," ",0,"RootSum(27*_t**3*b**4 - a, Lambda(_t, _t*log(9*_t**2*b**3/a + x))) - 1/(b*x)","A",0
1976,1,32,0,0.319755," ","integrate(1/(a+b/x**3)/x**6,x)","\operatorname{RootSum} {\left(27 t^{3} b^{5} + a^{2}, \left( t \mapsto t \log{\left(- \frac{3 t b^{2}}{a} + x \right)} \right)\right)} - \frac{1}{2 b x^{2}}"," ",0,"RootSum(27*_t**3*b**5 + a**2, Lambda(_t, _t*log(-3*_t*b**2/a + x))) - 1/(2*b*x**2)","A",0
1977,1,31,0,0.439341," ","integrate(1/(a+b/x**3)/x**7,x)","- \frac{a \log{\left(x \right)}}{b^{2}} + \frac{a \log{\left(x^{3} + \frac{b}{a} \right)}}{3 b^{2}} - \frac{1}{3 b x^{3}}"," ",0,"-a*log(x)/b**2 + a*log(x**3 + b/a)/(3*b**2) - 1/(3*b*x**3)","A",0
1978,1,53,0,0.397832," ","integrate(x**5/(a+b/x**3)**2,x)","\frac{b^{3}}{3 a^{5} x^{3} + 3 a^{4} b} + \frac{x^{6}}{6 a^{2}} - \frac{2 b x^{3}}{3 a^{3}} + \frac{b^{2} \log{\left(a x^{3} + b \right)}}{a^{4}}"," ",0,"b**3/(3*a**5*x**3 + 3*a**4*b) + x**6/(6*a**2) - 2*b*x**3/(3*a**3) + b**2*log(a*x**3 + b)/a**4","A",0
1979,1,70,0,0.413604," ","integrate(x**4/(a+b/x**3)**2,x)","- \frac{b^{2} x^{2}}{3 a^{4} x^{3} + 3 a^{3} b} + \operatorname{RootSum} {\left(729 t^{3} a^{11} + 512 b^{5}, \left( t \mapsto t \log{\left(\frac{81 t^{2} a^{7}}{64 b^{3}} + x \right)} \right)\right)} + \frac{x^{5}}{5 a^{2}} - \frac{b x^{2}}{a^{3}}"," ",0,"-b**2*x**2/(3*a**4*x**3 + 3*a**3*b) + RootSum(729*_t**3*a**11 + 512*b**5, Lambda(_t, _t*log(81*_t**2*a**7/(64*b**3) + x))) + x**5/(5*a**2) - b*x**2/a**3","A",0
1980,1,65,0,0.388670," ","integrate(x**3/(a+b/x**3)**2,x)","- \frac{b^{2} x}{3 a^{4} x^{3} + 3 a^{3} b} + \operatorname{RootSum} {\left(729 t^{3} a^{10} - 343 b^{4}, \left( t \mapsto t \log{\left(\frac{9 t a^{3}}{7 b} + x \right)} \right)\right)} + \frac{x^{4}}{4 a^{2}} - \frac{2 b x}{a^{3}}"," ",0,"-b**2*x/(3*a**4*x**3 + 3*a**3*b) + RootSum(729*_t**3*a**10 - 343*b**4, Lambda(_t, _t*log(9*_t*a**3/(7*b) + x))) + x**4/(4*a**2) - 2*b*x/a**3","A",0
1981,1,42,0,0.368463," ","integrate(x**2/(a+b/x**3)**2,x)","- \frac{b^{2}}{3 a^{4} x^{3} + 3 a^{3} b} + \frac{x^{3}}{3 a^{2}} - \frac{2 b \log{\left(a x^{3} + b \right)}}{3 a^{3}}"," ",0,"-b**2/(3*a**4*x**3 + 3*a**3*b) + x**3/(3*a**2) - 2*b*log(a*x**3 + b)/(3*a**3)","A",0
1982,1,58,0,0.417284," ","integrate(x/(a+b/x**3)**2,x)","\frac{b x^{2}}{3 a^{3} x^{3} + 3 a^{2} b} + \operatorname{RootSum} {\left(729 t^{3} a^{8} - 125 b^{2}, \left( t \mapsto t \log{\left(\frac{81 t^{2} a^{5}}{25 b} + x \right)} \right)\right)} + \frac{x^{2}}{2 a^{2}}"," ",0,"b*x**2/(3*a**3*x**3 + 3*a**2*b) + RootSum(729*_t**3*a**8 - 125*b**2, Lambda(_t, _t*log(81*_t**2*a**5/(25*b) + x))) + x**2/(2*a**2)","A",0
1983,1,48,0,0.336718," ","integrate(1/(a+b/x**3)**2,x)","\frac{b x}{3 a^{3} x^{3} + 3 a^{2} b} + \operatorname{RootSum} {\left(729 t^{3} a^{7} + 64 b, \left( t \mapsto t \log{\left(- \frac{9 t a^{2}}{4} + x \right)} \right)\right)} + \frac{x}{a^{2}}"," ",0,"b*x/(3*a**3*x**3 + 3*a**2*b) + RootSum(729*_t**3*a**7 + 64*b, Lambda(_t, _t*log(-9*_t*a**2/4 + x))) + x/a**2","A",0
1984,1,29,0,0.377823," ","integrate(1/(a+b/x**3)**2/x,x)","\frac{b}{3 a^{3} x^{3} + 3 a^{2} b} + \frac{\log{\left(a x^{3} + b \right)}}{3 a^{2}}"," ",0,"b/(3*a**3*x**3 + 3*a**2*b) + log(a*x**3 + b)/(3*a**2)","A",0
1985,1,44,0,0.319208," ","integrate(1/(a+b/x**3)**2/x**2,x)","- \frac{x^{2}}{3 a^{2} x^{3} + 3 a b} + \operatorname{RootSum} {\left(729 t^{3} a^{5} b + 8, \left( t \mapsto t \log{\left(\frac{81 t^{2} a^{3} b}{4} + x \right)} \right)\right)}"," ",0,"-x**2/(3*a**2*x**3 + 3*a*b) + RootSum(729*_t**3*a**5*b + 8, Lambda(_t, _t*log(81*_t**2*a**3*b/4 + x)))","A",0
1986,1,39,0,0.307887," ","integrate(1/(a+b/x**3)**2/x**3,x)","- \frac{x}{3 a^{2} x^{3} + 3 a b} + \operatorname{RootSum} {\left(729 t^{3} a^{4} b^{2} - 1, \left( t \mapsto t \log{\left(9 t a b + x \right)} \right)\right)}"," ",0,"-x/(3*a**2*x**3 + 3*a*b) + RootSum(729*_t**3*a**4*b**2 - 1, Lambda(_t, _t*log(9*_t*a*b + x)))","A",0
1987,1,15,0,0.272395," ","integrate(1/(a+b/x**3)**2/x**4,x)","- \frac{1}{3 a^{2} x^{3} + 3 a b}"," ",0,"-1/(3*a**2*x**3 + 3*a*b)","A",0
1988,1,44,0,0.499414," ","integrate(1/(a+b/x**3)**2/x**5,x)","\frac{x^{2}}{3 a b x^{3} + 3 b^{2}} + \operatorname{RootSum} {\left(729 t^{3} a^{2} b^{4} + 1, \left( t \mapsto t \log{\left(81 t^{2} a b^{3} + x \right)} \right)\right)}"," ",0,"x**2/(3*a*b*x**3 + 3*b**2) + RootSum(729*_t**3*a**2*b**4 + 1, Lambda(_t, _t*log(81*_t**2*a*b**3 + x)))","A",0
1989,1,39,0,0.332303," ","integrate(1/(a+b/x**3)**2/x**6,x)","\frac{x}{3 a b x^{3} + 3 b^{2}} + \operatorname{RootSum} {\left(729 t^{3} a b^{5} - 8, \left( t \mapsto t \log{\left(\frac{9 t b^{2}}{2} + x \right)} \right)\right)}"," ",0,"x/(3*a*b*x**3 + 3*b**2) + RootSum(729*_t**3*a*b**5 - 8, Lambda(_t, _t*log(9*_t*b**2/2 + x)))","A",0
1990,1,34,0,0.426135," ","integrate(1/(a+b/x**3)**2/x**7,x)","\frac{1}{3 a b x^{3} + 3 b^{2}} + \frac{\log{\left(x \right)}}{b^{2}} - \frac{\log{\left(x^{3} + \frac{b}{a} \right)}}{3 b^{2}}"," ",0,"1/(3*a*b*x**3 + 3*b**2) + log(x)/b**2 - log(x**3 + b/a)/(3*b**2)","A",0
1991,1,100,0,4.529604," ","integrate(x**5*(a+b/x**3)**(1/2),x)","\frac{a x^{\frac{15}{2}}}{6 \sqrt{b} \sqrt{\frac{a x^{3}}{b} + 1}} + \frac{\sqrt{b} x^{\frac{9}{2}}}{4 \sqrt{\frac{a x^{3}}{b} + 1}} + \frac{b^{\frac{3}{2}} x^{\frac{3}{2}}}{12 a \sqrt{\frac{a x^{3}}{b} + 1}} - \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{3}{2}}}{\sqrt{b}} \right)}}{12 a^{\frac{3}{2}}}"," ",0,"a*x**(15/2)/(6*sqrt(b)*sqrt(a*x**3/b + 1)) + sqrt(b)*x**(9/2)/(4*sqrt(a*x**3/b + 1)) + b**(3/2)*x**(3/2)/(12*a*sqrt(a*x**3/b + 1)) - b**2*asinh(sqrt(a)*x**(3/2)/sqrt(b))/(12*a**(3/2))","A",0
1992,1,48,0,2.441401," ","integrate(x**2*(a+b/x**3)**(1/2),x)","\frac{\sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{3} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{3}{2}}}{\sqrt{b}} \right)}}{3 \sqrt{a}}"," ",0,"sqrt(b)*x**(3/2)*sqrt(a*x**3/b + 1)/3 + b*asinh(sqrt(a)*x**(3/2)/sqrt(b))/(3*sqrt(a))","A",0
1993,1,76,0,1.746823," ","integrate((a+b/x**3)**(1/2)/x,x)","\frac{2 \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{3}{2}}}{\sqrt{b}} \right)}}{3} - \frac{2 a x^{\frac{3}{2}}}{3 \sqrt{b} \sqrt{\frac{a x^{3}}{b} + 1}} - \frac{2 \sqrt{b}}{3 x^{\frac{3}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}"," ",0,"2*sqrt(a)*asinh(sqrt(a)*x**(3/2)/sqrt(b))/3 - 2*a*x**(3/2)/(3*sqrt(b)*sqrt(a*x**3/b + 1)) - 2*sqrt(b)/(3*x**(3/2)*sqrt(a*x**3/b + 1))","B",0
1994,1,46,0,1.228243," ","integrate((a+b/x**3)**(1/2)/x**4,x)","- \frac{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{3}}}}{9 b} - \frac{2 \sqrt{a} \sqrt{1 + \frac{b}{a x^{3}}}}{9 x^{3}}"," ",0,"-2*a**(3/2)*sqrt(1 + b/(a*x**3))/(9*b) - 2*sqrt(a)*sqrt(1 + b/(a*x**3))/(9*x**3)","B",0
1995,1,313,0,1.795304," ","integrate((a+b/x**3)**(1/2)/x**7,x)","\frac{4 a^{\frac{11}{2}} b^{\frac{3}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} + \frac{2 a^{\frac{9}{2}} b^{\frac{5}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} - \frac{8 a^{\frac{7}{2}} b^{\frac{7}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} - \frac{6 a^{\frac{5}{2}} b^{\frac{9}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} - \frac{4 a^{6} b x^{\frac{21}{2}}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} - \frac{4 a^{5} b^{2} x^{\frac{15}{2}}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}}"," ",0,"4*a**(11/2)*b**(3/2)*x**9*sqrt(a*x**3/b + 1)/(45*a**(7/2)*b**3*x**(21/2) + 45*a**(5/2)*b**4*x**(15/2)) + 2*a**(9/2)*b**(5/2)*x**6*sqrt(a*x**3/b + 1)/(45*a**(7/2)*b**3*x**(21/2) + 45*a**(5/2)*b**4*x**(15/2)) - 8*a**(7/2)*b**(7/2)*x**3*sqrt(a*x**3/b + 1)/(45*a**(7/2)*b**3*x**(21/2) + 45*a**(5/2)*b**4*x**(15/2)) - 6*a**(5/2)*b**(9/2)*sqrt(a*x**3/b + 1)/(45*a**(7/2)*b**3*x**(21/2) + 45*a**(5/2)*b**4*x**(15/2)) - 4*a**6*b*x**(21/2)/(45*a**(7/2)*b**3*x**(21/2) + 45*a**(5/2)*b**4*x**(15/2)) - 4*a**5*b**2*x**(15/2)/(45*a**(7/2)*b**3*x**(21/2) + 45*a**(5/2)*b**4*x**(15/2))","B",0
1996,1,913,0,2.914310," ","integrate((a+b/x**3)**(1/2)/x**10,x)","- \frac{16 a^{\frac{19}{2}} b^{\frac{9}{2}} x^{18} \sqrt{\frac{a x^{3}}{b} + 1}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}} - \frac{40 a^{\frac{17}{2}} b^{\frac{11}{2}} x^{15} \sqrt{\frac{a x^{3}}{b} + 1}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}} - \frac{30 a^{\frac{15}{2}} b^{\frac{13}{2}} x^{12} \sqrt{\frac{a x^{3}}{b} + 1}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}} - \frac{40 a^{\frac{13}{2}} b^{\frac{15}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}} - \frac{100 a^{\frac{11}{2}} b^{\frac{17}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}} - \frac{96 a^{\frac{9}{2}} b^{\frac{19}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}} - \frac{30 a^{\frac{7}{2}} b^{\frac{21}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}} + \frac{16 a^{10} b^{4} x^{\frac{39}{2}}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}} + \frac{48 a^{9} b^{5} x^{\frac{33}{2}}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}} + \frac{48 a^{8} b^{6} x^{\frac{27}{2}}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}} + \frac{16 a^{7} b^{7} x^{\frac{21}{2}}}{315 a^{\frac{13}{2}} b^{7} x^{\frac{39}{2}} + 945 a^{\frac{11}{2}} b^{8} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{9} x^{\frac{27}{2}} + 315 a^{\frac{7}{2}} b^{10} x^{\frac{21}{2}}}"," ",0,"-16*a**(19/2)*b**(9/2)*x**18*sqrt(a*x**3/b + 1)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2)) - 40*a**(17/2)*b**(11/2)*x**15*sqrt(a*x**3/b + 1)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2)) - 30*a**(15/2)*b**(13/2)*x**12*sqrt(a*x**3/b + 1)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2)) - 40*a**(13/2)*b**(15/2)*x**9*sqrt(a*x**3/b + 1)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2)) - 100*a**(11/2)*b**(17/2)*x**6*sqrt(a*x**3/b + 1)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2)) - 96*a**(9/2)*b**(19/2)*x**3*sqrt(a*x**3/b + 1)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2)) - 30*a**(7/2)*b**(21/2)*sqrt(a*x**3/b + 1)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2)) + 16*a**10*b**4*x**(39/2)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2)) + 48*a**9*b**5*x**(33/2)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2)) + 48*a**8*b**6*x**(27/2)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2)) + 16*a**7*b**7*x**(21/2)/(315*a**(13/2)*b**7*x**(39/2) + 945*a**(11/2)*b**8*x**(33/2) + 945*a**(9/2)*b**9*x**(27/2) + 315*a**(7/2)*b**10*x**(21/2))","B",0
1997,1,2317,0,4.284444," ","integrate((a+b/x**3)**(1/2)/x**13,x)","\frac{32 a^{\frac{29}{2}} b^{\frac{23}{2}} x^{30} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} + \frac{176 a^{\frac{27}{2}} b^{\frac{25}{2}} x^{27} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} + \frac{396 a^{\frac{25}{2}} b^{\frac{27}{2}} x^{24} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} + \frac{462 a^{\frac{23}{2}} b^{\frac{29}{2}} x^{21} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} + \frac{210 a^{\frac{21}{2}} b^{\frac{31}{2}} x^{18} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{378 a^{\frac{19}{2}} b^{\frac{33}{2}} x^{15} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{1134 a^{\frac{17}{2}} b^{\frac{35}{2}} x^{12} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{1494 a^{\frac{15}{2}} b^{\frac{37}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{1098 a^{\frac{13}{2}} b^{\frac{39}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{430 a^{\frac{11}{2}} b^{\frac{41}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{70 a^{\frac{9}{2}} b^{\frac{43}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{32 a^{15} b^{11} x^{\frac{63}{2}}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{192 a^{14} b^{12} x^{\frac{57}{2}}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{480 a^{13} b^{13} x^{\frac{51}{2}}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{640 a^{12} b^{14} x^{\frac{45}{2}}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{480 a^{11} b^{15} x^{\frac{39}{2}}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{192 a^{10} b^{16} x^{\frac{33}{2}}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}} - \frac{32 a^{9} b^{17} x^{\frac{27}{2}}}{945 a^{\frac{21}{2}} b^{15} x^{\frac{63}{2}} + 5670 a^{\frac{19}{2}} b^{16} x^{\frac{57}{2}} + 14175 a^{\frac{17}{2}} b^{17} x^{\frac{51}{2}} + 18900 a^{\frac{15}{2}} b^{18} x^{\frac{45}{2}} + 14175 a^{\frac{13}{2}} b^{19} x^{\frac{39}{2}} + 5670 a^{\frac{11}{2}} b^{20} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{21} x^{\frac{27}{2}}}"," ",0,"32*a**(29/2)*b**(23/2)*x**30*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) + 176*a**(27/2)*b**(25/2)*x**27*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) + 396*a**(25/2)*b**(27/2)*x**24*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) + 462*a**(23/2)*b**(29/2)*x**21*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) + 210*a**(21/2)*b**(31/2)*x**18*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 378*a**(19/2)*b**(33/2)*x**15*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 1134*a**(17/2)*b**(35/2)*x**12*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 1494*a**(15/2)*b**(37/2)*x**9*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 1098*a**(13/2)*b**(39/2)*x**6*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 430*a**(11/2)*b**(41/2)*x**3*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 70*a**(9/2)*b**(43/2)*sqrt(a*x**3/b + 1)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 32*a**15*b**11*x**(63/2)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 192*a**14*b**12*x**(57/2)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 480*a**13*b**13*x**(51/2)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 640*a**12*b**14*x**(45/2)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 480*a**11*b**15*x**(39/2)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 192*a**10*b**16*x**(33/2)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2)) - 32*a**9*b**17*x**(27/2)/(945*a**(21/2)*b**15*x**(63/2) + 5670*a**(19/2)*b**16*x**(57/2) + 14175*a**(17/2)*b**17*x**(51/2) + 18900*a**(15/2)*b**18*x**(45/2) + 14175*a**(13/2)*b**19*x**(39/2) + 5670*a**(11/2)*b**20*x**(33/2) + 945*a**(9/2)*b**21*x**(27/2))","B",0
1998,1,48,0,1.586824," ","integrate(x**7*(a+b/x**3)**(1/2),x)","- \frac{\sqrt{a} x^{8} \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, - \frac{1}{2} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \Gamma\left(- \frac{5}{3}\right)}"," ",0,"-sqrt(a)*x**8*gamma(-8/3)*hyper((-8/3, -1/2), (-5/3,), b*exp_polar(I*pi)/(a*x**3))/(3*gamma(-5/3))","A",0
1999,1,48,0,1.290606," ","integrate(x**4*(a+b/x**3)**(1/2),x)","- \frac{\sqrt{a} x^{5} \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \Gamma\left(- \frac{2}{3}\right)}"," ",0,"-sqrt(a)*x**5*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*exp_polar(I*pi)/(a*x**3))/(3*gamma(-2/3))","A",0
2000,1,44,0,1.090680," ","integrate(x*(a+b/x**3)**(1/2),x)","- \frac{\sqrt{a} x^{2} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \Gamma\left(\frac{1}{3}\right)}"," ",0,"-sqrt(a)*x**2*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*exp_polar(I*pi)/(a*x**3))/(3*gamma(1/3))","A",0
2001,1,39,0,1.090249," ","integrate((a+b/x**3)**(1/2)/x**2,x)","- \frac{\sqrt{a} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 x \Gamma\left(\frac{4}{3}\right)}"," ",0,"-sqrt(a)*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*exp_polar(I*pi)/(a*x**3))/(3*x*gamma(4/3))","A",0
2002,1,41,0,1.336639," ","integrate((a+b/x**3)**(1/2)/x**5,x)","- \frac{\sqrt{a} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 x^{4} \Gamma\left(\frac{7}{3}\right)}"," ",0,"-sqrt(a)*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*exp_polar(I*pi)/(a*x**3))/(3*x**4*gamma(7/3))","A",0
2003,1,41,0,1.722652," ","integrate((a+b/x**3)**(1/2)/x**8,x)","- \frac{\sqrt{a} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 x^{7} \Gamma\left(\frac{10}{3}\right)}"," ",0,"-sqrt(a)*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*exp_polar(I*pi)/(a*x**3))/(3*x**7*gamma(10/3))","A",0
2004,1,48,0,1.613443," ","integrate(x**6*(a+b/x**3)**(1/2),x)","- \frac{\sqrt{a} x^{7} \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, - \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \Gamma\left(- \frac{4}{3}\right)}"," ",0,"-sqrt(a)*x**7*gamma(-7/3)*hyper((-7/3, -1/2), (-4/3,), b*exp_polar(I*pi)/(a*x**3))/(3*gamma(-4/3))","A",0
2005,1,48,0,1.363707," ","integrate(x**3*(a+b/x**3)**(1/2),x)","- \frac{\sqrt{a} x^{4} \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \Gamma\left(- \frac{1}{3}\right)}"," ",0,"-sqrt(a)*x**4*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*exp_polar(I*pi)/(a*x**3))/(3*gamma(-1/3))","A",0
2006,1,42,0,0.997408," ","integrate((a+b/x**3)**(1/2),x)","- \frac{\sqrt{a} x \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \Gamma\left(\frac{2}{3}\right)}"," ",0,"-sqrt(a)*x*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*exp_polar(I*pi)/(a*x**3))/(3*gamma(2/3))","A",0
2007,1,41,0,1.267841," ","integrate((a+b/x**3)**(1/2)/x**3,x)","- \frac{\sqrt{a} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 x^{2} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-sqrt(a)*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*exp_polar(I*pi)/(a*x**3))/(3*x**2*gamma(5/3))","A",0
2008,1,41,0,1.457672," ","integrate((a+b/x**3)**(1/2)/x**6,x)","- \frac{\sqrt{a} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 x^{5} \Gamma\left(\frac{8}{3}\right)}"," ",0,"-sqrt(a)*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*exp_polar(I*pi)/(a*x**3))/(3*x**5*gamma(8/3))","A",0
2009,1,41,0,1.803387," ","integrate((a+b/x**3)**(1/2)/x**9,x)","- \frac{\sqrt{a} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 x^{8} \Gamma\left(\frac{11}{3}\right)}"," ",0,"-sqrt(a)*gamma(8/3)*hyper((-1/2, 8/3), (11/3,), b*exp_polar(I*pi)/(a*x**3))/(3*x**8*gamma(11/3))","A",0
2010,1,76,0,3.872976," ","integrate((a+b/x**3)**(3/2)*x**5,x)","\frac{a \sqrt{b} x^{\frac{9}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{6} + \frac{5 b^{\frac{3}{2}} x^{\frac{3}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{12} + \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{3}{2}}}{\sqrt{b}} \right)}}{4 \sqrt{a}}"," ",0,"a*sqrt(b)*x**(9/2)*sqrt(a*x**3/b + 1)/6 + 5*b**(3/2)*x**(3/2)*sqrt(a*x**3/b + 1)/12 + b**2*asinh(sqrt(a)*x**(3/2)/sqrt(b))/(4*sqrt(a))","A",0
2011,1,100,0,2.997139," ","integrate((a+b/x**3)**(3/2)*x**2,x)","\sqrt{a} b \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{3}{2}}}{\sqrt{b}} \right)} + \frac{a^{2} x^{\frac{9}{2}}}{3 \sqrt{b} \sqrt{\frac{a x^{3}}{b} + 1}} - \frac{a \sqrt{b} x^{\frac{3}{2}}}{3 \sqrt{\frac{a x^{3}}{b} + 1}} - \frac{2 b^{\frac{3}{2}}}{3 x^{\frac{3}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}"," ",0,"sqrt(a)*b*asinh(sqrt(a)*x**(3/2)/sqrt(b)) + a**2*x**(9/2)/(3*sqrt(b)*sqrt(a*x**3/b + 1)) - a*sqrt(b)*x**(3/2)/(3*sqrt(a*x**3/b + 1)) - 2*b**(3/2)/(3*x**(3/2)*sqrt(a*x**3/b + 1))","B",0
2012,1,83,0,2.377522," ","integrate((a+b/x**3)**(3/2)/x,x)","- \frac{8 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{3}}}}{9} - \frac{a^{\frac{3}{2}} \log{\left(\frac{b}{a x^{3}} \right)}}{3} + \frac{2 a^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{b}{a x^{3}}} + 1 \right)}}{3} - \frac{2 \sqrt{a} b \sqrt{1 + \frac{b}{a x^{3}}}}{9 x^{3}}"," ",0,"-8*a**(3/2)*sqrt(1 + b/(a*x**3))/9 - a**(3/2)*log(b/(a*x**3))/3 + 2*a**(3/2)*log(sqrt(1 + b/(a*x**3)) + 1)/3 - 2*sqrt(a)*b*sqrt(1 + b/(a*x**3))/(9*x**3)","A",0
2013,1,71,0,1.357560," ","integrate((a+b/x**3)**(3/2)/x**4,x)","- \frac{2 a^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x^{3}}}}{15 b} - \frac{4 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{3}}}}{15 x^{3}} - \frac{2 \sqrt{a} b \sqrt{1 + \frac{b}{a x^{3}}}}{15 x^{6}}"," ",0,"-2*a**(5/2)*sqrt(1 + b/(a*x**3))/(15*b) - 4*a**(3/2)*sqrt(1 + b/(a*x**3))/(15*x**3) - 2*sqrt(a)*b*sqrt(1 + b/(a*x**3))/(15*x**6)","B",0
2014,1,371,0,2.053891," ","integrate((a+b/x**3)**(3/2)/x**7,x)","\frac{4 a^{\frac{15}{2}} b^{\frac{3}{2}} x^{12} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{9}{2}} b^{3} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{4} x^{\frac{21}{2}}} + \frac{2 a^{\frac{13}{2}} b^{\frac{5}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{9}{2}} b^{3} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{4} x^{\frac{21}{2}}} - \frac{18 a^{\frac{11}{2}} b^{\frac{7}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{9}{2}} b^{3} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{4} x^{\frac{21}{2}}} - \frac{26 a^{\frac{9}{2}} b^{\frac{9}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{9}{2}} b^{3} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{4} x^{\frac{21}{2}}} - \frac{10 a^{\frac{7}{2}} b^{\frac{11}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{9}{2}} b^{3} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{4} x^{\frac{21}{2}}} - \frac{4 a^{8} b x^{\frac{27}{2}}}{105 a^{\frac{9}{2}} b^{3} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{4} x^{\frac{21}{2}}} - \frac{4 a^{7} b^{2} x^{\frac{21}{2}}}{105 a^{\frac{9}{2}} b^{3} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{4} x^{\frac{21}{2}}}"," ",0,"4*a**(15/2)*b**(3/2)*x**12*sqrt(a*x**3/b + 1)/(105*a**(9/2)*b**3*x**(27/2) + 105*a**(7/2)*b**4*x**(21/2)) + 2*a**(13/2)*b**(5/2)*x**9*sqrt(a*x**3/b + 1)/(105*a**(9/2)*b**3*x**(27/2) + 105*a**(7/2)*b**4*x**(21/2)) - 18*a**(11/2)*b**(7/2)*x**6*sqrt(a*x**3/b + 1)/(105*a**(9/2)*b**3*x**(27/2) + 105*a**(7/2)*b**4*x**(21/2)) - 26*a**(9/2)*b**(9/2)*x**3*sqrt(a*x**3/b + 1)/(105*a**(9/2)*b**3*x**(27/2) + 105*a**(7/2)*b**4*x**(21/2)) - 10*a**(7/2)*b**(11/2)*sqrt(a*x**3/b + 1)/(105*a**(9/2)*b**3*x**(27/2) + 105*a**(7/2)*b**4*x**(21/2)) - 4*a**8*b*x**(27/2)/(105*a**(9/2)*b**3*x**(27/2) + 105*a**(7/2)*b**4*x**(21/2)) - 4*a**7*b**2*x**(21/2)/(105*a**(9/2)*b**3*x**(27/2) + 105*a**(7/2)*b**4*x**(21/2))","B",0
2015,1,1001,0,3.236591," ","integrate((a+b/x**3)**(3/2)/x**10,x)","- \frac{16 a^{\frac{23}{2}} b^{\frac{9}{2}} x^{21} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} - \frac{40 a^{\frac{21}{2}} b^{\frac{11}{2}} x^{18} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} - \frac{30 a^{\frac{19}{2}} b^{\frac{13}{2}} x^{15} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} - \frac{110 a^{\frac{17}{2}} b^{\frac{15}{2}} x^{12} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} - \frac{380 a^{\frac{15}{2}} b^{\frac{17}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} - \frac{516 a^{\frac{13}{2}} b^{\frac{19}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} - \frac{310 a^{\frac{11}{2}} b^{\frac{21}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} - \frac{70 a^{\frac{9}{2}} b^{\frac{23}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} + \frac{16 a^{12} b^{4} x^{\frac{45}{2}}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} + \frac{48 a^{11} b^{5} x^{\frac{39}{2}}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} + \frac{48 a^{10} b^{6} x^{\frac{33}{2}}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}} + \frac{16 a^{9} b^{7} x^{\frac{27}{2}}}{945 a^{\frac{15}{2}} b^{7} x^{\frac{45}{2}} + 2835 a^{\frac{13}{2}} b^{8} x^{\frac{39}{2}} + 2835 a^{\frac{11}{2}} b^{9} x^{\frac{33}{2}} + 945 a^{\frac{9}{2}} b^{10} x^{\frac{27}{2}}}"," ",0,"-16*a**(23/2)*b**(9/2)*x**21*sqrt(a*x**3/b + 1)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) - 40*a**(21/2)*b**(11/2)*x**18*sqrt(a*x**3/b + 1)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) - 30*a**(19/2)*b**(13/2)*x**15*sqrt(a*x**3/b + 1)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) - 110*a**(17/2)*b**(15/2)*x**12*sqrt(a*x**3/b + 1)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) - 380*a**(15/2)*b**(17/2)*x**9*sqrt(a*x**3/b + 1)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) - 516*a**(13/2)*b**(19/2)*x**6*sqrt(a*x**3/b + 1)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) - 310*a**(11/2)*b**(21/2)*x**3*sqrt(a*x**3/b + 1)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) - 70*a**(9/2)*b**(23/2)*sqrt(a*x**3/b + 1)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) + 16*a**12*b**4*x**(45/2)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) + 48*a**11*b**5*x**(39/2)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) + 48*a**10*b**6*x**(33/2)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2)) + 16*a**9*b**7*x**(27/2)/(945*a**(15/2)*b**7*x**(45/2) + 2835*a**(13/2)*b**8*x**(39/2) + 2835*a**(11/2)*b**9*x**(33/2) + 945*a**(9/2)*b**10*x**(27/2))","B",0
2016,1,2317,0,4.750525," ","integrate((a+b/x**3)**(3/2)/x**13,x)","\frac{32 a^{\frac{33}{2}} b^{\frac{23}{2}} x^{33} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} + \frac{176 a^{\frac{31}{2}} b^{\frac{25}{2}} x^{30} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} + \frac{396 a^{\frac{29}{2}} b^{\frac{27}{2}} x^{27} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} + \frac{462 a^{\frac{27}{2}} b^{\frac{29}{2}} x^{24} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{1848 a^{\frac{23}{2}} b^{\frac{33}{2}} x^{18} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{5544 a^{\frac{21}{2}} b^{\frac{35}{2}} x^{15} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{8844 a^{\frac{19}{2}} b^{\frac{37}{2}} x^{12} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{8448 a^{\frac{17}{2}} b^{\frac{39}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{4840 a^{\frac{15}{2}} b^{\frac{41}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{1540 a^{\frac{13}{2}} b^{\frac{43}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{210 a^{\frac{11}{2}} b^{\frac{45}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{32 a^{17} b^{11} x^{\frac{69}{2}}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{192 a^{16} b^{12} x^{\frac{63}{2}}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{480 a^{15} b^{13} x^{\frac{57}{2}}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{640 a^{14} b^{14} x^{\frac{51}{2}}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{480 a^{13} b^{15} x^{\frac{45}{2}}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{192 a^{12} b^{16} x^{\frac{39}{2}}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}} - \frac{32 a^{11} b^{17} x^{\frac{33}{2}}}{3465 a^{\frac{23}{2}} b^{15} x^{\frac{69}{2}} + 20790 a^{\frac{21}{2}} b^{16} x^{\frac{63}{2}} + 51975 a^{\frac{19}{2}} b^{17} x^{\frac{57}{2}} + 69300 a^{\frac{17}{2}} b^{18} x^{\frac{51}{2}} + 51975 a^{\frac{15}{2}} b^{19} x^{\frac{45}{2}} + 20790 a^{\frac{13}{2}} b^{20} x^{\frac{39}{2}} + 3465 a^{\frac{11}{2}} b^{21} x^{\frac{33}{2}}}"," ",0,"32*a**(33/2)*b**(23/2)*x**33*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) + 176*a**(31/2)*b**(25/2)*x**30*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) + 396*a**(29/2)*b**(27/2)*x**27*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) + 462*a**(27/2)*b**(29/2)*x**24*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 1848*a**(23/2)*b**(33/2)*x**18*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 5544*a**(21/2)*b**(35/2)*x**15*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 8844*a**(19/2)*b**(37/2)*x**12*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 8448*a**(17/2)*b**(39/2)*x**9*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 4840*a**(15/2)*b**(41/2)*x**6*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 1540*a**(13/2)*b**(43/2)*x**3*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 210*a**(11/2)*b**(45/2)*sqrt(a*x**3/b + 1)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 32*a**17*b**11*x**(69/2)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 192*a**16*b**12*x**(63/2)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 480*a**15*b**13*x**(57/2)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 640*a**14*b**14*x**(51/2)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 480*a**13*b**15*x**(45/2)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 192*a**12*b**16*x**(39/2)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2)) - 32*a**11*b**17*x**(33/2)/(3465*a**(23/2)*b**15*x**(69/2) + 20790*a**(21/2)*b**16*x**(63/2) + 51975*a**(19/2)*b**17*x**(57/2) + 69300*a**(17/2)*b**18*x**(51/2) + 51975*a**(15/2)*b**19*x**(45/2) + 20790*a**(13/2)*b**20*x**(39/2) + 3465*a**(11/2)*b**21*x**(33/2))","B",0
2017,1,102,0,5.785566," ","integrate(x**5/(a+b/x**3)**(1/2),x)","\frac{x^{\frac{15}{2}}}{6 \sqrt{b} \sqrt{\frac{a x^{3}}{b} + 1}} - \frac{\sqrt{b} x^{\frac{9}{2}}}{12 a \sqrt{\frac{a x^{3}}{b} + 1}} - \frac{b^{\frac{3}{2}} x^{\frac{3}{2}}}{4 a^{2} \sqrt{\frac{a x^{3}}{b} + 1}} + \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{3}{2}}}{\sqrt{b}} \right)}}{4 a^{\frac{5}{2}}}"," ",0,"x**(15/2)/(6*sqrt(b)*sqrt(a*x**3/b + 1)) - sqrt(b)*x**(9/2)/(12*a*sqrt(a*x**3/b + 1)) - b**(3/2)*x**(3/2)/(4*a**2*sqrt(a*x**3/b + 1)) + b**2*asinh(sqrt(a)*x**(3/2)/sqrt(b))/(4*a**(5/2))","A",0
2018,1,49,0,2.632221," ","integrate(x**2/(a+b/x**3)**(1/2),x)","\frac{\sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{3 a} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{3}{2}}}{\sqrt{b}} \right)}}{3 a^{\frac{3}{2}}}"," ",0,"sqrt(b)*x**(3/2)*sqrt(a*x**3/b + 1)/(3*a) - b*asinh(sqrt(a)*x**(3/2)/sqrt(b))/(3*a**(3/2))","A",0
2019,1,24,0,1.368080," ","integrate(1/x/(a+b/x**3)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{3}{2}}}{\sqrt{b}} \right)}}{3 \sqrt{a}}"," ",0,"2*asinh(sqrt(a)*x**(3/2)/sqrt(b))/(3*sqrt(a))","A",0
2020,1,29,0,2.039153," ","integrate(1/x**4/(a+b/x**3)**(1/2),x)","\begin{cases} - \frac{2 \sqrt{a + \frac{b}{x^{3}}}}{3 b} & \text{for}\: b \neq 0 \\- \frac{1}{3 \sqrt{a} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(a + b/x**3)/(3*b), Ne(b, 0)), (-1/(3*sqrt(a)*x**3), True))","A",0
2021,1,255,0,1.961808," ","integrate(1/x**7/(a+b/x**3)**(1/2),x)","\frac{4 a^{\frac{7}{2}} b^{\frac{3}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{9 a^{\frac{5}{2}} b^{3} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{4} x^{\frac{9}{2}}} + \frac{2 a^{\frac{5}{2}} b^{\frac{5}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{9 a^{\frac{5}{2}} b^{3} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{4} x^{\frac{9}{2}}} - \frac{2 a^{\frac{3}{2}} b^{\frac{7}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{9 a^{\frac{5}{2}} b^{3} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{4} x^{\frac{9}{2}}} - \frac{4 a^{4} b x^{\frac{15}{2}}}{9 a^{\frac{5}{2}} b^{3} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{4} x^{\frac{9}{2}}} - \frac{4 a^{3} b^{2} x^{\frac{9}{2}}}{9 a^{\frac{5}{2}} b^{3} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{4} x^{\frac{9}{2}}}"," ",0,"4*a**(7/2)*b**(3/2)*x**6*sqrt(a*x**3/b + 1)/(9*a**(5/2)*b**3*x**(15/2) + 9*a**(3/2)*b**4*x**(9/2)) + 2*a**(5/2)*b**(5/2)*x**3*sqrt(a*x**3/b + 1)/(9*a**(5/2)*b**3*x**(15/2) + 9*a**(3/2)*b**4*x**(9/2)) - 2*a**(3/2)*b**(7/2)*sqrt(a*x**3/b + 1)/(9*a**(5/2)*b**3*x**(15/2) + 9*a**(3/2)*b**4*x**(9/2)) - 4*a**4*b*x**(15/2)/(9*a**(5/2)*b**3*x**(15/2) + 9*a**(3/2)*b**4*x**(9/2)) - 4*a**3*b**2*x**(9/2)/(9*a**(5/2)*b**3*x**(15/2) + 9*a**(3/2)*b**4*x**(9/2))","B",0
2022,1,824,0,3.192758," ","integrate(1/x**10/(a+b/x**3)**(1/2),x)","- \frac{16 a^{\frac{15}{2}} b^{\frac{9}{2}} x^{15} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{11}{2}} b^{7} x^{\frac{33}{2}} + 135 a^{\frac{9}{2}} b^{8} x^{\frac{27}{2}} + 135 a^{\frac{7}{2}} b^{9} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{10} x^{\frac{15}{2}}} - \frac{40 a^{\frac{13}{2}} b^{\frac{11}{2}} x^{12} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{11}{2}} b^{7} x^{\frac{33}{2}} + 135 a^{\frac{9}{2}} b^{8} x^{\frac{27}{2}} + 135 a^{\frac{7}{2}} b^{9} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{10} x^{\frac{15}{2}}} - \frac{30 a^{\frac{11}{2}} b^{\frac{13}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{11}{2}} b^{7} x^{\frac{33}{2}} + 135 a^{\frac{9}{2}} b^{8} x^{\frac{27}{2}} + 135 a^{\frac{7}{2}} b^{9} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{10} x^{\frac{15}{2}}} - \frac{10 a^{\frac{9}{2}} b^{\frac{15}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{11}{2}} b^{7} x^{\frac{33}{2}} + 135 a^{\frac{9}{2}} b^{8} x^{\frac{27}{2}} + 135 a^{\frac{7}{2}} b^{9} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{10} x^{\frac{15}{2}}} - \frac{10 a^{\frac{7}{2}} b^{\frac{17}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{11}{2}} b^{7} x^{\frac{33}{2}} + 135 a^{\frac{9}{2}} b^{8} x^{\frac{27}{2}} + 135 a^{\frac{7}{2}} b^{9} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{10} x^{\frac{15}{2}}} - \frac{6 a^{\frac{5}{2}} b^{\frac{19}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{11}{2}} b^{7} x^{\frac{33}{2}} + 135 a^{\frac{9}{2}} b^{8} x^{\frac{27}{2}} + 135 a^{\frac{7}{2}} b^{9} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{10} x^{\frac{15}{2}}} + \frac{16 a^{8} b^{4} x^{\frac{33}{2}}}{45 a^{\frac{11}{2}} b^{7} x^{\frac{33}{2}} + 135 a^{\frac{9}{2}} b^{8} x^{\frac{27}{2}} + 135 a^{\frac{7}{2}} b^{9} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{10} x^{\frac{15}{2}}} + \frac{48 a^{7} b^{5} x^{\frac{27}{2}}}{45 a^{\frac{11}{2}} b^{7} x^{\frac{33}{2}} + 135 a^{\frac{9}{2}} b^{8} x^{\frac{27}{2}} + 135 a^{\frac{7}{2}} b^{9} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{10} x^{\frac{15}{2}}} + \frac{48 a^{6} b^{6} x^{\frac{21}{2}}}{45 a^{\frac{11}{2}} b^{7} x^{\frac{33}{2}} + 135 a^{\frac{9}{2}} b^{8} x^{\frac{27}{2}} + 135 a^{\frac{7}{2}} b^{9} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{10} x^{\frac{15}{2}}} + \frac{16 a^{5} b^{7} x^{\frac{15}{2}}}{45 a^{\frac{11}{2}} b^{7} x^{\frac{33}{2}} + 135 a^{\frac{9}{2}} b^{8} x^{\frac{27}{2}} + 135 a^{\frac{7}{2}} b^{9} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{10} x^{\frac{15}{2}}}"," ",0,"-16*a**(15/2)*b**(9/2)*x**15*sqrt(a*x**3/b + 1)/(45*a**(11/2)*b**7*x**(33/2) + 135*a**(9/2)*b**8*x**(27/2) + 135*a**(7/2)*b**9*x**(21/2) + 45*a**(5/2)*b**10*x**(15/2)) - 40*a**(13/2)*b**(11/2)*x**12*sqrt(a*x**3/b + 1)/(45*a**(11/2)*b**7*x**(33/2) + 135*a**(9/2)*b**8*x**(27/2) + 135*a**(7/2)*b**9*x**(21/2) + 45*a**(5/2)*b**10*x**(15/2)) - 30*a**(11/2)*b**(13/2)*x**9*sqrt(a*x**3/b + 1)/(45*a**(11/2)*b**7*x**(33/2) + 135*a**(9/2)*b**8*x**(27/2) + 135*a**(7/2)*b**9*x**(21/2) + 45*a**(5/2)*b**10*x**(15/2)) - 10*a**(9/2)*b**(15/2)*x**6*sqrt(a*x**3/b + 1)/(45*a**(11/2)*b**7*x**(33/2) + 135*a**(9/2)*b**8*x**(27/2) + 135*a**(7/2)*b**9*x**(21/2) + 45*a**(5/2)*b**10*x**(15/2)) - 10*a**(7/2)*b**(17/2)*x**3*sqrt(a*x**3/b + 1)/(45*a**(11/2)*b**7*x**(33/2) + 135*a**(9/2)*b**8*x**(27/2) + 135*a**(7/2)*b**9*x**(21/2) + 45*a**(5/2)*b**10*x**(15/2)) - 6*a**(5/2)*b**(19/2)*sqrt(a*x**3/b + 1)/(45*a**(11/2)*b**7*x**(33/2) + 135*a**(9/2)*b**8*x**(27/2) + 135*a**(7/2)*b**9*x**(21/2) + 45*a**(5/2)*b**10*x**(15/2)) + 16*a**8*b**4*x**(33/2)/(45*a**(11/2)*b**7*x**(33/2) + 135*a**(9/2)*b**8*x**(27/2) + 135*a**(7/2)*b**9*x**(21/2) + 45*a**(5/2)*b**10*x**(15/2)) + 48*a**7*b**5*x**(27/2)/(45*a**(11/2)*b**7*x**(33/2) + 135*a**(9/2)*b**8*x**(27/2) + 135*a**(7/2)*b**9*x**(21/2) + 45*a**(5/2)*b**10*x**(15/2)) + 48*a**6*b**6*x**(21/2)/(45*a**(11/2)*b**7*x**(33/2) + 135*a**(9/2)*b**8*x**(27/2) + 135*a**(7/2)*b**9*x**(21/2) + 45*a**(5/2)*b**10*x**(15/2)) + 16*a**5*b**7*x**(15/2)/(45*a**(11/2)*b**7*x**(33/2) + 135*a**(9/2)*b**8*x**(27/2) + 135*a**(7/2)*b**9*x**(21/2) + 45*a**(5/2)*b**10*x**(15/2))","B",0
2023,1,2183,0,4.743406," ","integrate(1/x**13/(a+b/x**3)**(1/2),x)","\frac{32 a^{\frac{25}{2}} b^{\frac{23}{2}} x^{27} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} + \frac{176 a^{\frac{23}{2}} b^{\frac{25}{2}} x^{24} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} + \frac{396 a^{\frac{21}{2}} b^{\frac{27}{2}} x^{21} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} + \frac{462 a^{\frac{19}{2}} b^{\frac{29}{2}} x^{18} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} + \frac{280 a^{\frac{17}{2}} b^{\frac{31}{2}} x^{15} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} + \frac{42 a^{\frac{15}{2}} b^{\frac{33}{2}} x^{12} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{84 a^{\frac{13}{2}} b^{\frac{35}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{94 a^{\frac{11}{2}} b^{\frac{37}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{48 a^{\frac{9}{2}} b^{\frac{39}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{10 a^{\frac{7}{2}} b^{\frac{41}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{32 a^{13} b^{11} x^{\frac{57}{2}}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{192 a^{12} b^{12} x^{\frac{51}{2}}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{480 a^{11} b^{13} x^{\frac{45}{2}}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{640 a^{10} b^{14} x^{\frac{39}{2}}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{480 a^{9} b^{15} x^{\frac{33}{2}}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{192 a^{8} b^{16} x^{\frac{27}{2}}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}} - \frac{32 a^{7} b^{17} x^{\frac{21}{2}}}{105 a^{\frac{19}{2}} b^{15} x^{\frac{57}{2}} + 630 a^{\frac{17}{2}} b^{16} x^{\frac{51}{2}} + 1575 a^{\frac{15}{2}} b^{17} x^{\frac{45}{2}} + 2100 a^{\frac{13}{2}} b^{18} x^{\frac{39}{2}} + 1575 a^{\frac{11}{2}} b^{19} x^{\frac{33}{2}} + 630 a^{\frac{9}{2}} b^{20} x^{\frac{27}{2}} + 105 a^{\frac{7}{2}} b^{21} x^{\frac{21}{2}}}"," ",0,"32*a**(25/2)*b**(23/2)*x**27*sqrt(a*x**3/b + 1)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) + 176*a**(23/2)*b**(25/2)*x**24*sqrt(a*x**3/b + 1)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) + 396*a**(21/2)*b**(27/2)*x**21*sqrt(a*x**3/b + 1)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) + 462*a**(19/2)*b**(29/2)*x**18*sqrt(a*x**3/b + 1)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) + 280*a**(17/2)*b**(31/2)*x**15*sqrt(a*x**3/b + 1)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) + 42*a**(15/2)*b**(33/2)*x**12*sqrt(a*x**3/b + 1)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 84*a**(13/2)*b**(35/2)*x**9*sqrt(a*x**3/b + 1)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 94*a**(11/2)*b**(37/2)*x**6*sqrt(a*x**3/b + 1)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 48*a**(9/2)*b**(39/2)*x**3*sqrt(a*x**3/b + 1)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 10*a**(7/2)*b**(41/2)*sqrt(a*x**3/b + 1)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 32*a**13*b**11*x**(57/2)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 192*a**12*b**12*x**(51/2)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 480*a**11*b**13*x**(45/2)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 640*a**10*b**14*x**(39/2)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 480*a**9*b**15*x**(33/2)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 192*a**8*b**16*x**(27/2)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2)) - 32*a**7*b**17*x**(21/2)/(105*a**(19/2)*b**15*x**(57/2) + 630*a**(17/2)*b**16*x**(51/2) + 1575*a**(15/2)*b**17*x**(45/2) + 2100*a**(13/2)*b**18*x**(39/2) + 1575*a**(11/2)*b**19*x**(33/2) + 630*a**(9/2)*b**20*x**(27/2) + 105*a**(7/2)*b**21*x**(21/2))","B",0
2024,1,46,0,1.461915," ","integrate(x**7/(a+b/x**3)**(1/2),x)","- \frac{x^{8} \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, \frac{1}{2} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} \Gamma\left(- \frac{5}{3}\right)}"," ",0,"-x**8*gamma(-8/3)*hyper((-8/3, 1/2), (-5/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*gamma(-5/3))","A",0
2025,1,46,0,1.199198," ","integrate(x**4/(a+b/x**3)**(1/2),x)","- \frac{x^{5} \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"-x**5*gamma(-5/3)*hyper((-5/3, 1/2), (-2/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*gamma(-2/3))","A",0
2026,1,42,0,1.029756," ","integrate(x/(a+b/x**3)**(1/2),x)","- \frac{x^{2} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{1}{3}\right)}"," ",0,"-x**2*gamma(-2/3)*hyper((-2/3, 1/2), (1/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*gamma(1/3))","A",0
2027,1,37,0,1.148977," ","integrate(1/x**2/(a+b/x**3)**(1/2),x)","- \frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} x \Gamma\left(\frac{4}{3}\right)}"," ",0,"-gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*x*gamma(4/3))","A",0
2028,1,39,0,1.346337," ","integrate(1/x**5/(a+b/x**3)**(1/2),x)","- \frac{\Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} x^{4} \Gamma\left(\frac{7}{3}\right)}"," ",0,"-gamma(4/3)*hyper((1/2, 4/3), (7/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*x**4*gamma(7/3))","A",0
2029,1,39,0,1.676037," ","integrate(1/x**8/(a+b/x**3)**(1/2),x)","- \frac{\Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} x^{7} \Gamma\left(\frac{10}{3}\right)}"," ",0,"-gamma(7/3)*hyper((1/2, 7/3), (10/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*x**7*gamma(10/3))","A",0
2030,1,46,0,1.314847," ","integrate(x**6/(a+b/x**3)**(1/2),x)","- \frac{x^{7} \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} \Gamma\left(- \frac{4}{3}\right)}"," ",0,"-x**7*gamma(-7/3)*hyper((-7/3, 1/2), (-4/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*gamma(-4/3))","A",0
2031,1,46,0,1.138248," ","integrate(x**3/(a+b/x**3)**(1/2),x)","- \frac{x^{4} \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"-x**4*gamma(-4/3)*hyper((-4/3, 1/2), (-1/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*gamma(-1/3))","A",0
2032,1,41,0,1.042011," ","integrate(1/(a+b/x**3)**(1/2),x)","- \frac{x \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{2}{3}\right)}"," ",0,"-x*gamma(-1/3)*hyper((-1/3, 1/2), (2/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*gamma(2/3))","A",0
2033,1,39,0,1.196521," ","integrate(1/x**3/(a+b/x**3)**(1/2),x)","- \frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} x^{2} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*x**2*gamma(5/3))","A",0
2034,1,39,0,1.465675," ","integrate(1/x**6/(a+b/x**3)**(1/2),x)","- \frac{\Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} x^{5} \Gamma\left(\frac{8}{3}\right)}"," ",0,"-gamma(5/3)*hyper((1/2, 5/3), (8/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*x**5*gamma(8/3))","A",0
2035,1,39,0,1.792639," ","integrate(1/x**9/(a+b/x**3)**(1/2),x)","- \frac{\Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} x^{8} \Gamma\left(\frac{11}{3}\right)}"," ",0,"-gamma(8/3)*hyper((1/2, 8/3), (11/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*x**8*gamma(11/3))","A",0
2036,1,39,0,2.252945," ","integrate(1/x**12/(a+b/x**3)**(1/2),x)","- \frac{\Gamma\left(\frac{11}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{3} \\ \frac{14}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 \sqrt{a} x^{11} \Gamma\left(\frac{14}{3}\right)}"," ",0,"-gamma(11/3)*hyper((1/2, 11/3), (14/3,), b*exp_polar(I*pi)/(a*x**3))/(3*sqrt(a)*x**11*gamma(14/3))","A",0
2037,1,110,0,6.164083," ","integrate(x**5/(a+b/x**3)**(3/2),x)","\frac{x^{\frac{15}{2}}}{6 a \sqrt{b} \sqrt{\frac{a x^{3}}{b} + 1}} - \frac{5 \sqrt{b} x^{\frac{9}{2}}}{12 a^{2} \sqrt{\frac{a x^{3}}{b} + 1}} - \frac{5 b^{\frac{3}{2}} x^{\frac{3}{2}}}{4 a^{3} \sqrt{\frac{a x^{3}}{b} + 1}} + \frac{5 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{3}{2}}}{\sqrt{b}} \right)}}{4 a^{\frac{7}{2}}}"," ",0,"x**(15/2)/(6*a*sqrt(b)*sqrt(a*x**3/b + 1)) - 5*sqrt(b)*x**(9/2)/(12*a**2*sqrt(a*x**3/b + 1)) - 5*b**(3/2)*x**(3/2)/(4*a**3*sqrt(a*x**3/b + 1)) + 5*b**2*asinh(sqrt(a)*x**(3/2)/sqrt(b))/(4*a**(7/2))","A",0
2038,1,73,0,3.582279," ","integrate(x**2/(a+b/x**3)**(3/2),x)","\frac{x^{\frac{9}{2}}}{3 a \sqrt{b} \sqrt{\frac{a x^{3}}{b} + 1}} + \frac{\sqrt{b} x^{\frac{3}{2}}}{a^{2} \sqrt{\frac{a x^{3}}{b} + 1}} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{3}{2}}}{\sqrt{b}} \right)}}{a^{\frac{5}{2}}}"," ",0,"x**(9/2)/(3*a*sqrt(b)*sqrt(a*x**3/b + 1)) + sqrt(b)*x**(3/2)/(a**2*sqrt(a*x**3/b + 1)) - b*asinh(sqrt(a)*x**(3/2)/sqrt(b))/a**(5/2)","A",0
2039,1,187,0,2.221816," ","integrate(1/(a+b/x**3)**(3/2)/x,x)","- \frac{2 a^{3} x^{3} \sqrt{1 + \frac{b}{a x^{3}}}}{3 a^{\frac{9}{2}} x^{3} + 3 a^{\frac{7}{2}} b} - \frac{a^{3} x^{3} \log{\left(\frac{b}{a x^{3}} \right)}}{3 a^{\frac{9}{2}} x^{3} + 3 a^{\frac{7}{2}} b} + \frac{2 a^{3} x^{3} \log{\left(\sqrt{1 + \frac{b}{a x^{3}}} + 1 \right)}}{3 a^{\frac{9}{2}} x^{3} + 3 a^{\frac{7}{2}} b} - \frac{a^{2} b \log{\left(\frac{b}{a x^{3}} \right)}}{3 a^{\frac{9}{2}} x^{3} + 3 a^{\frac{7}{2}} b} + \frac{2 a^{2} b \log{\left(\sqrt{1 + \frac{b}{a x^{3}}} + 1 \right)}}{3 a^{\frac{9}{2}} x^{3} + 3 a^{\frac{7}{2}} b}"," ",0,"-2*a**3*x**3*sqrt(1 + b/(a*x**3))/(3*a**(9/2)*x**3 + 3*a**(7/2)*b) - a**3*x**3*log(b/(a*x**3))/(3*a**(9/2)*x**3 + 3*a**(7/2)*b) + 2*a**3*x**3*log(sqrt(1 + b/(a*x**3)) + 1)/(3*a**(9/2)*x**3 + 3*a**(7/2)*b) - a**2*b*log(b/(a*x**3))/(3*a**(9/2)*x**3 + 3*a**(7/2)*b) + 2*a**2*b*log(sqrt(1 + b/(a*x**3)) + 1)/(3*a**(9/2)*x**3 + 3*a**(7/2)*b)","B",0
2040,1,27,0,3.197303," ","integrate(1/(a+b/x**3)**(3/2)/x**4,x)","\begin{cases} \frac{2}{3 b \sqrt{a + \frac{b}{x^{3}}}} & \text{for}\: b \neq 0 \\- \frac{1}{3 a^{\frac{3}{2}} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2/(3*b*sqrt(a + b/x**3)), Ne(b, 0)), (-1/(3*a**(3/2)*x**3), True))","A",0
2041,1,51,0,6.153721," ","integrate(1/(a+b/x**3)**(3/2)/x**7,x)","\begin{cases} - \frac{4 a}{3 b^{2} \sqrt{a + \frac{b}{x^{3}}}} - \frac{2}{3 b x^{3} \sqrt{a + \frac{b}{x^{3}}}} & \text{for}\: b \neq 0 \\- \frac{1}{6 a^{\frac{3}{2}} x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a/(3*b**2*sqrt(a + b/x**3)) - 2/(3*b*x**3*sqrt(a + b/x**3)), Ne(b, 0)), (-1/(6*a**(3/2)*x**6), True))","A",0
2042,1,466,0,3.480216," ","integrate(1/(a+b/x**3)**(3/2)/x**10,x)","\frac{16 a^{\frac{9}{2}} b^{\frac{7}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{9 a^{\frac{7}{2}} b^{6} x^{\frac{21}{2}} + 18 a^{\frac{5}{2}} b^{7} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{8} x^{\frac{9}{2}}} + \frac{24 a^{\frac{7}{2}} b^{\frac{9}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{9 a^{\frac{7}{2}} b^{6} x^{\frac{21}{2}} + 18 a^{\frac{5}{2}} b^{7} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{8} x^{\frac{9}{2}}} + \frac{6 a^{\frac{5}{2}} b^{\frac{11}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{9 a^{\frac{7}{2}} b^{6} x^{\frac{21}{2}} + 18 a^{\frac{5}{2}} b^{7} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{8} x^{\frac{9}{2}}} - \frac{2 a^{\frac{3}{2}} b^{\frac{13}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{9 a^{\frac{7}{2}} b^{6} x^{\frac{21}{2}} + 18 a^{\frac{5}{2}} b^{7} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{8} x^{\frac{9}{2}}} - \frac{16 a^{5} b^{3} x^{\frac{21}{2}}}{9 a^{\frac{7}{2}} b^{6} x^{\frac{21}{2}} + 18 a^{\frac{5}{2}} b^{7} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{8} x^{\frac{9}{2}}} - \frac{32 a^{4} b^{4} x^{\frac{15}{2}}}{9 a^{\frac{7}{2}} b^{6} x^{\frac{21}{2}} + 18 a^{\frac{5}{2}} b^{7} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{8} x^{\frac{9}{2}}} - \frac{16 a^{3} b^{5} x^{\frac{9}{2}}}{9 a^{\frac{7}{2}} b^{6} x^{\frac{21}{2}} + 18 a^{\frac{5}{2}} b^{7} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{8} x^{\frac{9}{2}}}"," ",0,"16*a**(9/2)*b**(7/2)*x**9*sqrt(a*x**3/b + 1)/(9*a**(7/2)*b**6*x**(21/2) + 18*a**(5/2)*b**7*x**(15/2) + 9*a**(3/2)*b**8*x**(9/2)) + 24*a**(7/2)*b**(9/2)*x**6*sqrt(a*x**3/b + 1)/(9*a**(7/2)*b**6*x**(21/2) + 18*a**(5/2)*b**7*x**(15/2) + 9*a**(3/2)*b**8*x**(9/2)) + 6*a**(5/2)*b**(11/2)*x**3*sqrt(a*x**3/b + 1)/(9*a**(7/2)*b**6*x**(21/2) + 18*a**(5/2)*b**7*x**(15/2) + 9*a**(3/2)*b**8*x**(9/2)) - 2*a**(3/2)*b**(13/2)*sqrt(a*x**3/b + 1)/(9*a**(7/2)*b**6*x**(21/2) + 18*a**(5/2)*b**7*x**(15/2) + 9*a**(3/2)*b**8*x**(9/2)) - 16*a**5*b**3*x**(21/2)/(9*a**(7/2)*b**6*x**(21/2) + 18*a**(5/2)*b**7*x**(15/2) + 9*a**(3/2)*b**8*x**(9/2)) - 32*a**4*b**4*x**(15/2)/(9*a**(7/2)*b**6*x**(21/2) + 18*a**(5/2)*b**7*x**(15/2) + 9*a**(3/2)*b**8*x**(9/2)) - 16*a**3*b**5*x**(9/2)/(9*a**(7/2)*b**6*x**(21/2) + 18*a**(5/2)*b**7*x**(15/2) + 9*a**(3/2)*b**8*x**(9/2))","B",0
2043,1,2048,0,5.174484," ","integrate(1/(a+b/x**3)**(3/2)/x**13,x)","- \frac{32 a^{\frac{21}{2}} b^{\frac{23}{2}} x^{24} \sqrt{\frac{a x^{3}}{b} + 1}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} - \frac{176 a^{\frac{19}{2}} b^{\frac{25}{2}} x^{21} \sqrt{\frac{a x^{3}}{b} + 1}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} - \frac{396 a^{\frac{17}{2}} b^{\frac{27}{2}} x^{18} \sqrt{\frac{a x^{3}}{b} + 1}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} - \frac{462 a^{\frac{15}{2}} b^{\frac{29}{2}} x^{15} \sqrt{\frac{a x^{3}}{b} + 1}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} - \frac{290 a^{\frac{13}{2}} b^{\frac{31}{2}} x^{12} \sqrt{\frac{a x^{3}}{b} + 1}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} - \frac{92 a^{\frac{11}{2}} b^{\frac{33}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} - \frac{16 a^{\frac{9}{2}} b^{\frac{35}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} - \frac{6 a^{\frac{7}{2}} b^{\frac{37}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} - \frac{2 a^{\frac{5}{2}} b^{\frac{39}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} + \frac{32 a^{11} b^{11} x^{\frac{51}{2}}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} + \frac{192 a^{10} b^{12} x^{\frac{45}{2}}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} + \frac{480 a^{9} b^{13} x^{\frac{39}{2}}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} + \frac{640 a^{8} b^{14} x^{\frac{33}{2}}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} + \frac{480 a^{7} b^{15} x^{\frac{27}{2}}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} + \frac{192 a^{6} b^{16} x^{\frac{21}{2}}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}} + \frac{32 a^{5} b^{17} x^{\frac{15}{2}}}{15 a^{\frac{17}{2}} b^{15} x^{\frac{51}{2}} + 90 a^{\frac{15}{2}} b^{16} x^{\frac{45}{2}} + 225 a^{\frac{13}{2}} b^{17} x^{\frac{39}{2}} + 300 a^{\frac{11}{2}} b^{18} x^{\frac{33}{2}} + 225 a^{\frac{9}{2}} b^{19} x^{\frac{27}{2}} + 90 a^{\frac{7}{2}} b^{20} x^{\frac{21}{2}} + 15 a^{\frac{5}{2}} b^{21} x^{\frac{15}{2}}}"," ",0,"-32*a**(21/2)*b**(23/2)*x**24*sqrt(a*x**3/b + 1)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) - 176*a**(19/2)*b**(25/2)*x**21*sqrt(a*x**3/b + 1)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) - 396*a**(17/2)*b**(27/2)*x**18*sqrt(a*x**3/b + 1)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) - 462*a**(15/2)*b**(29/2)*x**15*sqrt(a*x**3/b + 1)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) - 290*a**(13/2)*b**(31/2)*x**12*sqrt(a*x**3/b + 1)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) - 92*a**(11/2)*b**(33/2)*x**9*sqrt(a*x**3/b + 1)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) - 16*a**(9/2)*b**(35/2)*x**6*sqrt(a*x**3/b + 1)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) - 6*a**(7/2)*b**(37/2)*x**3*sqrt(a*x**3/b + 1)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) - 2*a**(5/2)*b**(39/2)*sqrt(a*x**3/b + 1)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) + 32*a**11*b**11*x**(51/2)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) + 192*a**10*b**12*x**(45/2)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) + 480*a**9*b**13*x**(39/2)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) + 640*a**8*b**14*x**(33/2)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) + 480*a**7*b**15*x**(27/2)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) + 192*a**6*b**16*x**(21/2)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2)) + 32*a**5*b**17*x**(15/2)/(15*a**(17/2)*b**15*x**(51/2) + 90*a**(15/2)*b**16*x**(45/2) + 225*a**(13/2)*b**17*x**(39/2) + 300*a**(11/2)*b**18*x**(33/2) + 225*a**(9/2)*b**19*x**(27/2) + 90*a**(7/2)*b**20*x**(21/2) + 15*a**(5/2)*b**21*x**(15/2))","B",0
2044,1,46,0,1.589218," ","integrate(x**7/(a+b/x**3)**(3/2),x)","- \frac{x^{8} \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, \frac{3}{2} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(- \frac{5}{3}\right)}"," ",0,"-x**8*gamma(-8/3)*hyper((-8/3, 3/2), (-5/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*gamma(-5/3))","A",0
2045,1,46,0,1.378538," ","integrate(x**4/(a+b/x**3)**(3/2),x)","- \frac{x^{5} \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, \frac{3}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(- \frac{2}{3}\right)}"," ",0,"-x**5*gamma(-5/3)*hyper((-5/3, 3/2), (-2/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*gamma(-2/3))","A",0
2046,1,42,0,1.198202," ","integrate(x/(a+b/x**3)**(3/2),x)","- \frac{x^{2} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{3}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{1}{3}\right)}"," ",0,"-x**2*gamma(-2/3)*hyper((-2/3, 3/2), (1/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*gamma(1/3))","A",0
2047,1,37,0,1.415962," ","integrate(1/(a+b/x**3)**(3/2)/x**2,x)","- \frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} x \Gamma\left(\frac{4}{3}\right)}"," ",0,"-gamma(1/3)*hyper((1/3, 3/2), (4/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*x*gamma(4/3))","A",0
2048,1,39,0,2.149676," ","integrate(1/(a+b/x**3)**(3/2)/x**5,x)","- \frac{\Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{3}{2} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} x^{4} \Gamma\left(\frac{7}{3}\right)}"," ",0,"-gamma(4/3)*hyper((4/3, 3/2), (7/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*x**4*gamma(7/3))","A",0
2049,1,39,0,2.246561," ","integrate(1/(a+b/x**3)**(3/2)/x**8,x)","- \frac{\Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} x^{7} \Gamma\left(\frac{10}{3}\right)}"," ",0,"-gamma(7/3)*hyper((3/2, 7/3), (10/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*x**7*gamma(10/3))","A",0
2050,1,46,0,1.558279," ","integrate(x**6/(a+b/x**3)**(3/2),x)","- \frac{x^{7} \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, \frac{3}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(- \frac{4}{3}\right)}"," ",0,"-x**7*gamma(-7/3)*hyper((-7/3, 3/2), (-4/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*gamma(-4/3))","A",0
2051,1,46,0,1.447205," ","integrate(x**3/(a+b/x**3)**(3/2),x)","- \frac{x^{4} \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{3}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"-x**4*gamma(-4/3)*hyper((-4/3, 3/2), (-1/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*gamma(-1/3))","A",0
2052,1,41,0,1.242964," ","integrate(1/(a+b/x**3)**(3/2),x)","- \frac{x \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{3}{2} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{2}{3}\right)}"," ",0,"-x*gamma(-1/3)*hyper((-1/3, 3/2), (2/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*gamma(2/3))","A",0
2053,1,39,0,1.443985," ","integrate(1/(a+b/x**3)**(3/2)/x**3,x)","- \frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{3}{2} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} x^{2} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-gamma(2/3)*hyper((2/3, 3/2), (5/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*x**2*gamma(5/3))","A",0
2054,1,39,0,1.838999," ","integrate(1/(a+b/x**3)**(3/2)/x**6,x)","- \frac{\Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} x^{5} \Gamma\left(\frac{8}{3}\right)}"," ",0,"-gamma(5/3)*hyper((3/2, 5/3), (8/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*x**5*gamma(8/3))","A",0
2055,1,39,0,2.547306," ","integrate(1/(a+b/x**3)**(3/2)/x**9,x)","- \frac{\Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} x^{8} \Gamma\left(\frac{11}{3}\right)}"," ",0,"-gamma(8/3)*hyper((3/2, 8/3), (11/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*x**8*gamma(11/3))","A",0
2056,1,39,0,3.059884," ","integrate(1/(a+b/x**3)**(3/2)/x**12,x)","- \frac{\Gamma\left(\frac{11}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{11}{3} \\ \frac{14}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{3}}} \right)}}{3 a^{\frac{3}{2}} x^{11} \Gamma\left(\frac{14}{3}\right)}"," ",0,"-gamma(11/3)*hyper((3/2, 11/3), (14/3,), b*exp_polar(I*pi)/(a*x**3))/(3*a**(3/2)*x**11*gamma(14/3))","A",0
2057,1,22,0,0.210831," ","integrate(1/(a+b/x**4),x)","\operatorname{RootSum} {\left(256 t^{4} a^{5} + b, \left( t \mapsto t \log{\left(- 4 t a + x \right)} \right)\right)} + \frac{x}{a}"," ",0,"RootSum(256*_t**4*a**5 + b, Lambda(_t, _t*log(-4*_t*a + x))) + x/a","A",0
2058,1,44,0,2.500834," ","integrate(x**3*(a+b/x**4)**(1/2),x)","\frac{\sqrt{b} x^{2} \sqrt{\frac{a x^{4}}{b} + 1}}{4} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} x^{2}}{\sqrt{b}} \right)}}{4 \sqrt{a}}"," ",0,"sqrt(b)*x**2*sqrt(a*x**4/b + 1)/4 + b*asinh(sqrt(a)*x**2/sqrt(b))/(4*sqrt(a))","A",0
2059,1,66,0,1.794976," ","integrate(x*(a+b/x**4)**(1/2),x)","\frac{\sqrt{a} x^{2}}{2 \sqrt{1 + \frac{b}{a x^{4}}}} - \frac{\sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x^{2}} \right)}}{2} + \frac{b}{2 \sqrt{a} x^{2} \sqrt{1 + \frac{b}{a x^{4}}}}"," ",0,"sqrt(a)*x**2/(2*sqrt(1 + b/(a*x**4))) - sqrt(b)*asinh(sqrt(b)/(sqrt(a)*x**2))/2 + b/(2*sqrt(a)*x**2*sqrt(1 + b/(a*x**4)))","A",0
2060,1,66,0,1.777238," ","integrate((a+b/x**4)**(1/2)/x,x)","\frac{\sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a} x^{2}}{\sqrt{b}} \right)}}{2} - \frac{a x^{2}}{2 \sqrt{b} \sqrt{\frac{a x^{4}}{b} + 1}} - \frac{\sqrt{b}}{2 x^{2} \sqrt{\frac{a x^{4}}{b} + 1}}"," ",0,"sqrt(a)*asinh(sqrt(a)*x**2/sqrt(b))/2 - a*x**2/(2*sqrt(b)*sqrt(a*x**4/b + 1)) - sqrt(b)/(2*x**2*sqrt(a*x**4/b + 1))","A",0
2061,1,46,0,2.449543," ","integrate((a+b/x**4)**(1/2)/x**3,x)","- \frac{\sqrt{a} \sqrt{1 + \frac{b}{a x^{4}}}}{4 x^{2}} - \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x^{2}} \right)}}{4 \sqrt{b}}"," ",0,"-sqrt(a)*sqrt(1 + b/(a*x**4))/(4*x**2) - a*asinh(sqrt(b)/(sqrt(a)*x**2))/(4*sqrt(b))","A",0
2062,1,44,0,1.298126," ","integrate(x**2*(a+b/x**4)**(1/2),x)","- \frac{\sqrt{a} x^{3} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 \Gamma\left(\frac{1}{4}\right)}"," ",0,"-sqrt(a)*x**3*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*exp_polar(I*pi)/(a*x**4))/(4*gamma(1/4))","C",0
2063,1,42,0,1.170859," ","integrate((a+b/x**4)**(1/2),x)","- \frac{\sqrt{a} x \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}"," ",0,"-sqrt(a)*x*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*exp_polar(I*pi)/(a*x**4))/(4*gamma(3/4))","C",0
2064,1,39,0,1.211554," ","integrate((a+b/x**4)**(1/2)/x**2,x)","- \frac{\sqrt{a} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 x \Gamma\left(\frac{5}{4}\right)}"," ",0,"-sqrt(a)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*exp_polar(I*pi)/(a*x**4))/(4*x*gamma(5/4))","C",0
2065,1,41,0,1.438428," ","integrate((a+b/x**4)**(1/2)/x**4,x)","- \frac{\sqrt{a} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-sqrt(a)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*exp_polar(I*pi)/(a*x**4))/(4*x**3*gamma(7/4))","C",0
2066,1,95,0,3.275152," ","integrate((a+b/x**4)**(3/2)*x**3,x)","\frac{3 \sqrt{a} b \operatorname{asinh}{\left(\frac{\sqrt{a} x^{2}}{\sqrt{b}} \right)}}{4} + \frac{a^{2} x^{6}}{4 \sqrt{b} \sqrt{\frac{a x^{4}}{b} + 1}} - \frac{a \sqrt{b} x^{2}}{4 \sqrt{\frac{a x^{4}}{b} + 1}} - \frac{b^{\frac{3}{2}}}{2 x^{2} \sqrt{\frac{a x^{4}}{b} + 1}}"," ",0,"3*sqrt(a)*b*asinh(sqrt(a)*x**2/sqrt(b))/4 + a**2*x**6/(4*sqrt(b)*sqrt(a*x**4/b + 1)) - a*sqrt(b)*x**2/(4*sqrt(a*x**4/b + 1)) - b**(3/2)/(2*x**2*sqrt(a*x**4/b + 1))","A",0
2067,1,95,0,3.076335," ","integrate((a+b/x**4)**(3/2)*x,x)","\frac{a^{\frac{3}{2}} x^{2}}{2 \sqrt{1 + \frac{b}{a x^{4}}}} + \frac{\sqrt{a} b}{4 x^{2} \sqrt{1 + \frac{b}{a x^{4}}}} - \frac{3 a \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x^{2}} \right)}}{4} - \frac{b^{2}}{4 \sqrt{a} x^{6} \sqrt{1 + \frac{b}{a x^{4}}}}"," ",0,"a**(3/2)*x**2/(2*sqrt(1 + b/(a*x**4))) + sqrt(a)*b/(4*x**2*sqrt(1 + b/(a*x**4))) - 3*a*sqrt(b)*asinh(sqrt(b)/(sqrt(a)*x**2))/4 - b**2/(4*sqrt(a)*x**6*sqrt(1 + b/(a*x**4)))","A",0
2068,1,80,0,2.475827," ","integrate((a+b/x**4)**(3/2)/x,x)","- \frac{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{4}}}}{3} - \frac{a^{\frac{3}{2}} \log{\left(\frac{b}{a x^{4}} \right)}}{4} + \frac{a^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{2} - \frac{\sqrt{a} b \sqrt{1 + \frac{b}{a x^{4}}}}{6 x^{4}}"," ",0,"-2*a**(3/2)*sqrt(1 + b/(a*x**4))/3 - a**(3/2)*log(b/(a*x**4))/4 + a**(3/2)*log(sqrt(1 + b/(a*x**4)) + 1)/2 - sqrt(a)*b*sqrt(1 + b/(a*x**4))/(6*x**4)","A",0
2069,1,75,0,3.633515," ","integrate((a+b/x**4)**(3/2)/x**3,x)","- \frac{5 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{4}}}}{16 x^{2}} - \frac{\sqrt{a} b \sqrt{1 + \frac{b}{a x^{4}}}}{8 x^{6}} - \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x^{2}} \right)}}{16 \sqrt{b}}"," ",0,"-5*a**(3/2)*sqrt(1 + b/(a*x**4))/(16*x**2) - sqrt(a)*b*sqrt(1 + b/(a*x**4))/(8*x**6) - 3*a**2*asinh(sqrt(b)/(sqrt(a)*x**2))/(16*sqrt(b))","A",0
2070,1,44,0,1.609320," ","integrate((a+b/x**4)**(3/2)*x**2,x)","- \frac{a^{\frac{3}{2}} x^{3} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 \Gamma\left(\frac{1}{4}\right)}"," ",0,"-a**(3/2)*x**3*gamma(-3/4)*hyper((-3/2, -3/4), (1/4,), b*exp_polar(I*pi)/(a*x**4))/(4*gamma(1/4))","C",0
2071,1,42,0,1.378531," ","integrate((a+b/x**4)**(3/2),x)","- \frac{a^{\frac{3}{2}} x \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}"," ",0,"-a**(3/2)*x*gamma(-1/4)*hyper((-3/2, -1/4), (3/4,), b*exp_polar(I*pi)/(a*x**4))/(4*gamma(3/4))","C",0
2072,1,39,0,1.417730," ","integrate((a+b/x**4)**(3/2)/x**2,x)","- \frac{a^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 x \Gamma\left(\frac{5}{4}\right)}"," ",0,"-a**(3/2)*gamma(1/4)*hyper((-3/2, 1/4), (5/4,), b*exp_polar(I*pi)/(a*x**4))/(4*x*gamma(5/4))","C",0
2073,1,41,0,1.505868," ","integrate((a+b/x**4)**(3/2)/x**4,x)","- \frac{a^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-a**(3/2)*gamma(3/4)*hyper((-3/2, 3/4), (7/4,), b*exp_polar(I*pi)/(a*x**4))/(4*x**3*gamma(7/4))","C",0
2074,1,112,0,4.602833," ","integrate((a+b/x**4)**(5/2)*x**3,x)","\frac{a^{\frac{5}{2}} x^{4} \sqrt{1 + \frac{b}{a x^{4}}}}{4} - \frac{7 a^{\frac{3}{2}} b \sqrt{1 + \frac{b}{a x^{4}}}}{6} - \frac{5 a^{\frac{3}{2}} b \log{\left(\frac{b}{a x^{4}} \right)}}{8} + \frac{5 a^{\frac{3}{2}} b \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{4} - \frac{\sqrt{a} b^{2} \sqrt{1 + \frac{b}{a x^{4}}}}{6 x^{4}}"," ",0,"a**(5/2)*x**4*sqrt(1 + b/(a*x**4))/4 - 7*a**(3/2)*b*sqrt(1 + b/(a*x**4))/6 - 5*a**(3/2)*b*log(b/(a*x**4))/8 + 5*a**(3/2)*b*log(sqrt(1 + b/(a*x**4)) + 1)/4 - sqrt(a)*b**2*sqrt(1 + b/(a*x**4))/(6*x**4)","A",0
2075,1,124,0,4.969201," ","integrate((a+b/x**4)**(5/2)*x,x)","\frac{a^{\frac{5}{2}} x^{2}}{2 \sqrt{1 + \frac{b}{a x^{4}}}} - \frac{a^{\frac{3}{2}} b}{16 x^{2} \sqrt{1 + \frac{b}{a x^{4}}}} - \frac{11 \sqrt{a} b^{2}}{16 x^{6} \sqrt{1 + \frac{b}{a x^{4}}}} - \frac{15 a^{2} \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x^{2}} \right)}}{16} - \frac{b^{3}}{8 \sqrt{a} x^{10} \sqrt{1 + \frac{b}{a x^{4}}}}"," ",0,"a**(5/2)*x**2/(2*sqrt(1 + b/(a*x**4))) - a**(3/2)*b/(16*x**2*sqrt(1 + b/(a*x**4))) - 11*sqrt(a)*b**2/(16*x**6*sqrt(1 + b/(a*x**4))) - 15*a**2*sqrt(b)*asinh(sqrt(b)/(sqrt(a)*x**2))/16 - b**3/(8*sqrt(a)*x**10*sqrt(1 + b/(a*x**4)))","A",0
2076,1,107,0,6.299814," ","integrate((a+b/x**4)**(5/2)/x,x)","- \frac{23 a^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x^{4}}}}{30} - \frac{a^{\frac{5}{2}} \log{\left(\frac{b}{a x^{4}} \right)}}{4} + \frac{a^{\frac{5}{2}} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{2} - \frac{11 a^{\frac{3}{2}} b \sqrt{1 + \frac{b}{a x^{4}}}}{30 x^{4}} - \frac{\sqrt{a} b^{2} \sqrt{1 + \frac{b}{a x^{4}}}}{10 x^{8}}"," ",0,"-23*a**(5/2)*sqrt(1 + b/(a*x**4))/30 - a**(5/2)*log(b/(a*x**4))/4 + a**(5/2)*log(sqrt(1 + b/(a*x**4)) + 1)/2 - 11*a**(3/2)*b*sqrt(1 + b/(a*x**4))/(30*x**4) - sqrt(a)*b**2*sqrt(1 + b/(a*x**4))/(10*x**8)","A",0
2077,1,102,0,6.227945," ","integrate((a+b/x**4)**(5/2)/x**3,x)","- \frac{11 a^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x^{4}}}}{32 x^{2}} - \frac{13 a^{\frac{3}{2}} b \sqrt{1 + \frac{b}{a x^{4}}}}{48 x^{6}} - \frac{\sqrt{a} b^{2} \sqrt{1 + \frac{b}{a x^{4}}}}{12 x^{10}} - \frac{5 a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x^{2}} \right)}}{32 \sqrt{b}}"," ",0,"-11*a**(5/2)*sqrt(1 + b/(a*x**4))/(32*x**2) - 13*a**(3/2)*b*sqrt(1 + b/(a*x**4))/(48*x**6) - sqrt(a)*b**2*sqrt(1 + b/(a*x**4))/(12*x**10) - 5*a**3*asinh(sqrt(b)/(sqrt(a)*x**2))/(32*sqrt(b))","A",0
2078,1,44,0,2.240241," ","integrate((a+b/x**4)**(5/2)*x**2,x)","- \frac{a^{\frac{5}{2}} x^{3} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 \Gamma\left(\frac{1}{4}\right)}"," ",0,"-a**(5/2)*x**3*gamma(-3/4)*hyper((-5/2, -3/4), (1/4,), b*exp_polar(I*pi)/(a*x**4))/(4*gamma(1/4))","C",0
2079,1,42,0,1.975980," ","integrate((a+b/x**4)**(5/2),x)","- \frac{a^{\frac{5}{2}} x \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}"," ",0,"-a**(5/2)*x*gamma(-1/4)*hyper((-5/2, -1/4), (3/4,), b*exp_polar(I*pi)/(a*x**4))/(4*gamma(3/4))","C",0
2080,1,39,0,2.205929," ","integrate((a+b/x**4)**(5/2)/x**2,x)","- \frac{a^{\frac{5}{2}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 x \Gamma\left(\frac{5}{4}\right)}"," ",0,"-a**(5/2)*gamma(1/4)*hyper((-5/2, 1/4), (5/4,), b*exp_polar(I*pi)/(a*x**4))/(4*x*gamma(5/4))","C",0
2081,1,41,0,1.894869," ","integrate((a+b/x**4)**(5/2)/x**4,x)","- \frac{a^{\frac{5}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-a**(5/2)*gamma(3/4)*hyper((-5/2, 3/4), (7/4,), b*exp_polar(I*pi)/(a*x**4))/(4*x**3*gamma(7/4))","C",0
2082,1,46,0,2.758115," ","integrate(x**3/(a+b/x**4)**(1/2),x)","\frac{\sqrt{b} x^{2} \sqrt{\frac{a x^{4}}{b} + 1}}{4 a} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} x^{2}}{\sqrt{b}} \right)}}{4 a^{\frac{3}{2}}}"," ",0,"sqrt(b)*x**2*sqrt(a*x**4/b + 1)/(4*a) - b*asinh(sqrt(a)*x**2/sqrt(b))/(4*a**(3/2))","A",0
2083,1,19,0,0.870336," ","integrate(x/(a+b/x**4)**(1/2),x)","\frac{\sqrt{b} \sqrt{\frac{a x^{4}}{b} + 1}}{2 a}"," ",0,"sqrt(b)*sqrt(a*x**4/b + 1)/(2*a)","A",0
2084,1,20,0,1.452722," ","integrate(1/x/(a+b/x**4)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{a} x^{2}}{\sqrt{b}} \right)}}{2 \sqrt{a}}"," ",0,"asinh(sqrt(a)*x**2/sqrt(b))/(2*sqrt(a))","A",0
2085,1,22,0,1.633461," ","integrate(1/x**3/(a+b/x**4)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{\sqrt{b}}{\sqrt{a} x^{2}} \right)}}{2 \sqrt{b}}"," ",0,"-asinh(sqrt(b)/(sqrt(a)*x**2))/(2*sqrt(b))","A",0
2086,1,42,0,1.301138," ","integrate(x**2/(a+b/x**4)**(1/2),x)","- \frac{x^{3} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{1}{4}\right)}"," ",0,"-x**3*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), b*exp_polar(I*pi)/(a*x**4))/(4*sqrt(a)*gamma(1/4))","C",0
2087,1,41,0,1.112546," ","integrate(1/(a+b/x**4)**(1/2),x)","- \frac{x \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{3}{4}\right)}"," ",0,"-x*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), b*exp_polar(I*pi)/(a*x**4))/(4*sqrt(a)*gamma(3/4))","C",0
2088,1,37,0,1.238635," ","integrate(1/x**2/(a+b/x**4)**(1/2),x)","- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 \sqrt{a} x \Gamma\left(\frac{5}{4}\right)}"," ",0,"-gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*exp_polar(I*pi)/(a*x**4))/(4*sqrt(a)*x*gamma(5/4))","C",0
2089,1,39,0,1.494484," ","integrate(1/x**4/(a+b/x**4)**(1/2),x)","- \frac{\Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 \sqrt{a} x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*exp_polar(I*pi)/(a*x**4))/(4*sqrt(a)*x**3*gamma(7/4))","C",0
2090,1,75,0,4.007100," ","integrate(x**3/(a+b/x**4)**(3/2),x)","\frac{x^{6}}{4 a \sqrt{b} \sqrt{\frac{a x^{4}}{b} + 1}} + \frac{3 \sqrt{b} x^{2}}{4 a^{2} \sqrt{\frac{a x^{4}}{b} + 1}} - \frac{3 b \operatorname{asinh}{\left(\frac{\sqrt{a} x^{2}}{\sqrt{b}} \right)}}{4 a^{\frac{5}{2}}}"," ",0,"x**6/(4*a*sqrt(b)*sqrt(a*x**4/b + 1)) + 3*sqrt(b)*x**2/(4*a**2*sqrt(a*x**4/b + 1)) - 3*b*asinh(sqrt(a)*x**2/sqrt(b))/(4*a**(5/2))","A",0
2091,1,42,0,1.206389," ","integrate(x/(a+b/x**4)**(3/2),x)","\frac{x^{4}}{2 a \sqrt{b} \sqrt{\frac{a x^{4}}{b} + 1}} + \frac{\sqrt{b}}{a^{2} \sqrt{\frac{a x^{4}}{b} + 1}}"," ",0,"x**4/(2*a*sqrt(b)*sqrt(a*x**4/b + 1)) + sqrt(b)/(a**2*sqrt(a*x**4/b + 1))","A",0
2092,1,187,0,2.331330," ","integrate(1/(a+b/x**4)**(3/2)/x,x)","- \frac{2 a^{3} x^{4} \sqrt{1 + \frac{b}{a x^{4}}}}{4 a^{\frac{9}{2}} x^{4} + 4 a^{\frac{7}{2}} b} - \frac{a^{3} x^{4} \log{\left(\frac{b}{a x^{4}} \right)}}{4 a^{\frac{9}{2}} x^{4} + 4 a^{\frac{7}{2}} b} + \frac{2 a^{3} x^{4} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{4 a^{\frac{9}{2}} x^{4} + 4 a^{\frac{7}{2}} b} - \frac{a^{2} b \log{\left(\frac{b}{a x^{4}} \right)}}{4 a^{\frac{9}{2}} x^{4} + 4 a^{\frac{7}{2}} b} + \frac{2 a^{2} b \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{4 a^{\frac{9}{2}} x^{4} + 4 a^{\frac{7}{2}} b}"," ",0,"-2*a**3*x**4*sqrt(1 + b/(a*x**4))/(4*a**(9/2)*x**4 + 4*a**(7/2)*b) - a**3*x**4*log(b/(a*x**4))/(4*a**(9/2)*x**4 + 4*a**(7/2)*b) + 2*a**3*x**4*log(sqrt(1 + b/(a*x**4)) + 1)/(4*a**(9/2)*x**4 + 4*a**(7/2)*b) - a**2*b*log(b/(a*x**4))/(4*a**(9/2)*x**4 + 4*a**(7/2)*b) + 2*a**2*b*log(sqrt(1 + b/(a*x**4)) + 1)/(4*a**(9/2)*x**4 + 4*a**(7/2)*b)","B",0
2093,1,22,0,1.396627," ","integrate(1/(a+b/x**4)**(3/2)/x**3,x)","- \frac{1}{2 a \sqrt{b} \sqrt{\frac{a x^{4}}{b} + 1}}"," ",0,"-1/(2*a*sqrt(b)*sqrt(a*x**4/b + 1))","A",0
2094,1,42,0,1.285491," ","integrate(x**2/(a+b/x**4)**(3/2),x)","- \frac{x^{3} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"-x**3*gamma(-3/4)*hyper((-3/4, 3/2), (1/4,), b*exp_polar(I*pi)/(a*x**4))/(4*a**(3/2)*gamma(1/4))","C",0
2095,1,41,0,1.300129," ","integrate(1/(a+b/x**4)**(3/2),x)","- \frac{x \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right)}"," ",0,"-x*gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), b*exp_polar(I*pi)/(a*x**4))/(4*a**(3/2)*gamma(3/4))","C",0
2096,1,37,0,1.504779," ","integrate(1/(a+b/x**4)**(3/2)/x**2,x)","- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 a^{\frac{3}{2}} x \Gamma\left(\frac{5}{4}\right)}"," ",0,"-gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*exp_polar(I*pi)/(a*x**4))/(4*a**(3/2)*x*gamma(5/4))","C",0
2097,1,39,0,1.709699," ","integrate(1/(a+b/x**4)**(3/2)/x**4,x)","- \frac{\Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 a^{\frac{3}{2}} x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-gamma(3/4)*hyper((3/4, 3/2), (7/4,), b*exp_polar(I*pi)/(a*x**4))/(4*a**(3/2)*x**3*gamma(7/4))","C",0
2098,1,819,0,6.203936," ","integrate(x**3/(a+b/x**4)**(5/2),x)","\frac{6 a^{17} x^{16} \sqrt{1 + \frac{b}{a x^{4}}}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} + \frac{46 a^{16} b x^{12} \sqrt{1 + \frac{b}{a x^{4}}}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} + \frac{15 a^{16} b x^{12} \log{\left(\frac{b}{a x^{4}} \right)}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} - \frac{30 a^{16} b x^{12} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} + \frac{70 a^{15} b^{2} x^{8} \sqrt{1 + \frac{b}{a x^{4}}}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} + \frac{45 a^{15} b^{2} x^{8} \log{\left(\frac{b}{a x^{4}} \right)}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} - \frac{90 a^{15} b^{2} x^{8} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} + \frac{30 a^{14} b^{3} x^{4} \sqrt{1 + \frac{b}{a x^{4}}}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} + \frac{45 a^{14} b^{3} x^{4} \log{\left(\frac{b}{a x^{4}} \right)}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} - \frac{90 a^{14} b^{3} x^{4} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} + \frac{15 a^{13} b^{4} \log{\left(\frac{b}{a x^{4}} \right)}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}} - \frac{30 a^{13} b^{4} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{24 a^{\frac{39}{2}} x^{12} + 72 a^{\frac{37}{2}} b x^{8} + 72 a^{\frac{35}{2}} b^{2} x^{4} + 24 a^{\frac{33}{2}} b^{3}}"," ",0,"6*a**17*x**16*sqrt(1 + b/(a*x**4))/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) + 46*a**16*b*x**12*sqrt(1 + b/(a*x**4))/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) + 15*a**16*b*x**12*log(b/(a*x**4))/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) - 30*a**16*b*x**12*log(sqrt(1 + b/(a*x**4)) + 1)/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) + 70*a**15*b**2*x**8*sqrt(1 + b/(a*x**4))/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) + 45*a**15*b**2*x**8*log(b/(a*x**4))/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) - 90*a**15*b**2*x**8*log(sqrt(1 + b/(a*x**4)) + 1)/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) + 30*a**14*b**3*x**4*sqrt(1 + b/(a*x**4))/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) + 45*a**14*b**3*x**4*log(b/(a*x**4))/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) - 90*a**14*b**3*x**4*log(sqrt(1 + b/(a*x**4)) + 1)/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) + 15*a**13*b**4*log(b/(a*x**4))/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3) - 30*a**13*b**4*log(sqrt(1 + b/(a*x**4)) + 1)/(24*a**(39/2)*x**12 + 72*a**(37/2)*b*x**8 + 72*a**(35/2)*b**2*x**4 + 24*a**(33/2)*b**3)","B",0
2099,1,163,0,1.663548," ","integrate(x/(a+b/x**4)**(5/2),x)","\frac{3 a^{2} b^{\frac{9}{2}} x^{8} \sqrt{\frac{a x^{4}}{b} + 1}}{6 a^{5} b^{4} x^{8} + 12 a^{4} b^{5} x^{4} + 6 a^{3} b^{6}} + \frac{12 a b^{\frac{11}{2}} x^{4} \sqrt{\frac{a x^{4}}{b} + 1}}{6 a^{5} b^{4} x^{8} + 12 a^{4} b^{5} x^{4} + 6 a^{3} b^{6}} + \frac{8 b^{\frac{13}{2}} \sqrt{\frac{a x^{4}}{b} + 1}}{6 a^{5} b^{4} x^{8} + 12 a^{4} b^{5} x^{4} + 6 a^{3} b^{6}}"," ",0,"3*a**2*b**(9/2)*x**8*sqrt(a*x**4/b + 1)/(6*a**5*b**4*x**8 + 12*a**4*b**5*x**4 + 6*a**3*b**6) + 12*a*b**(11/2)*x**4*sqrt(a*x**4/b + 1)/(6*a**5*b**4*x**8 + 12*a**4*b**5*x**4 + 6*a**3*b**6) + 8*b**(13/2)*sqrt(a*x**4/b + 1)/(6*a**5*b**4*x**8 + 12*a**4*b**5*x**4 + 6*a**3*b**6)","B",0
2100,1,743,0,3.694362," ","integrate(1/(a+b/x**4)**(5/2)/x,x)","- \frac{8 a^{7} x^{12} \sqrt{1 + \frac{b}{a x^{4}}}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}} - \frac{3 a^{7} x^{12} \log{\left(\frac{b}{a x^{4}} \right)}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}} + \frac{6 a^{7} x^{12} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}} - \frac{14 a^{6} b x^{8} \sqrt{1 + \frac{b}{a x^{4}}}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}} - \frac{9 a^{6} b x^{8} \log{\left(\frac{b}{a x^{4}} \right)}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}} + \frac{18 a^{6} b x^{8} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}} - \frac{6 a^{5} b^{2} x^{4} \sqrt{1 + \frac{b}{a x^{4}}}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}} - \frac{9 a^{5} b^{2} x^{4} \log{\left(\frac{b}{a x^{4}} \right)}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}} + \frac{18 a^{5} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}} - \frac{3 a^{4} b^{3} \log{\left(\frac{b}{a x^{4}} \right)}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}} + \frac{6 a^{4} b^{3} \log{\left(\sqrt{1 + \frac{b}{a x^{4}}} + 1 \right)}}{12 a^{\frac{19}{2}} x^{12} + 36 a^{\frac{17}{2}} b x^{8} + 36 a^{\frac{15}{2}} b^{2} x^{4} + 12 a^{\frac{13}{2}} b^{3}}"," ",0,"-8*a**7*x**12*sqrt(1 + b/(a*x**4))/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3) - 3*a**7*x**12*log(b/(a*x**4))/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3) + 6*a**7*x**12*log(sqrt(1 + b/(a*x**4)) + 1)/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3) - 14*a**6*b*x**8*sqrt(1 + b/(a*x**4))/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3) - 9*a**6*b*x**8*log(b/(a*x**4))/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3) + 18*a**6*b*x**8*log(sqrt(1 + b/(a*x**4)) + 1)/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3) - 6*a**5*b**2*x**4*sqrt(1 + b/(a*x**4))/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3) - 9*a**5*b**2*x**4*log(b/(a*x**4))/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3) + 18*a**5*b**2*x**4*log(sqrt(1 + b/(a*x**4)) + 1)/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3) - 3*a**4*b**3*log(b/(a*x**4))/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3) + 6*a**4*b**3*log(sqrt(1 + b/(a*x**4)) + 1)/(12*a**(19/2)*x**12 + 36*a**(17/2)*b*x**8 + 36*a**(15/2)*b**2*x**4 + 12*a**(13/2)*b**3)","B",0
2101,1,105,0,1.920583," ","integrate(1/(a+b/x**4)**(5/2)/x**3,x)","- \frac{3 a x^{4}}{6 a^{3} \sqrt{b} x^{4} \sqrt{\frac{a x^{4}}{b} + 1} + 6 a^{2} b^{\frac{3}{2}} \sqrt{\frac{a x^{4}}{b} + 1}} - \frac{2 b}{6 a^{3} \sqrt{b} x^{4} \sqrt{\frac{a x^{4}}{b} + 1} + 6 a^{2} b^{\frac{3}{2}} \sqrt{\frac{a x^{4}}{b} + 1}}"," ",0,"-3*a*x**4/(6*a**3*sqrt(b)*x**4*sqrt(a*x**4/b + 1) + 6*a**2*b**(3/2)*sqrt(a*x**4/b + 1)) - 2*b/(6*a**3*sqrt(b)*x**4*sqrt(a*x**4/b + 1) + 6*a**2*b**(3/2)*sqrt(a*x**4/b + 1))","B",0
2102,1,42,0,1.512755," ","integrate(x**2/(a+b/x**4)**(5/2),x)","- \frac{x^{3} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{5}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 a^{\frac{5}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"-x**3*gamma(-3/4)*hyper((-3/4, 5/2), (1/4,), b*exp_polar(I*pi)/(a*x**4))/(4*a**(5/2)*gamma(1/4))","C",0
2103,1,41,0,1.548274," ","integrate(1/(a+b/x**4)**(5/2),x)","- \frac{x \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 a^{\frac{5}{2}} \Gamma\left(\frac{3}{4}\right)}"," ",0,"-x*gamma(-1/4)*hyper((-1/4, 5/2), (3/4,), b*exp_polar(I*pi)/(a*x**4))/(4*a**(5/2)*gamma(3/4))","C",0
2104,1,37,0,1.850348," ","integrate(1/(a+b/x**4)**(5/2)/x**2,x)","- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 a^{\frac{5}{2}} x \Gamma\left(\frac{5}{4}\right)}"," ",0,"-gamma(1/4)*hyper((1/4, 5/2), (5/4,), b*exp_polar(I*pi)/(a*x**4))/(4*a**(5/2)*x*gamma(5/4))","C",0
2105,1,39,0,2.107738," ","integrate(1/(a+b/x**4)**(5/2)/x**4,x)","- \frac{\Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{4}}} \right)}}{4 a^{\frac{5}{2}} x^{3} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-gamma(3/4)*hyper((3/4, 5/2), (7/4,), b*exp_polar(I*pi)/(a*x**4))/(4*a**(5/2)*x**3*gamma(7/4))","C",0
2106,1,22,0,0.204447," ","integrate(1/(a+b/x**5),x)","\operatorname{RootSum} {\left(3125 t^{5} a^{6} + b, \left( t \mapsto t \log{\left(- 5 t a + x \right)} \right)\right)} + \frac{x}{a}"," ",0,"RootSum(3125*_t**5*a**6 + b, Lambda(_t, _t*log(-5*_t*a + x))) + x/a","A",0
2107,1,24,0,1.441851," ","integrate(1/x/(a+b/x**5)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{\sqrt{a} x^{\frac{5}{2}}}{\sqrt{b}} \right)}}{5 \sqrt{a}}"," ",0,"2*asinh(sqrt(a)*x**(5/2)/sqrt(b))/(5*sqrt(a))","A",0
2108,1,60,0,1.576694," ","integrate(1/x/(-a+b/x**5)**(1/2),x)","\begin{cases} - \frac{2 i \operatorname{acosh}{\left(\frac{\sqrt{a} x^{\frac{5}{2}}}{\sqrt{b}} \right)}}{5 \sqrt{a}} & \text{for}\: \left|{\frac{a x^{5}}{b}}\right| > 1 \\\frac{2 \operatorname{asin}{\left(\frac{\sqrt{a} x^{\frac{5}{2}}}{\sqrt{b}} \right)}}{5 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(a)*x**(5/2)/sqrt(b))/(5*sqrt(a)), Abs(a*x**5/b) > 1), (2*asin(sqrt(a)*x**(5/2)/sqrt(b))/(5*sqrt(a)), True))","A",0
2109,1,22,0,0.210889," ","integrate(1/(a+b/x**6),x)","\operatorname{RootSum} {\left(46656 t^{6} a^{7} + b, \left( t \mapsto t \log{\left(- 6 t a + x \right)} \right)\right)} + \frac{x}{a}"," ",0,"RootSum(46656*_t**6*a**7 + b, Lambda(_t, _t*log(-6*_t*a + x))) + x/a","A",0
2110,1,22,0,0.221573," ","integrate(1/(a+b/x**8),x)","\operatorname{RootSum} {\left(16777216 t^{8} a^{9} + b, \left( t \mapsto t \log{\left(- 8 t a + x \right)} \right)\right)} + \frac{x}{a}"," ",0,"RootSum(16777216*_t**8*a**9 + b, Lambda(_t, _t*log(-8*_t*a + x))) + x/a","A",0
2111,1,15,0,1.475217," ","integrate(x**4*(a+b*x**(1/2)),x)","\frac{a x^{5}}{5} + \frac{2 b x^{\frac{11}{2}}}{11}"," ",0,"a*x**5/5 + 2*b*x**(11/2)/11","A",0
2112,1,15,0,1.410279," ","integrate(x**3*(a+b*x**(1/2)),x)","\frac{a x^{4}}{4} + \frac{2 b x^{\frac{9}{2}}}{9}"," ",0,"a*x**4/4 + 2*b*x**(9/2)/9","A",0
2113,1,15,0,1.354757," ","integrate(x**2*(a+b*x**(1/2)),x)","\frac{a x^{3}}{3} + \frac{2 b x^{\frac{7}{2}}}{7}"," ",0,"a*x**3/3 + 2*b*x**(7/2)/7","A",0
2114,1,15,0,1.188897," ","integrate(x*(a+b*x**(1/2)),x)","\frac{a x^{2}}{2} + \frac{2 b x^{\frac{5}{2}}}{5}"," ",0,"a*x**2/2 + 2*b*x**(5/2)/5","A",0
2115,1,12,0,0.062771," ","integrate(a+b*x**(1/2),x)","a x + \frac{2 b x^{\frac{3}{2}}}{3}"," ",0,"a*x + 2*b*x**(3/2)/3","A",0
2116,1,12,0,0.183898," ","integrate((a+b*x**(1/2))/x,x)","a \log{\left(x \right)} + 2 b \sqrt{x}"," ",0,"a*log(x) + 2*b*sqrt(x)","A",0
2117,1,12,0,0.437910," ","integrate((a+b*x**(1/2))/x**2,x)","- \frac{a}{x} - \frac{2 b}{\sqrt{x}}"," ",0,"-a/x - 2*b/sqrt(x)","A",0
2118,1,17,0,0.664866," ","integrate((a+b*x**(1/2))/x**3,x)","- \frac{a}{2 x^{2}} - \frac{2 b}{3 x^{\frac{3}{2}}}"," ",0,"-a/(2*x**2) - 2*b/(3*x**(3/2))","A",0
2119,1,17,0,0.973100," ","integrate((a+b*x**(1/2))/x**4,x)","- \frac{a}{3 x^{3}} - \frac{2 b}{5 x^{\frac{5}{2}}}"," ",0,"-a/(3*x**3) - 2*b/(5*x**(5/2))","A",0
2120,1,27,0,1.458559," ","integrate(x**4*(a+b*x**(1/2))**2,x)","\frac{a^{2} x^{5}}{5} + \frac{4 a b x^{\frac{11}{2}}}{11} + \frac{b^{2} x^{6}}{6}"," ",0,"a**2*x**5/5 + 4*a*b*x**(11/2)/11 + b**2*x**6/6","A",0
2121,1,27,0,0.900343," ","integrate(x**3*(a+b*x**(1/2))**2,x)","\frac{a^{2} x^{4}}{4} + \frac{4 a b x^{\frac{9}{2}}}{9} + \frac{b^{2} x^{5}}{5}"," ",0,"a**2*x**4/4 + 4*a*b*x**(9/2)/9 + b**2*x**5/5","A",0
2122,1,27,0,0.494690," ","integrate(x**2*(a+b*x**(1/2))**2,x)","\frac{a^{2} x^{3}}{3} + \frac{4 a b x^{\frac{7}{2}}}{7} + \frac{b^{2} x^{4}}{4}"," ",0,"a**2*x**3/3 + 4*a*b*x**(7/2)/7 + b**2*x**4/4","A",0
2123,1,27,0,0.302977," ","integrate(x*(a+b*x**(1/2))**2,x)","\frac{a^{2} x^{2}}{2} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{b^{2} x^{3}}{3}"," ",0,"a**2*x**2/2 + 4*a*b*x**(5/2)/5 + b**2*x**3/3","A",0
2124,1,24,0,0.178931," ","integrate((a+b*x**(1/2))**2,x)","a^{2} x + \frac{4 a b x^{\frac{3}{2}}}{3} + \frac{b^{2} x^{2}}{2}"," ",0,"a**2*x + 4*a*b*x**(3/2)/3 + b**2*x**2/2","A",0
2125,1,20,0,0.308573," ","integrate((a+b*x**(1/2))**2/x,x)","a^{2} \log{\left(x \right)} + 4 a b \sqrt{x} + b^{2} x"," ",0,"a**2*log(x) + 4*a*b*sqrt(x) + b**2*x","A",0
2126,1,20,0,0.449186," ","integrate((a+b*x**(1/2))**2/x**2,x)","- \frac{a^{2}}{x} - \frac{4 a b}{\sqrt{x}} + b^{2} \log{\left(x \right)}"," ",0,"-a**2/x - 4*a*b/sqrt(x) + b**2*log(x)","A",0
2127,1,26,0,0.700716," ","integrate((a+b*x**(1/2))**2/x**3,x)","- \frac{a^{2}}{2 x^{2}} - \frac{4 a b}{3 x^{\frac{3}{2}}} - \frac{b^{2}}{x}"," ",0,"-a**2/(2*x**2) - 4*a*b/(3*x**(3/2)) - b**2/x","A",0
2128,1,29,0,1.055642," ","integrate((a+b*x**(1/2))**2/x**4,x)","- \frac{a^{2}}{3 x^{3}} - \frac{4 a b}{5 x^{\frac{5}{2}}} - \frac{b^{2}}{2 x^{2}}"," ",0,"-a**2/(3*x**3) - 4*a*b/(5*x**(5/2)) - b**2/(2*x**2)","A",0
2129,1,29,0,1.355751," ","integrate((a+b*x**(1/2))**2/x**5,x)","- \frac{a^{2}}{4 x^{4}} - \frac{4 a b}{7 x^{\frac{7}{2}}} - \frac{b^{2}}{3 x^{3}}"," ",0,"-a**2/(4*x**4) - 4*a*b/(7*x**(7/2)) - b**2/(3*x**3)","A",0
2130,1,42,0,2.091971," ","integrate(x**4*(a+b*x**(1/2))**3,x)","\frac{a^{3} x^{5}}{5} + \frac{6 a^{2} b x^{\frac{11}{2}}}{11} + \frac{a b^{2} x^{6}}{2} + \frac{2 b^{3} x^{\frac{13}{2}}}{13}"," ",0,"a**3*x**5/5 + 6*a**2*b*x**(11/2)/11 + a*b**2*x**6/2 + 2*b**3*x**(13/2)/13","A",0
2131,1,44,0,1.919313," ","integrate(x**3*(a+b*x**(1/2))**3,x)","\frac{a^{3} x^{4}}{4} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{3 a b^{2} x^{5}}{5} + \frac{2 b^{3} x^{\frac{11}{2}}}{11}"," ",0,"a**3*x**4/4 + 2*a**2*b*x**(9/2)/3 + 3*a*b**2*x**5/5 + 2*b**3*x**(11/2)/11","A",0
2132,1,44,0,1.941948," ","integrate(x**2*(a+b*x**(1/2))**3,x)","\frac{a^{3} x^{3}}{3} + \frac{6 a^{2} b x^{\frac{7}{2}}}{7} + \frac{3 a b^{2} x^{4}}{4} + \frac{2 b^{3} x^{\frac{9}{2}}}{9}"," ",0,"a**3*x**3/3 + 6*a**2*b*x**(7/2)/7 + 3*a*b**2*x**4/4 + 2*b**3*x**(9/2)/9","A",0
2133,1,41,0,1.858745," ","integrate(x*(a+b*x**(1/2))**3,x)","\frac{a^{3} x^{2}}{2} + \frac{6 a^{2} b x^{\frac{5}{2}}}{5} + a b^{2} x^{3} + \frac{2 b^{3} x^{\frac{7}{2}}}{7}"," ",0,"a**3*x**2/2 + 6*a**2*b*x**(5/2)/5 + a*b**2*x**3 + 2*b**3*x**(7/2)/7","A",0
2134,1,39,0,1.747465," ","integrate((a+b*x**(1/2))**3,x)","a^{3} x + 2 a^{2} b x^{\frac{3}{2}} + \frac{3 a b^{2} x^{2}}{2} + \frac{2 b^{3} x^{\frac{5}{2}}}{5}"," ",0,"a**3*x + 2*a**2*b*x**(3/2) + 3*a*b**2*x**2/2 + 2*b**3*x**(5/2)/5","A",0
2135,1,37,0,0.262832," ","integrate((a+b*x**(1/2))**3/x,x)","a^{3} \log{\left(x \right)} + 6 a^{2} b \sqrt{x} + 3 a b^{2} x + \frac{2 b^{3} x^{\frac{3}{2}}}{3}"," ",0,"a**3*log(x) + 6*a**2*b*sqrt(x) + 3*a*b**2*x + 2*b**3*x**(3/2)/3","A",0
2136,1,36,0,0.486944," ","integrate((a+b*x**(1/2))**3/x**2,x)","- \frac{a^{3}}{x} - \frac{6 a^{2} b}{\sqrt{x}} + 3 a b^{2} \log{\left(x \right)} + 2 b^{3} \sqrt{x}"," ",0,"-a**3/x - 6*a**2*b/sqrt(x) + 3*a*b**2*log(x) + 2*b**3*sqrt(x)","A",0
2137,1,39,0,0.686382," ","integrate((a+b*x**(1/2))**3/x**3,x)","- \frac{a^{3}}{2 x^{2}} - \frac{2 a^{2} b}{x^{\frac{3}{2}}} - \frac{3 a b^{2}}{x} - \frac{2 b^{3}}{\sqrt{x}}"," ",0,"-a**3/(2*x**2) - 2*a**2*b/x**(3/2) - 3*a*b**2/x - 2*b**3/sqrt(x)","B",0
2138,1,46,0,1.104800," ","integrate((a+b*x**(1/2))**3/x**4,x)","- \frac{a^{3}}{3 x^{3}} - \frac{6 a^{2} b}{5 x^{\frac{5}{2}}} - \frac{3 a b^{2}}{2 x^{2}} - \frac{2 b^{3}}{3 x^{\frac{3}{2}}}"," ",0,"-a**3/(3*x**3) - 6*a**2*b/(5*x**(5/2)) - 3*a*b**2/(2*x**2) - 2*b**3/(3*x**(3/2))","A",0
2139,1,42,0,1.548593," ","integrate((a+b*x**(1/2))**3/x**5,x)","- \frac{a^{3}}{4 x^{4}} - \frac{6 a^{2} b}{7 x^{\frac{7}{2}}} - \frac{a b^{2}}{x^{3}} - \frac{2 b^{3}}{5 x^{\frac{5}{2}}}"," ",0,"-a**3/(4*x**4) - 6*a**2*b/(7*x**(7/2)) - a*b**2/x**3 - 2*b**3/(5*x**(5/2))","A",0
2140,1,46,0,2.222708," ","integrate((a+b*x**(1/2))**3/x**6,x)","- \frac{a^{3}}{5 x^{5}} - \frac{2 a^{2} b}{3 x^{\frac{9}{2}}} - \frac{3 a b^{2}}{4 x^{4}} - \frac{2 b^{3}}{7 x^{\frac{7}{2}}}"," ",0,"-a**3/(5*x**5) - 2*a**2*b/(3*x**(9/2)) - 3*a*b**2/(4*x**4) - 2*b**3/(7*x**(7/2))","A",0
2141,1,73,0,2.731263," ","integrate(x**4*(a+b*x**(1/2))**5,x)","\frac{a^{5} x^{5}}{5} + \frac{10 a^{4} b x^{\frac{11}{2}}}{11} + \frac{5 a^{3} b^{2} x^{6}}{3} + \frac{20 a^{2} b^{3} x^{\frac{13}{2}}}{13} + \frac{5 a b^{4} x^{7}}{7} + \frac{2 b^{5} x^{\frac{15}{2}}}{15}"," ",0,"a**5*x**5/5 + 10*a**4*b*x**(11/2)/11 + 5*a**3*b**2*x**6/3 + 20*a**2*b**3*x**(13/2)/13 + 5*a*b**4*x**7/7 + 2*b**5*x**(15/2)/15","A",0
2142,1,71,0,2.556261," ","integrate(x**3*(a+b*x**(1/2))**5,x)","\frac{a^{5} x^{4}}{4} + \frac{10 a^{4} b x^{\frac{9}{2}}}{9} + 2 a^{3} b^{2} x^{5} + \frac{20 a^{2} b^{3} x^{\frac{11}{2}}}{11} + \frac{5 a b^{4} x^{6}}{6} + \frac{2 b^{5} x^{\frac{13}{2}}}{13}"," ",0,"a**5*x**4/4 + 10*a**4*b*x**(9/2)/9 + 2*a**3*b**2*x**5 + 20*a**2*b**3*x**(11/2)/11 + 5*a*b**4*x**6/6 + 2*b**5*x**(13/2)/13","A",0
2143,1,70,0,2.336982," ","integrate(x**2*(a+b*x**(1/2))**5,x)","\frac{a^{5} x^{3}}{3} + \frac{10 a^{4} b x^{\frac{7}{2}}}{7} + \frac{5 a^{3} b^{2} x^{4}}{2} + \frac{20 a^{2} b^{3} x^{\frac{9}{2}}}{9} + a b^{4} x^{5} + \frac{2 b^{5} x^{\frac{11}{2}}}{11}"," ",0,"a**5*x**3/3 + 10*a**4*b*x**(7/2)/7 + 5*a**3*b**2*x**4/2 + 20*a**2*b**3*x**(9/2)/9 + a*b**4*x**5 + 2*b**5*x**(11/2)/11","A",0
2144,1,71,0,2.339653," ","integrate(x*(a+b*x**(1/2))**5,x)","\frac{a^{5} x^{2}}{2} + 2 a^{4} b x^{\frac{5}{2}} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{20 a^{2} b^{3} x^{\frac{7}{2}}}{7} + \frac{5 a b^{4} x^{4}}{4} + \frac{2 b^{5} x^{\frac{9}{2}}}{9}"," ",0,"a**5*x**2/2 + 2*a**4*b*x**(5/2) + 10*a**3*b**2*x**3/3 + 20*a**2*b**3*x**(7/2)/7 + 5*a*b**4*x**4/4 + 2*b**5*x**(9/2)/9","A",0
2145,1,66,0,2.237754," ","integrate((a+b*x**(1/2))**5,x)","a^{5} x + \frac{10 a^{4} b x^{\frac{3}{2}}}{3} + 5 a^{3} b^{2} x^{2} + 4 a^{2} b^{3} x^{\frac{5}{2}} + \frac{5 a b^{4} x^{3}}{3} + \frac{2 b^{5} x^{\frac{7}{2}}}{7}"," ",0,"a**5*x + 10*a**4*b*x**(3/2)/3 + 5*a**3*b**2*x**2 + 4*a**2*b**3*x**(5/2) + 5*a*b**4*x**3/3 + 2*b**5*x**(7/2)/7","B",0
2146,1,66,0,0.456910," ","integrate((a+b*x**(1/2))**5/x,x)","a^{5} \log{\left(x \right)} + 10 a^{4} b \sqrt{x} + 10 a^{3} b^{2} x + \frac{20 a^{2} b^{3} x^{\frac{3}{2}}}{3} + \frac{5 a b^{4} x^{2}}{2} + \frac{2 b^{5} x^{\frac{5}{2}}}{5}"," ",0,"a**5*log(x) + 10*a**4*b*sqrt(x) + 10*a**3*b**2*x + 20*a**2*b**3*x**(3/2)/3 + 5*a*b**4*x**2/2 + 2*b**5*x**(5/2)/5","A",0
2147,1,61,0,0.645642," ","integrate((a+b*x**(1/2))**5/x**2,x)","- \frac{a^{5}}{x} - \frac{10 a^{4} b}{\sqrt{x}} + 10 a^{3} b^{2} \log{\left(x \right)} + 20 a^{2} b^{3} \sqrt{x} + 5 a b^{4} x + \frac{2 b^{5} x^{\frac{3}{2}}}{3}"," ",0,"-a**5/x - 10*a**4*b/sqrt(x) + 10*a**3*b**2*log(x) + 20*a**2*b**3*sqrt(x) + 5*a*b**4*x + 2*b**5*x**(3/2)/3","A",0
2148,1,65,0,0.738102," ","integrate((a+b*x**(1/2))**5/x**3,x)","- \frac{a^{5}}{2 x^{2}} - \frac{10 a^{4} b}{3 x^{\frac{3}{2}}} - \frac{10 a^{3} b^{2}}{x} - \frac{20 a^{2} b^{3}}{\sqrt{x}} + 5 a b^{4} \log{\left(x \right)} + 2 b^{5} \sqrt{x}"," ",0,"-a**5/(2*x**2) - 10*a**4*b/(3*x**(3/2)) - 10*a**3*b**2/x - 20*a**2*b**3/sqrt(x) + 5*a*b**4*log(x) + 2*b**5*sqrt(x)","A",0
2149,1,66,0,1.110020," ","integrate((a+b*x**(1/2))**5/x**4,x)","- \frac{a^{5}}{3 x^{3}} - \frac{2 a^{4} b}{x^{\frac{5}{2}}} - \frac{5 a^{3} b^{2}}{x^{2}} - \frac{20 a^{2} b^{3}}{3 x^{\frac{3}{2}}} - \frac{5 a b^{4}}{x} - \frac{2 b^{5}}{\sqrt{x}}"," ",0,"-a**5/(3*x**3) - 2*a**4*b/x**(5/2) - 5*a**3*b**2/x**2 - 20*a**2*b**3/(3*x**(3/2)) - 5*a*b**4/x - 2*b**5/sqrt(x)","B",0
2150,1,73,0,1.637529," ","integrate((a+b*x**(1/2))**5/x**5,x)","- \frac{a^{5}}{4 x^{4}} - \frac{10 a^{4} b}{7 x^{\frac{7}{2}}} - \frac{10 a^{3} b^{2}}{3 x^{3}} - \frac{4 a^{2} b^{3}}{x^{\frac{5}{2}}} - \frac{5 a b^{4}}{2 x^{2}} - \frac{2 b^{5}}{3 x^{\frac{3}{2}}}"," ",0,"-a**5/(4*x**4) - 10*a**4*b/(7*x**(7/2)) - 10*a**3*b**2/(3*x**3) - 4*a**2*b**3/x**(5/2) - 5*a*b**4/(2*x**2) - 2*b**5/(3*x**(3/2))","A",0
2151,1,75,0,2.208892," ","integrate((a+b*x**(1/2))**5/x**6,x)","- \frac{a^{5}}{5 x^{5}} - \frac{10 a^{4} b}{9 x^{\frac{9}{2}}} - \frac{5 a^{3} b^{2}}{2 x^{4}} - \frac{20 a^{2} b^{3}}{7 x^{\frac{7}{2}}} - \frac{5 a b^{4}}{3 x^{3}} - \frac{2 b^{5}}{5 x^{\frac{5}{2}}}"," ",0,"-a**5/(5*x**5) - 10*a**4*b/(9*x**(9/2)) - 5*a**3*b**2/(2*x**4) - 20*a**2*b**3/(7*x**(7/2)) - 5*a*b**4/(3*x**3) - 2*b**5/(5*x**(5/2))","A",0
2152,1,73,0,3.214390," ","integrate((a+b*x**(1/2))**5/x**7,x)","- \frac{a^{5}}{6 x^{6}} - \frac{10 a^{4} b}{11 x^{\frac{11}{2}}} - \frac{2 a^{3} b^{2}}{x^{5}} - \frac{20 a^{2} b^{3}}{9 x^{\frac{9}{2}}} - \frac{5 a b^{4}}{4 x^{4}} - \frac{2 b^{5}}{7 x^{\frac{7}{2}}}"," ",0,"-a**5/(6*x**6) - 10*a**4*b/(11*x**(11/2)) - 2*a**3*b**2/x**5 - 20*a**2*b**3/(9*x**(9/2)) - 5*a*b**4/(4*x**4) - 2*b**5/(7*x**(7/2))","A",0
2153,1,139,0,7.818644," ","integrate(x**4*(a+b*x**(1/2))**10,x)","\frac{a^{10} x^{5}}{5} + \frac{20 a^{9} b x^{\frac{11}{2}}}{11} + \frac{15 a^{8} b^{2} x^{6}}{2} + \frac{240 a^{7} b^{3} x^{\frac{13}{2}}}{13} + 30 a^{6} b^{4} x^{7} + \frac{168 a^{5} b^{5} x^{\frac{15}{2}}}{5} + \frac{105 a^{4} b^{6} x^{8}}{4} + \frac{240 a^{3} b^{7} x^{\frac{17}{2}}}{17} + 5 a^{2} b^{8} x^{9} + \frac{20 a b^{9} x^{\frac{19}{2}}}{19} + \frac{b^{10} x^{10}}{10}"," ",0,"a**10*x**5/5 + 20*a**9*b*x**(11/2)/11 + 15*a**8*b**2*x**6/2 + 240*a**7*b**3*x**(13/2)/13 + 30*a**6*b**4*x**7 + 168*a**5*b**5*x**(15/2)/5 + 105*a**4*b**6*x**8/4 + 240*a**3*b**7*x**(17/2)/17 + 5*a**2*b**8*x**9 + 20*a*b**9*x**(19/2)/19 + b**10*x**10/10","A",0
2154,1,136,0,6.048248," ","integrate(x**3*(a+b*x**(1/2))**10,x)","\frac{a^{10} x^{4}}{4} + \frac{20 a^{9} b x^{\frac{9}{2}}}{9} + 9 a^{8} b^{2} x^{5} + \frac{240 a^{7} b^{3} x^{\frac{11}{2}}}{11} + 35 a^{6} b^{4} x^{6} + \frac{504 a^{5} b^{5} x^{\frac{13}{2}}}{13} + 30 a^{4} b^{6} x^{7} + 16 a^{3} b^{7} x^{\frac{15}{2}} + \frac{45 a^{2} b^{8} x^{8}}{8} + \frac{20 a b^{9} x^{\frac{17}{2}}}{17} + \frac{b^{10} x^{9}}{9}"," ",0,"a**10*x**4/4 + 20*a**9*b*x**(9/2)/9 + 9*a**8*b**2*x**5 + 240*a**7*b**3*x**(11/2)/11 + 35*a**6*b**4*x**6 + 504*a**5*b**5*x**(13/2)/13 + 30*a**4*b**6*x**7 + 16*a**3*b**7*x**(15/2) + 45*a**2*b**8*x**8/8 + 20*a*b**9*x**(17/2)/17 + b**10*x**9/9","A",0
2155,1,139,0,4.008893," ","integrate(x**2*(a+b*x**(1/2))**10,x)","\frac{a^{10} x^{3}}{3} + \frac{20 a^{9} b x^{\frac{7}{2}}}{7} + \frac{45 a^{8} b^{2} x^{4}}{4} + \frac{80 a^{7} b^{3} x^{\frac{9}{2}}}{3} + 42 a^{6} b^{4} x^{5} + \frac{504 a^{5} b^{5} x^{\frac{11}{2}}}{11} + 35 a^{4} b^{6} x^{6} + \frac{240 a^{3} b^{7} x^{\frac{13}{2}}}{13} + \frac{45 a^{2} b^{8} x^{7}}{7} + \frac{4 a b^{9} x^{\frac{15}{2}}}{3} + \frac{b^{10} x^{8}}{8}"," ",0,"a**10*x**3/3 + 20*a**9*b*x**(7/2)/7 + 45*a**8*b**2*x**4/4 + 80*a**7*b**3*x**(9/2)/3 + 42*a**6*b**4*x**5 + 504*a**5*b**5*x**(11/2)/11 + 35*a**4*b**6*x**6 + 240*a**3*b**7*x**(13/2)/13 + 45*a**2*b**8*x**7/7 + 4*a*b**9*x**(15/2)/3 + b**10*x**8/8","A",0
2156,1,136,0,2.755852," ","integrate(x*(a+b*x**(1/2))**10,x)","\frac{a^{10} x^{2}}{2} + 4 a^{9} b x^{\frac{5}{2}} + 15 a^{8} b^{2} x^{3} + \frac{240 a^{7} b^{3} x^{\frac{7}{2}}}{7} + \frac{105 a^{6} b^{4} x^{4}}{2} + 56 a^{5} b^{5} x^{\frac{9}{2}} + 42 a^{4} b^{6} x^{5} + \frac{240 a^{3} b^{7} x^{\frac{11}{2}}}{11} + \frac{15 a^{2} b^{8} x^{6}}{2} + \frac{20 a b^{9} x^{\frac{13}{2}}}{13} + \frac{b^{10} x^{7}}{7}"," ",0,"a**10*x**2/2 + 4*a**9*b*x**(5/2) + 15*a**8*b**2*x**3 + 240*a**7*b**3*x**(7/2)/7 + 105*a**6*b**4*x**4/2 + 56*a**5*b**5*x**(9/2) + 42*a**4*b**6*x**5 + 240*a**3*b**7*x**(11/2)/11 + 15*a**2*b**8*x**6/2 + 20*a*b**9*x**(13/2)/13 + b**10*x**7/7","A",0
2157,1,133,0,1.825253," ","integrate((a+b*x**(1/2))**10,x)","a^{10} x + \frac{20 a^{9} b x^{\frac{3}{2}}}{3} + \frac{45 a^{8} b^{2} x^{2}}{2} + 48 a^{7} b^{3} x^{\frac{5}{2}} + 70 a^{6} b^{4} x^{3} + 72 a^{5} b^{5} x^{\frac{7}{2}} + \frac{105 a^{4} b^{6} x^{4}}{2} + \frac{80 a^{3} b^{7} x^{\frac{9}{2}}}{3} + 9 a^{2} b^{8} x^{5} + \frac{20 a b^{9} x^{\frac{11}{2}}}{11} + \frac{b^{10} x^{6}}{6}"," ",0,"a**10*x + 20*a**9*b*x**(3/2)/3 + 45*a**8*b**2*x**2/2 + 48*a**7*b**3*x**(5/2) + 70*a**6*b**4*x**3 + 72*a**5*b**5*x**(7/2) + 105*a**4*b**6*x**4/2 + 80*a**3*b**7*x**(9/2)/3 + 9*a**2*b**8*x**5 + 20*a*b**9*x**(11/2)/11 + b**10*x**6/6","B",0
2158,1,131,0,2.120873," ","integrate((a+b*x**(1/2))**10/x,x)","a^{10} \log{\left(x \right)} + 20 a^{9} b \sqrt{x} + 45 a^{8} b^{2} x + 80 a^{7} b^{3} x^{\frac{3}{2}} + 105 a^{6} b^{4} x^{2} + \frac{504 a^{5} b^{5} x^{\frac{5}{2}}}{5} + 70 a^{4} b^{6} x^{3} + \frac{240 a^{3} b^{7} x^{\frac{7}{2}}}{7} + \frac{45 a^{2} b^{8} x^{4}}{4} + \frac{20 a b^{9} x^{\frac{9}{2}}}{9} + \frac{b^{10} x^{5}}{5}"," ",0,"a**10*log(x) + 20*a**9*b*sqrt(x) + 45*a**8*b**2*x + 80*a**7*b**3*x**(3/2) + 105*a**6*b**4*x**2 + 504*a**5*b**5*x**(5/2)/5 + 70*a**4*b**6*x**3 + 240*a**3*b**7*x**(7/2)/7 + 45*a**2*b**8*x**4/4 + 20*a*b**9*x**(9/2)/9 + b**10*x**5/5","A",0
2159,1,124,0,2.176187," ","integrate((a+b*x**(1/2))**10/x**2,x)","- \frac{a^{10}}{x} - \frac{20 a^{9} b}{\sqrt{x}} + 45 a^{8} b^{2} \log{\left(x \right)} + 240 a^{7} b^{3} \sqrt{x} + 210 a^{6} b^{4} x + 168 a^{5} b^{5} x^{\frac{3}{2}} + 105 a^{4} b^{6} x^{2} + 48 a^{3} b^{7} x^{\frac{5}{2}} + 15 a^{2} b^{8} x^{3} + \frac{20 a b^{9} x^{\frac{7}{2}}}{7} + \frac{b^{10} x^{4}}{4}"," ",0,"-a**10/x - 20*a**9*b/sqrt(x) + 45*a**8*b**2*log(x) + 240*a**7*b**3*sqrt(x) + 210*a**6*b**4*x + 168*a**5*b**5*x**(3/2) + 105*a**4*b**6*x**2 + 48*a**3*b**7*x**(5/2) + 15*a**2*b**8*x**3 + 20*a*b**9*x**(7/2)/7 + b**10*x**4/4","A",0
2160,1,128,0,1.953676," ","integrate((a+b*x**(1/2))**10/x**3,x)","- \frac{a^{10}}{2 x^{2}} - \frac{20 a^{9} b}{3 x^{\frac{3}{2}}} - \frac{45 a^{8} b^{2}}{x} - \frac{240 a^{7} b^{3}}{\sqrt{x}} + 210 a^{6} b^{4} \log{\left(x \right)} + 504 a^{5} b^{5} \sqrt{x} + 210 a^{4} b^{6} x + 80 a^{3} b^{7} x^{\frac{3}{2}} + \frac{45 a^{2} b^{8} x^{2}}{2} + 4 a b^{9} x^{\frac{5}{2}} + \frac{b^{10} x^{3}}{3}"," ",0,"-a**10/(2*x**2) - 20*a**9*b/(3*x**(3/2)) - 45*a**8*b**2/x - 240*a**7*b**3/sqrt(x) + 210*a**6*b**4*log(x) + 504*a**5*b**5*sqrt(x) + 210*a**4*b**6*x + 80*a**3*b**7*x**(3/2) + 45*a**2*b**8*x**2/2 + 4*a*b**9*x**(5/2) + b**10*x**3/3","A",0
2161,1,128,0,2.003791," ","integrate((a+b*x**(1/2))**10/x**4,x)","- \frac{a^{10}}{3 x^{3}} - \frac{4 a^{9} b}{x^{\frac{5}{2}}} - \frac{45 a^{8} b^{2}}{2 x^{2}} - \frac{80 a^{7} b^{3}}{x^{\frac{3}{2}}} - \frac{210 a^{6} b^{4}}{x} - \frac{504 a^{5} b^{5}}{\sqrt{x}} + 210 a^{4} b^{6} \log{\left(x \right)} + 240 a^{3} b^{7} \sqrt{x} + 45 a^{2} b^{8} x + \frac{20 a b^{9} x^{\frac{3}{2}}}{3} + \frac{b^{10} x^{2}}{2}"," ",0,"-a**10/(3*x**3) - 4*a**9*b/x**(5/2) - 45*a**8*b**2/(2*x**2) - 80*a**7*b**3/x**(3/2) - 210*a**6*b**4/x - 504*a**5*b**5/sqrt(x) + 210*a**4*b**6*log(x) + 240*a**3*b**7*sqrt(x) + 45*a**2*b**8*x + 20*a*b**9*x**(3/2)/3 + b**10*x**2/2","A",0
2162,1,124,0,2.012111," ","integrate((a+b*x**(1/2))**10/x**5,x)","- \frac{a^{10}}{4 x^{4}} - \frac{20 a^{9} b}{7 x^{\frac{7}{2}}} - \frac{15 a^{8} b^{2}}{x^{3}} - \frac{48 a^{7} b^{3}}{x^{\frac{5}{2}}} - \frac{105 a^{6} b^{4}}{x^{2}} - \frac{168 a^{5} b^{5}}{x^{\frac{3}{2}}} - \frac{210 a^{4} b^{6}}{x} - \frac{240 a^{3} b^{7}}{\sqrt{x}} + 45 a^{2} b^{8} \log{\left(x \right)} + 20 a b^{9} \sqrt{x} + b^{10} x"," ",0,"-a**10/(4*x**4) - 20*a**9*b/(7*x**(7/2)) - 15*a**8*b**2/x**3 - 48*a**7*b**3/x**(5/2) - 105*a**6*b**4/x**2 - 168*a**5*b**5/x**(3/2) - 210*a**4*b**6/x - 240*a**3*b**7/sqrt(x) + 45*a**2*b**8*log(x) + 20*a*b**9*sqrt(x) + b**10*x","A",0
2163,1,131,0,2.729455," ","integrate((a+b*x**(1/2))**10/x**6,x)","- \frac{a^{10}}{5 x^{5}} - \frac{20 a^{9} b}{9 x^{\frac{9}{2}}} - \frac{45 a^{8} b^{2}}{4 x^{4}} - \frac{240 a^{7} b^{3}}{7 x^{\frac{7}{2}}} - \frac{70 a^{6} b^{4}}{x^{3}} - \frac{504 a^{5} b^{5}}{5 x^{\frac{5}{2}}} - \frac{105 a^{4} b^{6}}{x^{2}} - \frac{80 a^{3} b^{7}}{x^{\frac{3}{2}}} - \frac{45 a^{2} b^{8}}{x} - \frac{20 a b^{9}}{\sqrt{x}} + b^{10} \log{\left(x \right)}"," ",0,"-a**10/(5*x**5) - 20*a**9*b/(9*x**(9/2)) - 45*a**8*b**2/(4*x**4) - 240*a**7*b**3/(7*x**(7/2)) - 70*a**6*b**4/x**3 - 504*a**5*b**5/(5*x**(5/2)) - 105*a**4*b**6/x**2 - 80*a**3*b**7/x**(3/2) - 45*a**2*b**8/x - 20*a*b**9/sqrt(x) + b**10*log(x)","A",0
2164,1,134,0,3.635193," ","integrate((a+b*x**(1/2))**10/x**7,x)","- \frac{a^{10}}{6 x^{6}} - \frac{20 a^{9} b}{11 x^{\frac{11}{2}}} - \frac{9 a^{8} b^{2}}{x^{5}} - \frac{80 a^{7} b^{3}}{3 x^{\frac{9}{2}}} - \frac{105 a^{6} b^{4}}{2 x^{4}} - \frac{72 a^{5} b^{5}}{x^{\frac{7}{2}}} - \frac{70 a^{4} b^{6}}{x^{3}} - \frac{48 a^{3} b^{7}}{x^{\frac{5}{2}}} - \frac{45 a^{2} b^{8}}{2 x^{2}} - \frac{20 a b^{9}}{3 x^{\frac{3}{2}}} - \frac{b^{10}}{x}"," ",0,"-a**10/(6*x**6) - 20*a**9*b/(11*x**(11/2)) - 9*a**8*b**2/x**5 - 80*a**7*b**3/(3*x**(9/2)) - 105*a**6*b**4/(2*x**4) - 72*a**5*b**5/x**(7/2) - 70*a**4*b**6/x**3 - 48*a**3*b**7/x**(5/2) - 45*a**2*b**8/(2*x**2) - 20*a*b**9/(3*x**(3/2)) - b**10/x","B",0
2165,1,138,0,4.891885," ","integrate((a+b*x**(1/2))**10/x**8,x)","- \frac{a^{10}}{7 x^{7}} - \frac{20 a^{9} b}{13 x^{\frac{13}{2}}} - \frac{15 a^{8} b^{2}}{2 x^{6}} - \frac{240 a^{7} b^{3}}{11 x^{\frac{11}{2}}} - \frac{42 a^{6} b^{4}}{x^{5}} - \frac{56 a^{5} b^{5}}{x^{\frac{9}{2}}} - \frac{105 a^{4} b^{6}}{2 x^{4}} - \frac{240 a^{3} b^{7}}{7 x^{\frac{7}{2}}} - \frac{15 a^{2} b^{8}}{x^{3}} - \frac{4 a b^{9}}{x^{\frac{5}{2}}} - \frac{b^{10}}{2 x^{2}}"," ",0,"-a**10/(7*x**7) - 20*a**9*b/(13*x**(13/2)) - 15*a**8*b**2/(2*x**6) - 240*a**7*b**3/(11*x**(11/2)) - 42*a**6*b**4/x**5 - 56*a**5*b**5/x**(9/2) - 105*a**4*b**6/(2*x**4) - 240*a**3*b**7/(7*x**(7/2)) - 15*a**2*b**8/x**3 - 4*a*b**9/x**(5/2) - b**10/(2*x**2)","A",0
2166,1,141,0,7.271572," ","integrate((a+b*x**(1/2))**10/x**9,x)","- \frac{a^{10}}{8 x^{8}} - \frac{4 a^{9} b}{3 x^{\frac{15}{2}}} - \frac{45 a^{8} b^{2}}{7 x^{7}} - \frac{240 a^{7} b^{3}}{13 x^{\frac{13}{2}}} - \frac{35 a^{6} b^{4}}{x^{6}} - \frac{504 a^{5} b^{5}}{11 x^{\frac{11}{2}}} - \frac{42 a^{4} b^{6}}{x^{5}} - \frac{80 a^{3} b^{7}}{3 x^{\frac{9}{2}}} - \frac{45 a^{2} b^{8}}{4 x^{4}} - \frac{20 a b^{9}}{7 x^{\frac{7}{2}}} - \frac{b^{10}}{3 x^{3}}"," ",0,"-a**10/(8*x**8) - 4*a**9*b/(3*x**(15/2)) - 45*a**8*b**2/(7*x**7) - 240*a**7*b**3/(13*x**(13/2)) - 35*a**6*b**4/x**6 - 504*a**5*b**5/(11*x**(11/2)) - 42*a**4*b**6/x**5 - 80*a**3*b**7/(3*x**(9/2)) - 45*a**2*b**8/(4*x**4) - 20*a*b**9/(7*x**(7/2)) - b**10/(3*x**3)","A",0
2167,1,138,0,9.419196," ","integrate((a+b*x**(1/2))**10/x**10,x)","- \frac{a^{10}}{9 x^{9}} - \frac{20 a^{9} b}{17 x^{\frac{17}{2}}} - \frac{45 a^{8} b^{2}}{8 x^{8}} - \frac{16 a^{7} b^{3}}{x^{\frac{15}{2}}} - \frac{30 a^{6} b^{4}}{x^{7}} - \frac{504 a^{5} b^{5}}{13 x^{\frac{13}{2}}} - \frac{35 a^{4} b^{6}}{x^{6}} - \frac{240 a^{3} b^{7}}{11 x^{\frac{11}{2}}} - \frac{9 a^{2} b^{8}}{x^{5}} - \frac{20 a b^{9}}{9 x^{\frac{9}{2}}} - \frac{b^{10}}{4 x^{4}}"," ",0,"-a**10/(9*x**9) - 20*a**9*b/(17*x**(17/2)) - 45*a**8*b**2/(8*x**8) - 16*a**7*b**3/x**(15/2) - 30*a**6*b**4/x**7 - 504*a**5*b**5/(13*x**(13/2)) - 35*a**4*b**6/x**6 - 240*a**3*b**7/(11*x**(11/2)) - 9*a**2*b**8/x**5 - 20*a*b**9/(9*x**(9/2)) - b**10/(4*x**4)","A",0
2168,1,141,0,12.380460," ","integrate((a+b*x**(1/2))**10/x**11,x)","- \frac{a^{10}}{10 x^{10}} - \frac{20 a^{9} b}{19 x^{\frac{19}{2}}} - \frac{5 a^{8} b^{2}}{x^{9}} - \frac{240 a^{7} b^{3}}{17 x^{\frac{17}{2}}} - \frac{105 a^{6} b^{4}}{4 x^{8}} - \frac{168 a^{5} b^{5}}{5 x^{\frac{15}{2}}} - \frac{30 a^{4} b^{6}}{x^{7}} - \frac{240 a^{3} b^{7}}{13 x^{\frac{13}{2}}} - \frac{15 a^{2} b^{8}}{2 x^{6}} - \frac{20 a b^{9}}{11 x^{\frac{11}{2}}} - \frac{b^{10}}{5 x^{5}}"," ",0,"-a**10/(10*x**10) - 20*a**9*b/(19*x**(19/2)) - 5*a**8*b**2/x**9 - 240*a**7*b**3/(17*x**(17/2)) - 105*a**6*b**4/(4*x**8) - 168*a**5*b**5/(5*x**(15/2)) - 30*a**4*b**6/x**7 - 240*a**3*b**7/(13*x**(13/2)) - 15*a**2*b**8/(2*x**6) - 20*a*b**9/(11*x**(11/2)) - b**10/(5*x**5)","A",0
2169,1,214,0,7.544041," ","integrate(x**5*(a+b*x**(1/2))**15,x)","\frac{a^{15} x^{6}}{6} + \frac{30 a^{14} b x^{\frac{13}{2}}}{13} + 15 a^{13} b^{2} x^{7} + \frac{182 a^{12} b^{3} x^{\frac{15}{2}}}{3} + \frac{1365 a^{11} b^{4} x^{8}}{8} + \frac{6006 a^{10} b^{5} x^{\frac{17}{2}}}{17} + \frac{5005 a^{9} b^{6} x^{9}}{9} + \frac{12870 a^{8} b^{7} x^{\frac{19}{2}}}{19} + \frac{1287 a^{7} b^{8} x^{10}}{2} + \frac{1430 a^{6} b^{9} x^{\frac{21}{2}}}{3} + 273 a^{5} b^{10} x^{11} + \frac{2730 a^{4} b^{11} x^{\frac{23}{2}}}{23} + \frac{455 a^{3} b^{12} x^{12}}{12} + \frac{42 a^{2} b^{13} x^{\frac{25}{2}}}{5} + \frac{15 a b^{14} x^{13}}{13} + \frac{2 b^{15} x^{\frac{27}{2}}}{27}"," ",0,"a**15*x**6/6 + 30*a**14*b*x**(13/2)/13 + 15*a**13*b**2*x**7 + 182*a**12*b**3*x**(15/2)/3 + 1365*a**11*b**4*x**8/8 + 6006*a**10*b**5*x**(17/2)/17 + 5005*a**9*b**6*x**9/9 + 12870*a**8*b**7*x**(19/2)/19 + 1287*a**7*b**8*x**10/2 + 1430*a**6*b**9*x**(21/2)/3 + 273*a**5*b**10*x**11 + 2730*a**4*b**11*x**(23/2)/23 + 455*a**3*b**12*x**12/12 + 42*a**2*b**13*x**(25/2)/5 + 15*a*b**14*x**13/13 + 2*b**15*x**(27/2)/27","A",0
2170,1,211,0,6.728145," ","integrate(x**4*(a+b*x**(1/2))**15,x)","\frac{a^{15} x^{5}}{5} + \frac{30 a^{14} b x^{\frac{11}{2}}}{11} + \frac{35 a^{13} b^{2} x^{6}}{2} + 70 a^{12} b^{3} x^{\frac{13}{2}} + 195 a^{11} b^{4} x^{7} + \frac{2002 a^{10} b^{5} x^{\frac{15}{2}}}{5} + \frac{5005 a^{9} b^{6} x^{8}}{8} + \frac{12870 a^{8} b^{7} x^{\frac{17}{2}}}{17} + 715 a^{7} b^{8} x^{9} + \frac{10010 a^{6} b^{9} x^{\frac{19}{2}}}{19} + \frac{3003 a^{5} b^{10} x^{10}}{10} + 130 a^{4} b^{11} x^{\frac{21}{2}} + \frac{455 a^{3} b^{12} x^{11}}{11} + \frac{210 a^{2} b^{13} x^{\frac{23}{2}}}{23} + \frac{5 a b^{14} x^{12}}{4} + \frac{2 b^{15} x^{\frac{25}{2}}}{25}"," ",0,"a**15*x**5/5 + 30*a**14*b*x**(11/2)/11 + 35*a**13*b**2*x**6/2 + 70*a**12*b**3*x**(13/2) + 195*a**11*b**4*x**7 + 2002*a**10*b**5*x**(15/2)/5 + 5005*a**9*b**6*x**8/8 + 12870*a**8*b**7*x**(17/2)/17 + 715*a**7*b**8*x**9 + 10010*a**6*b**9*x**(19/2)/19 + 3003*a**5*b**10*x**10/10 + 130*a**4*b**11*x**(21/2) + 455*a**3*b**12*x**11/11 + 210*a**2*b**13*x**(23/2)/23 + 5*a*b**14*x**12/4 + 2*b**15*x**(25/2)/25","A",0
2171,1,209,0,6.354768," ","integrate(x**3*(a+b*x**(1/2))**15,x)","\frac{a^{15} x^{4}}{4} + \frac{10 a^{14} b x^{\frac{9}{2}}}{3} + 21 a^{13} b^{2} x^{5} + \frac{910 a^{12} b^{3} x^{\frac{11}{2}}}{11} + \frac{455 a^{11} b^{4} x^{6}}{2} + 462 a^{10} b^{5} x^{\frac{13}{2}} + 715 a^{9} b^{6} x^{7} + 858 a^{8} b^{7} x^{\frac{15}{2}} + \frac{6435 a^{7} b^{8} x^{8}}{8} + \frac{10010 a^{6} b^{9} x^{\frac{17}{2}}}{17} + \frac{1001 a^{5} b^{10} x^{9}}{3} + \frac{2730 a^{4} b^{11} x^{\frac{19}{2}}}{19} + \frac{91 a^{3} b^{12} x^{10}}{2} + 10 a^{2} b^{13} x^{\frac{21}{2}} + \frac{15 a b^{14} x^{11}}{11} + \frac{2 b^{15} x^{\frac{23}{2}}}{23}"," ",0,"a**15*x**4/4 + 10*a**14*b*x**(9/2)/3 + 21*a**13*b**2*x**5 + 910*a**12*b**3*x**(11/2)/11 + 455*a**11*b**4*x**6/2 + 462*a**10*b**5*x**(13/2) + 715*a**9*b**6*x**7 + 858*a**8*b**7*x**(15/2) + 6435*a**7*b**8*x**8/8 + 10010*a**6*b**9*x**(17/2)/17 + 1001*a**5*b**10*x**9/3 + 2730*a**4*b**11*x**(19/2)/19 + 91*a**3*b**12*x**10/2 + 10*a**2*b**13*x**(21/2) + 15*a*b**14*x**11/11 + 2*b**15*x**(23/2)/23","A",0
2172,1,212,0,6.041822," ","integrate(x**2*(a+b*x**(1/2))**15,x)","\frac{a^{15} x^{3}}{3} + \frac{30 a^{14} b x^{\frac{7}{2}}}{7} + \frac{105 a^{13} b^{2} x^{4}}{4} + \frac{910 a^{12} b^{3} x^{\frac{9}{2}}}{9} + 273 a^{11} b^{4} x^{5} + 546 a^{10} b^{5} x^{\frac{11}{2}} + \frac{5005 a^{9} b^{6} x^{6}}{6} + 990 a^{8} b^{7} x^{\frac{13}{2}} + \frac{6435 a^{7} b^{8} x^{7}}{7} + \frac{2002 a^{6} b^{9} x^{\frac{15}{2}}}{3} + \frac{3003 a^{5} b^{10} x^{8}}{8} + \frac{2730 a^{4} b^{11} x^{\frac{17}{2}}}{17} + \frac{455 a^{3} b^{12} x^{9}}{9} + \frac{210 a^{2} b^{13} x^{\frac{19}{2}}}{19} + \frac{3 a b^{14} x^{10}}{2} + \frac{2 b^{15} x^{\frac{21}{2}}}{21}"," ",0,"a**15*x**3/3 + 30*a**14*b*x**(7/2)/7 + 105*a**13*b**2*x**4/4 + 910*a**12*b**3*x**(9/2)/9 + 273*a**11*b**4*x**5 + 546*a**10*b**5*x**(11/2) + 5005*a**9*b**6*x**6/6 + 990*a**8*b**7*x**(13/2) + 6435*a**7*b**8*x**7/7 + 2002*a**6*b**9*x**(15/2)/3 + 3003*a**5*b**10*x**8/8 + 2730*a**4*b**11*x**(17/2)/17 + 455*a**3*b**12*x**9/9 + 210*a**2*b**13*x**(19/2)/19 + 3*a*b**14*x**10/2 + 2*b**15*x**(21/2)/21","A",0
2173,1,204,0,5.786125," ","integrate(x*(a+b*x**(1/2))**15,x)","\frac{a^{15} x^{2}}{2} + 6 a^{14} b x^{\frac{5}{2}} + 35 a^{13} b^{2} x^{3} + 130 a^{12} b^{3} x^{\frac{7}{2}} + \frac{1365 a^{11} b^{4} x^{4}}{4} + \frac{2002 a^{10} b^{5} x^{\frac{9}{2}}}{3} + 1001 a^{9} b^{6} x^{5} + 1170 a^{8} b^{7} x^{\frac{11}{2}} + \frac{2145 a^{7} b^{8} x^{6}}{2} + 770 a^{6} b^{9} x^{\frac{13}{2}} + 429 a^{5} b^{10} x^{7} + 182 a^{4} b^{11} x^{\frac{15}{2}} + \frac{455 a^{3} b^{12} x^{8}}{8} + \frac{210 a^{2} b^{13} x^{\frac{17}{2}}}{17} + \frac{5 a b^{14} x^{9}}{3} + \frac{2 b^{15} x^{\frac{19}{2}}}{19}"," ",0,"a**15*x**2/2 + 6*a**14*b*x**(5/2) + 35*a**13*b**2*x**3 + 130*a**12*b**3*x**(7/2) + 1365*a**11*b**4*x**4/4 + 2002*a**10*b**5*x**(9/2)/3 + 1001*a**9*b**6*x**5 + 1170*a**8*b**7*x**(11/2) + 2145*a**7*b**8*x**6/2 + 770*a**6*b**9*x**(13/2) + 429*a**5*b**10*x**7 + 182*a**4*b**11*x**(15/2) + 455*a**3*b**12*x**8/8 + 210*a**2*b**13*x**(17/2)/17 + 5*a*b**14*x**9/3 + 2*b**15*x**(19/2)/19","B",0
2174,1,197,0,5.427712," ","integrate((a+b*x**(1/2))**15,x)","a^{15} x + 10 a^{14} b x^{\frac{3}{2}} + \frac{105 a^{13} b^{2} x^{2}}{2} + 182 a^{12} b^{3} x^{\frac{5}{2}} + 455 a^{11} b^{4} x^{3} + 858 a^{10} b^{5} x^{\frac{7}{2}} + \frac{5005 a^{9} b^{6} x^{4}}{4} + 1430 a^{8} b^{7} x^{\frac{9}{2}} + 1287 a^{7} b^{8} x^{5} + 910 a^{6} b^{9} x^{\frac{11}{2}} + \frac{1001 a^{5} b^{10} x^{6}}{2} + 210 a^{4} b^{11} x^{\frac{13}{2}} + 65 a^{3} b^{12} x^{7} + 14 a^{2} b^{13} x^{\frac{15}{2}} + \frac{15 a b^{14} x^{8}}{8} + \frac{2 b^{15} x^{\frac{17}{2}}}{17}"," ",0,"a**15*x + 10*a**14*b*x**(3/2) + 105*a**13*b**2*x**2/2 + 182*a**12*b**3*x**(5/2) + 455*a**11*b**4*x**3 + 858*a**10*b**5*x**(7/2) + 5005*a**9*b**6*x**4/4 + 1430*a**8*b**7*x**(9/2) + 1287*a**7*b**8*x**5 + 910*a**6*b**9*x**(11/2) + 1001*a**5*b**10*x**6/2 + 210*a**4*b**11*x**(13/2) + 65*a**3*b**12*x**7 + 14*a**2*b**13*x**(15/2) + 15*a*b**14*x**8/8 + 2*b**15*x**(17/2)/17","B",0
2175,1,211,0,6.026705," ","integrate((a+b*x**(1/2))**15/x,x)","a^{15} \log{\left(x \right)} + 30 a^{14} b \sqrt{x} + 105 a^{13} b^{2} x + \frac{910 a^{12} b^{3} x^{\frac{3}{2}}}{3} + \frac{1365 a^{11} b^{4} x^{2}}{2} + \frac{6006 a^{10} b^{5} x^{\frac{5}{2}}}{5} + \frac{5005 a^{9} b^{6} x^{3}}{3} + \frac{12870 a^{8} b^{7} x^{\frac{7}{2}}}{7} + \frac{6435 a^{7} b^{8} x^{4}}{4} + \frac{10010 a^{6} b^{9} x^{\frac{9}{2}}}{9} + \frac{3003 a^{5} b^{10} x^{5}}{5} + \frac{2730 a^{4} b^{11} x^{\frac{11}{2}}}{11} + \frac{455 a^{3} b^{12} x^{6}}{6} + \frac{210 a^{2} b^{13} x^{\frac{13}{2}}}{13} + \frac{15 a b^{14} x^{7}}{7} + \frac{2 b^{15} x^{\frac{15}{2}}}{15}"," ",0,"a**15*log(x) + 30*a**14*b*sqrt(x) + 105*a**13*b**2*x + 910*a**12*b**3*x**(3/2)/3 + 1365*a**11*b**4*x**2/2 + 6006*a**10*b**5*x**(5/2)/5 + 5005*a**9*b**6*x**3/3 + 12870*a**8*b**7*x**(7/2)/7 + 6435*a**7*b**8*x**4/4 + 10010*a**6*b**9*x**(9/2)/9 + 3003*a**5*b**10*x**5/5 + 2730*a**4*b**11*x**(11/2)/11 + 455*a**3*b**12*x**6/6 + 210*a**2*b**13*x**(13/2)/13 + 15*a*b**14*x**7/7 + 2*b**15*x**(15/2)/15","A",0
2176,1,197,0,5.807235," ","integrate((a+b*x**(1/2))**15/x**2,x)","- \frac{a^{15}}{x} - \frac{30 a^{14} b}{\sqrt{x}} + 105 a^{13} b^{2} \log{\left(x \right)} + 910 a^{12} b^{3} \sqrt{x} + 1365 a^{11} b^{4} x + 2002 a^{10} b^{5} x^{\frac{3}{2}} + \frac{5005 a^{9} b^{6} x^{2}}{2} + 2574 a^{8} b^{7} x^{\frac{5}{2}} + 2145 a^{7} b^{8} x^{3} + 1430 a^{6} b^{9} x^{\frac{7}{2}} + \frac{3003 a^{5} b^{10} x^{4}}{4} + \frac{910 a^{4} b^{11} x^{\frac{9}{2}}}{3} + 91 a^{3} b^{12} x^{5} + \frac{210 a^{2} b^{13} x^{\frac{11}{2}}}{11} + \frac{5 a b^{14} x^{6}}{2} + \frac{2 b^{15} x^{\frac{13}{2}}}{13}"," ",0,"-a**15/x - 30*a**14*b/sqrt(x) + 105*a**13*b**2*log(x) + 910*a**12*b**3*sqrt(x) + 1365*a**11*b**4*x + 2002*a**10*b**5*x**(3/2) + 5005*a**9*b**6*x**2/2 + 2574*a**8*b**7*x**(5/2) + 2145*a**7*b**8*x**3 + 1430*a**6*b**9*x**(7/2) + 3003*a**5*b**10*x**4/4 + 910*a**4*b**11*x**(9/2)/3 + 91*a**3*b**12*x**5 + 210*a**2*b**13*x**(11/2)/11 + 5*a*b**14*x**6/2 + 2*b**15*x**(13/2)/13","A",0
2177,1,196,0,5.626976," ","integrate((a+b*x**(1/2))**15/x**3,x)","- \frac{a^{15}}{2 x^{2}} - \frac{10 a^{14} b}{x^{\frac{3}{2}}} - \frac{105 a^{13} b^{2}}{x} - \frac{910 a^{12} b^{3}}{\sqrt{x}} + 1365 a^{11} b^{4} \log{\left(x \right)} + 6006 a^{10} b^{5} \sqrt{x} + 5005 a^{9} b^{6} x + 4290 a^{8} b^{7} x^{\frac{3}{2}} + \frac{6435 a^{7} b^{8} x^{2}}{2} + 2002 a^{6} b^{9} x^{\frac{5}{2}} + 1001 a^{5} b^{10} x^{3} + 390 a^{4} b^{11} x^{\frac{7}{2}} + \frac{455 a^{3} b^{12} x^{4}}{4} + \frac{70 a^{2} b^{13} x^{\frac{9}{2}}}{3} + 3 a b^{14} x^{5} + \frac{2 b^{15} x^{\frac{11}{2}}}{11}"," ",0,"-a**15/(2*x**2) - 10*a**14*b/x**(3/2) - 105*a**13*b**2/x - 910*a**12*b**3/sqrt(x) + 1365*a**11*b**4*log(x) + 6006*a**10*b**5*sqrt(x) + 5005*a**9*b**6*x + 4290*a**8*b**7*x**(3/2) + 6435*a**7*b**8*x**2/2 + 2002*a**6*b**9*x**(5/2) + 1001*a**5*b**10*x**3 + 390*a**4*b**11*x**(7/2) + 455*a**3*b**12*x**4/4 + 70*a**2*b**13*x**(9/2)/3 + 3*a*b**14*x**5 + 2*b**15*x**(11/2)/11","A",0
2178,1,201,0,5.371955," ","integrate((a+b*x**(1/2))**15/x**4,x)","- \frac{a^{15}}{3 x^{3}} - \frac{6 a^{14} b}{x^{\frac{5}{2}}} - \frac{105 a^{13} b^{2}}{2 x^{2}} - \frac{910 a^{12} b^{3}}{3 x^{\frac{3}{2}}} - \frac{1365 a^{11} b^{4}}{x} - \frac{6006 a^{10} b^{5}}{\sqrt{x}} + 5005 a^{9} b^{6} \log{\left(x \right)} + 12870 a^{8} b^{7} \sqrt{x} + 6435 a^{7} b^{8} x + \frac{10010 a^{6} b^{9} x^{\frac{3}{2}}}{3} + \frac{3003 a^{5} b^{10} x^{2}}{2} + 546 a^{4} b^{11} x^{\frac{5}{2}} + \frac{455 a^{3} b^{12} x^{3}}{3} + 30 a^{2} b^{13} x^{\frac{7}{2}} + \frac{15 a b^{14} x^{4}}{4} + \frac{2 b^{15} x^{\frac{9}{2}}}{9}"," ",0,"-a**15/(3*x**3) - 6*a**14*b/x**(5/2) - 105*a**13*b**2/(2*x**2) - 910*a**12*b**3/(3*x**(3/2)) - 1365*a**11*b**4/x - 6006*a**10*b**5/sqrt(x) + 5005*a**9*b**6*log(x) + 12870*a**8*b**7*sqrt(x) + 6435*a**7*b**8*x + 10010*a**6*b**9*x**(3/2)/3 + 3003*a**5*b**10*x**2/2 + 546*a**4*b**11*x**(5/2) + 455*a**3*b**12*x**3/3 + 30*a**2*b**13*x**(7/2) + 15*a*b**14*x**4/4 + 2*b**15*x**(9/2)/9","A",0
2179,1,199,0,5.046004," ","integrate((a+b*x**(1/2))**15/x**6,x)","- \frac{a^{15}}{5 x^{5}} - \frac{10 a^{14} b}{3 x^{\frac{9}{2}}} - \frac{105 a^{13} b^{2}}{4 x^{4}} - \frac{130 a^{12} b^{3}}{x^{\frac{7}{2}}} - \frac{455 a^{11} b^{4}}{x^{3}} - \frac{6006 a^{10} b^{5}}{5 x^{\frac{5}{2}}} - \frac{5005 a^{9} b^{6}}{2 x^{2}} - \frac{4290 a^{8} b^{7}}{x^{\frac{3}{2}}} - \frac{6435 a^{7} b^{8}}{x} - \frac{10010 a^{6} b^{9}}{\sqrt{x}} + 3003 a^{5} b^{10} \log{\left(x \right)} + 2730 a^{4} b^{11} \sqrt{x} + 455 a^{3} b^{12} x + 70 a^{2} b^{13} x^{\frac{3}{2}} + \frac{15 a b^{14} x^{2}}{2} + \frac{2 b^{15} x^{\frac{5}{2}}}{5}"," ",0,"-a**15/(5*x**5) - 10*a**14*b/(3*x**(9/2)) - 105*a**13*b**2/(4*x**4) - 130*a**12*b**3/x**(7/2) - 455*a**11*b**4/x**3 - 6006*a**10*b**5/(5*x**(5/2)) - 5005*a**9*b**6/(2*x**2) - 4290*a**8*b**7/x**(3/2) - 6435*a**7*b**8/x - 10010*a**6*b**9/sqrt(x) + 3003*a**5*b**10*log(x) + 2730*a**4*b**11*sqrt(x) + 455*a**3*b**12*x + 70*a**2*b**13*x**(3/2) + 15*a*b**14*x**2/2 + 2*b**15*x**(5/2)/5","A",0
2180,1,201,0,5.037886," ","integrate((a+b*x**(1/2))**15/x**7,x)","- \frac{a^{15}}{6 x^{6}} - \frac{30 a^{14} b}{11 x^{\frac{11}{2}}} - \frac{21 a^{13} b^{2}}{x^{5}} - \frac{910 a^{12} b^{3}}{9 x^{\frac{9}{2}}} - \frac{1365 a^{11} b^{4}}{4 x^{4}} - \frac{858 a^{10} b^{5}}{x^{\frac{7}{2}}} - \frac{5005 a^{9} b^{6}}{3 x^{3}} - \frac{2574 a^{8} b^{7}}{x^{\frac{5}{2}}} - \frac{6435 a^{7} b^{8}}{2 x^{2}} - \frac{10010 a^{6} b^{9}}{3 x^{\frac{3}{2}}} - \frac{3003 a^{5} b^{10}}{x} - \frac{2730 a^{4} b^{11}}{\sqrt{x}} + 455 a^{3} b^{12} \log{\left(x \right)} + 210 a^{2} b^{13} \sqrt{x} + 15 a b^{14} x + \frac{2 b^{15} x^{\frac{3}{2}}}{3}"," ",0,"-a**15/(6*x**6) - 30*a**14*b/(11*x**(11/2)) - 21*a**13*b**2/x**5 - 910*a**12*b**3/(9*x**(9/2)) - 1365*a**11*b**4/(4*x**4) - 858*a**10*b**5/x**(7/2) - 5005*a**9*b**6/(3*x**3) - 2574*a**8*b**7/x**(5/2) - 6435*a**7*b**8/(2*x**2) - 10010*a**6*b**9/(3*x**(3/2)) - 3003*a**5*b**10/x - 2730*a**4*b**11/sqrt(x) + 455*a**3*b**12*log(x) + 210*a**2*b**13*sqrt(x) + 15*a*b**14*x + 2*b**15*x**(3/2)/3","A",0
2181,1,202,0,5.871637," ","integrate((a+b*x**(1/2))**15/x**8,x)","- \frac{a^{15}}{7 x^{7}} - \frac{30 a^{14} b}{13 x^{\frac{13}{2}}} - \frac{35 a^{13} b^{2}}{2 x^{6}} - \frac{910 a^{12} b^{3}}{11 x^{\frac{11}{2}}} - \frac{273 a^{11} b^{4}}{x^{5}} - \frac{2002 a^{10} b^{5}}{3 x^{\frac{9}{2}}} - \frac{5005 a^{9} b^{6}}{4 x^{4}} - \frac{12870 a^{8} b^{7}}{7 x^{\frac{7}{2}}} - \frac{2145 a^{7} b^{8}}{x^{3}} - \frac{2002 a^{6} b^{9}}{x^{\frac{5}{2}}} - \frac{3003 a^{5} b^{10}}{2 x^{2}} - \frac{910 a^{4} b^{11}}{x^{\frac{3}{2}}} - \frac{455 a^{3} b^{12}}{x} - \frac{210 a^{2} b^{13}}{\sqrt{x}} + 15 a b^{14} \log{\left(x \right)} + 2 b^{15} \sqrt{x}"," ",0,"-a**15/(7*x**7) - 30*a**14*b/(13*x**(13/2)) - 35*a**13*b**2/(2*x**6) - 910*a**12*b**3/(11*x**(11/2)) - 273*a**11*b**4/x**5 - 2002*a**10*b**5/(3*x**(9/2)) - 5005*a**9*b**6/(4*x**4) - 12870*a**8*b**7/(7*x**(7/2)) - 2145*a**7*b**8/x**3 - 2002*a**6*b**9/x**(5/2) - 3003*a**5*b**10/(2*x**2) - 910*a**4*b**11/x**(3/2) - 455*a**3*b**12/x - 210*a**2*b**13/sqrt(x) + 15*a*b**14*log(x) + 2*b**15*sqrt(x)","A",0
2182,1,197,0,7.555276," ","integrate((a+b*x**(1/2))**15/x**9,x)","- \frac{a^{15}}{8 x^{8}} - \frac{2 a^{14} b}{x^{\frac{15}{2}}} - \frac{15 a^{13} b^{2}}{x^{7}} - \frac{70 a^{12} b^{3}}{x^{\frac{13}{2}}} - \frac{455 a^{11} b^{4}}{2 x^{6}} - \frac{546 a^{10} b^{5}}{x^{\frac{11}{2}}} - \frac{1001 a^{9} b^{6}}{x^{5}} - \frac{1430 a^{8} b^{7}}{x^{\frac{9}{2}}} - \frac{6435 a^{7} b^{8}}{4 x^{4}} - \frac{1430 a^{6} b^{9}}{x^{\frac{7}{2}}} - \frac{1001 a^{5} b^{10}}{x^{3}} - \frac{546 a^{4} b^{11}}{x^{\frac{5}{2}}} - \frac{455 a^{3} b^{12}}{2 x^{2}} - \frac{70 a^{2} b^{13}}{x^{\frac{3}{2}}} - \frac{15 a b^{14}}{x} - \frac{2 b^{15}}{\sqrt{x}}"," ",0,"-a**15/(8*x**8) - 2*a**14*b/x**(15/2) - 15*a**13*b**2/x**7 - 70*a**12*b**3/x**(13/2) - 455*a**11*b**4/(2*x**6) - 546*a**10*b**5/x**(11/2) - 1001*a**9*b**6/x**5 - 1430*a**8*b**7/x**(9/2) - 6435*a**7*b**8/(4*x**4) - 1430*a**6*b**9/x**(7/2) - 1001*a**5*b**10/x**3 - 546*a**4*b**11/x**(5/2) - 455*a**3*b**12/(2*x**2) - 70*a**2*b**13/x**(3/2) - 15*a*b**14/x - 2*b**15/sqrt(x)","B",0
2183,1,209,0,10.072855," ","integrate((a+b*x**(1/2))**15/x**10,x)","- \frac{a^{15}}{9 x^{9}} - \frac{30 a^{14} b}{17 x^{\frac{17}{2}}} - \frac{105 a^{13} b^{2}}{8 x^{8}} - \frac{182 a^{12} b^{3}}{3 x^{\frac{15}{2}}} - \frac{195 a^{11} b^{4}}{x^{7}} - \frac{462 a^{10} b^{5}}{x^{\frac{13}{2}}} - \frac{5005 a^{9} b^{6}}{6 x^{6}} - \frac{1170 a^{8} b^{7}}{x^{\frac{11}{2}}} - \frac{1287 a^{7} b^{8}}{x^{5}} - \frac{10010 a^{6} b^{9}}{9 x^{\frac{9}{2}}} - \frac{3003 a^{5} b^{10}}{4 x^{4}} - \frac{390 a^{4} b^{11}}{x^{\frac{7}{2}}} - \frac{455 a^{3} b^{12}}{3 x^{3}} - \frac{42 a^{2} b^{13}}{x^{\frac{5}{2}}} - \frac{15 a b^{14}}{2 x^{2}} - \frac{2 b^{15}}{3 x^{\frac{3}{2}}}"," ",0,"-a**15/(9*x**9) - 30*a**14*b/(17*x**(17/2)) - 105*a**13*b**2/(8*x**8) - 182*a**12*b**3/(3*x**(15/2)) - 195*a**11*b**4/x**7 - 462*a**10*b**5/x**(13/2) - 5005*a**9*b**6/(6*x**6) - 1170*a**8*b**7/x**(11/2) - 1287*a**7*b**8/x**5 - 10010*a**6*b**9/(9*x**(9/2)) - 3003*a**5*b**10/(4*x**4) - 390*a**4*b**11/x**(7/2) - 455*a**3*b**12/(3*x**3) - 42*a**2*b**13/x**(5/2) - 15*a*b**14/(2*x**2) - 2*b**15/(3*x**(3/2))","B",0
2184,1,211,0,13.033819," ","integrate((a+b*x**(1/2))**15/x**11,x)","- \frac{a^{15}}{10 x^{10}} - \frac{30 a^{14} b}{19 x^{\frac{19}{2}}} - \frac{35 a^{13} b^{2}}{3 x^{9}} - \frac{910 a^{12} b^{3}}{17 x^{\frac{17}{2}}} - \frac{1365 a^{11} b^{4}}{8 x^{8}} - \frac{2002 a^{10} b^{5}}{5 x^{\frac{15}{2}}} - \frac{715 a^{9} b^{6}}{x^{7}} - \frac{990 a^{8} b^{7}}{x^{\frac{13}{2}}} - \frac{2145 a^{7} b^{8}}{2 x^{6}} - \frac{910 a^{6} b^{9}}{x^{\frac{11}{2}}} - \frac{3003 a^{5} b^{10}}{5 x^{5}} - \frac{910 a^{4} b^{11}}{3 x^{\frac{9}{2}}} - \frac{455 a^{3} b^{12}}{4 x^{4}} - \frac{30 a^{2} b^{13}}{x^{\frac{7}{2}}} - \frac{5 a b^{14}}{x^{3}} - \frac{2 b^{15}}{5 x^{\frac{5}{2}}}"," ",0,"-a**15/(10*x**10) - 30*a**14*b/(19*x**(19/2)) - 35*a**13*b**2/(3*x**9) - 910*a**12*b**3/(17*x**(17/2)) - 1365*a**11*b**4/(8*x**8) - 2002*a**10*b**5/(5*x**(15/2)) - 715*a**9*b**6/x**7 - 990*a**8*b**7/x**(13/2) - 2145*a**7*b**8/(2*x**6) - 910*a**6*b**9/x**(11/2) - 3003*a**5*b**10/(5*x**5) - 910*a**4*b**11/(3*x**(9/2)) - 455*a**3*b**12/(4*x**4) - 30*a**2*b**13/x**(7/2) - 5*a*b**14/x**3 - 2*b**15/(5*x**(5/2))","A",0
2185,1,214,0,16.780920," ","integrate((a+b*x**(1/2))**15/x**12,x)","- \frac{a^{15}}{11 x^{11}} - \frac{10 a^{14} b}{7 x^{\frac{21}{2}}} - \frac{21 a^{13} b^{2}}{2 x^{10}} - \frac{910 a^{12} b^{3}}{19 x^{\frac{19}{2}}} - \frac{455 a^{11} b^{4}}{3 x^{9}} - \frac{6006 a^{10} b^{5}}{17 x^{\frac{17}{2}}} - \frac{5005 a^{9} b^{6}}{8 x^{8}} - \frac{858 a^{8} b^{7}}{x^{\frac{15}{2}}} - \frac{6435 a^{7} b^{8}}{7 x^{7}} - \frac{770 a^{6} b^{9}}{x^{\frac{13}{2}}} - \frac{1001 a^{5} b^{10}}{2 x^{6}} - \frac{2730 a^{4} b^{11}}{11 x^{\frac{11}{2}}} - \frac{91 a^{3} b^{12}}{x^{5}} - \frac{70 a^{2} b^{13}}{3 x^{\frac{9}{2}}} - \frac{15 a b^{14}}{4 x^{4}} - \frac{2 b^{15}}{7 x^{\frac{7}{2}}}"," ",0,"-a**15/(11*x**11) - 10*a**14*b/(7*x**(21/2)) - 21*a**13*b**2/(2*x**10) - 910*a**12*b**3/(19*x**(19/2)) - 455*a**11*b**4/(3*x**9) - 6006*a**10*b**5/(17*x**(17/2)) - 5005*a**9*b**6/(8*x**8) - 858*a**8*b**7/x**(15/2) - 6435*a**7*b**8/(7*x**7) - 770*a**6*b**9/x**(13/2) - 1001*a**5*b**10/(2*x**6) - 2730*a**4*b**11/(11*x**(11/2)) - 91*a**3*b**12/x**5 - 70*a**2*b**13/(3*x**(9/2)) - 15*a*b**14/(4*x**4) - 2*b**15/(7*x**(7/2))","A",0
2186,1,214,0,21.119135," ","integrate((a+b*x**(1/2))**15/x**13,x)","- \frac{a^{15}}{12 x^{12}} - \frac{30 a^{14} b}{23 x^{\frac{23}{2}}} - \frac{105 a^{13} b^{2}}{11 x^{11}} - \frac{130 a^{12} b^{3}}{3 x^{\frac{21}{2}}} - \frac{273 a^{11} b^{4}}{2 x^{10}} - \frac{6006 a^{10} b^{5}}{19 x^{\frac{19}{2}}} - \frac{5005 a^{9} b^{6}}{9 x^{9}} - \frac{12870 a^{8} b^{7}}{17 x^{\frac{17}{2}}} - \frac{6435 a^{7} b^{8}}{8 x^{8}} - \frac{2002 a^{6} b^{9}}{3 x^{\frac{15}{2}}} - \frac{429 a^{5} b^{10}}{x^{7}} - \frac{210 a^{4} b^{11}}{x^{\frac{13}{2}}} - \frac{455 a^{3} b^{12}}{6 x^{6}} - \frac{210 a^{2} b^{13}}{11 x^{\frac{11}{2}}} - \frac{3 a b^{14}}{x^{5}} - \frac{2 b^{15}}{9 x^{\frac{9}{2}}}"," ",0,"-a**15/(12*x**12) - 30*a**14*b/(23*x**(23/2)) - 105*a**13*b**2/(11*x**11) - 130*a**12*b**3/(3*x**(21/2)) - 273*a**11*b**4/(2*x**10) - 6006*a**10*b**5/(19*x**(19/2)) - 5005*a**9*b**6/(9*x**9) - 12870*a**8*b**7/(17*x**(17/2)) - 6435*a**7*b**8/(8*x**8) - 2002*a**6*b**9/(3*x**(15/2)) - 429*a**5*b**10/x**7 - 210*a**4*b**11/x**(13/2) - 455*a**3*b**12/(6*x**6) - 210*a**2*b**13/(11*x**(11/2)) - 3*a*b**14/x**5 - 2*b**15/(9*x**(9/2))","A",0
2187,1,212,0,27.382480," ","integrate((a+b*x**(1/2))**15/x**14,x)","- \frac{a^{15}}{13 x^{13}} - \frac{6 a^{14} b}{5 x^{\frac{25}{2}}} - \frac{35 a^{13} b^{2}}{4 x^{12}} - \frac{910 a^{12} b^{3}}{23 x^{\frac{23}{2}}} - \frac{1365 a^{11} b^{4}}{11 x^{11}} - \frac{286 a^{10} b^{5}}{x^{\frac{21}{2}}} - \frac{1001 a^{9} b^{6}}{2 x^{10}} - \frac{12870 a^{8} b^{7}}{19 x^{\frac{19}{2}}} - \frac{715 a^{7} b^{8}}{x^{9}} - \frac{10010 a^{6} b^{9}}{17 x^{\frac{17}{2}}} - \frac{3003 a^{5} b^{10}}{8 x^{8}} - \frac{182 a^{4} b^{11}}{x^{\frac{15}{2}}} - \frac{65 a^{3} b^{12}}{x^{7}} - \frac{210 a^{2} b^{13}}{13 x^{\frac{13}{2}}} - \frac{5 a b^{14}}{2 x^{6}} - \frac{2 b^{15}}{11 x^{\frac{11}{2}}}"," ",0,"-a**15/(13*x**13) - 6*a**14*b/(5*x**(25/2)) - 35*a**13*b**2/(4*x**12) - 910*a**12*b**3/(23*x**(23/2)) - 1365*a**11*b**4/(11*x**11) - 286*a**10*b**5/x**(21/2) - 1001*a**9*b**6/(2*x**10) - 12870*a**8*b**7/(19*x**(19/2)) - 715*a**7*b**8/x**9 - 10010*a**6*b**9/(17*x**(17/2)) - 3003*a**5*b**10/(8*x**8) - 182*a**4*b**11/x**(15/2) - 65*a**3*b**12/x**7 - 210*a**2*b**13/(13*x**(13/2)) - 5*a*b**14/(2*x**6) - 2*b**15/(11*x**(11/2))","A",0
2188,1,216,0,34.854454," ","integrate((a+b*x**(1/2))**15/x**15,x)","- \frac{a^{15}}{14 x^{14}} - \frac{10 a^{14} b}{9 x^{\frac{27}{2}}} - \frac{105 a^{13} b^{2}}{13 x^{13}} - \frac{182 a^{12} b^{3}}{5 x^{\frac{25}{2}}} - \frac{455 a^{11} b^{4}}{4 x^{12}} - \frac{6006 a^{10} b^{5}}{23 x^{\frac{23}{2}}} - \frac{455 a^{9} b^{6}}{x^{11}} - \frac{4290 a^{8} b^{7}}{7 x^{\frac{21}{2}}} - \frac{1287 a^{7} b^{8}}{2 x^{10}} - \frac{10010 a^{6} b^{9}}{19 x^{\frac{19}{2}}} - \frac{1001 a^{5} b^{10}}{3 x^{9}} - \frac{2730 a^{4} b^{11}}{17 x^{\frac{17}{2}}} - \frac{455 a^{3} b^{12}}{8 x^{8}} - \frac{14 a^{2} b^{13}}{x^{\frac{15}{2}}} - \frac{15 a b^{14}}{7 x^{7}} - \frac{2 b^{15}}{13 x^{\frac{13}{2}}}"," ",0,"-a**15/(14*x**14) - 10*a**14*b/(9*x**(27/2)) - 105*a**13*b**2/(13*x**13) - 182*a**12*b**3/(5*x**(25/2)) - 455*a**11*b**4/(4*x**12) - 6006*a**10*b**5/(23*x**(23/2)) - 455*a**9*b**6/x**11 - 4290*a**8*b**7/(7*x**(21/2)) - 1287*a**7*b**8/(2*x**10) - 10010*a**6*b**9/(19*x**(19/2)) - 1001*a**5*b**10/(3*x**9) - 2730*a**4*b**11/(17*x**(17/2)) - 455*a**3*b**12/(8*x**8) - 14*a**2*b**13/x**(15/2) - 15*a*b**14/(7*x**7) - 2*b**15/(13*x**(13/2))","A",0
2189,1,216,0,48.089332," ","integrate((a+b*x**(1/2))**15/x**16,x)","- \frac{a^{15}}{15 x^{15}} - \frac{30 a^{14} b}{29 x^{\frac{29}{2}}} - \frac{15 a^{13} b^{2}}{2 x^{14}} - \frac{910 a^{12} b^{3}}{27 x^{\frac{27}{2}}} - \frac{105 a^{11} b^{4}}{x^{13}} - \frac{6006 a^{10} b^{5}}{25 x^{\frac{25}{2}}} - \frac{5005 a^{9} b^{6}}{12 x^{12}} - \frac{12870 a^{8} b^{7}}{23 x^{\frac{23}{2}}} - \frac{585 a^{7} b^{8}}{x^{11}} - \frac{1430 a^{6} b^{9}}{3 x^{\frac{21}{2}}} - \frac{3003 a^{5} b^{10}}{10 x^{10}} - \frac{2730 a^{4} b^{11}}{19 x^{\frac{19}{2}}} - \frac{455 a^{3} b^{12}}{9 x^{9}} - \frac{210 a^{2} b^{13}}{17 x^{\frac{17}{2}}} - \frac{15 a b^{14}}{8 x^{8}} - \frac{2 b^{15}}{15 x^{\frac{15}{2}}}"," ",0,"-a**15/(15*x**15) - 30*a**14*b/(29*x**(29/2)) - 15*a**13*b**2/(2*x**14) - 910*a**12*b**3/(27*x**(27/2)) - 105*a**11*b**4/x**13 - 6006*a**10*b**5/(25*x**(25/2)) - 5005*a**9*b**6/(12*x**12) - 12870*a**8*b**7/(23*x**(23/2)) - 585*a**7*b**8/x**11 - 1430*a**6*b**9/(3*x**(21/2)) - 3003*a**5*b**10/(10*x**10) - 2730*a**4*b**11/(19*x**(19/2)) - 455*a**3*b**12/(9*x**9) - 210*a**2*b**13/(17*x**(17/2)) - 15*a*b**14/(8*x**8) - 2*b**15/(15*x**(15/2))","A",0
2190,1,212,0,51.039030," ","integrate((a+b*x**(1/2))**15/x**17,x)","- \frac{a^{15}}{16 x^{16}} - \frac{30 a^{14} b}{31 x^{\frac{31}{2}}} - \frac{7 a^{13} b^{2}}{x^{15}} - \frac{910 a^{12} b^{3}}{29 x^{\frac{29}{2}}} - \frac{195 a^{11} b^{4}}{2 x^{14}} - \frac{2002 a^{10} b^{5}}{9 x^{\frac{27}{2}}} - \frac{385 a^{9} b^{6}}{x^{13}} - \frac{2574 a^{8} b^{7}}{5 x^{\frac{25}{2}}} - \frac{2145 a^{7} b^{8}}{4 x^{12}} - \frac{10010 a^{6} b^{9}}{23 x^{\frac{23}{2}}} - \frac{273 a^{5} b^{10}}{x^{11}} - \frac{130 a^{4} b^{11}}{x^{\frac{21}{2}}} - \frac{91 a^{3} b^{12}}{2 x^{10}} - \frac{210 a^{2} b^{13}}{19 x^{\frac{19}{2}}} - \frac{5 a b^{14}}{3 x^{9}} - \frac{2 b^{15}}{17 x^{\frac{17}{2}}}"," ",0,"-a**15/(16*x**16) - 30*a**14*b/(31*x**(31/2)) - 7*a**13*b**2/x**15 - 910*a**12*b**3/(29*x**(29/2)) - 195*a**11*b**4/(2*x**14) - 2002*a**10*b**5/(9*x**(27/2)) - 385*a**9*b**6/x**13 - 2574*a**8*b**7/(5*x**(25/2)) - 2145*a**7*b**8/(4*x**12) - 10010*a**6*b**9/(23*x**(23/2)) - 273*a**5*b**10/x**11 - 130*a**4*b**11/x**(21/2) - 91*a**3*b**12/(2*x**10) - 210*a**2*b**13/(19*x**(19/2)) - 5*a*b**14/(3*x**9) - 2*b**15/(17*x**(17/2))","A",0
2191,1,109,0,1.088401," ","integrate(x**3/(a+b*x**(1/2)),x)","\begin{cases} - \frac{2 a^{7} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{b^{8}} + \frac{2 a^{6} \sqrt{x}}{b^{7}} - \frac{a^{5} x}{b^{6}} + \frac{2 a^{4} x^{\frac{3}{2}}}{3 b^{5}} - \frac{a^{3} x^{2}}{2 b^{4}} + \frac{2 a^{2} x^{\frac{5}{2}}}{5 b^{3}} - \frac{a x^{3}}{3 b^{2}} + \frac{2 x^{\frac{7}{2}}}{7 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**7*log(a/b + sqrt(x))/b**8 + 2*a**6*sqrt(x)/b**7 - a**5*x/b**6 + 2*a**4*x**(3/2)/(3*b**5) - a**3*x**2/(2*b**4) + 2*a**2*x**(5/2)/(5*b**3) - a*x**3/(3*b**2) + 2*x**(7/2)/(7*b), Ne(b, 0)), (x**4/(4*a), True))","A",0
2192,1,82,0,0.653547," ","integrate(x**2/(a+b*x**(1/2)),x)","\begin{cases} - \frac{2 a^{5} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{b^{6}} + \frac{2 a^{4} \sqrt{x}}{b^{5}} - \frac{a^{3} x}{b^{4}} + \frac{2 a^{2} x^{\frac{3}{2}}}{3 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{2 x^{\frac{5}{2}}}{5 b} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**5*log(a/b + sqrt(x))/b**6 + 2*a**4*sqrt(x)/b**5 - a**3*x/b**4 + 2*a**2*x**(3/2)/(3*b**3) - a*x**2/(2*b**2) + 2*x**(5/2)/(5*b), Ne(b, 0)), (x**3/(3*a), True))","A",0
2193,1,54,0,0.310537," ","integrate(x/(a+b*x**(1/2)),x)","\begin{cases} - \frac{2 a^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{b^{4}} + \frac{2 a^{2} \sqrt{x}}{b^{3}} - \frac{a x}{b^{2}} + \frac{2 x^{\frac{3}{2}}}{3 b} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*log(a/b + sqrt(x))/b**4 + 2*a**2*sqrt(x)/b**3 - a*x/b**2 + 2*x**(3/2)/(3*b), Ne(b, 0)), (x**2/(2*a), True))","A",0
2194,1,27,0,0.205572," ","integrate(1/(a+b*x**(1/2)),x)","\begin{cases} - \frac{2 a \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{b^{2}} + \frac{2 \sqrt{x}}{b} & \text{for}\: b \neq 0 \\\frac{x}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*log(a/b + sqrt(x))/b**2 + 2*sqrt(x)/b, Ne(b, 0)), (x/a, True))","A",0
2195,1,37,0,0.377407," ","integrate(1/x/(a+b*x**(1/2)),x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{b \sqrt{x}} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{a} - \frac{2 \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (-2/(b*sqrt(x)), Eq(a, 0)), (log(x)/a, Eq(b, 0)), (log(x)/a - 2*log(a/b + sqrt(x))/a, True))","A",0
2196,1,68,0,1.783697," ","integrate(1/x**2/(a+b*x**(1/2)),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{3 b x^{\frac{3}{2}}} & \text{for}\: a = 0 \\- \frac{1}{a x} & \text{for}\: b = 0 \\- \frac{1}{a x} + \frac{2 b}{a^{2} \sqrt{x}} + \frac{b^{2} \log{\left(x \right)}}{a^{3}} - \frac{2 b^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (-2/(3*b*x**(3/2)), Eq(a, 0)), (-1/(a*x), Eq(b, 0)), (-1/(a*x) + 2*b/(a**2*sqrt(x)) + b**2*log(x)/a**3 - 2*b**2*log(a/b + sqrt(x))/a**3, True))","A",0
2197,1,99,0,4.526669," ","integrate(1/x**3/(a+b*x**(1/2)),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{5 b x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{1}{2 a x^{2}} & \text{for}\: b = 0 \\- \frac{1}{2 a x^{2}} + \frac{2 b}{3 a^{2} x^{\frac{3}{2}}} - \frac{b^{2}}{a^{3} x} + \frac{2 b^{3}}{a^{4} \sqrt{x}} + \frac{b^{4} \log{\left(x \right)}}{a^{5}} - \frac{2 b^{4} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(5*b*x**(5/2)), Eq(a, 0)), (-1/(2*a*x**2), Eq(b, 0)), (-1/(2*a*x**2) + 2*b/(3*a**2*x**(3/2)) - b**2/(a**3*x) + 2*b**3/(a**4*sqrt(x)) + b**4*log(x)/a**5 - 2*b**4*log(a/b + sqrt(x))/a**5, True))","A",0
2198,1,126,0,10.185966," ","integrate(1/x**4/(a+b*x**(1/2)),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{7 b x^{\frac{7}{2}}} & \text{for}\: a = 0 \\- \frac{1}{3 a x^{3}} & \text{for}\: b = 0 \\- \frac{1}{3 a x^{3}} + \frac{2 b}{5 a^{2} x^{\frac{5}{2}}} - \frac{b^{2}}{2 a^{3} x^{2}} + \frac{2 b^{3}}{3 a^{4} x^{\frac{3}{2}}} - \frac{b^{4}}{a^{5} x} + \frac{2 b^{5}}{a^{6} \sqrt{x}} + \frac{b^{6} \log{\left(x \right)}}{a^{7}} - \frac{2 b^{6} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{7}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (-2/(7*b*x**(7/2)), Eq(a, 0)), (-1/(3*a*x**3), Eq(b, 0)), (-1/(3*a*x**3) + 2*b/(5*a**2*x**(5/2)) - b**2/(2*a**3*x**2) + 2*b**3/(3*a**4*x**(3/2)) - b**4/(a**5*x) + 2*b**5/(a**6*sqrt(x)) + b**6*log(x)/a**7 - 2*b**6*log(a/b + sqrt(x))/a**7, True))","A",0
2199,1,272,0,2.613430," ","integrate(x**3/(a+b*x**(1/2))**2,x)","\begin{cases} \frac{420 a^{7} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{30 a b^{8} + 30 b^{9} \sqrt{x}} + \frac{420 a^{7}}{30 a b^{8} + 30 b^{9} \sqrt{x}} + \frac{420 a^{6} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{30 a b^{8} + 30 b^{9} \sqrt{x}} - \frac{210 a^{5} b^{2} x}{30 a b^{8} + 30 b^{9} \sqrt{x}} + \frac{70 a^{4} b^{3} x^{\frac{3}{2}}}{30 a b^{8} + 30 b^{9} \sqrt{x}} - \frac{35 a^{3} b^{4} x^{2}}{30 a b^{8} + 30 b^{9} \sqrt{x}} + \frac{21 a^{2} b^{5} x^{\frac{5}{2}}}{30 a b^{8} + 30 b^{9} \sqrt{x}} - \frac{14 a b^{6} x^{3}}{30 a b^{8} + 30 b^{9} \sqrt{x}} + \frac{10 b^{7} x^{\frac{7}{2}}}{30 a b^{8} + 30 b^{9} \sqrt{x}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((420*a**7*log(a/b + sqrt(x))/(30*a*b**8 + 30*b**9*sqrt(x)) + 420*a**7/(30*a*b**8 + 30*b**9*sqrt(x)) + 420*a**6*b*sqrt(x)*log(a/b + sqrt(x))/(30*a*b**8 + 30*b**9*sqrt(x)) - 210*a**5*b**2*x/(30*a*b**8 + 30*b**9*sqrt(x)) + 70*a**4*b**3*x**(3/2)/(30*a*b**8 + 30*b**9*sqrt(x)) - 35*a**3*b**4*x**2/(30*a*b**8 + 30*b**9*sqrt(x)) + 21*a**2*b**5*x**(5/2)/(30*a*b**8 + 30*b**9*sqrt(x)) - 14*a*b**6*x**3/(30*a*b**8 + 30*b**9*sqrt(x)) + 10*b**7*x**(7/2)/(30*a*b**8 + 30*b**9*sqrt(x)), Ne(b, 0)), (x**4/(4*a**2), True))","A",0
2200,1,212,0,1.260834," ","integrate(x**2/(a+b*x**(1/2))**2,x)","\begin{cases} \frac{60 a^{5} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a b^{6} + 6 b^{7} \sqrt{x}} + \frac{60 a^{5}}{6 a b^{6} + 6 b^{7} \sqrt{x}} + \frac{60 a^{4} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a b^{6} + 6 b^{7} \sqrt{x}} - \frac{30 a^{3} b^{2} x}{6 a b^{6} + 6 b^{7} \sqrt{x}} + \frac{10 a^{2} b^{3} x^{\frac{3}{2}}}{6 a b^{6} + 6 b^{7} \sqrt{x}} - \frac{5 a b^{4} x^{2}}{6 a b^{6} + 6 b^{7} \sqrt{x}} + \frac{3 b^{5} x^{\frac{5}{2}}}{6 a b^{6} + 6 b^{7} \sqrt{x}} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((60*a**5*log(a/b + sqrt(x))/(6*a*b**6 + 6*b**7*sqrt(x)) + 60*a**5/(6*a*b**6 + 6*b**7*sqrt(x)) + 60*a**4*b*sqrt(x)*log(a/b + sqrt(x))/(6*a*b**6 + 6*b**7*sqrt(x)) - 30*a**3*b**2*x/(6*a*b**6 + 6*b**7*sqrt(x)) + 10*a**2*b**3*x**(3/2)/(6*a*b**6 + 6*b**7*sqrt(x)) - 5*a*b**4*x**2/(6*a*b**6 + 6*b**7*sqrt(x)) + 3*b**5*x**(5/2)/(6*a*b**6 + 6*b**7*sqrt(x)), Ne(b, 0)), (x**3/(3*a**2), True))","A",0
2201,1,134,0,0.476873," ","integrate(x/(a+b*x**(1/2))**2,x)","\begin{cases} \frac{6 a^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a b^{4} + b^{5} \sqrt{x}} + \frac{6 a^{3}}{a b^{4} + b^{5} \sqrt{x}} + \frac{6 a^{2} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a b^{4} + b^{5} \sqrt{x}} - \frac{3 a b^{2} x}{a b^{4} + b^{5} \sqrt{x}} + \frac{b^{3} x^{\frac{3}{2}}}{a b^{4} + b^{5} \sqrt{x}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*a**3*log(a/b + sqrt(x))/(a*b**4 + b**5*sqrt(x)) + 6*a**3/(a*b**4 + b**5*sqrt(x)) + 6*a**2*b*sqrt(x)*log(a/b + sqrt(x))/(a*b**4 + b**5*sqrt(x)) - 3*a*b**2*x/(a*b**4 + b**5*sqrt(x)) + b**3*x**(3/2)/(a*b**4 + b**5*sqrt(x)), Ne(b, 0)), (x**2/(2*a**2), True))","A",0
2202,1,80,0,0.627632," ","integrate(1/(a+b*x**(1/2))**2,x)","\begin{cases} \frac{2 a \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a b^{2} + b^{3} \sqrt{x}} + \frac{2 a}{a b^{2} + b^{3} \sqrt{x}} + \frac{2 b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a b^{2} + b^{3} \sqrt{x}} & \text{for}\: b \neq 0 \\\frac{x}{a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*log(a/b + sqrt(x))/(a*b**2 + b**3*sqrt(x)) + 2*a/(a*b**2 + b**3*sqrt(x)) + 2*b*sqrt(x)*log(a/b + sqrt(x))/(a*b**2 + b**3*sqrt(x)), Ne(b, 0)), (x/a**2, True))","A",0
2203,1,151,0,1.469894," ","integrate(1/x/(a+b*x**(1/2))**2,x)","\begin{cases} \frac{\tilde{\infty}}{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\log{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \\- \frac{1}{b^{2} x} & \text{for}\: a = 0 \\\frac{a \sqrt{x} \log{\left(x \right)}}{a^{3} \sqrt{x} + a^{2} b x} - \frac{2 a \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{3} \sqrt{x} + a^{2} b x} + \frac{2 a \sqrt{x}}{a^{3} \sqrt{x} + a^{2} b x} + \frac{b x \log{\left(x \right)}}{a^{3} \sqrt{x} + a^{2} b x} - \frac{2 b x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{3} \sqrt{x} + a^{2} b x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x, Eq(a, 0) & Eq(b, 0)), (log(x)/a**2, Eq(b, 0)), (-1/(b**2*x), Eq(a, 0)), (a*sqrt(x)*log(x)/(a**3*sqrt(x) + a**2*b*x) - 2*a*sqrt(x)*log(a/b + sqrt(x))/(a**3*sqrt(x) + a**2*b*x) + 2*a*sqrt(x)/(a**3*sqrt(x) + a**2*b*x) + b*x*log(x)/(a**3*sqrt(x) + a**2*b*x) - 2*b*x*log(a/b + sqrt(x))/(a**3*sqrt(x) + a**2*b*x), True))","A",0
2204,1,238,0,1.823229," ","integrate(1/x**2/(a+b*x**(1/2))**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{2}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{a^{2} x} & \text{for}\: b = 0 \\- \frac{1}{2 b^{2} x^{2}} & \text{for}\: a = 0 \\- \frac{a^{3} \sqrt{x}}{a^{5} x^{\frac{3}{2}} + a^{4} b x^{2}} + \frac{3 a^{2} b x}{a^{5} x^{\frac{3}{2}} + a^{4} b x^{2}} + \frac{3 a b^{2} x^{\frac{3}{2}} \log{\left(x \right)}}{a^{5} x^{\frac{3}{2}} + a^{4} b x^{2}} - \frac{6 a b^{2} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{5} x^{\frac{3}{2}} + a^{4} b x^{2}} + \frac{6 a b^{2} x^{\frac{3}{2}}}{a^{5} x^{\frac{3}{2}} + a^{4} b x^{2}} + \frac{3 b^{3} x^{2} \log{\left(x \right)}}{a^{5} x^{\frac{3}{2}} + a^{4} b x^{2}} - \frac{6 b^{3} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{5} x^{\frac{3}{2}} + a^{4} b x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**2, Eq(a, 0) & Eq(b, 0)), (-1/(a**2*x), Eq(b, 0)), (-1/(2*b**2*x**2), Eq(a, 0)), (-a**3*sqrt(x)/(a**5*x**(3/2) + a**4*b*x**2) + 3*a**2*b*x/(a**5*x**(3/2) + a**4*b*x**2) + 3*a*b**2*x**(3/2)*log(x)/(a**5*x**(3/2) + a**4*b*x**2) - 6*a*b**2*x**(3/2)*log(a/b + sqrt(x))/(a**5*x**(3/2) + a**4*b*x**2) + 6*a*b**2*x**(3/2)/(a**5*x**(3/2) + a**4*b*x**2) + 3*b**3*x**2*log(x)/(a**5*x**(3/2) + a**4*b*x**2) - 6*b**3*x**2*log(a/b + sqrt(x))/(a**5*x**(3/2) + a**4*b*x**2), True))","A",0
2205,1,333,0,4.073916," ","integrate(1/x**3/(a+b*x**(1/2))**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{3}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{3 b^{2} x^{3}} & \text{for}\: a = 0 \\- \frac{1}{2 a^{2} x^{2}} & \text{for}\: b = 0 \\- \frac{3 a^{5} \sqrt{x}}{6 a^{7} x^{\frac{5}{2}} + 6 a^{6} b x^{3}} + \frac{5 a^{4} b x}{6 a^{7} x^{\frac{5}{2}} + 6 a^{6} b x^{3}} - \frac{10 a^{3} b^{2} x^{\frac{3}{2}}}{6 a^{7} x^{\frac{5}{2}} + 6 a^{6} b x^{3}} + \frac{30 a^{2} b^{3} x^{2}}{6 a^{7} x^{\frac{5}{2}} + 6 a^{6} b x^{3}} + \frac{30 a b^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{6 a^{7} x^{\frac{5}{2}} + 6 a^{6} b x^{3}} - \frac{60 a b^{4} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{7} x^{\frac{5}{2}} + 6 a^{6} b x^{3}} + \frac{60 a b^{4} x^{\frac{5}{2}}}{6 a^{7} x^{\frac{5}{2}} + 6 a^{6} b x^{3}} + \frac{30 b^{5} x^{3} \log{\left(x \right)}}{6 a^{7} x^{\frac{5}{2}} + 6 a^{6} b x^{3}} - \frac{60 b^{5} x^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{7} x^{\frac{5}{2}} + 6 a^{6} b x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**3, Eq(a, 0) & Eq(b, 0)), (-1/(3*b**2*x**3), Eq(a, 0)), (-1/(2*a**2*x**2), Eq(b, 0)), (-3*a**5*sqrt(x)/(6*a**7*x**(5/2) + 6*a**6*b*x**3) + 5*a**4*b*x/(6*a**7*x**(5/2) + 6*a**6*b*x**3) - 10*a**3*b**2*x**(3/2)/(6*a**7*x**(5/2) + 6*a**6*b*x**3) + 30*a**2*b**3*x**2/(6*a**7*x**(5/2) + 6*a**6*b*x**3) + 30*a*b**4*x**(5/2)*log(x)/(6*a**7*x**(5/2) + 6*a**6*b*x**3) - 60*a*b**4*x**(5/2)*log(a/b + sqrt(x))/(6*a**7*x**(5/2) + 6*a**6*b*x**3) + 60*a*b**4*x**(5/2)/(6*a**7*x**(5/2) + 6*a**6*b*x**3) + 30*b**5*x**3*log(x)/(6*a**7*x**(5/2) + 6*a**6*b*x**3) - 60*b**5*x**3*log(a/b + sqrt(x))/(6*a**7*x**(5/2) + 6*a**6*b*x**3), True))","A",0
2206,1,400,0,5.649001," ","integrate(1/x**4/(a+b*x**(1/2))**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{4}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{4 b^{2} x^{4}} & \text{for}\: a = 0 \\- \frac{1}{3 a^{2} x^{3}} & \text{for}\: b = 0 \\- \frac{10 a^{7} \sqrt{x}}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} + \frac{14 a^{6} b x}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} - \frac{21 a^{5} b^{2} x^{\frac{3}{2}}}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} + \frac{35 a^{4} b^{3} x^{2}}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} - \frac{70 a^{3} b^{4} x^{\frac{5}{2}}}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} + \frac{210 a^{2} b^{5} x^{3}}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} + \frac{210 a b^{6} x^{\frac{7}{2}} \log{\left(x \right)}}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} - \frac{420 a b^{6} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} + \frac{420 a b^{6} x^{\frac{7}{2}}}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} + \frac{210 b^{7} x^{4} \log{\left(x \right)}}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} - \frac{420 b^{7} x^{4} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{30 a^{9} x^{\frac{7}{2}} + 30 a^{8} b x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**4, Eq(a, 0) & Eq(b, 0)), (-1/(4*b**2*x**4), Eq(a, 0)), (-1/(3*a**2*x**3), Eq(b, 0)), (-10*a**7*sqrt(x)/(30*a**9*x**(7/2) + 30*a**8*b*x**4) + 14*a**6*b*x/(30*a**9*x**(7/2) + 30*a**8*b*x**4) - 21*a**5*b**2*x**(3/2)/(30*a**9*x**(7/2) + 30*a**8*b*x**4) + 35*a**4*b**3*x**2/(30*a**9*x**(7/2) + 30*a**8*b*x**4) - 70*a**3*b**4*x**(5/2)/(30*a**9*x**(7/2) + 30*a**8*b*x**4) + 210*a**2*b**5*x**3/(30*a**9*x**(7/2) + 30*a**8*b*x**4) + 210*a*b**6*x**(7/2)*log(x)/(30*a**9*x**(7/2) + 30*a**8*b*x**4) - 420*a*b**6*x**(7/2)*log(a/b + sqrt(x))/(30*a**9*x**(7/2) + 30*a**8*b*x**4) + 420*a*b**6*x**(7/2)/(30*a**9*x**(7/2) + 30*a**8*b*x**4) + 210*b**7*x**4*log(x)/(30*a**9*x**(7/2) + 30*a**8*b*x**4) - 420*b**7*x**4*log(a/b + sqrt(x))/(30*a**9*x**(7/2) + 30*a**8*b*x**4), True))","A",0
2207,1,413,0,3.159618," ","integrate(x**3/(a+b*x**(1/2))**3,x)","\begin{cases} - \frac{420 a^{7} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{10 a^{2} b^{8} + 20 a b^{9} \sqrt{x} + 10 b^{10} x} - \frac{630 a^{7}}{10 a^{2} b^{8} + 20 a b^{9} \sqrt{x} + 10 b^{10} x} - \frac{840 a^{6} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{10 a^{2} b^{8} + 20 a b^{9} \sqrt{x} + 10 b^{10} x} - \frac{840 a^{6} b \sqrt{x}}{10 a^{2} b^{8} + 20 a b^{9} \sqrt{x} + 10 b^{10} x} - \frac{420 a^{5} b^{2} x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{10 a^{2} b^{8} + 20 a b^{9} \sqrt{x} + 10 b^{10} x} + \frac{140 a^{4} b^{3} x^{\frac{3}{2}}}{10 a^{2} b^{8} + 20 a b^{9} \sqrt{x} + 10 b^{10} x} - \frac{35 a^{3} b^{4} x^{2}}{10 a^{2} b^{8} + 20 a b^{9} \sqrt{x} + 10 b^{10} x} + \frac{14 a^{2} b^{5} x^{\frac{5}{2}}}{10 a^{2} b^{8} + 20 a b^{9} \sqrt{x} + 10 b^{10} x} - \frac{7 a b^{6} x^{3}}{10 a^{2} b^{8} + 20 a b^{9} \sqrt{x} + 10 b^{10} x} + \frac{4 b^{7} x^{\frac{7}{2}}}{10 a^{2} b^{8} + 20 a b^{9} \sqrt{x} + 10 b^{10} x} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-420*a**7*log(a/b + sqrt(x))/(10*a**2*b**8 + 20*a*b**9*sqrt(x) + 10*b**10*x) - 630*a**7/(10*a**2*b**8 + 20*a*b**9*sqrt(x) + 10*b**10*x) - 840*a**6*b*sqrt(x)*log(a/b + sqrt(x))/(10*a**2*b**8 + 20*a*b**9*sqrt(x) + 10*b**10*x) - 840*a**6*b*sqrt(x)/(10*a**2*b**8 + 20*a*b**9*sqrt(x) + 10*b**10*x) - 420*a**5*b**2*x*log(a/b + sqrt(x))/(10*a**2*b**8 + 20*a*b**9*sqrt(x) + 10*b**10*x) + 140*a**4*b**3*x**(3/2)/(10*a**2*b**8 + 20*a*b**9*sqrt(x) + 10*b**10*x) - 35*a**3*b**4*x**2/(10*a**2*b**8 + 20*a*b**9*sqrt(x) + 10*b**10*x) + 14*a**2*b**5*x**(5/2)/(10*a**2*b**8 + 20*a*b**9*sqrt(x) + 10*b**10*x) - 7*a*b**6*x**3/(10*a**2*b**8 + 20*a*b**9*sqrt(x) + 10*b**10*x) + 4*b**7*x**(7/2)/(10*a**2*b**8 + 20*a*b**9*sqrt(x) + 10*b**10*x), Ne(b, 0)), (x**4/(4*a**3), True))","A",0
2208,1,333,0,1.457247," ","integrate(x**2/(a+b*x**(1/2))**3,x)","\begin{cases} - \frac{60 a^{5} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{3 a^{2} b^{6} + 6 a b^{7} \sqrt{x} + 3 b^{8} x} - \frac{90 a^{5}}{3 a^{2} b^{6} + 6 a b^{7} \sqrt{x} + 3 b^{8} x} - \frac{120 a^{4} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{3 a^{2} b^{6} + 6 a b^{7} \sqrt{x} + 3 b^{8} x} - \frac{120 a^{4} b \sqrt{x}}{3 a^{2} b^{6} + 6 a b^{7} \sqrt{x} + 3 b^{8} x} - \frac{60 a^{3} b^{2} x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{3 a^{2} b^{6} + 6 a b^{7} \sqrt{x} + 3 b^{8} x} + \frac{20 a^{2} b^{3} x^{\frac{3}{2}}}{3 a^{2} b^{6} + 6 a b^{7} \sqrt{x} + 3 b^{8} x} - \frac{5 a b^{4} x^{2}}{3 a^{2} b^{6} + 6 a b^{7} \sqrt{x} + 3 b^{8} x} + \frac{2 b^{5} x^{\frac{5}{2}}}{3 a^{2} b^{6} + 6 a b^{7} \sqrt{x} + 3 b^{8} x} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-60*a**5*log(a/b + sqrt(x))/(3*a**2*b**6 + 6*a*b**7*sqrt(x) + 3*b**8*x) - 90*a**5/(3*a**2*b**6 + 6*a*b**7*sqrt(x) + 3*b**8*x) - 120*a**4*b*sqrt(x)*log(a/b + sqrt(x))/(3*a**2*b**6 + 6*a*b**7*sqrt(x) + 3*b**8*x) - 120*a**4*b*sqrt(x)/(3*a**2*b**6 + 6*a*b**7*sqrt(x) + 3*b**8*x) - 60*a**3*b**2*x*log(a/b + sqrt(x))/(3*a**2*b**6 + 6*a*b**7*sqrt(x) + 3*b**8*x) + 20*a**2*b**3*x**(3/2)/(3*a**2*b**6 + 6*a*b**7*sqrt(x) + 3*b**8*x) - 5*a*b**4*x**2/(3*a**2*b**6 + 6*a*b**7*sqrt(x) + 3*b**8*x) + 2*b**5*x**(5/2)/(3*a**2*b**6 + 6*a*b**7*sqrt(x) + 3*b**8*x), Ne(b, 0)), (x**3/(3*a**3), True))","A",0
2209,1,233,0,0.949864," ","integrate(x/(a+b*x**(1/2))**3,x)","\begin{cases} - \frac{6 a^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{2} b^{4} + 2 a b^{5} \sqrt{x} + b^{6} x} - \frac{9 a^{3}}{a^{2} b^{4} + 2 a b^{5} \sqrt{x} + b^{6} x} - \frac{12 a^{2} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{2} b^{4} + 2 a b^{5} \sqrt{x} + b^{6} x} - \frac{12 a^{2} b \sqrt{x}}{a^{2} b^{4} + 2 a b^{5} \sqrt{x} + b^{6} x} - \frac{6 a b^{2} x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{2} b^{4} + 2 a b^{5} \sqrt{x} + b^{6} x} + \frac{2 b^{3} x^{\frac{3}{2}}}{a^{2} b^{4} + 2 a b^{5} \sqrt{x} + b^{6} x} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a**3*log(a/b + sqrt(x))/(a**2*b**4 + 2*a*b**5*sqrt(x) + b**6*x) - 9*a**3/(a**2*b**4 + 2*a*b**5*sqrt(x) + b**6*x) - 12*a**2*b*sqrt(x)*log(a/b + sqrt(x))/(a**2*b**4 + 2*a*b**5*sqrt(x) + b**6*x) - 12*a**2*b*sqrt(x)/(a**2*b**4 + 2*a*b**5*sqrt(x) + b**6*x) - 6*a*b**2*x*log(a/b + sqrt(x))/(a**2*b**4 + 2*a*b**5*sqrt(x) + b**6*x) + 2*b**3*x**(3/2)/(a**2*b**4 + 2*a*b**5*sqrt(x) + b**6*x), Ne(b, 0)), (x**2/(2*a**3), True))","A",0
2210,1,63,0,1.149784," ","integrate(1/(a+b*x**(1/2))**3,x)","\begin{cases} - \frac{a}{a^{2} b^{2} + 2 a b^{3} \sqrt{x} + b^{4} x} - \frac{2 b \sqrt{x}}{a^{2} b^{2} + 2 a b^{3} \sqrt{x} + b^{4} x} & \text{for}\: b \neq 0 \\\frac{x}{a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(a**2*b**2 + 2*a*b**3*sqrt(x) + b**4*x) - 2*b*sqrt(x)/(a**2*b**2 + 2*a*b**3*sqrt(x) + b**4*x), Ne(b, 0)), (x/a**3, True))","A",0
2211,1,364,0,2.594379," ","integrate(1/x/(a+b*x**(1/2))**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\log{\left(x \right)}}{a^{3}} & \text{for}\: b = 0 \\- \frac{2}{3 b^{3} x^{\frac{3}{2}}} & \text{for}\: a = 0 \\\frac{a^{2} \sqrt{x} \log{\left(x \right)}}{a^{5} \sqrt{x} + 2 a^{4} b x + a^{3} b^{2} x^{\frac{3}{2}}} - \frac{2 a^{2} \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{5} \sqrt{x} + 2 a^{4} b x + a^{3} b^{2} x^{\frac{3}{2}}} + \frac{3 a^{2} \sqrt{x}}{a^{5} \sqrt{x} + 2 a^{4} b x + a^{3} b^{2} x^{\frac{3}{2}}} + \frac{2 a b x \log{\left(x \right)}}{a^{5} \sqrt{x} + 2 a^{4} b x + a^{3} b^{2} x^{\frac{3}{2}}} - \frac{4 a b x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{5} \sqrt{x} + 2 a^{4} b x + a^{3} b^{2} x^{\frac{3}{2}}} + \frac{2 a b x}{a^{5} \sqrt{x} + 2 a^{4} b x + a^{3} b^{2} x^{\frac{3}{2}}} + \frac{b^{2} x^{\frac{3}{2}} \log{\left(x \right)}}{a^{5} \sqrt{x} + 2 a^{4} b x + a^{3} b^{2} x^{\frac{3}{2}}} - \frac{2 b^{2} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{5} \sqrt{x} + 2 a^{4} b x + a^{3} b^{2} x^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (log(x)/a**3, Eq(b, 0)), (-2/(3*b**3*x**(3/2)), Eq(a, 0)), (a**2*sqrt(x)*log(x)/(a**5*sqrt(x) + 2*a**4*b*x + a**3*b**2*x**(3/2)) - 2*a**2*sqrt(x)*log(a/b + sqrt(x))/(a**5*sqrt(x) + 2*a**4*b*x + a**3*b**2*x**(3/2)) + 3*a**2*sqrt(x)/(a**5*sqrt(x) + 2*a**4*b*x + a**3*b**2*x**(3/2)) + 2*a*b*x*log(x)/(a**5*sqrt(x) + 2*a**4*b*x + a**3*b**2*x**(3/2)) - 4*a*b*x*log(a/b + sqrt(x))/(a**5*sqrt(x) + 2*a**4*b*x + a**3*b**2*x**(3/2)) + 2*a*b*x/(a**5*sqrt(x) + 2*a**4*b*x + a**3*b**2*x**(3/2)) + b**2*x**(3/2)*log(x)/(a**5*sqrt(x) + 2*a**4*b*x + a**3*b**2*x**(3/2)) - 2*b**2*x**(3/2)*log(a/b + sqrt(x))/(a**5*sqrt(x) + 2*a**4*b*x + a**3*b**2*x**(3/2)), True))","A",0
2212,1,481,0,4.983529," ","integrate(1/x**2/(a+b*x**(1/2))**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{a^{3} x} & \text{for}\: b = 0 \\- \frac{2}{5 b^{3} x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{a^{4} \sqrt{x}}{a^{7} x^{\frac{3}{2}} + 2 a^{6} b x^{2} + a^{5} b^{2} x^{\frac{5}{2}}} + \frac{4 a^{3} b x}{a^{7} x^{\frac{3}{2}} + 2 a^{6} b x^{2} + a^{5} b^{2} x^{\frac{5}{2}}} + \frac{6 a^{2} b^{2} x^{\frac{3}{2}} \log{\left(x \right)}}{a^{7} x^{\frac{3}{2}} + 2 a^{6} b x^{2} + a^{5} b^{2} x^{\frac{5}{2}}} - \frac{12 a^{2} b^{2} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{7} x^{\frac{3}{2}} + 2 a^{6} b x^{2} + a^{5} b^{2} x^{\frac{5}{2}}} + \frac{18 a^{2} b^{2} x^{\frac{3}{2}}}{a^{7} x^{\frac{3}{2}} + 2 a^{6} b x^{2} + a^{5} b^{2} x^{\frac{5}{2}}} + \frac{12 a b^{3} x^{2} \log{\left(x \right)}}{a^{7} x^{\frac{3}{2}} + 2 a^{6} b x^{2} + a^{5} b^{2} x^{\frac{5}{2}}} - \frac{24 a b^{3} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{7} x^{\frac{3}{2}} + 2 a^{6} b x^{2} + a^{5} b^{2} x^{\frac{5}{2}}} + \frac{12 a b^{3} x^{2}}{a^{7} x^{\frac{3}{2}} + 2 a^{6} b x^{2} + a^{5} b^{2} x^{\frac{5}{2}}} + \frac{6 b^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{a^{7} x^{\frac{3}{2}} + 2 a^{6} b x^{2} + a^{5} b^{2} x^{\frac{5}{2}}} - \frac{12 b^{4} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{a^{7} x^{\frac{3}{2}} + 2 a^{6} b x^{2} + a^{5} b^{2} x^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-1/(a**3*x), Eq(b, 0)), (-2/(5*b**3*x**(5/2)), Eq(a, 0)), (-a**4*sqrt(x)/(a**7*x**(3/2) + 2*a**6*b*x**2 + a**5*b**2*x**(5/2)) + 4*a**3*b*x/(a**7*x**(3/2) + 2*a**6*b*x**2 + a**5*b**2*x**(5/2)) + 6*a**2*b**2*x**(3/2)*log(x)/(a**7*x**(3/2) + 2*a**6*b*x**2 + a**5*b**2*x**(5/2)) - 12*a**2*b**2*x**(3/2)*log(a/b + sqrt(x))/(a**7*x**(3/2) + 2*a**6*b*x**2 + a**5*b**2*x**(5/2)) + 18*a**2*b**2*x**(3/2)/(a**7*x**(3/2) + 2*a**6*b*x**2 + a**5*b**2*x**(5/2)) + 12*a*b**3*x**2*log(x)/(a**7*x**(3/2) + 2*a**6*b*x**2 + a**5*b**2*x**(5/2)) - 24*a*b**3*x**2*log(a/b + sqrt(x))/(a**7*x**(3/2) + 2*a**6*b*x**2 + a**5*b**2*x**(5/2)) + 12*a*b**3*x**2/(a**7*x**(3/2) + 2*a**6*b*x**2 + a**5*b**2*x**(5/2)) + 6*b**4*x**(5/2)*log(x)/(a**7*x**(3/2) + 2*a**6*b*x**2 + a**5*b**2*x**(5/2)) - 12*b**4*x**(5/2)*log(a/b + sqrt(x))/(a**7*x**(3/2) + 2*a**6*b*x**2 + a**5*b**2*x**(5/2)), True))","A",0
2213,1,612,0,11.058365," ","integrate(1/x**3/(a+b*x**(1/2))**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{7 b^{3} x^{\frac{7}{2}}} & \text{for}\: a = 0 \\- \frac{1}{2 a^{3} x^{2}} & \text{for}\: b = 0 \\- \frac{a^{6} \sqrt{x}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} + \frac{2 a^{5} b x}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} - \frac{5 a^{4} b^{2} x^{\frac{3}{2}}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} + \frac{20 a^{3} b^{3} x^{2}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} + \frac{30 a^{2} b^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} - \frac{60 a^{2} b^{4} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} + \frac{90 a^{2} b^{4} x^{\frac{5}{2}}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} + \frac{60 a b^{5} x^{3} \log{\left(x \right)}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} - \frac{120 a b^{5} x^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} + \frac{60 a b^{5} x^{3}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} + \frac{30 b^{6} x^{\frac{7}{2}} \log{\left(x \right)}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} - \frac{60 b^{6} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{2 a^{9} x^{\frac{5}{2}} + 4 a^{8} b x^{3} + 2 a^{7} b^{2} x^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (-2/(7*b**3*x**(7/2)), Eq(a, 0)), (-1/(2*a**3*x**2), Eq(b, 0)), (-a**6*sqrt(x)/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) + 2*a**5*b*x/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) - 5*a**4*b**2*x**(3/2)/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) + 20*a**3*b**3*x**2/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) + 30*a**2*b**4*x**(5/2)*log(x)/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) - 60*a**2*b**4*x**(5/2)*log(a/b + sqrt(x))/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) + 90*a**2*b**4*x**(5/2)/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) + 60*a*b**5*x**3*log(x)/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) - 120*a*b**5*x**3*log(a/b + sqrt(x))/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) + 60*a*b**5*x**3/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) + 30*b**6*x**(7/2)*log(x)/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)) - 60*b**6*x**(7/2)*log(a/b + sqrt(x))/(2*a**9*x**(5/2) + 4*a**8*b*x**3 + 2*a**7*b**2*x**(7/2)), True))","A",0
2214,1,707,0,19.334545," ","integrate(1/x**4/(a+b*x**(1/2))**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{9}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{3 a^{3} x^{3}} & \text{for}\: b = 0 \\- \frac{2}{9 b^{3} x^{\frac{9}{2}}} & \text{for}\: a = 0 \\- \frac{5 a^{8} \sqrt{x}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} + \frac{8 a^{7} b x}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} - \frac{14 a^{6} b^{2} x^{\frac{3}{2}}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} + \frac{28 a^{5} b^{3} x^{2}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} - \frac{70 a^{4} b^{4} x^{\frac{5}{2}}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} + \frac{280 a^{3} b^{5} x^{3}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} + \frac{420 a^{2} b^{6} x^{\frac{7}{2}} \log{\left(x \right)}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} - \frac{840 a^{2} b^{6} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} + \frac{1260 a^{2} b^{6} x^{\frac{7}{2}}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} + \frac{840 a b^{7} x^{4} \log{\left(x \right)}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} - \frac{1680 a b^{7} x^{4} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} + \frac{840 a b^{7} x^{4}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} + \frac{420 b^{8} x^{\frac{9}{2}} \log{\left(x \right)}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} - \frac{840 b^{8} x^{\frac{9}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{15 a^{11} x^{\frac{7}{2}} + 30 a^{10} b x^{4} + 15 a^{9} b^{2} x^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(9/2), Eq(a, 0) & Eq(b, 0)), (-1/(3*a**3*x**3), Eq(b, 0)), (-2/(9*b**3*x**(9/2)), Eq(a, 0)), (-5*a**8*sqrt(x)/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) + 8*a**7*b*x/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) - 14*a**6*b**2*x**(3/2)/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) + 28*a**5*b**3*x**2/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) - 70*a**4*b**4*x**(5/2)/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) + 280*a**3*b**5*x**3/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) + 420*a**2*b**6*x**(7/2)*log(x)/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) - 840*a**2*b**6*x**(7/2)*log(a/b + sqrt(x))/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) + 1260*a**2*b**6*x**(7/2)/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) + 840*a*b**7*x**4*log(x)/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) - 1680*a*b**7*x**4*log(a/b + sqrt(x))/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) + 840*a*b**7*x**4/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) + 420*b**8*x**(9/2)*log(x)/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)) - 840*b**8*x**(9/2)*log(a/b + sqrt(x))/(15*a**11*x**(7/2) + 30*a**10*b*x**4 + 15*a**9*b**2*x**(9/2)), True))","A",0
2215,1,949,0,5.948234," ","integrate(x**4/(a+b*x**(1/2))**5,x)","\begin{cases} - \frac{2520 a^{9} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} - \frac{5250 a^{9}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} - \frac{10080 a^{8} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} - \frac{18480 a^{8} b \sqrt{x}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} - \frac{15120 a^{7} b^{2} x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} - \frac{22680 a^{7} b^{2} x}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} - \frac{10080 a^{6} b^{3} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} - \frac{10080 a^{6} b^{3} x^{\frac{3}{2}}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} - \frac{2520 a^{5} b^{4} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} + \frac{504 a^{4} b^{5} x^{\frac{5}{2}}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} - \frac{84 a^{3} b^{6} x^{3}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} + \frac{24 a^{2} b^{7} x^{\frac{7}{2}}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} - \frac{9 a b^{8} x^{4}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} + \frac{4 b^{9} x^{\frac{9}{2}}}{10 a^{4} b^{10} + 40 a^{3} b^{11} \sqrt{x} + 60 a^{2} b^{12} x + 40 a b^{13} x^{\frac{3}{2}} + 10 b^{14} x^{2}} & \text{for}\: b \neq 0 \\\frac{x^{5}}{5 a^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2520*a**9*log(a/b + sqrt(x))/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) - 5250*a**9/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) - 10080*a**8*b*sqrt(x)*log(a/b + sqrt(x))/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) - 18480*a**8*b*sqrt(x)/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) - 15120*a**7*b**2*x*log(a/b + sqrt(x))/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) - 22680*a**7*b**2*x/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) - 10080*a**6*b**3*x**(3/2)*log(a/b + sqrt(x))/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) - 10080*a**6*b**3*x**(3/2)/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) - 2520*a**5*b**4*x**2*log(a/b + sqrt(x))/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) + 504*a**4*b**5*x**(5/2)/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) - 84*a**3*b**6*x**3/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) + 24*a**2*b**7*x**(7/2)/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) - 9*a*b**8*x**4/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2) + 4*b**9*x**(9/2)/(10*a**4*b**10 + 40*a**3*b**11*sqrt(x) + 60*a**2*b**12*x + 40*a*b**13*x**(3/2) + 10*b**14*x**2), Ne(b, 0)), (x**5/(5*a**5), True))","A",0
2216,1,818,0,3.027221," ","integrate(x**3/(a+b*x**(1/2))**5,x)","\begin{cases} - \frac{420 a^{7} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} - \frac{875 a^{7}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} - \frac{1680 a^{6} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} - \frac{3080 a^{6} b \sqrt{x}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} - \frac{2520 a^{5} b^{2} x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} - \frac{3780 a^{5} b^{2} x}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} - \frac{1680 a^{4} b^{3} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} - \frac{1680 a^{4} b^{3} x^{\frac{3}{2}}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} - \frac{420 a^{3} b^{4} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} + \frac{84 a^{2} b^{5} x^{\frac{5}{2}}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} - \frac{14 a b^{6} x^{3}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} + \frac{4 b^{7} x^{\frac{7}{2}}}{6 a^{4} b^{8} + 24 a^{3} b^{9} \sqrt{x} + 36 a^{2} b^{10} x + 24 a b^{11} x^{\frac{3}{2}} + 6 b^{12} x^{2}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-420*a**7*log(a/b + sqrt(x))/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) - 875*a**7/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) - 1680*a**6*b*sqrt(x)*log(a/b + sqrt(x))/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) - 3080*a**6*b*sqrt(x)/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) - 2520*a**5*b**2*x*log(a/b + sqrt(x))/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) - 3780*a**5*b**2*x/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) - 1680*a**4*b**3*x**(3/2)*log(a/b + sqrt(x))/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) - 1680*a**4*b**3*x**(3/2)/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) - 420*a**3*b**4*x**2*log(a/b + sqrt(x))/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) + 84*a**2*b**5*x**(5/2)/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) - 14*a*b**6*x**3/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2) + 4*b**7*x**(7/2)/(6*a**4*b**8 + 24*a**3*b**9*sqrt(x) + 36*a**2*b**10*x + 24*a*b**11*x**(3/2) + 6*b**12*x**2), Ne(b, 0)), (x**4/(4*a**5), True))","A",0
2217,1,687,0,2.165881," ","integrate(x**2/(a+b*x**(1/2))**5,x)","\begin{cases} - \frac{60 a^{5} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{4} b^{6} + 24 a^{3} b^{7} \sqrt{x} + 36 a^{2} b^{8} x + 24 a b^{9} x^{\frac{3}{2}} + 6 b^{10} x^{2}} - \frac{125 a^{5}}{6 a^{4} b^{6} + 24 a^{3} b^{7} \sqrt{x} + 36 a^{2} b^{8} x + 24 a b^{9} x^{\frac{3}{2}} + 6 b^{10} x^{2}} - \frac{240 a^{4} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{4} b^{6} + 24 a^{3} b^{7} \sqrt{x} + 36 a^{2} b^{8} x + 24 a b^{9} x^{\frac{3}{2}} + 6 b^{10} x^{2}} - \frac{440 a^{4} b \sqrt{x}}{6 a^{4} b^{6} + 24 a^{3} b^{7} \sqrt{x} + 36 a^{2} b^{8} x + 24 a b^{9} x^{\frac{3}{2}} + 6 b^{10} x^{2}} - \frac{360 a^{3} b^{2} x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{4} b^{6} + 24 a^{3} b^{7} \sqrt{x} + 36 a^{2} b^{8} x + 24 a b^{9} x^{\frac{3}{2}} + 6 b^{10} x^{2}} - \frac{540 a^{3} b^{2} x}{6 a^{4} b^{6} + 24 a^{3} b^{7} \sqrt{x} + 36 a^{2} b^{8} x + 24 a b^{9} x^{\frac{3}{2}} + 6 b^{10} x^{2}} - \frac{240 a^{2} b^{3} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{4} b^{6} + 24 a^{3} b^{7} \sqrt{x} + 36 a^{2} b^{8} x + 24 a b^{9} x^{\frac{3}{2}} + 6 b^{10} x^{2}} - \frac{240 a^{2} b^{3} x^{\frac{3}{2}}}{6 a^{4} b^{6} + 24 a^{3} b^{7} \sqrt{x} + 36 a^{2} b^{8} x + 24 a b^{9} x^{\frac{3}{2}} + 6 b^{10} x^{2}} - \frac{60 a b^{4} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{4} b^{6} + 24 a^{3} b^{7} \sqrt{x} + 36 a^{2} b^{8} x + 24 a b^{9} x^{\frac{3}{2}} + 6 b^{10} x^{2}} + \frac{12 b^{5} x^{\frac{5}{2}}}{6 a^{4} b^{6} + 24 a^{3} b^{7} \sqrt{x} + 36 a^{2} b^{8} x + 24 a b^{9} x^{\frac{3}{2}} + 6 b^{10} x^{2}} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-60*a**5*log(a/b + sqrt(x))/(6*a**4*b**6 + 24*a**3*b**7*sqrt(x) + 36*a**2*b**8*x + 24*a*b**9*x**(3/2) + 6*b**10*x**2) - 125*a**5/(6*a**4*b**6 + 24*a**3*b**7*sqrt(x) + 36*a**2*b**8*x + 24*a*b**9*x**(3/2) + 6*b**10*x**2) - 240*a**4*b*sqrt(x)*log(a/b + sqrt(x))/(6*a**4*b**6 + 24*a**3*b**7*sqrt(x) + 36*a**2*b**8*x + 24*a*b**9*x**(3/2) + 6*b**10*x**2) - 440*a**4*b*sqrt(x)/(6*a**4*b**6 + 24*a**3*b**7*sqrt(x) + 36*a**2*b**8*x + 24*a*b**9*x**(3/2) + 6*b**10*x**2) - 360*a**3*b**2*x*log(a/b + sqrt(x))/(6*a**4*b**6 + 24*a**3*b**7*sqrt(x) + 36*a**2*b**8*x + 24*a*b**9*x**(3/2) + 6*b**10*x**2) - 540*a**3*b**2*x/(6*a**4*b**6 + 24*a**3*b**7*sqrt(x) + 36*a**2*b**8*x + 24*a*b**9*x**(3/2) + 6*b**10*x**2) - 240*a**2*b**3*x**(3/2)*log(a/b + sqrt(x))/(6*a**4*b**6 + 24*a**3*b**7*sqrt(x) + 36*a**2*b**8*x + 24*a*b**9*x**(3/2) + 6*b**10*x**2) - 240*a**2*b**3*x**(3/2)/(6*a**4*b**6 + 24*a**3*b**7*sqrt(x) + 36*a**2*b**8*x + 24*a*b**9*x**(3/2) + 6*b**10*x**2) - 60*a*b**4*x**2*log(a/b + sqrt(x))/(6*a**4*b**6 + 24*a**3*b**7*sqrt(x) + 36*a**2*b**8*x + 24*a*b**9*x**(3/2) + 6*b**10*x**2) + 12*b**5*x**(5/2)/(6*a**4*b**6 + 24*a**3*b**7*sqrt(x) + 36*a**2*b**8*x + 24*a*b**9*x**(3/2) + 6*b**10*x**2), Ne(b, 0)), (x**3/(3*a**5), True))","A",0
2218,1,253,0,1.848035," ","integrate(x/(a+b*x**(1/2))**5,x)","\begin{cases} - \frac{a^{3}}{2 a^{4} b^{4} + 8 a^{3} b^{5} \sqrt{x} + 12 a^{2} b^{6} x + 8 a b^{7} x^{\frac{3}{2}} + 2 b^{8} x^{2}} - \frac{4 a^{2} b \sqrt{x}}{2 a^{4} b^{4} + 8 a^{3} b^{5} \sqrt{x} + 12 a^{2} b^{6} x + 8 a b^{7} x^{\frac{3}{2}} + 2 b^{8} x^{2}} - \frac{6 a b^{2} x}{2 a^{4} b^{4} + 8 a^{3} b^{5} \sqrt{x} + 12 a^{2} b^{6} x + 8 a b^{7} x^{\frac{3}{2}} + 2 b^{8} x^{2}} - \frac{4 b^{3} x^{\frac{3}{2}}}{2 a^{4} b^{4} + 8 a^{3} b^{5} \sqrt{x} + 12 a^{2} b^{6} x + 8 a b^{7} x^{\frac{3}{2}} + 2 b^{8} x^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3/(2*a**4*b**4 + 8*a**3*b**5*sqrt(x) + 12*a**2*b**6*x + 8*a*b**7*x**(3/2) + 2*b**8*x**2) - 4*a**2*b*sqrt(x)/(2*a**4*b**4 + 8*a**3*b**5*sqrt(x) + 12*a**2*b**6*x + 8*a*b**7*x**(3/2) + 2*b**8*x**2) - 6*a*b**2*x/(2*a**4*b**4 + 8*a**3*b**5*sqrt(x) + 12*a**2*b**6*x + 8*a*b**7*x**(3/2) + 2*b**8*x**2) - 4*b**3*x**(3/2)/(2*a**4*b**4 + 8*a**3*b**5*sqrt(x) + 12*a**2*b**6*x + 8*a*b**7*x**(3/2) + 2*b**8*x**2), Ne(b, 0)), (x**2/(2*a**5), True))","A",0
2219,1,121,0,1.808925," ","integrate(1/(a+b*x**(1/2))**5,x)","\begin{cases} - \frac{a}{6 a^{4} b^{2} + 24 a^{3} b^{3} \sqrt{x} + 36 a^{2} b^{4} x + 24 a b^{5} x^{\frac{3}{2}} + 6 b^{6} x^{2}} - \frac{4 b \sqrt{x}}{6 a^{4} b^{2} + 24 a^{3} b^{3} \sqrt{x} + 36 a^{2} b^{4} x + 24 a b^{5} x^{\frac{3}{2}} + 6 b^{6} x^{2}} & \text{for}\: b \neq 0 \\\frac{x}{a^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(6*a**4*b**2 + 24*a**3*b**3*sqrt(x) + 36*a**2*b**4*x + 24*a*b**5*x**(3/2) + 6*b**6*x**2) - 4*b*sqrt(x)/(6*a**4*b**2 + 24*a**3*b**3*sqrt(x) + 36*a**2*b**4*x + 24*a*b**5*x**(3/2) + 6*b**6*x**2), Ne(b, 0)), (x/a**5, True))","A",0
2220,1,1049,0,5.827944," ","integrate(1/x/(a+b*x**(1/2))**5,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\log{\left(x \right)}}{a^{5}} & \text{for}\: b = 0 \\- \frac{2}{5 b^{5} x^{\frac{5}{2}}} & \text{for}\: a = 0 \\\frac{6 a^{4} \sqrt{x} \log{\left(x \right)}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} - \frac{12 a^{4} \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} + \frac{25 a^{4} \sqrt{x}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} + \frac{24 a^{3} b x \log{\left(x \right)}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} - \frac{48 a^{3} b x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} + \frac{52 a^{3} b x}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} + \frac{36 a^{2} b^{2} x^{\frac{3}{2}} \log{\left(x \right)}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} - \frac{72 a^{2} b^{2} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} + \frac{42 a^{2} b^{2} x^{\frac{3}{2}}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} + \frac{24 a b^{3} x^{2} \log{\left(x \right)}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} - \frac{48 a b^{3} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} + \frac{12 a b^{3} x^{2}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} + \frac{6 b^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} - \frac{12 b^{4} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{9} \sqrt{x} + 24 a^{8} b x + 36 a^{7} b^{2} x^{\frac{3}{2}} + 24 a^{6} b^{3} x^{2} + 6 a^{5} b^{4} x^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (log(x)/a**5, Eq(b, 0)), (-2/(5*b**5*x**(5/2)), Eq(a, 0)), (6*a**4*sqrt(x)*log(x)/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) - 12*a**4*sqrt(x)*log(a/b + sqrt(x))/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) + 25*a**4*sqrt(x)/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) + 24*a**3*b*x*log(x)/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) - 48*a**3*b*x*log(a/b + sqrt(x))/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) + 52*a**3*b*x/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) + 36*a**2*b**2*x**(3/2)*log(x)/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) - 72*a**2*b**2*x**(3/2)*log(a/b + sqrt(x))/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) + 42*a**2*b**2*x**(3/2)/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) + 24*a*b**3*x**2*log(x)/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) - 48*a*b**3*x**2*log(a/b + sqrt(x))/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) + 12*a*b**3*x**2/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) + 6*b**4*x**(5/2)*log(x)/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)) - 12*b**4*x**(5/2)*log(a/b + sqrt(x))/(6*a**9*sqrt(x) + 24*a**8*b*x + 36*a**7*b**2*x**(3/2) + 24*a**6*b**3*x**2 + 6*a**5*b**4*x**(5/2)), True))","A",0
2221,1,1232,0,12.840447," ","integrate(1/x**2/(a+b*x**(1/2))**5,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{a^{5} x} & \text{for}\: b = 0 \\- \frac{2}{7 b^{5} x^{\frac{7}{2}}} & \text{for}\: a = 0 \\- \frac{2 a^{6} \sqrt{x}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} + \frac{12 a^{5} b x}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} + \frac{30 a^{4} b^{2} x^{\frac{3}{2}} \log{\left(x \right)}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} - \frac{60 a^{4} b^{2} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} + \frac{125 a^{4} b^{2} x^{\frac{3}{2}}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} + \frac{120 a^{3} b^{3} x^{2} \log{\left(x \right)}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} - \frac{240 a^{3} b^{3} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} + \frac{260 a^{3} b^{3} x^{2}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} + \frac{180 a^{2} b^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} - \frac{360 a^{2} b^{4} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} + \frac{210 a^{2} b^{4} x^{\frac{5}{2}}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} + \frac{120 a b^{5} x^{3} \log{\left(x \right)}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} - \frac{240 a b^{5} x^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} + \frac{60 a b^{5} x^{3}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} + \frac{30 b^{6} x^{\frac{7}{2}} \log{\left(x \right)}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} - \frac{60 b^{6} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{2 a^{11} x^{\frac{3}{2}} + 8 a^{10} b x^{2} + 12 a^{9} b^{2} x^{\frac{5}{2}} + 8 a^{8} b^{3} x^{3} + 2 a^{7} b^{4} x^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (-1/(a**5*x), Eq(b, 0)), (-2/(7*b**5*x**(7/2)), Eq(a, 0)), (-2*a**6*sqrt(x)/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) + 12*a**5*b*x/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) + 30*a**4*b**2*x**(3/2)*log(x)/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) - 60*a**4*b**2*x**(3/2)*log(a/b + sqrt(x))/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) + 125*a**4*b**2*x**(3/2)/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) + 120*a**3*b**3*x**2*log(x)/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) - 240*a**3*b**3*x**2*log(a/b + sqrt(x))/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) + 260*a**3*b**3*x**2/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) + 180*a**2*b**4*x**(5/2)*log(x)/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) - 360*a**2*b**4*x**(5/2)*log(a/b + sqrt(x))/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) + 210*a**2*b**4*x**(5/2)/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) + 120*a*b**5*x**3*log(x)/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) - 240*a*b**5*x**3*log(a/b + sqrt(x))/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) + 60*a*b**5*x**3/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) + 30*b**6*x**(7/2)*log(x)/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)) - 60*b**6*x**(7/2)*log(a/b + sqrt(x))/(2*a**11*x**(3/2) + 8*a**10*b*x**2 + 12*a**9*b**2*x**(5/2) + 8*a**8*b**3*x**3 + 2*a**7*b**4*x**(7/2)), True))","A",0
2222,1,1380,0,22.061005," ","integrate(1/x**3/(a+b*x**(1/2))**5,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{9}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{2 a^{5} x^{2}} & \text{for}\: b = 0 \\- \frac{2}{9 b^{5} x^{\frac{9}{2}}} & \text{for}\: a = 0 \\- \frac{3 a^{8} \sqrt{x}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{8 a^{7} b x}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} - \frac{28 a^{6} b^{2} x^{\frac{3}{2}}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{168 a^{5} b^{3} x^{2}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{420 a^{4} b^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} - \frac{840 a^{4} b^{4} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{1750 a^{4} b^{4} x^{\frac{5}{2}}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{1680 a^{3} b^{5} x^{3} \log{\left(x \right)}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} - \frac{3360 a^{3} b^{5} x^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{3640 a^{3} b^{5} x^{3}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{2520 a^{2} b^{6} x^{\frac{7}{2}} \log{\left(x \right)}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} - \frac{5040 a^{2} b^{6} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{2940 a^{2} b^{6} x^{\frac{7}{2}}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{1680 a b^{7} x^{4} \log{\left(x \right)}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} - \frac{3360 a b^{7} x^{4} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{840 a b^{7} x^{4}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} + \frac{420 b^{8} x^{\frac{9}{2}} \log{\left(x \right)}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} - \frac{840 b^{8} x^{\frac{9}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{6 a^{13} x^{\frac{5}{2}} + 24 a^{12} b x^{3} + 36 a^{11} b^{2} x^{\frac{7}{2}} + 24 a^{10} b^{3} x^{4} + 6 a^{9} b^{4} x^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(9/2), Eq(a, 0) & Eq(b, 0)), (-1/(2*a**5*x**2), Eq(b, 0)), (-2/(9*b**5*x**(9/2)), Eq(a, 0)), (-3*a**8*sqrt(x)/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 8*a**7*b*x/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) - 28*a**6*b**2*x**(3/2)/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 168*a**5*b**3*x**2/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 420*a**4*b**4*x**(5/2)*log(x)/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) - 840*a**4*b**4*x**(5/2)*log(a/b + sqrt(x))/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 1750*a**4*b**4*x**(5/2)/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 1680*a**3*b**5*x**3*log(x)/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) - 3360*a**3*b**5*x**3*log(a/b + sqrt(x))/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 3640*a**3*b**5*x**3/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 2520*a**2*b**6*x**(7/2)*log(x)/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) - 5040*a**2*b**6*x**(7/2)*log(a/b + sqrt(x))/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 2940*a**2*b**6*x**(7/2)/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 1680*a*b**7*x**4*log(x)/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) - 3360*a*b**7*x**4*log(a/b + sqrt(x))/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 840*a*b**7*x**4/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) + 420*b**8*x**(9/2)*log(x)/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)) - 840*b**8*x**(9/2)*log(a/b + sqrt(x))/(6*a**13*x**(5/2) + 24*a**12*b*x**3 + 36*a**11*b**2*x**(7/2) + 24*a**10*b**3*x**4 + 6*a**9*b**4*x**(9/2)), True))","A",0
2223,1,2048,0,14.039398," ","integrate(x**5/(a+b*x**(1/2))**8,x)","\begin{cases} \frac{27720 a^{11} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{71874 a^{11}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{194040 a^{10} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{475398 a^{10} b \sqrt{x}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{582120 a^{9} b^{2} x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{1329174 a^{9} b^{2} x}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{970200 a^{8} b^{3} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{2021250 a^{8} b^{3} x^{\frac{3}{2}}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{970200 a^{7} b^{4} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{1778700 a^{7} b^{4} x^{2}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{582120 a^{6} b^{5} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{873180 a^{6} b^{5} x^{\frac{5}{2}}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{194040 a^{5} b^{6} x^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{194040 a^{5} b^{6} x^{3}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{27720 a^{4} b^{7} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} - \frac{3465 a^{3} b^{8} x^{4}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{385 a^{2} b^{9} x^{\frac{9}{2}}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} - \frac{77 a b^{10} x^{5}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} + \frac{21 b^{11} x^{\frac{11}{2}}}{42 a^{7} b^{12} + 294 a^{6} b^{13} \sqrt{x} + 882 a^{5} b^{14} x + 1470 a^{4} b^{15} x^{\frac{3}{2}} + 1470 a^{3} b^{16} x^{2} + 882 a^{2} b^{17} x^{\frac{5}{2}} + 294 a b^{18} x^{3} + 42 b^{19} x^{\frac{7}{2}}} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((27720*a**11*log(a/b + sqrt(x))/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 71874*a**11/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 194040*a**10*b*sqrt(x)*log(a/b + sqrt(x))/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 475398*a**10*b*sqrt(x)/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 582120*a**9*b**2*x*log(a/b + sqrt(x))/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 1329174*a**9*b**2*x/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 970200*a**8*b**3*x**(3/2)*log(a/b + sqrt(x))/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 2021250*a**8*b**3*x**(3/2)/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 970200*a**7*b**4*x**2*log(a/b + sqrt(x))/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 1778700*a**7*b**4*x**2/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 582120*a**6*b**5*x**(5/2)*log(a/b + sqrt(x))/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 873180*a**6*b**5*x**(5/2)/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 194040*a**5*b**6*x**3*log(a/b + sqrt(x))/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 194040*a**5*b**6*x**3/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 27720*a**4*b**7*x**(7/2)*log(a/b + sqrt(x))/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) - 3465*a**3*b**8*x**4/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 385*a**2*b**9*x**(9/2)/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) - 77*a*b**10*x**5/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)) + 21*b**11*x**(11/2)/(42*a**7*b**12 + 294*a**6*b**13*sqrt(x) + 882*a**5*b**14*x + 1470*a**4*b**15*x**(3/2) + 1470*a**3*b**16*x**2 + 882*a**2*b**17*x**(5/2) + 294*a*b**18*x**3 + 42*b**19*x**(7/2)), Ne(b, 0)), (x**6/(6*a**8), True))","A",0
2224,1,1839,0,6.980996," ","integrate(x**4/(a+b*x**(1/2))**8,x)","\begin{cases} \frac{2520 a^{9} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{6534 a^{9}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{17640 a^{8} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{43218 a^{8} b \sqrt{x}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{52920 a^{7} b^{2} x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{120834 a^{7} b^{2} x}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{88200 a^{6} b^{3} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{183750 a^{6} b^{3} x^{\frac{3}{2}}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{88200 a^{5} b^{4} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{161700 a^{5} b^{4} x^{2}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{52920 a^{4} b^{5} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{79380 a^{4} b^{5} x^{\frac{5}{2}}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{17640 a^{3} b^{6} x^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{17640 a^{3} b^{6} x^{3}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{2520 a^{2} b^{7} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} - \frac{315 a b^{8} x^{4}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} + \frac{35 b^{9} x^{\frac{9}{2}}}{35 a^{7} b^{10} + 245 a^{6} b^{11} \sqrt{x} + 735 a^{5} b^{12} x + 1225 a^{4} b^{13} x^{\frac{3}{2}} + 1225 a^{3} b^{14} x^{2} + 735 a^{2} b^{15} x^{\frac{5}{2}} + 245 a b^{16} x^{3} + 35 b^{17} x^{\frac{7}{2}}} & \text{for}\: b \neq 0 \\\frac{x^{5}}{5 a^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2520*a**9*log(a/b + sqrt(x))/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 6534*a**9/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 17640*a**8*b*sqrt(x)*log(a/b + sqrt(x))/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 43218*a**8*b*sqrt(x)/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 52920*a**7*b**2*x*log(a/b + sqrt(x))/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 120834*a**7*b**2*x/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 88200*a**6*b**3*x**(3/2)*log(a/b + sqrt(x))/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 183750*a**6*b**3*x**(3/2)/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 88200*a**5*b**4*x**2*log(a/b + sqrt(x))/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 161700*a**5*b**4*x**2/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 52920*a**4*b**5*x**(5/2)*log(a/b + sqrt(x))/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 79380*a**4*b**5*x**(5/2)/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 17640*a**3*b**6*x**3*log(a/b + sqrt(x))/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 17640*a**3*b**6*x**3/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 2520*a**2*b**7*x**(7/2)*log(a/b + sqrt(x))/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) - 315*a*b**8*x**4/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)) + 35*b**9*x**(9/2)/(35*a**7*b**10 + 245*a**6*b**11*sqrt(x) + 735*a**5*b**12*x + 1225*a**4*b**13*x**(3/2) + 1225*a**3*b**14*x**2 + 735*a**2*b**15*x**(5/2) + 245*a*b**16*x**3 + 35*b**17*x**(7/2)), Ne(b, 0)), (x**5/(5*a**8), True))","A",0
2225,1,1629,0,6.907432," ","integrate(x**3/(a+b*x**(1/2))**8,x)","\begin{cases} \frac{420 a^{7} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{1089 a^{7}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{2940 a^{6} b \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{7203 a^{6} b \sqrt{x}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{8820 a^{5} b^{2} x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{20139 a^{5} b^{2} x}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{14700 a^{4} b^{3} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{30625 a^{4} b^{3} x^{\frac{3}{2}}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{14700 a^{3} b^{4} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{26950 a^{3} b^{4} x^{2}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{8820 a^{2} b^{5} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{13230 a^{2} b^{5} x^{\frac{5}{2}}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{2940 a b^{6} x^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{2940 a b^{6} x^{3}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} + \frac{420 b^{7} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{7} b^{8} + 1470 a^{6} b^{9} \sqrt{x} + 4410 a^{5} b^{10} x + 7350 a^{4} b^{11} x^{\frac{3}{2}} + 7350 a^{3} b^{12} x^{2} + 4410 a^{2} b^{13} x^{\frac{5}{2}} + 1470 a b^{14} x^{3} + 210 b^{15} x^{\frac{7}{2}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((420*a**7*log(a/b + sqrt(x))/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 1089*a**7/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 2940*a**6*b*sqrt(x)*log(a/b + sqrt(x))/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 7203*a**6*b*sqrt(x)/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 8820*a**5*b**2*x*log(a/b + sqrt(x))/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 20139*a**5*b**2*x/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 14700*a**4*b**3*x**(3/2)*log(a/b + sqrt(x))/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 30625*a**4*b**3*x**(3/2)/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 14700*a**3*b**4*x**2*log(a/b + sqrt(x))/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 26950*a**3*b**4*x**2/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 8820*a**2*b**5*x**(5/2)*log(a/b + sqrt(x))/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 13230*a**2*b**5*x**(5/2)/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 2940*a*b**6*x**3*log(a/b + sqrt(x))/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 2940*a*b**6*x**3/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)) + 420*b**7*x**(7/2)*log(a/b + sqrt(x))/(210*a**7*b**8 + 1470*a**6*b**9*sqrt(x) + 4410*a**5*b**10*x + 7350*a**4*b**11*x**(3/2) + 7350*a**3*b**12*x**2 + 4410*a**2*b**13*x**(5/2) + 1470*a*b**14*x**3 + 210*b**15*x**(7/2)), Ne(b, 0)), (x**4/(4*a**8), True))","A",0
2226,1,619,0,6.491866," ","integrate(x**2/(a+b*x**(1/2))**8,x)","\begin{cases} - \frac{a^{5}}{21 a^{7} b^{6} + 147 a^{6} b^{7} \sqrt{x} + 441 a^{5} b^{8} x + 735 a^{4} b^{9} x^{\frac{3}{2}} + 735 a^{3} b^{10} x^{2} + 441 a^{2} b^{11} x^{\frac{5}{2}} + 147 a b^{12} x^{3} + 21 b^{13} x^{\frac{7}{2}}} - \frac{7 a^{4} b \sqrt{x}}{21 a^{7} b^{6} + 147 a^{6} b^{7} \sqrt{x} + 441 a^{5} b^{8} x + 735 a^{4} b^{9} x^{\frac{3}{2}} + 735 a^{3} b^{10} x^{2} + 441 a^{2} b^{11} x^{\frac{5}{2}} + 147 a b^{12} x^{3} + 21 b^{13} x^{\frac{7}{2}}} - \frac{21 a^{3} b^{2} x}{21 a^{7} b^{6} + 147 a^{6} b^{7} \sqrt{x} + 441 a^{5} b^{8} x + 735 a^{4} b^{9} x^{\frac{3}{2}} + 735 a^{3} b^{10} x^{2} + 441 a^{2} b^{11} x^{\frac{5}{2}} + 147 a b^{12} x^{3} + 21 b^{13} x^{\frac{7}{2}}} - \frac{35 a^{2} b^{3} x^{\frac{3}{2}}}{21 a^{7} b^{6} + 147 a^{6} b^{7} \sqrt{x} + 441 a^{5} b^{8} x + 735 a^{4} b^{9} x^{\frac{3}{2}} + 735 a^{3} b^{10} x^{2} + 441 a^{2} b^{11} x^{\frac{5}{2}} + 147 a b^{12} x^{3} + 21 b^{13} x^{\frac{7}{2}}} - \frac{35 a b^{4} x^{2}}{21 a^{7} b^{6} + 147 a^{6} b^{7} \sqrt{x} + 441 a^{5} b^{8} x + 735 a^{4} b^{9} x^{\frac{3}{2}} + 735 a^{3} b^{10} x^{2} + 441 a^{2} b^{11} x^{\frac{5}{2}} + 147 a b^{12} x^{3} + 21 b^{13} x^{\frac{7}{2}}} - \frac{21 b^{5} x^{\frac{5}{2}}}{21 a^{7} b^{6} + 147 a^{6} b^{7} \sqrt{x} + 441 a^{5} b^{8} x + 735 a^{4} b^{9} x^{\frac{3}{2}} + 735 a^{3} b^{10} x^{2} + 441 a^{2} b^{11} x^{\frac{5}{2}} + 147 a b^{12} x^{3} + 21 b^{13} x^{\frac{7}{2}}} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**5/(21*a**7*b**6 + 147*a**6*b**7*sqrt(x) + 441*a**5*b**8*x + 735*a**4*b**9*x**(3/2) + 735*a**3*b**10*x**2 + 441*a**2*b**11*x**(5/2) + 147*a*b**12*x**3 + 21*b**13*x**(7/2)) - 7*a**4*b*sqrt(x)/(21*a**7*b**6 + 147*a**6*b**7*sqrt(x) + 441*a**5*b**8*x + 735*a**4*b**9*x**(3/2) + 735*a**3*b**10*x**2 + 441*a**2*b**11*x**(5/2) + 147*a*b**12*x**3 + 21*b**13*x**(7/2)) - 21*a**3*b**2*x/(21*a**7*b**6 + 147*a**6*b**7*sqrt(x) + 441*a**5*b**8*x + 735*a**4*b**9*x**(3/2) + 735*a**3*b**10*x**2 + 441*a**2*b**11*x**(5/2) + 147*a*b**12*x**3 + 21*b**13*x**(7/2)) - 35*a**2*b**3*x**(3/2)/(21*a**7*b**6 + 147*a**6*b**7*sqrt(x) + 441*a**5*b**8*x + 735*a**4*b**9*x**(3/2) + 735*a**3*b**10*x**2 + 441*a**2*b**11*x**(5/2) + 147*a*b**12*x**3 + 21*b**13*x**(7/2)) - 35*a*b**4*x**2/(21*a**7*b**6 + 147*a**6*b**7*sqrt(x) + 441*a**5*b**8*x + 735*a**4*b**9*x**(3/2) + 735*a**3*b**10*x**2 + 441*a**2*b**11*x**(5/2) + 147*a*b**12*x**3 + 21*b**13*x**(7/2)) - 21*b**5*x**(5/2)/(21*a**7*b**6 + 147*a**6*b**7*sqrt(x) + 441*a**5*b**8*x + 735*a**4*b**9*x**(3/2) + 735*a**3*b**10*x**2 + 441*a**2*b**11*x**(5/2) + 147*a*b**12*x**3 + 21*b**13*x**(7/2)), Ne(b, 0)), (x**3/(3*a**8), True))","A",0
2227,1,410,0,6.164780," ","integrate(x/(a+b*x**(1/2))**8,x)","\begin{cases} - \frac{a^{3}}{70 a^{7} b^{4} + 490 a^{6} b^{5} \sqrt{x} + 1470 a^{5} b^{6} x + 2450 a^{4} b^{7} x^{\frac{3}{2}} + 2450 a^{3} b^{8} x^{2} + 1470 a^{2} b^{9} x^{\frac{5}{2}} + 490 a b^{10} x^{3} + 70 b^{11} x^{\frac{7}{2}}} - \frac{7 a^{2} b \sqrt{x}}{70 a^{7} b^{4} + 490 a^{6} b^{5} \sqrt{x} + 1470 a^{5} b^{6} x + 2450 a^{4} b^{7} x^{\frac{3}{2}} + 2450 a^{3} b^{8} x^{2} + 1470 a^{2} b^{9} x^{\frac{5}{2}} + 490 a b^{10} x^{3} + 70 b^{11} x^{\frac{7}{2}}} - \frac{21 a b^{2} x}{70 a^{7} b^{4} + 490 a^{6} b^{5} \sqrt{x} + 1470 a^{5} b^{6} x + 2450 a^{4} b^{7} x^{\frac{3}{2}} + 2450 a^{3} b^{8} x^{2} + 1470 a^{2} b^{9} x^{\frac{5}{2}} + 490 a b^{10} x^{3} + 70 b^{11} x^{\frac{7}{2}}} - \frac{35 b^{3} x^{\frac{3}{2}}}{70 a^{7} b^{4} + 490 a^{6} b^{5} \sqrt{x} + 1470 a^{5} b^{6} x + 2450 a^{4} b^{7} x^{\frac{3}{2}} + 2450 a^{3} b^{8} x^{2} + 1470 a^{2} b^{9} x^{\frac{5}{2}} + 490 a b^{10} x^{3} + 70 b^{11} x^{\frac{7}{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3/(70*a**7*b**4 + 490*a**6*b**5*sqrt(x) + 1470*a**5*b**6*x + 2450*a**4*b**7*x**(3/2) + 2450*a**3*b**8*x**2 + 1470*a**2*b**9*x**(5/2) + 490*a*b**10*x**3 + 70*b**11*x**(7/2)) - 7*a**2*b*sqrt(x)/(70*a**7*b**4 + 490*a**6*b**5*sqrt(x) + 1470*a**5*b**6*x + 2450*a**4*b**7*x**(3/2) + 2450*a**3*b**8*x**2 + 1470*a**2*b**9*x**(5/2) + 490*a*b**10*x**3 + 70*b**11*x**(7/2)) - 21*a*b**2*x/(70*a**7*b**4 + 490*a**6*b**5*sqrt(x) + 1470*a**5*b**6*x + 2450*a**4*b**7*x**(3/2) + 2450*a**3*b**8*x**2 + 1470*a**2*b**9*x**(5/2) + 490*a*b**10*x**3 + 70*b**11*x**(7/2)) - 35*b**3*x**(3/2)/(70*a**7*b**4 + 490*a**6*b**5*sqrt(x) + 1470*a**5*b**6*x + 2450*a**4*b**7*x**(3/2) + 2450*a**3*b**8*x**2 + 1470*a**2*b**9*x**(5/2) + 490*a*b**10*x**3 + 70*b**11*x**(7/2)), Ne(b, 0)), (x**2/(2*a**8), True))","A",0
2228,1,199,0,5.668474," ","integrate(1/(a+b*x**(1/2))**8,x)","\begin{cases} - \frac{a}{21 a^{7} b^{2} + 147 a^{6} b^{3} \sqrt{x} + 441 a^{5} b^{4} x + 735 a^{4} b^{5} x^{\frac{3}{2}} + 735 a^{3} b^{6} x^{2} + 441 a^{2} b^{7} x^{\frac{5}{2}} + 147 a b^{8} x^{3} + 21 b^{9} x^{\frac{7}{2}}} - \frac{7 b \sqrt{x}}{21 a^{7} b^{2} + 147 a^{6} b^{3} \sqrt{x} + 441 a^{5} b^{4} x + 735 a^{4} b^{5} x^{\frac{3}{2}} + 735 a^{3} b^{6} x^{2} + 441 a^{2} b^{7} x^{\frac{5}{2}} + 147 a b^{8} x^{3} + 21 b^{9} x^{\frac{7}{2}}} & \text{for}\: b \neq 0 \\\frac{x}{a^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(21*a**7*b**2 + 147*a**6*b**3*sqrt(x) + 441*a**5*b**4*x + 735*a**4*b**5*x**(3/2) + 735*a**3*b**6*x**2 + 441*a**2*b**7*x**(5/2) + 147*a*b**8*x**3 + 21*b**9*x**(7/2)) - 7*b*sqrt(x)/(21*a**7*b**2 + 147*a**6*b**3*sqrt(x) + 441*a**5*b**4*x + 735*a**4*b**5*x**(3/2) + 735*a**3*b**6*x**2 + 441*a**2*b**7*x**(5/2) + 147*a*b**8*x**3 + 21*b**9*x**(7/2)), Ne(b, 0)), (x/a**8, True))","A",0
2229,1,2581,0,11.353989," ","integrate(1/x/(a+b*x**(1/2))**8,x)","\begin{cases} \frac{\tilde{\infty}}{x^{4}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\log{\left(x \right)}}{a^{8}} & \text{for}\: b = 0 \\- \frac{1}{4 b^{8} x^{4}} & \text{for}\: a = 0 \\\frac{210 a^{7} \sqrt{x} \log{\left(x \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} - \frac{420 a^{7} \sqrt{x} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{1089 a^{7} \sqrt{x}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{1470 a^{6} b x \log{\left(x \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} - \frac{2940 a^{6} b x \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{4683 a^{6} b x}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{4410 a^{5} b^{2} x^{\frac{3}{2}} \log{\left(x \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} - \frac{8820 a^{5} b^{2} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{9639 a^{5} b^{2} x^{\frac{3}{2}}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{7350 a^{4} b^{3} x^{2} \log{\left(x \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} - \frac{14700 a^{4} b^{3} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{11165 a^{4} b^{3} x^{2}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{7350 a^{3} b^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} - \frac{14700 a^{3} b^{4} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{7490 a^{3} b^{4} x^{\frac{5}{2}}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{4410 a^{2} b^{5} x^{3} \log{\left(x \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} - \frac{8820 a^{2} b^{5} x^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{2730 a^{2} b^{5} x^{3}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{1470 a b^{6} x^{\frac{7}{2}} \log{\left(x \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} - \frac{2940 a b^{6} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{420 a b^{6} x^{\frac{7}{2}}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} + \frac{210 b^{7} x^{4} \log{\left(x \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} - \frac{420 b^{7} x^{4} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{210 a^{15} \sqrt{x} + 1470 a^{14} b x + 4410 a^{13} b^{2} x^{\frac{3}{2}} + 7350 a^{12} b^{3} x^{2} + 7350 a^{11} b^{4} x^{\frac{5}{2}} + 4410 a^{10} b^{5} x^{3} + 1470 a^{9} b^{6} x^{\frac{7}{2}} + 210 a^{8} b^{7} x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**4, Eq(a, 0) & Eq(b, 0)), (log(x)/a**8, Eq(b, 0)), (-1/(4*b**8*x**4), Eq(a, 0)), (210*a**7*sqrt(x)*log(x)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) - 420*a**7*sqrt(x)*log(a/b + sqrt(x))/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 1089*a**7*sqrt(x)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 1470*a**6*b*x*log(x)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) - 2940*a**6*b*x*log(a/b + sqrt(x))/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 4683*a**6*b*x/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 4410*a**5*b**2*x**(3/2)*log(x)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) - 8820*a**5*b**2*x**(3/2)*log(a/b + sqrt(x))/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 9639*a**5*b**2*x**(3/2)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 7350*a**4*b**3*x**2*log(x)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) - 14700*a**4*b**3*x**2*log(a/b + sqrt(x))/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 11165*a**4*b**3*x**2/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 7350*a**3*b**4*x**(5/2)*log(x)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) - 14700*a**3*b**4*x**(5/2)*log(a/b + sqrt(x))/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 7490*a**3*b**4*x**(5/2)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 4410*a**2*b**5*x**3*log(x)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) - 8820*a**2*b**5*x**3*log(a/b + sqrt(x))/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 2730*a**2*b**5*x**3/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 1470*a*b**6*x**(7/2)*log(x)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) - 2940*a*b**6*x**(7/2)*log(a/b + sqrt(x))/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 420*a*b**6*x**(7/2)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) + 210*b**7*x**4*log(x)/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4) - 420*b**7*x**4*log(a/b + sqrt(x))/(210*a**15*sqrt(x) + 1470*a**14*b*x + 4410*a**13*b**2*x**(3/2) + 7350*a**12*b**3*x**2 + 7350*a**11*b**4*x**(5/2) + 4410*a**10*b**5*x**3 + 1470*a**9*b**6*x**(7/2) + 210*a**8*b**7*x**4), True))","A",0
2230,1,2854,0,20.424919," ","integrate(1/x**2/(a+b*x**(1/2))**8,x)","\begin{cases} \frac{\tilde{\infty}}{x^{5}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{a^{8} x} & \text{for}\: b = 0 \\- \frac{1}{5 b^{8} x^{5}} & \text{for}\: a = 0 \\- \frac{35 a^{9} \sqrt{x}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{315 a^{8} b x}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{1260 a^{7} b^{2} x^{\frac{3}{2}} \log{\left(x \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} - \frac{2520 a^{7} b^{2} x^{\frac{3}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{6534 a^{7} b^{2} x^{\frac{3}{2}}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{8820 a^{6} b^{3} x^{2} \log{\left(x \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} - \frac{17640 a^{6} b^{3} x^{2} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{28098 a^{6} b^{3} x^{2}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{26460 a^{5} b^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} - \frac{52920 a^{5} b^{4} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{57834 a^{5} b^{4} x^{\frac{5}{2}}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{44100 a^{4} b^{5} x^{3} \log{\left(x \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} - \frac{88200 a^{4} b^{5} x^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{66990 a^{4} b^{5} x^{3}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{44100 a^{3} b^{6} x^{\frac{7}{2}} \log{\left(x \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} - \frac{88200 a^{3} b^{6} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{44940 a^{3} b^{6} x^{\frac{7}{2}}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{26460 a^{2} b^{7} x^{4} \log{\left(x \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} - \frac{52920 a^{2} b^{7} x^{4} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{16380 a^{2} b^{7} x^{4}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{8820 a b^{8} x^{\frac{9}{2}} \log{\left(x \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} - \frac{17640 a b^{8} x^{\frac{9}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{2520 a b^{8} x^{\frac{9}{2}}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} + \frac{1260 b^{9} x^{5} \log{\left(x \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} - \frac{2520 b^{9} x^{5} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{35 a^{17} x^{\frac{3}{2}} + 245 a^{16} b x^{2} + 735 a^{15} b^{2} x^{\frac{5}{2}} + 1225 a^{14} b^{3} x^{3} + 1225 a^{13} b^{4} x^{\frac{7}{2}} + 735 a^{12} b^{5} x^{4} + 245 a^{11} b^{6} x^{\frac{9}{2}} + 35 a^{10} b^{7} x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**5, Eq(a, 0) & Eq(b, 0)), (-1/(a**8*x), Eq(b, 0)), (-1/(5*b**8*x**5), Eq(a, 0)), (-35*a**9*sqrt(x)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 315*a**8*b*x/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 1260*a**7*b**2*x**(3/2)*log(x)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) - 2520*a**7*b**2*x**(3/2)*log(a/b + sqrt(x))/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 6534*a**7*b**2*x**(3/2)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 8820*a**6*b**3*x**2*log(x)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) - 17640*a**6*b**3*x**2*log(a/b + sqrt(x))/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 28098*a**6*b**3*x**2/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 26460*a**5*b**4*x**(5/2)*log(x)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) - 52920*a**5*b**4*x**(5/2)*log(a/b + sqrt(x))/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 57834*a**5*b**4*x**(5/2)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 44100*a**4*b**5*x**3*log(x)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) - 88200*a**4*b**5*x**3*log(a/b + sqrt(x))/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 66990*a**4*b**5*x**3/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 44100*a**3*b**6*x**(7/2)*log(x)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) - 88200*a**3*b**6*x**(7/2)*log(a/b + sqrt(x))/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 44940*a**3*b**6*x**(7/2)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 26460*a**2*b**7*x**4*log(x)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) - 52920*a**2*b**7*x**4*log(a/b + sqrt(x))/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 16380*a**2*b**7*x**4/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 8820*a*b**8*x**(9/2)*log(x)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) - 17640*a*b**8*x**(9/2)*log(a/b + sqrt(x))/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 2520*a*b**8*x**(9/2)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) + 1260*b**9*x**5*log(x)/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5) - 2520*b**9*x**5*log(a/b + sqrt(x))/(35*a**17*x**(3/2) + 245*a**16*b*x**2 + 735*a**15*b**2*x**(5/2) + 1225*a**14*b**3*x**3 + 1225*a**13*b**4*x**(7/2) + 735*a**12*b**5*x**4 + 245*a**11*b**6*x**(9/2) + 35*a**10*b**7*x**5), True))","A",0
2231,1,3077,0,30.478925," ","integrate(1/x**3/(a+b*x**(1/2))**8,x)","\begin{cases} \frac{\tilde{\infty}}{x^{6}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{2 a^{8} x^{2}} & \text{for}\: b = 0 \\- \frac{1}{6 b^{8} x^{6}} & \text{for}\: a = 0 \\- \frac{21 a^{11} \sqrt{x}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{77 a^{10} b x}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} - \frac{385 a^{9} b^{2} x^{\frac{3}{2}}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{3465 a^{8} b^{3} x^{2}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{13860 a^{7} b^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} - \frac{27720 a^{7} b^{4} x^{\frac{5}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{71874 a^{7} b^{4} x^{\frac{5}{2}}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{97020 a^{6} b^{5} x^{3} \log{\left(x \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} - \frac{194040 a^{6} b^{5} x^{3} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{309078 a^{6} b^{5} x^{3}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{291060 a^{5} b^{6} x^{\frac{7}{2}} \log{\left(x \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} - \frac{582120 a^{5} b^{6} x^{\frac{7}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{636174 a^{5} b^{6} x^{\frac{7}{2}}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{485100 a^{4} b^{7} x^{4} \log{\left(x \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} - \frac{970200 a^{4} b^{7} x^{4} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{736890 a^{4} b^{7} x^{4}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{485100 a^{3} b^{8} x^{\frac{9}{2}} \log{\left(x \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} - \frac{970200 a^{3} b^{8} x^{\frac{9}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{494340 a^{3} b^{8} x^{\frac{9}{2}}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{291060 a^{2} b^{9} x^{5} \log{\left(x \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} - \frac{582120 a^{2} b^{9} x^{5} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{180180 a^{2} b^{9} x^{5}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{97020 a b^{10} x^{\frac{11}{2}} \log{\left(x \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} - \frac{194040 a b^{10} x^{\frac{11}{2}} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{27720 a b^{10} x^{\frac{11}{2}}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} + \frac{13860 b^{11} x^{6} \log{\left(x \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} - \frac{27720 b^{11} x^{6} \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{42 a^{19} x^{\frac{5}{2}} + 294 a^{18} b x^{3} + 882 a^{17} b^{2} x^{\frac{7}{2}} + 1470 a^{16} b^{3} x^{4} + 1470 a^{15} b^{4} x^{\frac{9}{2}} + 882 a^{14} b^{5} x^{5} + 294 a^{13} b^{6} x^{\frac{11}{2}} + 42 a^{12} b^{7} x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**6, Eq(a, 0) & Eq(b, 0)), (-1/(2*a**8*x**2), Eq(b, 0)), (-1/(6*b**8*x**6), Eq(a, 0)), (-21*a**11*sqrt(x)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 77*a**10*b*x/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) - 385*a**9*b**2*x**(3/2)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 3465*a**8*b**3*x**2/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 13860*a**7*b**4*x**(5/2)*log(x)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) - 27720*a**7*b**4*x**(5/2)*log(a/b + sqrt(x))/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 71874*a**7*b**4*x**(5/2)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 97020*a**6*b**5*x**3*log(x)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) - 194040*a**6*b**5*x**3*log(a/b + sqrt(x))/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 309078*a**6*b**5*x**3/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 291060*a**5*b**6*x**(7/2)*log(x)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) - 582120*a**5*b**6*x**(7/2)*log(a/b + sqrt(x))/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 636174*a**5*b**6*x**(7/2)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 485100*a**4*b**7*x**4*log(x)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) - 970200*a**4*b**7*x**4*log(a/b + sqrt(x))/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 736890*a**4*b**7*x**4/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 485100*a**3*b**8*x**(9/2)*log(x)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) - 970200*a**3*b**8*x**(9/2)*log(a/b + sqrt(x))/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 494340*a**3*b**8*x**(9/2)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 291060*a**2*b**9*x**5*log(x)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) - 582120*a**2*b**9*x**5*log(a/b + sqrt(x))/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 180180*a**2*b**9*x**5/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 97020*a*b**10*x**(11/2)*log(x)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) - 194040*a*b**10*x**(11/2)*log(a/b + sqrt(x))/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 27720*a*b**10*x**(11/2)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) + 13860*b**11*x**6*log(x)/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6) - 27720*b**11*x**6*log(a/b + sqrt(x))/(42*a**19*x**(5/2) + 294*a**18*b*x**3 + 882*a**17*b**2*x**(7/2) + 1470*a**16*b**3*x**4 + 1470*a**15*b**4*x**(9/2) + 882*a**14*b**5*x**5 + 294*a**13*b**6*x**(11/2) + 42*a**12*b**7*x**6), True))","A",0
2232,1,19,0,0.467778," ","integrate(1/x/(2+b*x**(1/2)),x)","\begin{cases} \frac{\log{\left(x \right)}}{2} - \log{\left(\sqrt{x} + \frac{2}{b} \right)} & \text{for}\: b \neq 0 \\\frac{\log{\left(x \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/2 - log(sqrt(x) + 2/b), Ne(b, 0)), (log(x)/2, True))","A",0
2233,1,8588,0,10.054279," ","integrate(x**2*(a+b*x**(1/2))**(1/2),x)","- \frac{1024 a^{\frac{153}{2}} x^{18} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{1024 a^{\frac{153}{2}} x^{18}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{14848 a^{\frac{151}{2}} b x^{\frac{37}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{15360 a^{\frac{151}{2}} b x^{\frac{37}{2}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{100224 a^{\frac{149}{2}} b^{2} x^{19} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{107520 a^{\frac{149}{2}} b^{2} x^{19}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{417600 a^{\frac{147}{2}} b^{3} x^{\frac{39}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{465920 a^{\frac{147}{2}} b^{3} x^{\frac{39}{2}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{1200600 a^{\frac{145}{2}} b^{4} x^{20} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{1397760 a^{\frac{145}{2}} b^{4} x^{20}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{2521260 a^{\frac{143}{2}} b^{5} x^{\frac{41}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{3075072 a^{\frac{143}{2}} b^{5} x^{\frac{41}{2}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{3988992 a^{\frac{141}{2}} b^{6} x^{21} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{5125120 a^{\frac{141}{2}} b^{6} x^{21}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{4802592 a^{\frac{139}{2}} b^{7} x^{\frac{43}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{6589440 a^{\frac{139}{2}} b^{7} x^{\frac{43}{2}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{4232160 a^{\frac{137}{2}} b^{8} x^{22} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{6589440 a^{\frac{137}{2}} b^{8} x^{22}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{1935440 a^{\frac{135}{2}} b^{9} x^{\frac{45}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{5125120 a^{\frac{135}{2}} b^{9} x^{\frac{45}{2}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{2214784 a^{\frac{133}{2}} b^{10} x^{23} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{3075072 a^{\frac{133}{2}} b^{10} x^{23}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{8060832 a^{\frac{131}{2}} b^{11} x^{\frac{47}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{1397760 a^{\frac{131}{2}} b^{11} x^{\frac{47}{2}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{14375088 a^{\frac{129}{2}} b^{12} x^{24} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{465920 a^{\frac{129}{2}} b^{12} x^{24}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{18620280 a^{\frac{127}{2}} b^{13} x^{\frac{49}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{107520 a^{\frac{127}{2}} b^{13} x^{\frac{49}{2}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{18558720 a^{\frac{125}{2}} b^{14} x^{25} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{15360 a^{\frac{125}{2}} b^{14} x^{25}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{14360352 a^{\frac{123}{2}} b^{15} x^{\frac{51}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{1024 a^{\frac{123}{2}} b^{15} x^{\frac{51}{2}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{8569248 a^{\frac{121}{2}} b^{16} x^{26} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{3873456 a^{\frac{119}{2}} b^{17} x^{\frac{53}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{1283840 a^{\frac{117}{2}} b^{18} x^{27} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{294560 a^{\frac{115}{2}} b^{19} x^{\frac{55}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{41832 a^{\frac{113}{2}} b^{20} x^{28} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{2772 a^{\frac{111}{2}} b^{21} x^{\frac{57}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{9009 a^{70} b^{6} x^{18} + 135135 a^{69} b^{7} x^{\frac{37}{2}} + 945945 a^{68} b^{8} x^{19} + 4099095 a^{67} b^{9} x^{\frac{39}{2}} + 12297285 a^{66} b^{10} x^{20} + 27054027 a^{65} b^{11} x^{\frac{41}{2}} + 45090045 a^{64} b^{12} x^{21} + 57972915 a^{63} b^{13} x^{\frac{43}{2}} + 57972915 a^{62} b^{14} x^{22} + 45090045 a^{61} b^{15} x^{\frac{45}{2}} + 27054027 a^{60} b^{16} x^{23} + 12297285 a^{59} b^{17} x^{\frac{47}{2}} + 4099095 a^{58} b^{18} x^{24} + 945945 a^{57} b^{19} x^{\frac{49}{2}} + 135135 a^{56} b^{20} x^{25} + 9009 a^{55} b^{21} x^{\frac{51}{2}}}"," ",0,"-1024*a**(153/2)*x**18*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 1024*a**(153/2)*x**18/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) - 14848*a**(151/2)*b*x**(37/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 15360*a**(151/2)*b*x**(37/2)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) - 100224*a**(149/2)*b**2*x**19*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 107520*a**(149/2)*b**2*x**19/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) - 417600*a**(147/2)*b**3*x**(39/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 465920*a**(147/2)*b**3*x**(39/2)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) - 1200600*a**(145/2)*b**4*x**20*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 1397760*a**(145/2)*b**4*x**20/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) - 2521260*a**(143/2)*b**5*x**(41/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 3075072*a**(143/2)*b**5*x**(41/2)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) - 3988992*a**(141/2)*b**6*x**21*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 5125120*a**(141/2)*b**6*x**21/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) - 4802592*a**(139/2)*b**7*x**(43/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 6589440*a**(139/2)*b**7*x**(43/2)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) - 4232160*a**(137/2)*b**8*x**22*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 6589440*a**(137/2)*b**8*x**22/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) - 1935440*a**(135/2)*b**9*x**(45/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 5125120*a**(135/2)*b**9*x**(45/2)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 2214784*a**(133/2)*b**10*x**23*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 3075072*a**(133/2)*b**10*x**23/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 8060832*a**(131/2)*b**11*x**(47/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 1397760*a**(131/2)*b**11*x**(47/2)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 14375088*a**(129/2)*b**12*x**24*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 465920*a**(129/2)*b**12*x**24/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 18620280*a**(127/2)*b**13*x**(49/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 107520*a**(127/2)*b**13*x**(49/2)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 18558720*a**(125/2)*b**14*x**25*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 15360*a**(125/2)*b**14*x**25/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 14360352*a**(123/2)*b**15*x**(51/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 1024*a**(123/2)*b**15*x**(51/2)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 8569248*a**(121/2)*b**16*x**26*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 3873456*a**(119/2)*b**17*x**(53/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 1283840*a**(117/2)*b**18*x**27*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 294560*a**(115/2)*b**19*x**(55/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 41832*a**(113/2)*b**20*x**28*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2)) + 2772*a**(111/2)*b**21*x**(57/2)*sqrt(1 + b*sqrt(x)/a)/(9009*a**70*b**6*x**18 + 135135*a**69*b**7*x**(37/2) + 945945*a**68*b**8*x**19 + 4099095*a**67*b**9*x**(39/2) + 12297285*a**66*b**10*x**20 + 27054027*a**65*b**11*x**(41/2) + 45090045*a**64*b**12*x**21 + 57972915*a**63*b**13*x**(43/2) + 57972915*a**62*b**14*x**22 + 45090045*a**61*b**15*x**(45/2) + 27054027*a**60*b**16*x**23 + 12297285*a**59*b**17*x**(47/2) + 4099095*a**58*b**18*x**24 + 945945*a**57*b**19*x**(49/2) + 135135*a**56*b**20*x**25 + 9009*a**55*b**21*x**(51/2))","B",0
2234,1,1987,0,2.823373," ","integrate(x*(a+b*x**(1/2))**(1/2),x)","- \frac{64 a^{\frac{49}{2}} x^{8} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{64 a^{\frac{49}{2}} x^{8}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} - \frac{352 a^{\frac{47}{2}} b x^{\frac{17}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{384 a^{\frac{47}{2}} b x^{\frac{17}{2}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} - \frac{792 a^{\frac{45}{2}} b^{2} x^{9} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{960 a^{\frac{45}{2}} b^{2} x^{9}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} - \frac{924 a^{\frac{43}{2}} b^{3} x^{\frac{19}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{1280 a^{\frac{43}{2}} b^{3} x^{\frac{19}{2}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} - \frac{420 a^{\frac{41}{2}} b^{4} x^{10} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{960 a^{\frac{41}{2}} b^{4} x^{10}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{756 a^{\frac{39}{2}} b^{5} x^{\frac{21}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{384 a^{\frac{39}{2}} b^{5} x^{\frac{21}{2}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{2268 a^{\frac{37}{2}} b^{6} x^{11} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{64 a^{\frac{37}{2}} b^{6} x^{11}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{2988 a^{\frac{35}{2}} b^{7} x^{\frac{23}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{2196 a^{\frac{33}{2}} b^{8} x^{12} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{860 a^{\frac{31}{2}} b^{9} x^{\frac{25}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}} + \frac{140 a^{\frac{29}{2}} b^{10} x^{13} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{315 a^{20} b^{4} x^{8} + 1890 a^{19} b^{5} x^{\frac{17}{2}} + 4725 a^{18} b^{6} x^{9} + 6300 a^{17} b^{7} x^{\frac{19}{2}} + 4725 a^{16} b^{8} x^{10} + 1890 a^{15} b^{9} x^{\frac{21}{2}} + 315 a^{14} b^{10} x^{11}}"," ",0,"-64*a**(49/2)*x**8*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 64*a**(49/2)*x**8/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) - 352*a**(47/2)*b*x**(17/2)*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 384*a**(47/2)*b*x**(17/2)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) - 792*a**(45/2)*b**2*x**9*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 960*a**(45/2)*b**2*x**9/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) - 924*a**(43/2)*b**3*x**(19/2)*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 1280*a**(43/2)*b**3*x**(19/2)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) - 420*a**(41/2)*b**4*x**10*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 960*a**(41/2)*b**4*x**10/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 756*a**(39/2)*b**5*x**(21/2)*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 384*a**(39/2)*b**5*x**(21/2)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 2268*a**(37/2)*b**6*x**11*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 64*a**(37/2)*b**6*x**11/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 2988*a**(35/2)*b**7*x**(23/2)*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 2196*a**(33/2)*b**8*x**12*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 860*a**(31/2)*b**9*x**(25/2)*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11) + 140*a**(29/2)*b**10*x**13*sqrt(1 + b*sqrt(x)/a)/(315*a**20*b**4*x**8 + 1890*a**19*b**5*x**(17/2) + 4725*a**18*b**6*x**9 + 6300*a**17*b**7*x**(19/2) + 4725*a**16*b**8*x**10 + 1890*a**15*b**9*x**(21/2) + 315*a**14*b**10*x**11)","B",0
2235,1,272,0,1.235408," ","integrate((a+b*x**(1/2))**(1/2),x)","- \frac{8 a^{\frac{9}{2}} x^{2} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} + \frac{8 a^{\frac{9}{2}} x^{2}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} - \frac{4 a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} + \frac{8 a^{\frac{7}{2}} b x^{\frac{5}{2}}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} + \frac{16 a^{\frac{5}{2}} b^{2} x^{3} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} + \frac{12 a^{\frac{3}{2}} b^{3} x^{\frac{7}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}}"," ",0,"-8*a**(9/2)*x**2*sqrt(1 + b*sqrt(x)/a)/(15*a**2*b**2*x**2 + 15*a*b**3*x**(5/2)) + 8*a**(9/2)*x**2/(15*a**2*b**2*x**2 + 15*a*b**3*x**(5/2)) - 4*a**(7/2)*b*x**(5/2)*sqrt(1 + b*sqrt(x)/a)/(15*a**2*b**2*x**2 + 15*a*b**3*x**(5/2)) + 8*a**(7/2)*b*x**(5/2)/(15*a**2*b**2*x**2 + 15*a*b**3*x**(5/2)) + 16*a**(5/2)*b**2*x**3*sqrt(1 + b*sqrt(x)/a)/(15*a**2*b**2*x**2 + 15*a*b**3*x**(5/2)) + 12*a**(3/2)*b**3*x**(7/2)*sqrt(1 + b*sqrt(x)/a)/(15*a**2*b**2*x**2 + 15*a*b**3*x**(5/2))","B",0
2236,1,75,0,1.571030," ","integrate((a+b*x**(1/2))**(1/2)/x,x)","- 4 \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt[4]{x}} \right)} + \frac{4 a}{\sqrt{b} \sqrt[4]{x} \sqrt{\frac{a}{b \sqrt{x}} + 1}} + \frac{4 \sqrt{b} \sqrt[4]{x}}{\sqrt{\frac{a}{b \sqrt{x}} + 1}}"," ",0,"-4*sqrt(a)*asinh(sqrt(a)/(sqrt(b)*x**(1/4))) + 4*a/(sqrt(b)*x**(1/4)*sqrt(a/(b*sqrt(x)) + 1)) + 4*sqrt(b)*x**(1/4)/sqrt(a/(b*sqrt(x)) + 1)","B",0
2237,1,105,0,4.235329," ","integrate((a+b*x**(1/2))**(1/2)/x**2,x)","- \frac{a}{\sqrt{b} x^{\frac{5}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} - \frac{3 \sqrt{b}}{2 x^{\frac{3}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} - \frac{b^{\frac{3}{2}}}{2 a \sqrt[4]{x} \sqrt{\frac{a}{b \sqrt{x}} + 1}} + \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt[4]{x}} \right)}}{2 a^{\frac{3}{2}}}"," ",0,"-a/(sqrt(b)*x**(5/4)*sqrt(a/(b*sqrt(x)) + 1)) - 3*sqrt(b)/(2*x**(3/4)*sqrt(a/(b*sqrt(x)) + 1)) - b**(3/2)/(2*a*x**(1/4)*sqrt(a/(b*sqrt(x)) + 1)) + b**2*asinh(sqrt(a)/(sqrt(b)*x**(1/4)))/(2*a**(3/2))","A",0
2238,1,170,0,10.263283," ","integrate((a+b*x**(1/2))**(1/2)/x**3,x)","- \frac{a}{2 \sqrt{b} x^{\frac{9}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} - \frac{7 \sqrt{b}}{12 x^{\frac{7}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} + \frac{b^{\frac{3}{2}}}{48 a x^{\frac{5}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} - \frac{5 b^{\frac{5}{2}}}{96 a^{2} x^{\frac{3}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} - \frac{5 b^{\frac{7}{2}}}{32 a^{3} \sqrt[4]{x} \sqrt{\frac{a}{b \sqrt{x}} + 1}} + \frac{5 b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt[4]{x}} \right)}}{32 a^{\frac{7}{2}}}"," ",0,"-a/(2*sqrt(b)*x**(9/4)*sqrt(a/(b*sqrt(x)) + 1)) - 7*sqrt(b)/(12*x**(7/4)*sqrt(a/(b*sqrt(x)) + 1)) + b**(3/2)/(48*a*x**(5/4)*sqrt(a/(b*sqrt(x)) + 1)) - 5*b**(5/2)/(96*a**2*x**(3/4)*sqrt(a/(b*sqrt(x)) + 1)) - 5*b**(7/2)/(32*a**3*x**(1/4)*sqrt(a/(b*sqrt(x)) + 1)) + 5*b**4*asinh(sqrt(a)/(sqrt(b)*x**(1/4)))/(32*a**(7/2))","A",0
2239,1,8356,0,9.635747," ","integrate(x**2/(a+b*x**(1/2))**(1/2),x)","- \frac{1024 a^{\frac{151}{2}} x^{18} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{1024 a^{\frac{151}{2}} x^{18}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{14848 a^{\frac{149}{2}} b x^{\frac{37}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{15360 a^{\frac{149}{2}} b x^{\frac{37}{2}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{100224 a^{\frac{147}{2}} b^{2} x^{19} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{107520 a^{\frac{147}{2}} b^{2} x^{19}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{417600 a^{\frac{145}{2}} b^{3} x^{\frac{39}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{465920 a^{\frac{145}{2}} b^{3} x^{\frac{39}{2}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{1200600 a^{\frac{143}{2}} b^{4} x^{20} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{1397760 a^{\frac{143}{2}} b^{4} x^{20}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{2521260 a^{\frac{141}{2}} b^{5} x^{\frac{41}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{3075072 a^{\frac{141}{2}} b^{5} x^{\frac{41}{2}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{3991764 a^{\frac{139}{2}} b^{6} x^{21} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{5125120 a^{\frac{139}{2}} b^{6} x^{21}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{4844172 a^{\frac{137}{2}} b^{7} x^{\frac{43}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{6589440 a^{\frac{137}{2}} b^{7} x^{\frac{43}{2}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{4523220 a^{\frac{135}{2}} b^{8} x^{22} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{6589440 a^{\frac{135}{2}} b^{8} x^{22}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{3196700 a^{\frac{133}{2}} b^{9} x^{\frac{45}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{5125120 a^{\frac{133}{2}} b^{9} x^{\frac{45}{2}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{1568996 a^{\frac{131}{2}} b^{10} x^{23} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{3075072 a^{\frac{131}{2}} b^{10} x^{23}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} - \frac{263484 a^{\frac{129}{2}} b^{11} x^{\frac{47}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{1397760 a^{\frac{129}{2}} b^{11} x^{\frac{47}{2}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{501228 a^{\frac{127}{2}} b^{12} x^{24} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{465920 a^{\frac{127}{2}} b^{12} x^{24}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{782460 a^{\frac{125}{2}} b^{13} x^{\frac{49}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{107520 a^{\frac{125}{2}} b^{13} x^{\frac{49}{2}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{720900 a^{\frac{123}{2}} b^{14} x^{25} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{15360 a^{\frac{123}{2}} b^{14} x^{25}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{486492 a^{\frac{121}{2}} b^{15} x^{\frac{51}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{1024 a^{\frac{121}{2}} b^{15} x^{\frac{51}{2}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{244932 a^{\frac{119}{2}} b^{16} x^{26} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{89676 a^{\frac{117}{2}} b^{17} x^{\frac{53}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{22580 a^{\frac{115}{2}} b^{18} x^{27} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{3500 a^{\frac{113}{2}} b^{19} x^{\frac{55}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}} + \frac{252 a^{\frac{111}{2}} b^{20} x^{28} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{693 a^{70} b^{6} x^{18} + 10395 a^{69} b^{7} x^{\frac{37}{2}} + 72765 a^{68} b^{8} x^{19} + 315315 a^{67} b^{9} x^{\frac{39}{2}} + 945945 a^{66} b^{10} x^{20} + 2081079 a^{65} b^{11} x^{\frac{41}{2}} + 3468465 a^{64} b^{12} x^{21} + 4459455 a^{63} b^{13} x^{\frac{43}{2}} + 4459455 a^{62} b^{14} x^{22} + 3468465 a^{61} b^{15} x^{\frac{45}{2}} + 2081079 a^{60} b^{16} x^{23} + 945945 a^{59} b^{17} x^{\frac{47}{2}} + 315315 a^{58} b^{18} x^{24} + 72765 a^{57} b^{19} x^{\frac{49}{2}} + 10395 a^{56} b^{20} x^{25} + 693 a^{55} b^{21} x^{\frac{51}{2}}}"," ",0,"-1024*a**(151/2)*x**18*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 1024*a**(151/2)*x**18/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 14848*a**(149/2)*b*x**(37/2)*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 15360*a**(149/2)*b*x**(37/2)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 100224*a**(147/2)*b**2*x**19*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 107520*a**(147/2)*b**2*x**19/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 417600*a**(145/2)*b**3*x**(39/2)*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 465920*a**(145/2)*b**3*x**(39/2)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 1200600*a**(143/2)*b**4*x**20*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 1397760*a**(143/2)*b**4*x**20/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 2521260*a**(141/2)*b**5*x**(41/2)*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 3075072*a**(141/2)*b**5*x**(41/2)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 3991764*a**(139/2)*b**6*x**21*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 5125120*a**(139/2)*b**6*x**21/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 4844172*a**(137/2)*b**7*x**(43/2)*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 6589440*a**(137/2)*b**7*x**(43/2)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 4523220*a**(135/2)*b**8*x**22*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 6589440*a**(135/2)*b**8*x**22/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 3196700*a**(133/2)*b**9*x**(45/2)*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 5125120*a**(133/2)*b**9*x**(45/2)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 1568996*a**(131/2)*b**10*x**23*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 3075072*a**(131/2)*b**10*x**23/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) - 263484*a**(129/2)*b**11*x**(47/2)*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 1397760*a**(129/2)*b**11*x**(47/2)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 501228*a**(127/2)*b**12*x**24*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 465920*a**(127/2)*b**12*x**24/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 782460*a**(125/2)*b**13*x**(49/2)*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 107520*a**(125/2)*b**13*x**(49/2)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 720900*a**(123/2)*b**14*x**25*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 15360*a**(123/2)*b**14*x**25/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 486492*a**(121/2)*b**15*x**(51/2)*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 1024*a**(121/2)*b**15*x**(51/2)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 244932*a**(119/2)*b**16*x**26*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 89676*a**(117/2)*b**17*x**(53/2)*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 22580*a**(115/2)*b**18*x**27*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 3500*a**(113/2)*b**19*x**(55/2)*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2)) + 252*a**(111/2)*b**20*x**28*sqrt(1 + b*sqrt(x)/a)/(693*a**70*b**6*x**18 + 10395*a**69*b**7*x**(37/2) + 72765*a**68*b**8*x**19 + 315315*a**67*b**9*x**(39/2) + 945945*a**66*b**10*x**20 + 2081079*a**65*b**11*x**(41/2) + 3468465*a**64*b**12*x**21 + 4459455*a**63*b**13*x**(43/2) + 4459455*a**62*b**14*x**22 + 3468465*a**61*b**15*x**(45/2) + 2081079*a**60*b**16*x**23 + 945945*a**59*b**17*x**(47/2) + 315315*a**58*b**18*x**24 + 72765*a**57*b**19*x**(49/2) + 10395*a**56*b**20*x**25 + 693*a**55*b**21*x**(51/2))","B",0
2240,1,1872,0,2.954917," ","integrate(x/(a+b*x**(1/2))**(1/2),x)","- \frac{64 a^{\frac{47}{2}} x^{8} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{64 a^{\frac{47}{2}} x^{8}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} - \frac{352 a^{\frac{45}{2}} b x^{\frac{17}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{384 a^{\frac{45}{2}} b x^{\frac{17}{2}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} - \frac{792 a^{\frac{43}{2}} b^{2} x^{9} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{960 a^{\frac{43}{2}} b^{2} x^{9}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} - \frac{924 a^{\frac{41}{2}} b^{3} x^{\frac{19}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{1280 a^{\frac{41}{2}} b^{3} x^{\frac{19}{2}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} - \frac{560 a^{\frac{39}{2}} b^{4} x^{10} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{960 a^{\frac{39}{2}} b^{4} x^{10}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} - \frac{84 a^{\frac{37}{2}} b^{5} x^{\frac{21}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{384 a^{\frac{37}{2}} b^{5} x^{\frac{21}{2}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{168 a^{\frac{35}{2}} b^{6} x^{11} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{64 a^{\frac{35}{2}} b^{6} x^{11}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{188 a^{\frac{33}{2}} b^{7} x^{\frac{23}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{96 a^{\frac{31}{2}} b^{8} x^{12} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}} + \frac{20 a^{\frac{29}{2}} b^{9} x^{\frac{25}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{35 a^{20} b^{4} x^{8} + 210 a^{19} b^{5} x^{\frac{17}{2}} + 525 a^{18} b^{6} x^{9} + 700 a^{17} b^{7} x^{\frac{19}{2}} + 525 a^{16} b^{8} x^{10} + 210 a^{15} b^{9} x^{\frac{21}{2}} + 35 a^{14} b^{10} x^{11}}"," ",0,"-64*a**(47/2)*x**8*sqrt(1 + b*sqrt(x)/a)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 64*a**(47/2)*x**8/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) - 352*a**(45/2)*b*x**(17/2)*sqrt(1 + b*sqrt(x)/a)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 384*a**(45/2)*b*x**(17/2)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) - 792*a**(43/2)*b**2*x**9*sqrt(1 + b*sqrt(x)/a)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 960*a**(43/2)*b**2*x**9/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) - 924*a**(41/2)*b**3*x**(19/2)*sqrt(1 + b*sqrt(x)/a)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 1280*a**(41/2)*b**3*x**(19/2)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) - 560*a**(39/2)*b**4*x**10*sqrt(1 + b*sqrt(x)/a)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 960*a**(39/2)*b**4*x**10/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) - 84*a**(37/2)*b**5*x**(21/2)*sqrt(1 + b*sqrt(x)/a)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 384*a**(37/2)*b**5*x**(21/2)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 168*a**(35/2)*b**6*x**11*sqrt(1 + b*sqrt(x)/a)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 64*a**(35/2)*b**6*x**11/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 188*a**(33/2)*b**7*x**(23/2)*sqrt(1 + b*sqrt(x)/a)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 96*a**(31/2)*b**8*x**12*sqrt(1 + b*sqrt(x)/a)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11) + 20*a**(29/2)*b**9*x**(25/2)*sqrt(1 + b*sqrt(x)/a)/(35*a**20*b**4*x**8 + 210*a**19*b**5*x**(17/2) + 525*a**18*b**6*x**9 + 700*a**17*b**7*x**(19/2) + 525*a**16*b**8*x**10 + 210*a**15*b**9*x**(21/2) + 35*a**14*b**10*x**11)","B",0
2241,1,219,0,1.187415," ","integrate(1/(a+b*x**(1/2))**(1/2),x)","- \frac{8 a^{\frac{7}{2}} x^{2} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{3 a^{2} b^{2} x^{2} + 3 a b^{3} x^{\frac{5}{2}}} + \frac{8 a^{\frac{7}{2}} x^{2}}{3 a^{2} b^{2} x^{2} + 3 a b^{3} x^{\frac{5}{2}}} - \frac{4 a^{\frac{5}{2}} b x^{\frac{5}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{3 a^{2} b^{2} x^{2} + 3 a b^{3} x^{\frac{5}{2}}} + \frac{8 a^{\frac{5}{2}} b x^{\frac{5}{2}}}{3 a^{2} b^{2} x^{2} + 3 a b^{3} x^{\frac{5}{2}}} + \frac{4 a^{\frac{3}{2}} b^{2} x^{3} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{3 a^{2} b^{2} x^{2} + 3 a b^{3} x^{\frac{5}{2}}}"," ",0,"-8*a**(7/2)*x**2*sqrt(1 + b*sqrt(x)/a)/(3*a**2*b**2*x**2 + 3*a*b**3*x**(5/2)) + 8*a**(7/2)*x**2/(3*a**2*b**2*x**2 + 3*a*b**3*x**(5/2)) - 4*a**(5/2)*b*x**(5/2)*sqrt(1 + b*sqrt(x)/a)/(3*a**2*b**2*x**2 + 3*a*b**3*x**(5/2)) + 8*a**(5/2)*b*x**(5/2)/(3*a**2*b**2*x**2 + 3*a*b**3*x**(5/2)) + 4*a**(3/2)*b**2*x**3*sqrt(1 + b*sqrt(x)/a)/(3*a**2*b**2*x**2 + 3*a*b**3*x**(5/2))","B",0
2242,1,24,0,1.265721," ","integrate(1/x/(a+b*x**(1/2))**(1/2),x)","- \frac{4 \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt[4]{x}} \right)}}{\sqrt{a}}"," ",0,"-4*asinh(sqrt(a)/(sqrt(b)*x**(1/4)))/sqrt(a)","A",0
2243,1,110,0,4.860381," ","integrate(1/x**2/(a+b*x**(1/2))**(1/2),x)","- \frac{1}{\sqrt{b} x^{\frac{5}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} + \frac{\sqrt{b}}{2 a x^{\frac{3}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} + \frac{3 b^{\frac{3}{2}}}{2 a^{2} \sqrt[4]{x} \sqrt{\frac{a}{b \sqrt{x}} + 1}} - \frac{3 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt[4]{x}} \right)}}{2 a^{\frac{5}{2}}}"," ",0,"-1/(sqrt(b)*x**(5/4)*sqrt(a/(b*sqrt(x)) + 1)) + sqrt(b)/(2*a*x**(3/4)*sqrt(a/(b*sqrt(x)) + 1)) + 3*b**(3/2)/(2*a**2*x**(1/4)*sqrt(a/(b*sqrt(x)) + 1)) - 3*b**2*asinh(sqrt(a)/(sqrt(b)*x**(1/4)))/(2*a**(5/2))","A",0
2244,1,173,0,11.845989," ","integrate(1/x**3/(a+b*x**(1/2))**(1/2),x)","- \frac{1}{2 \sqrt{b} x^{\frac{9}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} + \frac{\sqrt{b}}{12 a x^{\frac{7}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} - \frac{7 b^{\frac{3}{2}}}{48 a^{2} x^{\frac{5}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} + \frac{35 b^{\frac{5}{2}}}{96 a^{3} x^{\frac{3}{4}} \sqrt{\frac{a}{b \sqrt{x}} + 1}} + \frac{35 b^{\frac{7}{2}}}{32 a^{4} \sqrt[4]{x} \sqrt{\frac{a}{b \sqrt{x}} + 1}} - \frac{35 b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt[4]{x}} \right)}}{32 a^{\frac{9}{2}}}"," ",0,"-1/(2*sqrt(b)*x**(9/4)*sqrt(a/(b*sqrt(x)) + 1)) + sqrt(b)/(12*a*x**(7/4)*sqrt(a/(b*sqrt(x)) + 1)) - 7*b**(3/2)/(48*a**2*x**(5/4)*sqrt(a/(b*sqrt(x)) + 1)) + 35*b**(5/2)/(96*a**3*x**(3/4)*sqrt(a/(b*sqrt(x)) + 1)) + 35*b**(7/2)/(32*a**4*x**(1/4)*sqrt(a/(b*sqrt(x)) + 1)) - 35*b**4*asinh(sqrt(a)/(sqrt(b)*x**(1/4)))/(32*a**(9/2))","A",0
2245,1,5039,0,4.319037," ","integrate(x**(1/2)*(a+b*x**(1/2))**n,x)","\frac{4 a^{6} a^{n} x^{\frac{9}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} - \frac{4 a^{6} a^{n} x^{\frac{9}{2}}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} - \frac{4 a^{5} a^{n} b n x^{5} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{12 a^{5} a^{n} b x^{5} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} - \frac{12 a^{5} a^{n} b x^{5}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{2 a^{4} a^{n} b^{2} n^{2} x^{\frac{11}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} - \frac{10 a^{4} a^{n} b^{2} n x^{\frac{11}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{12 a^{4} a^{n} b^{2} x^{\frac{11}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} - \frac{12 a^{4} a^{n} b^{2} x^{\frac{11}{2}}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{8 a^{3} a^{n} b^{3} n^{2} x^{6} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{8 a^{3} a^{n} b^{3} x^{6} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} - \frac{4 a^{3} a^{n} b^{3} x^{6}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{12 a^{2} a^{n} b^{4} n^{2} x^{\frac{13}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{20 a^{2} a^{n} b^{4} n x^{\frac{13}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{12 a^{2} a^{n} b^{4} x^{\frac{13}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{8 a a^{n} b^{5} n^{2} x^{7} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{20 a a^{n} b^{5} n x^{7} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{12 a a^{n} b^{5} x^{7} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{2 a^{n} b^{6} n^{2} x^{\frac{15}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{6 a^{n} b^{6} n x^{\frac{15}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}} + \frac{4 a^{n} b^{6} x^{\frac{15}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{n}}{a^{3} b^{3} n^{3} x^{\frac{9}{2}} + 6 a^{3} b^{3} n^{2} x^{\frac{9}{2}} + 11 a^{3} b^{3} n x^{\frac{9}{2}} + 6 a^{3} b^{3} x^{\frac{9}{2}} + 3 a^{2} b^{4} n^{3} x^{5} + 18 a^{2} b^{4} n^{2} x^{5} + 33 a^{2} b^{4} n x^{5} + 18 a^{2} b^{4} x^{5} + 3 a b^{5} n^{3} x^{\frac{11}{2}} + 18 a b^{5} n^{2} x^{\frac{11}{2}} + 33 a b^{5} n x^{\frac{11}{2}} + 18 a b^{5} x^{\frac{11}{2}} + b^{6} n^{3} x^{6} + 6 b^{6} n^{2} x^{6} + 11 b^{6} n x^{6} + 6 b^{6} x^{6}}"," ",0,"4*a**6*a**n*x**(9/2)*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) - 4*a**6*a**n*x**(9/2)/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) - 4*a**5*a**n*b*n*x**5*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 12*a**5*a**n*b*x**5*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) - 12*a**5*a**n*b*x**5/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 2*a**4*a**n*b**2*n**2*x**(11/2)*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) - 10*a**4*a**n*b**2*n*x**(11/2)*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 12*a**4*a**n*b**2*x**(11/2)*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) - 12*a**4*a**n*b**2*x**(11/2)/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 8*a**3*a**n*b**3*n**2*x**6*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 8*a**3*a**n*b**3*x**6*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) - 4*a**3*a**n*b**3*x**6/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 12*a**2*a**n*b**4*n**2*x**(13/2)*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 20*a**2*a**n*b**4*n*x**(13/2)*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 12*a**2*a**n*b**4*x**(13/2)*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 8*a*a**n*b**5*n**2*x**7*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 20*a*a**n*b**5*n*x**7*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 12*a*a**n*b**5*x**7*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 2*a**n*b**6*n**2*x**(15/2)*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 6*a**n*b**6*n*x**(15/2)*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6) + 4*a**n*b**6*x**(15/2)*(1 + b*sqrt(x)/a)**n/(a**3*b**3*n**3*x**(9/2) + 6*a**3*b**3*n**2*x**(9/2) + 11*a**3*b**3*n*x**(9/2) + 6*a**3*b**3*x**(9/2) + 3*a**2*b**4*n**3*x**5 + 18*a**2*b**4*n**2*x**5 + 33*a**2*b**4*n*x**5 + 18*a**2*b**4*x**5 + 3*a*b**5*n**3*x**(11/2) + 18*a*b**5*n**2*x**(11/2) + 33*a*b**5*n*x**(11/2) + 18*a*b**5*x**(11/2) + b**6*n**3*x**6 + 6*b**6*n**2*x**6 + 11*b**6*n*x**6 + 6*b**6*x**6)","B",0
2246,1,182,0,1.013370," ","integrate((a+b*x**(1/2))**n/x**(1/2),x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: a = 0 \wedge b = 0 \wedge n = -1 \\2 \cdot 0^{n} \sqrt{x} & \text{for}\: a = - b \sqrt{x} \\2 a^{n} \sqrt{x} & \text{for}\: b = 0 \\\frac{2 \log{\left(\frac{a}{b} + \sqrt{x} \right)}}{b} & \text{for}\: n = -1 \\\frac{2 a^{2} \left(a + b \sqrt{x}\right)^{n}}{a b n + a b + b^{2} n \sqrt{x} + b^{2} \sqrt{x}} + \frac{4 a b \sqrt{x} \left(a + b \sqrt{x}\right)^{n}}{a b n + a b + b^{2} n \sqrt{x} + b^{2} \sqrt{x}} + \frac{2 b^{2} x \left(a + b \sqrt{x}\right)^{n}}{a b n + a b + b^{2} n \sqrt{x} + b^{2} \sqrt{x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0) & Eq(n, -1)), (2*0**n*sqrt(x), Eq(a, -b*sqrt(x))), (2*a**n*sqrt(x), Eq(b, 0)), (2*log(a/b + sqrt(x))/b, Eq(n, -1)), (2*a**2*(a + b*sqrt(x))**n/(a*b*n + a*b + b**2*n*sqrt(x) + b**2*sqrt(x)) + 4*a*b*sqrt(x)*(a + b*sqrt(x))**n/(a*b*n + a*b + b**2*n*sqrt(x) + b**2*sqrt(x)) + 2*b**2*x*(a + b*sqrt(x))**n/(a*b*n + a*b + b**2*n*sqrt(x) + b**2*sqrt(x)), True))","A",0
2247,1,7,0,0.146971," ","integrate((1+x**(1/2))/x**(1/2),x)","2 \sqrt{x} + x"," ",0,"2*sqrt(x) + x","A",0
2248,1,17,0,0.154442," ","integrate((1+x**(1/2))**2/x**(1/2),x)","\frac{2 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + 2 x"," ",0,"2*x**(3/2)/3 + 2*sqrt(x) + 2*x","A",0
2249,1,20,0,0.193498," ","integrate((1+x**(1/2))**3/x**(1/2),x)","2 x^{\frac{3}{2}} + 2 \sqrt{x} + \frac{x^{2}}{2} + 3 x"," ",0,"2*x**(3/2) + 2*sqrt(x) + x**2/2 + 3*x","B",0
2250,1,17,0,0.154068," ","integrate(x**(1/2)/(1+x**(1/2)),x)","- 2 \sqrt{x} + x + 2 \log{\left(\sqrt{x} + 1 \right)}"," ",0,"-2*sqrt(x) + x + 2*log(sqrt(x) + 1)","A",0
2251,1,8,0,0.154337," ","integrate(1/x**(1/2)/(1+x**(1/2)),x)","2 \log{\left(\sqrt{x} + 1 \right)}"," ",0,"2*log(sqrt(x) + 1)","A",0
2252,1,8,0,0.355818," ","integrate(1/x**(1/2)/(1+x**(1/2))**2,x)","- \frac{2}{\sqrt{x} + 1}"," ",0,"-2/(sqrt(x) + 1)","A",0
2253,1,12,0,0.442610," ","integrate(1/x**(1/2)/(1+x**(1/2))**3,x)","- \frac{1}{2 \sqrt{x} + x + 1}"," ",0,"-1/(2*sqrt(x) + x + 1)","A",0
2254,1,398,0,1.388931," ","integrate(x**(1/2)*(1+x**(1/2))**(1/2),x)","\frac{60 x^{\frac{15}{2}} \sqrt{\sqrt{x} + 1}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}} + \frac{200 x^{\frac{13}{2}} \sqrt{\sqrt{x} + 1}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}} + \frac{60 x^{\frac{11}{2}} \sqrt{\sqrt{x} + 1}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}} - \frac{96 x^{\frac{11}{2}}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}} + \frac{32 x^{\frac{9}{2}} \sqrt{\sqrt{x} + 1}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}} - \frac{32 x^{\frac{9}{2}}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}} + \frac{192 x^{7} \sqrt{\sqrt{x} + 1}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}} + \frac{80 x^{6} \sqrt{\sqrt{x} + 1}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}} - \frac{32 x^{6}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}} + \frac{80 x^{5} \sqrt{\sqrt{x} + 1}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}} - \frac{96 x^{5}}{315 x^{\frac{11}{2}} + 105 x^{\frac{9}{2}} + 105 x^{6} + 315 x^{5}}"," ",0,"60*x**(15/2)*sqrt(sqrt(x) + 1)/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5) + 200*x**(13/2)*sqrt(sqrt(x) + 1)/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5) + 60*x**(11/2)*sqrt(sqrt(x) + 1)/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5) - 96*x**(11/2)/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5) + 32*x**(9/2)*sqrt(sqrt(x) + 1)/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5) - 32*x**(9/2)/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5) + 192*x**7*sqrt(sqrt(x) + 1)/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5) + 80*x**6*sqrt(sqrt(x) + 1)/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5) - 32*x**6/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5) + 80*x**5*sqrt(sqrt(x) + 1)/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5) - 96*x**5/(315*x**(11/2) + 105*x**(9/2) + 105*x**6 + 315*x**5)","B",0
2255,1,31,0,0.229599," ","integrate((1+x**(1/2))**(1/2)/x**(1/2),x)","\frac{4 \sqrt{x} \sqrt{\sqrt{x} + 1}}{3} + \frac{4 \sqrt{\sqrt{x} + 1}}{3}"," ",0,"4*sqrt(x)*sqrt(sqrt(x) + 1)/3 + 4*sqrt(sqrt(x) + 1)/3","B",0
2256,1,138,0,1.209942," ","integrate(x**(1/3)/(1+x**(1/2)),x)","\frac{16 x^{\frac{5}{6}} \Gamma\left(\frac{8}{3}\right)}{5 \Gamma\left(\frac{11}{3}\right)} - \frac{8 \sqrt[3]{x} \Gamma\left(\frac{8}{3}\right)}{\Gamma\left(\frac{11}{3}\right)} - \frac{16 e^{- \frac{2 i \pi}{3}} \log{\left(- \sqrt[6]{x} e^{\frac{i \pi}{3}} + 1 \right)} \Gamma\left(\frac{8}{3}\right)}{3 \Gamma\left(\frac{11}{3}\right)} - \frac{16 \log{\left(- \sqrt[6]{x} e^{i \pi} + 1 \right)} \Gamma\left(\frac{8}{3}\right)}{3 \Gamma\left(\frac{11}{3}\right)} - \frac{16 e^{\frac{2 i \pi}{3}} \log{\left(- \sqrt[6]{x} e^{\frac{5 i \pi}{3}} + 1 \right)} \Gamma\left(\frac{8}{3}\right)}{3 \Gamma\left(\frac{11}{3}\right)}"," ",0,"16*x**(5/6)*gamma(8/3)/(5*gamma(11/3)) - 8*x**(1/3)*gamma(8/3)/gamma(11/3) - 16*exp(-2*I*pi/3)*log(-x**(1/6)*exp_polar(I*pi/3) + 1)*gamma(8/3)/(3*gamma(11/3)) - 16*log(-x**(1/6)*exp_polar(I*pi) + 1)*gamma(8/3)/(3*gamma(11/3)) - 16*exp(2*I*pi/3)*log(-x**(1/6)*exp_polar(5*I*pi/3) + 1)*gamma(8/3)/(3*gamma(11/3))","C",0
2257,1,117,0,16.333756," ","integrate(x**m*(a+b*x**(1/2))**4,x)","a^{4} \left(\begin{cases} \frac{x^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + 8 a^{3} b \left(\begin{cases} \frac{x^{\frac{3}{2}} x^{m}}{2 m + 3} & \text{for}\: m \neq - \frac{3}{2} \\\log{\left(\sqrt{x} \right)} & \text{otherwise} \end{cases}\right) + 6 a^{2} b^{2} \left(\begin{cases} \frac{x^{2} x^{m}}{m + 2} & \text{for}\: m \neq -2 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + 4 a b^{3} \left(\begin{cases} \frac{2 x^{\frac{5}{2}} x^{m}}{2 m + 5} & \text{for}\: m \neq - \frac{5}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + b^{4} \left(\begin{cases} \frac{x^{3} x^{m}}{m + 3} & \text{for}\: m \neq -3 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a**4*Piecewise((x**(m + 1)/(m + 1), Ne(m, -1)), (log(x), True)) + 8*a**3*b*Piecewise((x**(3/2)*x**m/(2*m + 3), Ne(m, -3/2)), (log(sqrt(x)), True)) + 6*a**2*b**2*Piecewise((x**2*x**m/(m + 2), Ne(m, -2)), (log(x), True)) + 4*a*b**3*Piecewise((2*x**(5/2)*x**m/(2*m + 5), Ne(m, -5/2)), (log(x), True)) + b**4*Piecewise((x**3*x**m/(m + 3), Ne(m, -3)), (log(x), True))","A",0
2258,1,94,0,15.171514," ","integrate(x**m*(a+b*x**(1/2))**3,x)","a^{3} \left(\begin{cases} \frac{x^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + 6 a^{2} b \left(\begin{cases} \frac{x^{\frac{3}{2}} x^{m}}{2 m + 3} & \text{for}\: m \neq - \frac{3}{2} \\\log{\left(\sqrt{x} \right)} & \text{otherwise} \end{cases}\right) + 3 a b^{2} \left(\begin{cases} \frac{x^{2} x^{m}}{m + 2} & \text{for}\: m \neq -2 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + b^{3} \left(\begin{cases} \frac{2 x^{\frac{5}{2}} x^{m}}{2 m + 5} & \text{for}\: m \neq - \frac{5}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a**3*Piecewise((x**(m + 1)/(m + 1), Ne(m, -1)), (log(x), True)) + 6*a**2*b*Piecewise((x**(3/2)*x**m/(2*m + 3), Ne(m, -3/2)), (log(sqrt(x)), True)) + 3*a*b**2*Piecewise((x**2*x**m/(m + 2), Ne(m, -2)), (log(x), True)) + b**3*Piecewise((2*x**(5/2)*x**m/(2*m + 5), Ne(m, -5/2)), (log(x), True))","A",0
2259,1,63,0,3.197381," ","integrate(x**m*(a+b*x**(1/2))**2,x)","a^{2} \left(\begin{cases} \frac{x^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + 4 a b \left(\begin{cases} \frac{x^{\frac{3}{2}} x^{m}}{2 m + 3} & \text{for}\: m \neq - \frac{3}{2} \\\log{\left(\sqrt{x} \right)} & \text{otherwise} \end{cases}\right) + b^{2} \left(\begin{cases} \frac{x^{2} x^{m}}{m + 2} & \text{for}\: m \neq -2 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a**2*Piecewise((x**(m + 1)/(m + 1), Ne(m, -1)), (log(x), True)) + 4*a*b*Piecewise((x**(3/2)*x**m/(2*m + 3), Ne(m, -3/2)), (log(sqrt(x)), True)) + b**2*Piecewise((x**2*x**m/(m + 2), Ne(m, -2)), (log(x), True))","A",0
2260,1,41,0,2.541548," ","integrate(x**m*(a+b*x**(1/2)),x)","a \left(\begin{cases} \frac{x^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + 2 b \left(\begin{cases} \frac{x^{\frac{3}{2}} x^{m}}{2 m + 3} & \text{for}\: m \neq - \frac{3}{2} \\\log{\left(\sqrt{x} \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*Piecewise((x**(m + 1)/(m + 1), Ne(m, -1)), (log(x), True)) + 2*b*Piecewise((x**(3/2)*x**m/(2*m + 3), Ne(m, -3/2)), (log(sqrt(x)), True))","A",0
2261,1,82,0,1.107561," ","integrate(x**m/(a+b*x**(1/2)),x)","\frac{4 m x x^{m} \Phi\left(\frac{b \sqrt{x} e^{i \pi}}{a}, 1, 2 m + 2\right) \Gamma\left(2 m + 2\right)}{a \Gamma\left(2 m + 3\right)} + \frac{4 x x^{m} \Phi\left(\frac{b \sqrt{x} e^{i \pi}}{a}, 1, 2 m + 2\right) \Gamma\left(2 m + 2\right)}{a \Gamma\left(2 m + 3\right)}"," ",0,"4*m*x*x**m*lerchphi(b*sqrt(x)*exp_polar(I*pi)/a, 1, 2*m + 2)*gamma(2*m + 2)/(a*gamma(2*m + 3)) + 4*x*x**m*lerchphi(b*sqrt(x)*exp_polar(I*pi)/a, 1, 2*m + 2)*gamma(2*m + 2)/(a*gamma(2*m + 3))","C",0
2262,1,473,0,2.234076," ","integrate(x**m/(a+b*x**(1/2))**2,x)","- \frac{8 a m^{2} x x^{m} \Phi\left(\frac{b \sqrt{x} e^{i \pi}}{a}, 1, 2 m + 2\right) \Gamma\left(2 m + 2\right)}{a^{3} \Gamma\left(2 m + 3\right) + a^{2} b \sqrt{x} \Gamma\left(2 m + 3\right)} - \frac{12 a m x x^{m} \Phi\left(\frac{b \sqrt{x} e^{i \pi}}{a}, 1, 2 m + 2\right) \Gamma\left(2 m + 2\right)}{a^{3} \Gamma\left(2 m + 3\right) + a^{2} b \sqrt{x} \Gamma\left(2 m + 3\right)} + \frac{4 a m x x^{m} \Gamma\left(2 m + 2\right)}{a^{3} \Gamma\left(2 m + 3\right) + a^{2} b \sqrt{x} \Gamma\left(2 m + 3\right)} - \frac{4 a x x^{m} \Phi\left(\frac{b \sqrt{x} e^{i \pi}}{a}, 1, 2 m + 2\right) \Gamma\left(2 m + 2\right)}{a^{3} \Gamma\left(2 m + 3\right) + a^{2} b \sqrt{x} \Gamma\left(2 m + 3\right)} + \frac{4 a x x^{m} \Gamma\left(2 m + 2\right)}{a^{3} \Gamma\left(2 m + 3\right) + a^{2} b \sqrt{x} \Gamma\left(2 m + 3\right)} - \frac{8 b m^{2} x^{\frac{3}{2}} x^{m} \Phi\left(\frac{b \sqrt{x} e^{i \pi}}{a}, 1, 2 m + 2\right) \Gamma\left(2 m + 2\right)}{a^{3} \Gamma\left(2 m + 3\right) + a^{2} b \sqrt{x} \Gamma\left(2 m + 3\right)} - \frac{12 b m x^{\frac{3}{2}} x^{m} \Phi\left(\frac{b \sqrt{x} e^{i \pi}}{a}, 1, 2 m + 2\right) \Gamma\left(2 m + 2\right)}{a^{3} \Gamma\left(2 m + 3\right) + a^{2} b \sqrt{x} \Gamma\left(2 m + 3\right)} - \frac{4 b x^{\frac{3}{2}} x^{m} \Phi\left(\frac{b \sqrt{x} e^{i \pi}}{a}, 1, 2 m + 2\right) \Gamma\left(2 m + 2\right)}{a^{3} \Gamma\left(2 m + 3\right) + a^{2} b \sqrt{x} \Gamma\left(2 m + 3\right)}"," ",0,"-8*a*m**2*x*x**m*lerchphi(b*sqrt(x)*exp_polar(I*pi)/a, 1, 2*m + 2)*gamma(2*m + 2)/(a**3*gamma(2*m + 3) + a**2*b*sqrt(x)*gamma(2*m + 3)) - 12*a*m*x*x**m*lerchphi(b*sqrt(x)*exp_polar(I*pi)/a, 1, 2*m + 2)*gamma(2*m + 2)/(a**3*gamma(2*m + 3) + a**2*b*sqrt(x)*gamma(2*m + 3)) + 4*a*m*x*x**m*gamma(2*m + 2)/(a**3*gamma(2*m + 3) + a**2*b*sqrt(x)*gamma(2*m + 3)) - 4*a*x*x**m*lerchphi(b*sqrt(x)*exp_polar(I*pi)/a, 1, 2*m + 2)*gamma(2*m + 2)/(a**3*gamma(2*m + 3) + a**2*b*sqrt(x)*gamma(2*m + 3)) + 4*a*x*x**m*gamma(2*m + 2)/(a**3*gamma(2*m + 3) + a**2*b*sqrt(x)*gamma(2*m + 3)) - 8*b*m**2*x**(3/2)*x**m*lerchphi(b*sqrt(x)*exp_polar(I*pi)/a, 1, 2*m + 2)*gamma(2*m + 2)/(a**3*gamma(2*m + 3) + a**2*b*sqrt(x)*gamma(2*m + 3)) - 12*b*m*x**(3/2)*x**m*lerchphi(b*sqrt(x)*exp_polar(I*pi)/a, 1, 2*m + 2)*gamma(2*m + 2)/(a**3*gamma(2*m + 3) + a**2*b*sqrt(x)*gamma(2*m + 3)) - 4*b*x**(3/2)*x**m*lerchphi(b*sqrt(x)*exp_polar(I*pi)/a, 1, 2*m + 2)*gamma(2*m + 2)/(a**3*gamma(2*m + 3) + a**2*b*sqrt(x)*gamma(2*m + 3))","C",0
2263,1,46,0,36.185416," ","integrate(x**m*(a+b*x**(1/2))**p,x)","\frac{2 a^{p} x x^{m} \Gamma\left(2 m + 2\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 2 m + 2 \\ 2 m + 3 \end{matrix}\middle| {\frac{b \sqrt{x} e^{i \pi}}{a}} \right)}}{\Gamma\left(2 m + 3\right)}"," ",0,"2*a**p*x*x**m*gamma(2*m + 2)*hyper((-p, 2*m + 2), (2*m + 3,), b*sqrt(x)*exp_polar(I*pi)/a)/gamma(2*m + 3)","C",0
2264,-2,0,0,0.000000," ","integrate(x**3*(a+b*x**(1/2))**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2265,-1,0,0,0.000000," ","integrate(x**2*(a+b*x**(1/2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2266,-1,0,0,0.000000," ","integrate(x*(a+b*x**(1/2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2267,1,823,0,1.832010," ","integrate((a+b*x**(1/2))**p,x)","- \frac{2 a^{3} a^{p} x^{2} \left(1 + \frac{b \sqrt{x}}{a}\right)^{p}}{a b^{2} p^{2} x^{2} + 3 a b^{2} p x^{2} + 2 a b^{2} x^{2} + b^{3} p^{2} x^{\frac{5}{2}} + 3 b^{3} p x^{\frac{5}{2}} + 2 b^{3} x^{\frac{5}{2}}} + \frac{2 a^{3} a^{p} x^{2}}{a b^{2} p^{2} x^{2} + 3 a b^{2} p x^{2} + 2 a b^{2} x^{2} + b^{3} p^{2} x^{\frac{5}{2}} + 3 b^{3} p x^{\frac{5}{2}} + 2 b^{3} x^{\frac{5}{2}}} + \frac{2 a^{2} a^{p} b p x^{\frac{5}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{p}}{a b^{2} p^{2} x^{2} + 3 a b^{2} p x^{2} + 2 a b^{2} x^{2} + b^{3} p^{2} x^{\frac{5}{2}} + 3 b^{3} p x^{\frac{5}{2}} + 2 b^{3} x^{\frac{5}{2}}} - \frac{2 a^{2} a^{p} b x^{\frac{5}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{p}}{a b^{2} p^{2} x^{2} + 3 a b^{2} p x^{2} + 2 a b^{2} x^{2} + b^{3} p^{2} x^{\frac{5}{2}} + 3 b^{3} p x^{\frac{5}{2}} + 2 b^{3} x^{\frac{5}{2}}} + \frac{2 a^{2} a^{p} b x^{\frac{5}{2}}}{a b^{2} p^{2} x^{2} + 3 a b^{2} p x^{2} + 2 a b^{2} x^{2} + b^{3} p^{2} x^{\frac{5}{2}} + 3 b^{3} p x^{\frac{5}{2}} + 2 b^{3} x^{\frac{5}{2}}} + \frac{4 a a^{p} b^{2} p x^{3} \left(1 + \frac{b \sqrt{x}}{a}\right)^{p}}{a b^{2} p^{2} x^{2} + 3 a b^{2} p x^{2} + 2 a b^{2} x^{2} + b^{3} p^{2} x^{\frac{5}{2}} + 3 b^{3} p x^{\frac{5}{2}} + 2 b^{3} x^{\frac{5}{2}}} + \frac{2 a a^{p} b^{2} x^{3} \left(1 + \frac{b \sqrt{x}}{a}\right)^{p}}{a b^{2} p^{2} x^{2} + 3 a b^{2} p x^{2} + 2 a b^{2} x^{2} + b^{3} p^{2} x^{\frac{5}{2}} + 3 b^{3} p x^{\frac{5}{2}} + 2 b^{3} x^{\frac{5}{2}}} + \frac{2 a^{p} b^{3} p x^{\frac{7}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{p}}{a b^{2} p^{2} x^{2} + 3 a b^{2} p x^{2} + 2 a b^{2} x^{2} + b^{3} p^{2} x^{\frac{5}{2}} + 3 b^{3} p x^{\frac{5}{2}} + 2 b^{3} x^{\frac{5}{2}}} + \frac{2 a^{p} b^{3} x^{\frac{7}{2}} \left(1 + \frac{b \sqrt{x}}{a}\right)^{p}}{a b^{2} p^{2} x^{2} + 3 a b^{2} p x^{2} + 2 a b^{2} x^{2} + b^{3} p^{2} x^{\frac{5}{2}} + 3 b^{3} p x^{\frac{5}{2}} + 2 b^{3} x^{\frac{5}{2}}}"," ",0,"-2*a**3*a**p*x**2*(1 + b*sqrt(x)/a)**p/(a*b**2*p**2*x**2 + 3*a*b**2*p*x**2 + 2*a*b**2*x**2 + b**3*p**2*x**(5/2) + 3*b**3*p*x**(5/2) + 2*b**3*x**(5/2)) + 2*a**3*a**p*x**2/(a*b**2*p**2*x**2 + 3*a*b**2*p*x**2 + 2*a*b**2*x**2 + b**3*p**2*x**(5/2) + 3*b**3*p*x**(5/2) + 2*b**3*x**(5/2)) + 2*a**2*a**p*b*p*x**(5/2)*(1 + b*sqrt(x)/a)**p/(a*b**2*p**2*x**2 + 3*a*b**2*p*x**2 + 2*a*b**2*x**2 + b**3*p**2*x**(5/2) + 3*b**3*p*x**(5/2) + 2*b**3*x**(5/2)) - 2*a**2*a**p*b*x**(5/2)*(1 + b*sqrt(x)/a)**p/(a*b**2*p**2*x**2 + 3*a*b**2*p*x**2 + 2*a*b**2*x**2 + b**3*p**2*x**(5/2) + 3*b**3*p*x**(5/2) + 2*b**3*x**(5/2)) + 2*a**2*a**p*b*x**(5/2)/(a*b**2*p**2*x**2 + 3*a*b**2*p*x**2 + 2*a*b**2*x**2 + b**3*p**2*x**(5/2) + 3*b**3*p*x**(5/2) + 2*b**3*x**(5/2)) + 4*a*a**p*b**2*p*x**3*(1 + b*sqrt(x)/a)**p/(a*b**2*p**2*x**2 + 3*a*b**2*p*x**2 + 2*a*b**2*x**2 + b**3*p**2*x**(5/2) + 3*b**3*p*x**(5/2) + 2*b**3*x**(5/2)) + 2*a*a**p*b**2*x**3*(1 + b*sqrt(x)/a)**p/(a*b**2*p**2*x**2 + 3*a*b**2*p*x**2 + 2*a*b**2*x**2 + b**3*p**2*x**(5/2) + 3*b**3*p*x**(5/2) + 2*b**3*x**(5/2)) + 2*a**p*b**3*p*x**(7/2)*(1 + b*sqrt(x)/a)**p/(a*b**2*p**2*x**2 + 3*a*b**2*p*x**2 + 2*a*b**2*x**2 + b**3*p**2*x**(5/2) + 3*b**3*p*x**(5/2) + 2*b**3*x**(5/2)) + 2*a**p*b**3*x**(7/2)*(1 + b*sqrt(x)/a)**p/(a*b**2*p**2*x**2 + 3*a*b**2*p*x**2 + 2*a*b**2*x**2 + b**3*p**2*x**(5/2) + 3*b**3*p*x**(5/2) + 2*b**3*x**(5/2))","B",0
2268,1,41,0,2.038246," ","integrate((a+b*x**(1/2))**p/x,x)","- \frac{2 b^{p} x^{\frac{p}{2}} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b \sqrt{x}}} \right)}}{\Gamma\left(1 - p\right)}"," ",0,"-2*b**p*x**(p/2)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*sqrt(x)))/gamma(1 - p)","C",0
2269,1,42,0,5.345239," ","integrate((a+b*x**(1/2))**p/x**2,x)","- \frac{2 b^{p} x^{\frac{p}{2}} \Gamma\left(2 - p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 2 - p \\ 3 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b \sqrt{x}}} \right)}}{x \Gamma\left(3 - p\right)}"," ",0,"-2*b**p*x**(p/2)*gamma(2 - p)*hyper((-p, 2 - p), (3 - p,), a*exp_polar(I*pi)/(b*sqrt(x)))/(x*gamma(3 - p))","C",0
2270,1,24,0,0.216498," ","integrate(x**(1/2)/(1+x**(3/2)),x)","\frac{2 \log{\left(\sqrt{x} + 1 \right)}}{3} + \frac{2 \log{\left(- \sqrt{x} + x + 1 \right)}}{3}"," ",0,"2*log(sqrt(x) + 1)/3 + 2*log(-sqrt(x) + x + 1)/3","B",0
2271,1,41,0,2.121046," ","integrate(x**3/(a+b*x**(3/2))**(2/3),x)","\frac{2 x^{4} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{\frac{3}{2}} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{11}{3}\right)}"," ",0,"2*x**4*gamma(8/3)*hyper((2/3, 8/3), (11/3,), b*x**(3/2)*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(11/3))","C",0
2272,1,39,0,1.130189," ","integrate(1/(a+b*x**(3/2))**(2/3),x)","\frac{2 x \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{\frac{3}{2}} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"2*x*gamma(2/3)*hyper((2/3, 2/3), (5/3,), b*x**(3/2)*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(5/3))","C",0
2273,1,76,0,2.678741," ","integrate(1/x**3/(a+b*x**(3/2))**(2/3),x)","- \frac{2 \sqrt[3]{b} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{4}{3}\right)}{9 a x^{\frac{3}{2}} \Gamma\left(\frac{2}{3}\right)} + \frac{2 b^{\frac{4}{3}} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{4}{3}\right)}{3 a^{2} \Gamma\left(\frac{2}{3}\right)}"," ",0,"-2*b**(1/3)*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-4/3)/(9*a*x**(3/2)*gamma(2/3)) + 2*b**(4/3)*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-4/3)/(3*a**2*gamma(2/3))","A",0
2274,1,736,0,14.492724," ","integrate(1/x**6/(a+b*x**(3/2))**(2/3),x)","- \frac{56 a^{6} b^{\frac{28}{3}} x^{9} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{\frac{27}{2}} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{\frac{33}{2}} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} - \frac{96 a^{5} b^{\frac{31}{3}} x^{\frac{21}{2}} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{\frac{27}{2}} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{\frac{33}{2}} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} - \frac{60 a^{4} b^{\frac{34}{3}} x^{12} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{\frac{27}{2}} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{\frac{33}{2}} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} + \frac{160 a^{3} b^{\frac{37}{3}} x^{\frac{27}{2}} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{\frac{27}{2}} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{\frac{33}{2}} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} + \frac{720 a^{2} b^{\frac{40}{3}} x^{15} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{\frac{27}{2}} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{\frac{33}{2}} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} + \frac{864 a b^{\frac{43}{3}} x^{\frac{33}{2}} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{\frac{27}{2}} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{\frac{33}{2}} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)} + \frac{324 b^{\frac{46}{3}} x^{18} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{10}{3}\right)}{81 a^{7} b^{9} x^{\frac{27}{2}} \Gamma\left(\frac{2}{3}\right) + 243 a^{6} b^{10} x^{15} \Gamma\left(\frac{2}{3}\right) + 243 a^{5} b^{11} x^{\frac{33}{2}} \Gamma\left(\frac{2}{3}\right) + 81 a^{4} b^{12} x^{18} \Gamma\left(\frac{2}{3}\right)}"," ",0,"-56*a**6*b**(28/3)*x**9*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**(27/2)*gamma(2/3) + 243*a**6*b**10*x**15*gamma(2/3) + 243*a**5*b**11*x**(33/2)*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) - 96*a**5*b**(31/3)*x**(21/2)*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**(27/2)*gamma(2/3) + 243*a**6*b**10*x**15*gamma(2/3) + 243*a**5*b**11*x**(33/2)*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) - 60*a**4*b**(34/3)*x**12*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**(27/2)*gamma(2/3) + 243*a**6*b**10*x**15*gamma(2/3) + 243*a**5*b**11*x**(33/2)*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) + 160*a**3*b**(37/3)*x**(27/2)*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**(27/2)*gamma(2/3) + 243*a**6*b**10*x**15*gamma(2/3) + 243*a**5*b**11*x**(33/2)*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) + 720*a**2*b**(40/3)*x**15*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**(27/2)*gamma(2/3) + 243*a**6*b**10*x**15*gamma(2/3) + 243*a**5*b**11*x**(33/2)*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) + 864*a*b**(43/3)*x**(33/2)*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**(27/2)*gamma(2/3) + 243*a**6*b**10*x**15*gamma(2/3) + 243*a**5*b**11*x**(33/2)*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3)) + 324*b**(46/3)*x**18*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-10/3)/(81*a**7*b**9*x**(27/2)*gamma(2/3) + 243*a**6*b**10*x**15*gamma(2/3) + 243*a**5*b**11*x**(33/2)*gamma(2/3) + 81*a**4*b**12*x**18*gamma(2/3))","B",0
2275,1,1554,0,55.104240," ","integrate(1/x**9/(a+b*x**(3/2))**(2/3),x)","- \frac{7280 a^{10} b^{\frac{76}{3}} x^{30} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)} - \frac{28000 a^{9} b^{\frac{79}{3}} x^{\frac{63}{2}} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)} - \frac{40880 a^{8} b^{\frac{82}{3}} x^{33} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)} - \frac{26240 a^{7} b^{\frac{85}{3}} x^{\frac{69}{2}} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)} - \frac{7840 a^{6} b^{\frac{88}{3}} x^{36} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)} + \frac{24640 a^{5} b^{\frac{91}{3}} x^{\frac{75}{2}} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)} + \frac{184800 a^{4} b^{\frac{94}{3}} x^{39} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)} + \frac{443520 a^{3} b^{\frac{97}{3}} x^{\frac{81}{2}} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)} + \frac{498960 a^{2} b^{\frac{100}{3}} x^{42} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)} + \frac{272160 a b^{\frac{103}{3}} x^{\frac{87}{2}} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)} + \frac{58320 b^{\frac{106}{3}} x^{45} \sqrt[3]{\frac{a}{b x^{\frac{3}{2}}} + 1} \Gamma\left(- \frac{16}{3}\right)}{729 a^{11} b^{25} x^{\frac{75}{2}} \Gamma\left(\frac{2}{3}\right) + 3645 a^{10} b^{26} x^{39} \Gamma\left(\frac{2}{3}\right) + 7290 a^{9} b^{27} x^{\frac{81}{2}} \Gamma\left(\frac{2}{3}\right) + 7290 a^{8} b^{28} x^{42} \Gamma\left(\frac{2}{3}\right) + 3645 a^{7} b^{29} x^{\frac{87}{2}} \Gamma\left(\frac{2}{3}\right) + 729 a^{6} b^{30} x^{45} \Gamma\left(\frac{2}{3}\right)}"," ",0,"-7280*a**10*b**(76/3)*x**30*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3)) - 28000*a**9*b**(79/3)*x**(63/2)*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3)) - 40880*a**8*b**(82/3)*x**33*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3)) - 26240*a**7*b**(85/3)*x**(69/2)*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3)) - 7840*a**6*b**(88/3)*x**36*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3)) + 24640*a**5*b**(91/3)*x**(75/2)*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3)) + 184800*a**4*b**(94/3)*x**39*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3)) + 443520*a**3*b**(97/3)*x**(81/2)*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3)) + 498960*a**2*b**(100/3)*x**42*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3)) + 272160*a*b**(103/3)*x**(87/2)*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3)) + 58320*b**(106/3)*x**45*(a/(b*x**(3/2)) + 1)**(1/3)*gamma(-16/3)/(729*a**11*b**25*x**(75/2)*gamma(2/3) + 3645*a**10*b**26*x**39*gamma(2/3) + 7290*a**9*b**27*x**(81/2)*gamma(2/3) + 7290*a**8*b**28*x**42*gamma(2/3) + 3645*a**7*b**29*x**(87/2)*gamma(2/3) + 729*a**6*b**30*x**45*gamma(2/3))","B",0
2276,-1,0,0,0.000000," ","integrate(x**8/(a+b*x**(3/2))**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2277,1,102,0,39.171473," ","integrate(x**5/(a+b*x**(3/2))**(2/3),x)","\begin{cases} - \frac{81 a^{3} \sqrt[3]{a + b x^{\frac{3}{2}}}}{70 b^{4}} + \frac{27 a^{2} x^{\frac{3}{2}} \sqrt[3]{a + b x^{\frac{3}{2}}}}{70 b^{3}} - \frac{9 a x^{3} \sqrt[3]{a + b x^{\frac{3}{2}}}}{35 b^{2}} + \frac{x^{\frac{9}{2}} \sqrt[3]{a + b x^{\frac{3}{2}}}}{5 b} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{2}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-81*a**3*(a + b*x**(3/2))**(1/3)/(70*b**4) + 27*a**2*x**(3/2)*(a + b*x**(3/2))**(1/3)/(70*b**3) - 9*a*x**3*(a + b*x**(3/2))**(1/3)/(35*b**2) + x**(9/2)*(a + b*x**(3/2))**(1/3)/(5*b), Ne(b, 0)), (x**6/(6*a**(2/3)), True))","A",0
2278,1,49,0,1.582424," ","integrate(x**2/(a+b*x**(3/2))**(2/3),x)","\begin{cases} - \frac{3 a \sqrt[3]{a + b x^{\frac{3}{2}}}}{2 b^{2}} + \frac{x^{\frac{3}{2}} \sqrt[3]{a + b x^{\frac{3}{2}}}}{2 b} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{\frac{2}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a*(a + b*x**(3/2))**(1/3)/(2*b**2) + x**(3/2)*(a + b*x**(3/2))**(1/3)/(2*b), Ne(b, 0)), (x**3/(3*a**(2/3)), True))","A",0
2279,1,41,0,1.407979," ","integrate(1/x/(a+b*x**(3/2))**(2/3),x)","- \frac{2 \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{\frac{3}{2}}}} \right)}}{3 b^{\frac{2}{3}} x \Gamma\left(\frac{5}{3}\right)}"," ",0,"-2*gamma(2/3)*hyper((2/3, 2/3), (5/3,), a*exp_polar(I*pi)/(b*x**(3/2)))/(3*b**(2/3)*x*gamma(5/3))","C",0
2280,1,42,0,5.299632," ","integrate(1/x**4/(a+b*x**(3/2))**(2/3),x)","- \frac{2 \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{\frac{3}{2}}}} \right)}}{3 b^{\frac{2}{3}} x^{4} \Gamma\left(\frac{11}{3}\right)}"," ",0,"-2*gamma(8/3)*hyper((2/3, 8/3), (11/3,), a*exp_polar(I*pi)/(b*x**(3/2)))/(3*b**(2/3)*x**4*gamma(11/3))","C",0
2281,1,41,0,2.799835," ","integrate(x**4/(a+b*x**(3/2))**(2/3),x)","\frac{2 x^{5} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{10}{3} \\ \frac{13}{3} \end{matrix}\middle| {\frac{b x^{\frac{3}{2}} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{13}{3}\right)}"," ",0,"2*x**5*gamma(10/3)*hyper((2/3, 10/3), (13/3,), b*x**(3/2)*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(13/3))","C",0
2282,1,41,0,0.881843," ","integrate(x/(a+b*x**(3/2))**(2/3),x)","\frac{2 x^{2} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{\frac{3}{2}} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"2*x**2*gamma(4/3)*hyper((2/3, 4/3), (7/3,), b*x**(3/2)*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(7/3))","C",0
2283,1,42,0,1.734101," ","integrate(1/x**2/(a+b*x**(3/2))**(2/3),x)","\frac{2 \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{2}{3} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{\frac{3}{2}} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} x \Gamma\left(\frac{1}{3}\right)}"," ",0,"2*gamma(-2/3)*hyper((-2/3, 2/3), (1/3,), b*x**(3/2)*exp_polar(I*pi)/a)/(3*a**(2/3)*x*gamma(1/3))","C",0
2284,1,48,0,8.192830," ","integrate(1/x**5/(a+b*x**(3/2))**(2/3),x)","\frac{2 \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, \frac{2}{3} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b x^{\frac{3}{2}} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} x^{4} \Gamma\left(- \frac{5}{3}\right)}"," ",0,"2*gamma(-8/3)*hyper((-8/3, 2/3), (-5/3,), b*x**(3/2)*exp_polar(I*pi)/a)/(3*a**(2/3)*x**4*gamma(-5/3))","C",0
2285,1,15,0,1.746248," ","integrate((a+b*x**(1/3))*x**4,x)","\frac{a x^{5}}{5} + \frac{3 b x^{\frac{16}{3}}}{16}"," ",0,"a*x**5/5 + 3*b*x**(16/3)/16","A",0
2286,1,15,0,1.518752," ","integrate((a+b*x**(1/3))*x**3,x)","\frac{a x^{4}}{4} + \frac{3 b x^{\frac{13}{3}}}{13}"," ",0,"a*x**4/4 + 3*b*x**(13/3)/13","A",0
2287,1,15,0,1.348944," ","integrate((a+b*x**(1/3))*x**2,x)","\frac{a x^{3}}{3} + \frac{3 b x^{\frac{10}{3}}}{10}"," ",0,"a*x**3/3 + 3*b*x**(10/3)/10","A",0
2288,1,15,0,1.242216," ","integrate((a+b*x**(1/3))*x,x)","\frac{a x^{2}}{2} + \frac{3 b x^{\frac{7}{3}}}{7}"," ",0,"a*x**2/2 + 3*b*x**(7/3)/7","A",0
2289,1,12,0,0.060023," ","integrate(a+b*x**(1/3),x)","a x + \frac{3 b x^{\frac{4}{3}}}{4}"," ",0,"a*x + 3*b*x**(4/3)/4","A",0
2290,1,12,0,0.270181," ","integrate((a+b*x**(1/3))/x,x)","a \log{\left(x \right)} + 3 b \sqrt[3]{x}"," ",0,"a*log(x) + 3*b*x**(1/3)","A",0
2291,1,14,0,0.727414," ","integrate((a+b*x**(1/3))/x**2,x)","- \frac{a}{x} - \frac{3 b}{2 x^{\frac{2}{3}}}"," ",0,"-a/x - 3*b/(2*x**(2/3))","A",0
2292,1,17,0,1.270859," ","integrate((a+b*x**(1/3))/x**3,x)","- \frac{a}{2 x^{2}} - \frac{3 b}{5 x^{\frac{5}{3}}}"," ",0,"-a/(2*x**2) - 3*b/(5*x**(5/3))","A",0
2293,1,17,0,2.147841," ","integrate((a+b*x**(1/3))/x**4,x)","- \frac{a}{3 x^{3}} - \frac{3 b}{8 x^{\frac{8}{3}}}"," ",0,"-a/(3*x**3) - 3*b/(8*x**(8/3))","A",0
2294,1,31,0,2.024662," ","integrate((a+b*x**(1/3))**2*x**4,x)","\frac{a^{2} x^{5}}{5} + \frac{3 a b x^{\frac{16}{3}}}{8} + \frac{3 b^{2} x^{\frac{17}{3}}}{17}"," ",0,"a**2*x**5/5 + 3*a*b*x**(16/3)/8 + 3*b**2*x**(17/3)/17","A",0
2295,1,31,0,1.728433," ","integrate((a+b*x**(1/3))**2*x**3,x)","\frac{a^{2} x^{4}}{4} + \frac{6 a b x^{\frac{13}{3}}}{13} + \frac{3 b^{2} x^{\frac{14}{3}}}{14}"," ",0,"a**2*x**4/4 + 6*a*b*x**(13/3)/13 + 3*b**2*x**(14/3)/14","A",0
2296,1,31,0,1.606518," ","integrate((a+b*x**(1/3))**2*x**2,x)","\frac{a^{2} x^{3}}{3} + \frac{3 a b x^{\frac{10}{3}}}{5} + \frac{3 b^{2} x^{\frac{11}{3}}}{11}"," ",0,"a**2*x**3/3 + 3*a*b*x**(10/3)/5 + 3*b**2*x**(11/3)/11","A",0
2297,1,31,0,1.513216," ","integrate((a+b*x**(1/3))**2*x,x)","\frac{a^{2} x^{2}}{2} + \frac{6 a b x^{\frac{7}{3}}}{7} + \frac{3 b^{2} x^{\frac{8}{3}}}{8}"," ",0,"a**2*x**2/2 + 6*a*b*x**(7/3)/7 + 3*b**2*x**(8/3)/8","A",0
2298,1,27,0,1.386379," ","integrate((a+b*x**(1/3))**2,x)","a^{2} x + \frac{3 a b x^{\frac{4}{3}}}{2} + \frac{3 b^{2} x^{\frac{5}{3}}}{5}"," ",0,"a**2*x + 3*a*b*x**(4/3)/2 + 3*b**2*x**(5/3)/5","A",0
2299,1,27,0,0.236721," ","integrate((a+b*x**(1/3))**2/x,x)","a^{2} \log{\left(x \right)} + 6 a b \sqrt[3]{x} + \frac{3 b^{2} x^{\frac{2}{3}}}{2}"," ",0,"a**2*log(x) + 6*a*b*x**(1/3) + 3*b**2*x**(2/3)/2","A",0
2300,1,26,0,0.629244," ","integrate((a+b*x**(1/3))**2/x**2,x)","- \frac{a^{2}}{x} - \frac{3 a b}{x^{\frac{2}{3}}} - \frac{3 b^{2}}{\sqrt[3]{x}}"," ",0,"-a**2/x - 3*a*b/x**(2/3) - 3*b**2/x**(1/3)","A",0
2301,1,32,0,1.070996," ","integrate((a+b*x**(1/3))**2/x**3,x)","- \frac{a^{2}}{2 x^{2}} - \frac{6 a b}{5 x^{\frac{5}{3}}} - \frac{3 b^{2}}{4 x^{\frac{4}{3}}}"," ",0,"-a**2/(2*x**2) - 6*a*b/(5*x**(5/3)) - 3*b**2/(4*x**(4/3))","A",0
2302,1,32,0,1.881438," ","integrate((a+b*x**(1/3))**2/x**4,x)","- \frac{a^{2}}{3 x^{3}} - \frac{3 a b}{4 x^{\frac{8}{3}}} - \frac{3 b^{2}}{7 x^{\frac{7}{3}}}"," ",0,"-a**2/(3*x**3) - 3*a*b/(4*x**(8/3)) - 3*b**2/(7*x**(7/3))","A",0
2303,1,42,0,2.325085," ","integrate((a+b*x**(1/3))**3*x**4,x)","\frac{a^{3} x^{5}}{5} + \frac{9 a^{2} b x^{\frac{16}{3}}}{16} + \frac{9 a b^{2} x^{\frac{17}{3}}}{17} + \frac{b^{3} x^{6}}{6}"," ",0,"a**3*x**5/5 + 9*a**2*b*x**(16/3)/16 + 9*a*b**2*x**(17/3)/17 + b**3*x**6/6","A",0
2304,1,42,0,2.094714," ","integrate((a+b*x**(1/3))**3*x**3,x)","\frac{a^{3} x^{4}}{4} + \frac{9 a^{2} b x^{\frac{13}{3}}}{13} + \frac{9 a b^{2} x^{\frac{14}{3}}}{14} + \frac{b^{3} x^{5}}{5}"," ",0,"a**3*x**4/4 + 9*a**2*b*x**(13/3)/13 + 9*a*b**2*x**(14/3)/14 + b**3*x**5/5","A",0
2305,1,42,0,1.876889," ","integrate((a+b*x**(1/3))**3*x**2,x)","\frac{a^{3} x^{3}}{3} + \frac{9 a^{2} b x^{\frac{10}{3}}}{10} + \frac{9 a b^{2} x^{\frac{11}{3}}}{11} + \frac{b^{3} x^{4}}{4}"," ",0,"a**3*x**3/3 + 9*a**2*b*x**(10/3)/10 + 9*a*b**2*x**(11/3)/11 + b**3*x**4/4","A",0
2306,1,42,0,1.728903," ","integrate((a+b*x**(1/3))**3*x,x)","\frac{a^{3} x^{2}}{2} + \frac{9 a^{2} b x^{\frac{7}{3}}}{7} + \frac{9 a b^{2} x^{\frac{8}{3}}}{8} + \frac{b^{3} x^{3}}{3}"," ",0,"a**3*x**2/2 + 9*a**2*b*x**(7/3)/7 + 9*a*b**2*x**(8/3)/8 + b**3*x**3/3","A",0
2307,1,39,0,1.598387," ","integrate((a+b*x**(1/3))**3,x)","a^{3} x + \frac{9 a^{2} b x^{\frac{4}{3}}}{4} + \frac{9 a b^{2} x^{\frac{5}{3}}}{5} + \frac{b^{3} x^{2}}{2}"," ",0,"a**3*x + 9*a**2*b*x**(4/3)/4 + 9*a*b**2*x**(5/3)/5 + b**3*x**2/2","A",0
2308,1,36,0,0.250643," ","integrate((a+b*x**(1/3))**3/x,x)","a^{3} \log{\left(x \right)} + 9 a^{2} b \sqrt[3]{x} + \frac{9 a b^{2} x^{\frac{2}{3}}}{2} + b^{3} x"," ",0,"a**3*log(x) + 9*a**2*b*x**(1/3) + 9*a*b**2*x**(2/3)/2 + b**3*x","A",0
2309,1,36,0,0.652518," ","integrate((a+b*x**(1/3))**3/x**2,x)","- \frac{a^{3}}{x} - \frac{9 a^{2} b}{2 x^{\frac{2}{3}}} - \frac{9 a b^{2}}{\sqrt[3]{x}} + b^{3} \log{\left(x \right)}"," ",0,"-a**3/x - 9*a**2*b/(2*x**(2/3)) - 9*a*b**2/x**(1/3) + b**3*log(x)","A",0
2310,1,41,0,1.163257," ","integrate((a+b*x**(1/3))**3/x**3,x)","- \frac{a^{3}}{2 x^{2}} - \frac{9 a^{2} b}{5 x^{\frac{5}{3}}} - \frac{9 a b^{2}}{4 x^{\frac{4}{3}}} - \frac{b^{3}}{x}"," ",0,"-a**3/(2*x**2) - 9*a**2*b/(5*x**(5/3)) - 9*a*b**2/(4*x**(4/3)) - b**3/x","A",0
2311,1,44,0,1.951450," ","integrate((a+b*x**(1/3))**3/x**4,x)","- \frac{a^{3}}{3 x^{3}} - \frac{9 a^{2} b}{8 x^{\frac{8}{3}}} - \frac{9 a b^{2}}{7 x^{\frac{7}{3}}} - \frac{b^{3}}{2 x^{2}}"," ",0,"-a**3/(3*x**3) - 9*a**2*b/(8*x**(8/3)) - 9*a*b**2/(7*x**(7/3)) - b**3/(2*x**2)","A",0
2312,1,75,0,2.899953," ","integrate((a+b*x**(1/3))**5*x**4,x)","\frac{a^{5} x^{5}}{5} + \frac{15 a^{4} b x^{\frac{16}{3}}}{16} + \frac{30 a^{3} b^{2} x^{\frac{17}{3}}}{17} + \frac{5 a^{2} b^{3} x^{6}}{3} + \frac{15 a b^{4} x^{\frac{19}{3}}}{19} + \frac{3 b^{5} x^{\frac{20}{3}}}{20}"," ",0,"a**5*x**5/5 + 15*a**4*b*x**(16/3)/16 + 30*a**3*b**2*x**(17/3)/17 + 5*a**2*b**3*x**6/3 + 15*a*b**4*x**(19/3)/19 + 3*b**5*x**(20/3)/20","A",0
2313,1,73,0,2.612501," ","integrate((a+b*x**(1/3))**5*x**3,x)","\frac{a^{5} x^{4}}{4} + \frac{15 a^{4} b x^{\frac{13}{3}}}{13} + \frac{15 a^{3} b^{2} x^{\frac{14}{3}}}{7} + 2 a^{2} b^{3} x^{5} + \frac{15 a b^{4} x^{\frac{16}{3}}}{16} + \frac{3 b^{5} x^{\frac{17}{3}}}{17}"," ",0,"a**5*x**4/4 + 15*a**4*b*x**(13/3)/13 + 15*a**3*b**2*x**(14/3)/7 + 2*a**2*b**3*x**5 + 15*a*b**4*x**(16/3)/16 + 3*b**5*x**(17/3)/17","A",0
2314,1,75,0,2.383680," ","integrate((a+b*x**(1/3))**5*x**2,x)","\frac{a^{5} x^{3}}{3} + \frac{3 a^{4} b x^{\frac{10}{3}}}{2} + \frac{30 a^{3} b^{2} x^{\frac{11}{3}}}{11} + \frac{5 a^{2} b^{3} x^{4}}{2} + \frac{15 a b^{4} x^{\frac{13}{3}}}{13} + \frac{3 b^{5} x^{\frac{14}{3}}}{14}"," ",0,"a**5*x**3/3 + 3*a**4*b*x**(10/3)/2 + 30*a**3*b**2*x**(11/3)/11 + 5*a**2*b**3*x**4/2 + 15*a*b**4*x**(13/3)/13 + 3*b**5*x**(14/3)/14","A",0
2315,1,75,0,2.243171," ","integrate((a+b*x**(1/3))**5*x,x)","\frac{a^{5} x^{2}}{2} + \frac{15 a^{4} b x^{\frac{7}{3}}}{7} + \frac{15 a^{3} b^{2} x^{\frac{8}{3}}}{4} + \frac{10 a^{2} b^{3} x^{3}}{3} + \frac{3 a b^{4} x^{\frac{10}{3}}}{2} + \frac{3 b^{5} x^{\frac{11}{3}}}{11}"," ",0,"a**5*x**2/2 + 15*a**4*b*x**(7/3)/7 + 15*a**3*b**2*x**(8/3)/4 + 10*a**2*b**3*x**3/3 + 3*a*b**4*x**(10/3)/2 + 3*b**5*x**(11/3)/11","A",0
2316,1,68,0,2.081571," ","integrate((a+b*x**(1/3))**5,x)","a^{5} x + \frac{15 a^{4} b x^{\frac{4}{3}}}{4} + 6 a^{3} b^{2} x^{\frac{5}{3}} + 5 a^{2} b^{3} x^{2} + \frac{15 a b^{4} x^{\frac{7}{3}}}{7} + \frac{3 b^{5} x^{\frac{8}{3}}}{8}"," ",0,"a**5*x + 15*a**4*b*x**(4/3)/4 + 6*a**3*b**2*x**(5/3) + 5*a**2*b**3*x**2 + 15*a*b**4*x**(7/3)/7 + 3*b**5*x**(8/3)/8","A",0
2317,1,66,0,29.950916," ","integrate((a+b*x**(1/3))**5/x,x)","a^{5} \log{\left(x \right)} + 15 a^{4} b \sqrt[3]{x} + 15 a^{3} b^{2} x^{\frac{2}{3}} + 10 a^{2} b^{3} x + \frac{15 a b^{4} x^{\frac{4}{3}}}{4} + \frac{3 b^{5} x^{\frac{5}{3}}}{5}"," ",0,"a**5*log(x) + 15*a**4*b*x**(1/3) + 15*a**3*b**2*x**(2/3) + 10*a**2*b**3*x + 15*a*b**4*x**(4/3)/4 + 3*b**5*x**(5/3)/5","A",0
2318,1,66,0,0.712669," ","integrate((a+b*x**(1/3))**5/x**2,x)","- \frac{a^{5}}{x} - \frac{15 a^{4} b}{2 x^{\frac{2}{3}}} - \frac{30 a^{3} b^{2}}{\sqrt[3]{x}} + 10 a^{2} b^{3} \log{\left(x \right)} + 15 a b^{4} \sqrt[3]{x} + \frac{3 b^{5} x^{\frac{2}{3}}}{2}"," ",0,"-a**5/x - 15*a**4*b/(2*x**(2/3)) - 30*a**3*b**2/x**(1/3) + 10*a**2*b**3*log(x) + 15*a*b**4*x**(1/3) + 3*b**5*x**(2/3)/2","A",0
2319,1,70,0,1.239365," ","integrate((a+b*x**(1/3))**5/x**3,x)","- \frac{a^{5}}{2 x^{2}} - \frac{3 a^{4} b}{x^{\frac{5}{3}}} - \frac{15 a^{3} b^{2}}{2 x^{\frac{4}{3}}} - \frac{10 a^{2} b^{3}}{x} - \frac{15 a b^{4}}{2 x^{\frac{2}{3}}} - \frac{3 b^{5}}{\sqrt[3]{x}}"," ",0,"-a**5/(2*x**2) - 3*a**4*b/x**(5/3) - 15*a**3*b**2/(2*x**(4/3)) - 10*a**2*b**3/x - 15*a*b**4/(2*x**(2/3)) - 3*b**5/x**(1/3)","B",0
2320,1,73,0,2.147827," ","integrate((a+b*x**(1/3))**5/x**4,x)","- \frac{a^{5}}{3 x^{3}} - \frac{15 a^{4} b}{8 x^{\frac{8}{3}}} - \frac{30 a^{3} b^{2}}{7 x^{\frac{7}{3}}} - \frac{5 a^{2} b^{3}}{x^{2}} - \frac{3 a b^{4}}{x^{\frac{5}{3}}} - \frac{3 b^{5}}{4 x^{\frac{4}{3}}}"," ",0,"-a**5/(3*x**3) - 15*a**4*b/(8*x**(8/3)) - 30*a**3*b**2/(7*x**(7/3)) - 5*a**2*b**3/x**2 - 3*a*b**4/x**(5/3) - 3*b**5/(4*x**(4/3))","A",0
2321,1,75,0,3.530766," ","integrate((a+b*x**(1/3))**5/x**5,x)","- \frac{a^{5}}{4 x^{4}} - \frac{15 a^{4} b}{11 x^{\frac{11}{3}}} - \frac{3 a^{3} b^{2}}{x^{\frac{10}{3}}} - \frac{10 a^{2} b^{3}}{3 x^{3}} - \frac{15 a b^{4}}{8 x^{\frac{8}{3}}} - \frac{3 b^{5}}{7 x^{\frac{7}{3}}}"," ",0,"-a**5/(4*x**4) - 15*a**4*b/(11*x**(11/3)) - 3*a**3*b**2/x**(10/3) - 10*a**2*b**3/(3*x**3) - 15*a*b**4/(8*x**(8/3)) - 3*b**5/(7*x**(7/3))","A",0
2322,1,76,0,5.349303," ","integrate((a+b*x**(1/3))**5/x**6,x)","- \frac{a^{5}}{5 x^{5}} - \frac{15 a^{4} b}{14 x^{\frac{14}{3}}} - \frac{30 a^{3} b^{2}}{13 x^{\frac{13}{3}}} - \frac{5 a^{2} b^{3}}{2 x^{4}} - \frac{15 a b^{4}}{11 x^{\frac{11}{3}}} - \frac{3 b^{5}}{10 x^{\frac{10}{3}}}"," ",0,"-a**5/(5*x**5) - 15*a**4*b/(14*x**(14/3)) - 30*a**3*b**2/(13*x**(13/3)) - 5*a**2*b**3/(2*x**4) - 15*a*b**4/(11*x**(11/3)) - 3*b**5/(10*x**(10/3))","A",0
2323,1,75,0,8.508835," ","integrate((a+b*x**(1/3))**5/x**7,x)","- \frac{a^{5}}{6 x^{6}} - \frac{15 a^{4} b}{17 x^{\frac{17}{3}}} - \frac{15 a^{3} b^{2}}{8 x^{\frac{16}{3}}} - \frac{2 a^{2} b^{3}}{x^{5}} - \frac{15 a b^{4}}{14 x^{\frac{14}{3}}} - \frac{3 b^{5}}{13 x^{\frac{13}{3}}}"," ",0,"-a**5/(6*x**6) - 15*a**4*b/(17*x**(17/3)) - 15*a**3*b**2/(8*x**(16/3)) - 2*a**2*b**3/x**5 - 15*a*b**4/(14*x**(14/3)) - 3*b**5/(13*x**(13/3))","A",0
2324,1,144,0,4.665365," ","integrate((a+b*x**(1/3))**10*x**4,x)","\frac{a^{10} x^{5}}{5} + \frac{15 a^{9} b x^{\frac{16}{3}}}{8} + \frac{135 a^{8} b^{2} x^{\frac{17}{3}}}{17} + 20 a^{7} b^{3} x^{6} + \frac{630 a^{6} b^{4} x^{\frac{19}{3}}}{19} + \frac{189 a^{5} b^{5} x^{\frac{20}{3}}}{5} + 30 a^{4} b^{6} x^{7} + \frac{180 a^{3} b^{7} x^{\frac{22}{3}}}{11} + \frac{135 a^{2} b^{8} x^{\frac{23}{3}}}{23} + \frac{5 a b^{9} x^{8}}{4} + \frac{3 b^{10} x^{\frac{25}{3}}}{25}"," ",0,"a**10*x**5/5 + 15*a**9*b*x**(16/3)/8 + 135*a**8*b**2*x**(17/3)/17 + 20*a**7*b**3*x**6 + 630*a**6*b**4*x**(19/3)/19 + 189*a**5*b**5*x**(20/3)/5 + 30*a**4*b**6*x**7 + 180*a**3*b**7*x**(22/3)/11 + 135*a**2*b**8*x**(23/3)/23 + 5*a*b**9*x**8/4 + 3*b**10*x**(25/3)/25","A",0
2325,1,144,0,4.203351," ","integrate((a+b*x**(1/3))**10*x**3,x)","\frac{a^{10} x^{4}}{4} + \frac{30 a^{9} b x^{\frac{13}{3}}}{13} + \frac{135 a^{8} b^{2} x^{\frac{14}{3}}}{14} + 24 a^{7} b^{3} x^{5} + \frac{315 a^{6} b^{4} x^{\frac{16}{3}}}{8} + \frac{756 a^{5} b^{5} x^{\frac{17}{3}}}{17} + 35 a^{4} b^{6} x^{6} + \frac{360 a^{3} b^{7} x^{\frac{19}{3}}}{19} + \frac{27 a^{2} b^{8} x^{\frac{20}{3}}}{4} + \frac{10 a b^{9} x^{7}}{7} + \frac{3 b^{10} x^{\frac{22}{3}}}{22}"," ",0,"a**10*x**4/4 + 30*a**9*b*x**(13/3)/13 + 135*a**8*b**2*x**(14/3)/14 + 24*a**7*b**3*x**5 + 315*a**6*b**4*x**(16/3)/8 + 756*a**5*b**5*x**(17/3)/17 + 35*a**4*b**6*x**6 + 360*a**3*b**7*x**(19/3)/19 + 27*a**2*b**8*x**(20/3)/4 + 10*a*b**9*x**7/7 + 3*b**10*x**(22/3)/22","A",0
2326,1,141,0,3.873783," ","integrate((a+b*x**(1/3))**10*x**2,x)","\frac{a^{10} x^{3}}{3} + 3 a^{9} b x^{\frac{10}{3}} + \frac{135 a^{8} b^{2} x^{\frac{11}{3}}}{11} + 30 a^{7} b^{3} x^{4} + \frac{630 a^{6} b^{4} x^{\frac{13}{3}}}{13} + 54 a^{5} b^{5} x^{\frac{14}{3}} + 42 a^{4} b^{6} x^{5} + \frac{45 a^{3} b^{7} x^{\frac{16}{3}}}{2} + \frac{135 a^{2} b^{8} x^{\frac{17}{3}}}{17} + \frac{5 a b^{9} x^{6}}{3} + \frac{3 b^{10} x^{\frac{19}{3}}}{19}"," ",0,"a**10*x**3/3 + 3*a**9*b*x**(10/3) + 135*a**8*b**2*x**(11/3)/11 + 30*a**7*b**3*x**4 + 630*a**6*b**4*x**(13/3)/13 + 54*a**5*b**5*x**(14/3) + 42*a**4*b**6*x**5 + 45*a**3*b**7*x**(16/3)/2 + 135*a**2*b**8*x**(17/3)/17 + 5*a*b**9*x**6/3 + 3*b**10*x**(19/3)/19","A",0
2327,1,143,0,3.563118," ","integrate((a+b*x**(1/3))**10*x,x)","\frac{a^{10} x^{2}}{2} + \frac{30 a^{9} b x^{\frac{7}{3}}}{7} + \frac{135 a^{8} b^{2} x^{\frac{8}{3}}}{8} + 40 a^{7} b^{3} x^{3} + 63 a^{6} b^{4} x^{\frac{10}{3}} + \frac{756 a^{5} b^{5} x^{\frac{11}{3}}}{11} + \frac{105 a^{4} b^{6} x^{4}}{2} + \frac{360 a^{3} b^{7} x^{\frac{13}{3}}}{13} + \frac{135 a^{2} b^{8} x^{\frac{14}{3}}}{14} + 2 a b^{9} x^{5} + \frac{3 b^{10} x^{\frac{16}{3}}}{16}"," ",0,"a**10*x**2/2 + 30*a**9*b*x**(7/3)/7 + 135*a**8*b**2*x**(8/3)/8 + 40*a**7*b**3*x**3 + 63*a**6*b**4*x**(10/3) + 756*a**5*b**5*x**(11/3)/11 + 105*a**4*b**6*x**4/2 + 360*a**3*b**7*x**(13/3)/13 + 135*a**2*b**8*x**(14/3)/14 + 2*a*b**9*x**5 + 3*b**10*x**(16/3)/16","A",0
2328,1,136,0,3.417248," ","integrate((a+b*x**(1/3))**10,x)","a^{10} x + \frac{15 a^{9} b x^{\frac{4}{3}}}{2} + 27 a^{8} b^{2} x^{\frac{5}{3}} + 60 a^{7} b^{3} x^{2} + 90 a^{6} b^{4} x^{\frac{7}{3}} + \frac{189 a^{5} b^{5} x^{\frac{8}{3}}}{2} + 70 a^{4} b^{6} x^{3} + 36 a^{3} b^{7} x^{\frac{10}{3}} + \frac{135 a^{2} b^{8} x^{\frac{11}{3}}}{11} + \frac{5 a b^{9} x^{4}}{2} + \frac{3 b^{10} x^{\frac{13}{3}}}{13}"," ",0,"a**10*x + 15*a**9*b*x**(4/3)/2 + 27*a**8*b**2*x**(5/3) + 60*a**7*b**3*x**2 + 90*a**6*b**4*x**(7/3) + 189*a**5*b**5*x**(8/3)/2 + 70*a**4*b**6*x**3 + 36*a**3*b**7*x**(10/3) + 135*a**2*b**8*x**(11/3)/11 + 5*a*b**9*x**4/2 + 3*b**10*x**(13/3)/13","B",0
2329,1,139,0,66.358938," ","integrate((a+b*x**(1/3))**10/x,x)","a^{10} \log{\left(x \right)} + 30 a^{9} b \sqrt[3]{x} + \frac{135 a^{8} b^{2} x^{\frac{2}{3}}}{2} + 120 a^{7} b^{3} x + \frac{315 a^{6} b^{4} x^{\frac{4}{3}}}{2} + \frac{756 a^{5} b^{5} x^{\frac{5}{3}}}{5} + 105 a^{4} b^{6} x^{2} + \frac{360 a^{3} b^{7} x^{\frac{7}{3}}}{7} + \frac{135 a^{2} b^{8} x^{\frac{8}{3}}}{8} + \frac{10 a b^{9} x^{3}}{3} + \frac{3 b^{10} x^{\frac{10}{3}}}{10}"," ",0,"a**10*log(x) + 30*a**9*b*x**(1/3) + 135*a**8*b**2*x**(2/3)/2 + 120*a**7*b**3*x + 315*a**6*b**4*x**(4/3)/2 + 756*a**5*b**5*x**(5/3)/5 + 105*a**4*b**6*x**2 + 360*a**3*b**7*x**(7/3)/7 + 135*a**2*b**8*x**(8/3)/8 + 10*a*b**9*x**3/3 + 3*b**10*x**(10/3)/10","A",0
2330,1,131,0,15.710114," ","integrate((a+b*x**(1/3))**10/x**2,x)","- \frac{a^{10}}{x} - \frac{15 a^{9} b}{x^{\frac{2}{3}}} - \frac{135 a^{8} b^{2}}{\sqrt[3]{x}} + 360 a^{7} b^{3} \log{\left(\sqrt[3]{x} \right)} + 630 a^{6} b^{4} \sqrt[3]{x} + 378 a^{5} b^{5} x^{\frac{2}{3}} + 210 a^{4} b^{6} x + 90 a^{3} b^{7} x^{\frac{4}{3}} + 27 a^{2} b^{8} x^{\frac{5}{3}} + 5 a b^{9} x^{2} + \frac{3 b^{10} x^{\frac{7}{3}}}{7}"," ",0,"-a**10/x - 15*a**9*b/x**(2/3) - 135*a**8*b**2/x**(1/3) + 360*a**7*b**3*log(x**(1/3)) + 630*a**6*b**4*x**(1/3) + 378*a**5*b**5*x**(2/3) + 210*a**4*b**6*x + 90*a**3*b**7*x**(4/3) + 27*a**2*b**8*x**(5/3) + 5*a*b**9*x**2 + 3*b**10*x**(7/3)/7","A",0
2331,1,136,0,15.849177," ","integrate((a+b*x**(1/3))**10/x**3,x)","- \frac{a^{10}}{2 x^{2}} - \frac{6 a^{9} b}{x^{\frac{5}{3}}} - \frac{135 a^{8} b^{2}}{4 x^{\frac{4}{3}}} - \frac{120 a^{7} b^{3}}{x} - \frac{315 a^{6} b^{4}}{x^{\frac{2}{3}}} - \frac{756 a^{5} b^{5}}{\sqrt[3]{x}} + 630 a^{4} b^{6} \log{\left(\sqrt[3]{x} \right)} + 360 a^{3} b^{7} \sqrt[3]{x} + \frac{135 a^{2} b^{8} x^{\frac{2}{3}}}{2} + 10 a b^{9} x + \frac{3 b^{10} x^{\frac{4}{3}}}{4}"," ",0,"-a**10/(2*x**2) - 6*a**9*b/x**(5/3) - 135*a**8*b**2/(4*x**(4/3)) - 120*a**7*b**3/x - 315*a**6*b**4/x**(2/3) - 756*a**5*b**5/x**(1/3) + 630*a**4*b**6*log(x**(1/3)) + 360*a**3*b**7*x**(1/3) + 135*a**2*b**8*x**(2/3)/2 + 10*a*b**9*x + 3*b**10*x**(4/3)/4","A",0
2332,1,133,0,2.418900," ","integrate((a+b*x**(1/3))**10/x**4,x)","- \frac{a^{10}}{3 x^{3}} - \frac{15 a^{9} b}{4 x^{\frac{8}{3}}} - \frac{135 a^{8} b^{2}}{7 x^{\frac{7}{3}}} - \frac{60 a^{7} b^{3}}{x^{2}} - \frac{126 a^{6} b^{4}}{x^{\frac{5}{3}}} - \frac{189 a^{5} b^{5}}{x^{\frac{4}{3}}} - \frac{210 a^{4} b^{6}}{x} - \frac{180 a^{3} b^{7}}{x^{\frac{2}{3}}} - \frac{135 a^{2} b^{8}}{\sqrt[3]{x}} + 10 a b^{9} \log{\left(x \right)} + 3 b^{10} \sqrt[3]{x}"," ",0,"-a**10/(3*x**3) - 15*a**9*b/(4*x**(8/3)) - 135*a**8*b**2/(7*x**(7/3)) - 60*a**7*b**3/x**2 - 126*a**6*b**4/x**(5/3) - 189*a**5*b**5/x**(4/3) - 210*a**4*b**6/x - 180*a**3*b**7/x**(2/3) - 135*a**2*b**8/x**(1/3) + 10*a*b**9*log(x) + 3*b**10*x**(1/3)","A",0
2333,1,139,0,3.876258," ","integrate((a+b*x**(1/3))**10/x**5,x)","- \frac{a^{10}}{4 x^{4}} - \frac{30 a^{9} b}{11 x^{\frac{11}{3}}} - \frac{27 a^{8} b^{2}}{2 x^{\frac{10}{3}}} - \frac{40 a^{7} b^{3}}{x^{3}} - \frac{315 a^{6} b^{4}}{4 x^{\frac{8}{3}}} - \frac{108 a^{5} b^{5}}{x^{\frac{7}{3}}} - \frac{105 a^{4} b^{6}}{x^{2}} - \frac{72 a^{3} b^{7}}{x^{\frac{5}{3}}} - \frac{135 a^{2} b^{8}}{4 x^{\frac{4}{3}}} - \frac{10 a b^{9}}{x} - \frac{3 b^{10}}{2 x^{\frac{2}{3}}}"," ",0,"-a**10/(4*x**4) - 30*a**9*b/(11*x**(11/3)) - 27*a**8*b**2/(2*x**(10/3)) - 40*a**7*b**3/x**3 - 315*a**6*b**4/(4*x**(8/3)) - 108*a**5*b**5/x**(7/3) - 105*a**4*b**6/x**2 - 72*a**3*b**7/x**(5/3) - 135*a**2*b**8/(4*x**(4/3)) - 10*a*b**9/x - 3*b**10/(2*x**(2/3))","B",0
2334,1,143,0,6.118727," ","integrate((a+b*x**(1/3))**10/x**6,x)","- \frac{a^{10}}{5 x^{5}} - \frac{15 a^{9} b}{7 x^{\frac{14}{3}}} - \frac{135 a^{8} b^{2}}{13 x^{\frac{13}{3}}} - \frac{30 a^{7} b^{3}}{x^{4}} - \frac{630 a^{6} b^{4}}{11 x^{\frac{11}{3}}} - \frac{378 a^{5} b^{5}}{5 x^{\frac{10}{3}}} - \frac{70 a^{4} b^{6}}{x^{3}} - \frac{45 a^{3} b^{7}}{x^{\frac{8}{3}}} - \frac{135 a^{2} b^{8}}{7 x^{\frac{7}{3}}} - \frac{5 a b^{9}}{x^{2}} - \frac{3 b^{10}}{5 x^{\frac{5}{3}}}"," ",0,"-a**10/(5*x**5) - 15*a**9*b/(7*x**(14/3)) - 135*a**8*b**2/(13*x**(13/3)) - 30*a**7*b**3/x**4 - 630*a**6*b**4/(11*x**(11/3)) - 378*a**5*b**5/(5*x**(10/3)) - 70*a**4*b**6/x**3 - 45*a**3*b**7/x**(8/3) - 135*a**2*b**8/(7*x**(7/3)) - 5*a*b**9/x**2 - 3*b**10/(5*x**(5/3))","A",0
2335,1,146,0,9.501741," ","integrate((a+b*x**(1/3))**10/x**7,x)","- \frac{a^{10}}{6 x^{6}} - \frac{30 a^{9} b}{17 x^{\frac{17}{3}}} - \frac{135 a^{8} b^{2}}{16 x^{\frac{16}{3}}} - \frac{24 a^{7} b^{3}}{x^{5}} - \frac{45 a^{6} b^{4}}{x^{\frac{14}{3}}} - \frac{756 a^{5} b^{5}}{13 x^{\frac{13}{3}}} - \frac{105 a^{4} b^{6}}{2 x^{4}} - \frac{360 a^{3} b^{7}}{11 x^{\frac{11}{3}}} - \frac{27 a^{2} b^{8}}{2 x^{\frac{10}{3}}} - \frac{10 a b^{9}}{3 x^{3}} - \frac{3 b^{10}}{8 x^{\frac{8}{3}}}"," ",0,"-a**10/(6*x**6) - 30*a**9*b/(17*x**(17/3)) - 135*a**8*b**2/(16*x**(16/3)) - 24*a**7*b**3/x**5 - 45*a**6*b**4/x**(14/3) - 756*a**5*b**5/(13*x**(13/3)) - 105*a**4*b**6/(2*x**4) - 360*a**3*b**7/(11*x**(11/3)) - 27*a**2*b**8/(2*x**(10/3)) - 10*a*b**9/(3*x**3) - 3*b**10/(8*x**(8/3))","A",0
2336,1,146,0,13.721446," ","integrate((a+b*x**(1/3))**10/x**8,x)","- \frac{a^{10}}{7 x^{7}} - \frac{3 a^{9} b}{2 x^{\frac{20}{3}}} - \frac{135 a^{8} b^{2}}{19 x^{\frac{19}{3}}} - \frac{20 a^{7} b^{3}}{x^{6}} - \frac{630 a^{6} b^{4}}{17 x^{\frac{17}{3}}} - \frac{189 a^{5} b^{5}}{4 x^{\frac{16}{3}}} - \frac{42 a^{4} b^{6}}{x^{5}} - \frac{180 a^{3} b^{7}}{7 x^{\frac{14}{3}}} - \frac{135 a^{2} b^{8}}{13 x^{\frac{13}{3}}} - \frac{5 a b^{9}}{2 x^{4}} - \frac{3 b^{10}}{11 x^{\frac{11}{3}}}"," ",0,"-a**10/(7*x**7) - 3*a**9*b/(2*x**(20/3)) - 135*a**8*b**2/(19*x**(19/3)) - 20*a**7*b**3/x**6 - 630*a**6*b**4/(17*x**(17/3)) - 189*a**5*b**5/(4*x**(16/3)) - 42*a**4*b**6/x**5 - 180*a**3*b**7/(7*x**(14/3)) - 135*a**2*b**8/(13*x**(13/3)) - 5*a*b**9/(2*x**4) - 3*b**10/(11*x**(11/3))","A",0
2337,1,146,0,19.826189," ","integrate((a+b*x**(1/3))**10/x**9,x)","- \frac{a^{10}}{8 x^{8}} - \frac{30 a^{9} b}{23 x^{\frac{23}{3}}} - \frac{135 a^{8} b^{2}}{22 x^{\frac{22}{3}}} - \frac{120 a^{7} b^{3}}{7 x^{7}} - \frac{63 a^{6} b^{4}}{2 x^{\frac{20}{3}}} - \frac{756 a^{5} b^{5}}{19 x^{\frac{19}{3}}} - \frac{35 a^{4} b^{6}}{x^{6}} - \frac{360 a^{3} b^{7}}{17 x^{\frac{17}{3}}} - \frac{135 a^{2} b^{8}}{16 x^{\frac{16}{3}}} - \frac{2 a b^{9}}{x^{5}} - \frac{3 b^{10}}{14 x^{\frac{14}{3}}}"," ",0,"-a**10/(8*x**8) - 30*a**9*b/(23*x**(23/3)) - 135*a**8*b**2/(22*x**(22/3)) - 120*a**7*b**3/(7*x**7) - 63*a**6*b**4/(2*x**(20/3)) - 756*a**5*b**5/(19*x**(19/3)) - 35*a**4*b**6/x**6 - 360*a**3*b**7/(17*x**(17/3)) - 135*a**2*b**8/(16*x**(16/3)) - 2*a*b**9/x**5 - 3*b**10/(14*x**(14/3))","A",0
2338,1,144,0,27.836288," ","integrate((a+b*x**(1/3))**10/x**10,x)","- \frac{a^{10}}{9 x^{9}} - \frac{15 a^{9} b}{13 x^{\frac{26}{3}}} - \frac{27 a^{8} b^{2}}{5 x^{\frac{25}{3}}} - \frac{15 a^{7} b^{3}}{x^{8}} - \frac{630 a^{6} b^{4}}{23 x^{\frac{23}{3}}} - \frac{378 a^{5} b^{5}}{11 x^{\frac{22}{3}}} - \frac{30 a^{4} b^{6}}{x^{7}} - \frac{18 a^{3} b^{7}}{x^{\frac{20}{3}}} - \frac{135 a^{2} b^{8}}{19 x^{\frac{19}{3}}} - \frac{5 a b^{9}}{3 x^{6}} - \frac{3 b^{10}}{17 x^{\frac{17}{3}}}"," ",0,"-a**10/(9*x**9) - 15*a**9*b/(13*x**(26/3)) - 27*a**8*b**2/(5*x**(25/3)) - 15*a**7*b**3/x**8 - 630*a**6*b**4/(23*x**(23/3)) - 378*a**5*b**5/(11*x**(22/3)) - 30*a**4*b**6/x**7 - 18*a**3*b**7/x**(20/3) - 135*a**2*b**8/(19*x**(19/3)) - 5*a*b**9/(3*x**6) - 3*b**10/(17*x**(17/3))","A",0
2339,1,218,0,7.376467," ","integrate((a+b*x**(1/3))**15*x**5,x)","\frac{a^{15} x^{6}}{6} + \frac{45 a^{14} b x^{\frac{19}{3}}}{19} + \frac{63 a^{13} b^{2} x^{\frac{20}{3}}}{4} + 65 a^{12} b^{3} x^{7} + \frac{4095 a^{11} b^{4} x^{\frac{22}{3}}}{22} + \frac{9009 a^{10} b^{5} x^{\frac{23}{3}}}{23} + \frac{5005 a^{9} b^{6} x^{8}}{8} + \frac{3861 a^{8} b^{7} x^{\frac{25}{3}}}{5} + \frac{1485 a^{7} b^{8} x^{\frac{26}{3}}}{2} + \frac{5005 a^{6} b^{9} x^{9}}{9} + \frac{1287 a^{5} b^{10} x^{\frac{28}{3}}}{4} + \frac{4095 a^{4} b^{11} x^{\frac{29}{3}}}{29} + \frac{91 a^{3} b^{12} x^{10}}{2} + \frac{315 a^{2} b^{13} x^{\frac{31}{3}}}{31} + \frac{45 a b^{14} x^{\frac{32}{3}}}{32} + \frac{b^{15} x^{11}}{11}"," ",0,"a**15*x**6/6 + 45*a**14*b*x**(19/3)/19 + 63*a**13*b**2*x**(20/3)/4 + 65*a**12*b**3*x**7 + 4095*a**11*b**4*x**(22/3)/22 + 9009*a**10*b**5*x**(23/3)/23 + 5005*a**9*b**6*x**8/8 + 3861*a**8*b**7*x**(25/3)/5 + 1485*a**7*b**8*x**(26/3)/2 + 5005*a**6*b**9*x**9/9 + 1287*a**5*b**10*x**(28/3)/4 + 4095*a**4*b**11*x**(29/3)/29 + 91*a**3*b**12*x**10/2 + 315*a**2*b**13*x**(31/3)/31 + 45*a*b**14*x**(32/3)/32 + b**15*x**11/11","A",0
2340,1,218,0,6.795769," ","integrate((a+b*x**(1/3))**15*x**4,x)","\frac{a^{15} x^{5}}{5} + \frac{45 a^{14} b x^{\frac{16}{3}}}{16} + \frac{315 a^{13} b^{2} x^{\frac{17}{3}}}{17} + \frac{455 a^{12} b^{3} x^{6}}{6} + \frac{4095 a^{11} b^{4} x^{\frac{19}{3}}}{19} + \frac{9009 a^{10} b^{5} x^{\frac{20}{3}}}{20} + 715 a^{9} b^{6} x^{7} + \frac{1755 a^{8} b^{7} x^{\frac{22}{3}}}{2} + \frac{19305 a^{7} b^{8} x^{\frac{23}{3}}}{23} + \frac{5005 a^{6} b^{9} x^{8}}{8} + \frac{9009 a^{5} b^{10} x^{\frac{25}{3}}}{25} + \frac{315 a^{4} b^{11} x^{\frac{26}{3}}}{2} + \frac{455 a^{3} b^{12} x^{9}}{9} + \frac{45 a^{2} b^{13} x^{\frac{28}{3}}}{4} + \frac{45 a b^{14} x^{\frac{29}{3}}}{29} + \frac{b^{15} x^{10}}{10}"," ",0,"a**15*x**5/5 + 45*a**14*b*x**(16/3)/16 + 315*a**13*b**2*x**(17/3)/17 + 455*a**12*b**3*x**6/6 + 4095*a**11*b**4*x**(19/3)/19 + 9009*a**10*b**5*x**(20/3)/20 + 715*a**9*b**6*x**7 + 1755*a**8*b**7*x**(22/3)/2 + 19305*a**7*b**8*x**(23/3)/23 + 5005*a**6*b**9*x**8/8 + 9009*a**5*b**10*x**(25/3)/25 + 315*a**4*b**11*x**(26/3)/2 + 455*a**3*b**12*x**9/9 + 45*a**2*b**13*x**(28/3)/4 + 45*a*b**14*x**(29/3)/29 + b**15*x**10/10","A",0
2341,1,216,0,6.211868," ","integrate((a+b*x**(1/3))**15*x**3,x)","\frac{a^{15} x^{4}}{4} + \frac{45 a^{14} b x^{\frac{13}{3}}}{13} + \frac{45 a^{13} b^{2} x^{\frac{14}{3}}}{2} + 91 a^{12} b^{3} x^{5} + \frac{4095 a^{11} b^{4} x^{\frac{16}{3}}}{16} + \frac{9009 a^{10} b^{5} x^{\frac{17}{3}}}{17} + \frac{5005 a^{9} b^{6} x^{6}}{6} + \frac{19305 a^{8} b^{7} x^{\frac{19}{3}}}{19} + \frac{3861 a^{7} b^{8} x^{\frac{20}{3}}}{4} + 715 a^{6} b^{9} x^{7} + \frac{819 a^{5} b^{10} x^{\frac{22}{3}}}{2} + \frac{4095 a^{4} b^{11} x^{\frac{23}{3}}}{23} + \frac{455 a^{3} b^{12} x^{8}}{8} + \frac{63 a^{2} b^{13} x^{\frac{25}{3}}}{5} + \frac{45 a b^{14} x^{\frac{26}{3}}}{26} + \frac{b^{15} x^{9}}{9}"," ",0,"a**15*x**4/4 + 45*a**14*b*x**(13/3)/13 + 45*a**13*b**2*x**(14/3)/2 + 91*a**12*b**3*x**5 + 4095*a**11*b**4*x**(16/3)/16 + 9009*a**10*b**5*x**(17/3)/17 + 5005*a**9*b**6*x**6/6 + 19305*a**8*b**7*x**(19/3)/19 + 3861*a**7*b**8*x**(20/3)/4 + 715*a**6*b**9*x**7 + 819*a**5*b**10*x**(22/3)/2 + 4095*a**4*b**11*x**(23/3)/23 + 455*a**3*b**12*x**8/8 + 63*a**2*b**13*x**(25/3)/5 + 45*a*b**14*x**(26/3)/26 + b**15*x**9/9","A",0
2342,1,214,0,5.631456," ","integrate((a+b*x**(1/3))**15*x**2,x)","\frac{a^{15} x^{3}}{3} + \frac{9 a^{14} b x^{\frac{10}{3}}}{2} + \frac{315 a^{13} b^{2} x^{\frac{11}{3}}}{11} + \frac{455 a^{12} b^{3} x^{4}}{4} + 315 a^{11} b^{4} x^{\frac{13}{3}} + \frac{1287 a^{10} b^{5} x^{\frac{14}{3}}}{2} + 1001 a^{9} b^{6} x^{5} + \frac{19305 a^{8} b^{7} x^{\frac{16}{3}}}{16} + \frac{19305 a^{7} b^{8} x^{\frac{17}{3}}}{17} + \frac{5005 a^{6} b^{9} x^{6}}{6} + \frac{9009 a^{5} b^{10} x^{\frac{19}{3}}}{19} + \frac{819 a^{4} b^{11} x^{\frac{20}{3}}}{4} + 65 a^{3} b^{12} x^{7} + \frac{315 a^{2} b^{13} x^{\frac{22}{3}}}{22} + \frac{45 a b^{14} x^{\frac{23}{3}}}{23} + \frac{b^{15} x^{8}}{8}"," ",0,"a**15*x**3/3 + 9*a**14*b*x**(10/3)/2 + 315*a**13*b**2*x**(11/3)/11 + 455*a**12*b**3*x**4/4 + 315*a**11*b**4*x**(13/3) + 1287*a**10*b**5*x**(14/3)/2 + 1001*a**9*b**6*x**5 + 19305*a**8*b**7*x**(16/3)/16 + 19305*a**7*b**8*x**(17/3)/17 + 5005*a**6*b**9*x**6/6 + 9009*a**5*b**10*x**(19/3)/19 + 819*a**4*b**11*x**(20/3)/4 + 65*a**3*b**12*x**7 + 315*a**2*b**13*x**(22/3)/22 + 45*a*b**14*x**(23/3)/23 + b**15*x**8/8","A",0
2343,1,214,0,5.099610," ","integrate((a+b*x**(1/3))**15*x,x)","\frac{a^{15} x^{2}}{2} + \frac{45 a^{14} b x^{\frac{7}{3}}}{7} + \frac{315 a^{13} b^{2} x^{\frac{8}{3}}}{8} + \frac{455 a^{12} b^{3} x^{3}}{3} + \frac{819 a^{11} b^{4} x^{\frac{10}{3}}}{2} + 819 a^{10} b^{5} x^{\frac{11}{3}} + \frac{5005 a^{9} b^{6} x^{4}}{4} + 1485 a^{8} b^{7} x^{\frac{13}{3}} + \frac{19305 a^{7} b^{8} x^{\frac{14}{3}}}{14} + 1001 a^{6} b^{9} x^{5} + \frac{9009 a^{5} b^{10} x^{\frac{16}{3}}}{16} + \frac{4095 a^{4} b^{11} x^{\frac{17}{3}}}{17} + \frac{455 a^{3} b^{12} x^{6}}{6} + \frac{315 a^{2} b^{13} x^{\frac{19}{3}}}{19} + \frac{9 a b^{14} x^{\frac{20}{3}}}{4} + \frac{b^{15} x^{7}}{7}"," ",0,"a**15*x**2/2 + 45*a**14*b*x**(7/3)/7 + 315*a**13*b**2*x**(8/3)/8 + 455*a**12*b**3*x**3/3 + 819*a**11*b**4*x**(10/3)/2 + 819*a**10*b**5*x**(11/3) + 5005*a**9*b**6*x**4/4 + 1485*a**8*b**7*x**(13/3) + 19305*a**7*b**8*x**(14/3)/14 + 1001*a**6*b**9*x**5 + 9009*a**5*b**10*x**(16/3)/16 + 4095*a**4*b**11*x**(17/3)/17 + 455*a**3*b**12*x**6/6 + 315*a**2*b**13*x**(19/3)/19 + 9*a*b**14*x**(20/3)/4 + b**15*x**7/7","A",0
2344,1,207,0,4.785474," ","integrate((a+b*x**(1/3))**15,x)","a^{15} x + \frac{45 a^{14} b x^{\frac{4}{3}}}{4} + 63 a^{13} b^{2} x^{\frac{5}{3}} + \frac{455 a^{12} b^{3} x^{2}}{2} + 585 a^{11} b^{4} x^{\frac{7}{3}} + \frac{9009 a^{10} b^{5} x^{\frac{8}{3}}}{8} + \frac{5005 a^{9} b^{6} x^{3}}{3} + \frac{3861 a^{8} b^{7} x^{\frac{10}{3}}}{2} + 1755 a^{7} b^{8} x^{\frac{11}{3}} + \frac{5005 a^{6} b^{9} x^{4}}{4} + 693 a^{5} b^{10} x^{\frac{13}{3}} + \frac{585 a^{4} b^{11} x^{\frac{14}{3}}}{2} + 91 a^{3} b^{12} x^{5} + \frac{315 a^{2} b^{13} x^{\frac{16}{3}}}{16} + \frac{45 a b^{14} x^{\frac{17}{3}}}{17} + \frac{b^{15} x^{6}}{6}"," ",0,"a**15*x + 45*a**14*b*x**(4/3)/4 + 63*a**13*b**2*x**(5/3) + 455*a**12*b**3*x**2/2 + 585*a**11*b**4*x**(7/3) + 9009*a**10*b**5*x**(8/3)/8 + 5005*a**9*b**6*x**3/3 + 3861*a**8*b**7*x**(10/3)/2 + 1755*a**7*b**8*x**(11/3) + 5005*a**6*b**9*x**4/4 + 693*a**5*b**10*x**(13/3) + 585*a**4*b**11*x**(14/3)/2 + 91*a**3*b**12*x**5 + 315*a**2*b**13*x**(16/3)/16 + 45*a*b**14*x**(17/3)/17 + b**15*x**6/6","B",0
2345,1,212,0,4.719601," ","integrate((a+b*x**(1/3))**15/x,x)","a^{15} \log{\left(x \right)} + 45 a^{14} b \sqrt[3]{x} + \frac{315 a^{13} b^{2} x^{\frac{2}{3}}}{2} + 455 a^{12} b^{3} x + \frac{4095 a^{11} b^{4} x^{\frac{4}{3}}}{4} + \frac{9009 a^{10} b^{5} x^{\frac{5}{3}}}{5} + \frac{5005 a^{9} b^{6} x^{2}}{2} + \frac{19305 a^{8} b^{7} x^{\frac{7}{3}}}{7} + \frac{19305 a^{7} b^{8} x^{\frac{8}{3}}}{8} + \frac{5005 a^{6} b^{9} x^{3}}{3} + \frac{9009 a^{5} b^{10} x^{\frac{10}{3}}}{10} + \frac{4095 a^{4} b^{11} x^{\frac{11}{3}}}{11} + \frac{455 a^{3} b^{12} x^{4}}{4} + \frac{315 a^{2} b^{13} x^{\frac{13}{3}}}{13} + \frac{45 a b^{14} x^{\frac{14}{3}}}{14} + \frac{b^{15} x^{5}}{5}"," ",0,"a**15*log(x) + 45*a**14*b*x**(1/3) + 315*a**13*b**2*x**(2/3)/2 + 455*a**12*b**3*x + 4095*a**11*b**4*x**(4/3)/4 + 9009*a**10*b**5*x**(5/3)/5 + 5005*a**9*b**6*x**2/2 + 19305*a**8*b**7*x**(7/3)/7 + 19305*a**7*b**8*x**(8/3)/8 + 5005*a**6*b**9*x**3/3 + 9009*a**5*b**10*x**(10/3)/10 + 4095*a**4*b**11*x**(11/3)/11 + 455*a**3*b**12*x**4/4 + 315*a**2*b**13*x**(13/3)/13 + 45*a*b**14*x**(14/3)/14 + b**15*x**5/5","A",0
2346,1,204,0,4.851565," ","integrate((a+b*x**(1/3))**15/x**2,x)","- \frac{a^{15}}{x} - \frac{45 a^{14} b}{2 x^{\frac{2}{3}}} - \frac{315 a^{13} b^{2}}{\sqrt[3]{x}} + 455 a^{12} b^{3} \log{\left(x \right)} + 4095 a^{11} b^{4} \sqrt[3]{x} + \frac{9009 a^{10} b^{5} x^{\frac{2}{3}}}{2} + 5005 a^{9} b^{6} x + \frac{19305 a^{8} b^{7} x^{\frac{4}{3}}}{4} + 3861 a^{7} b^{8} x^{\frac{5}{3}} + \frac{5005 a^{6} b^{9} x^{2}}{2} + 1287 a^{5} b^{10} x^{\frac{7}{3}} + \frac{4095 a^{4} b^{11} x^{\frac{8}{3}}}{8} + \frac{455 a^{3} b^{12} x^{3}}{3} + \frac{63 a^{2} b^{13} x^{\frac{10}{3}}}{2} + \frac{45 a b^{14} x^{\frac{11}{3}}}{11} + \frac{b^{15} x^{4}}{4}"," ",0,"-a**15/x - 45*a**14*b/(2*x**(2/3)) - 315*a**13*b**2/x**(1/3) + 455*a**12*b**3*log(x) + 4095*a**11*b**4*x**(1/3) + 9009*a**10*b**5*x**(2/3)/2 + 5005*a**9*b**6*x + 19305*a**8*b**7*x**(4/3)/4 + 3861*a**7*b**8*x**(5/3) + 5005*a**6*b**9*x**2/2 + 1287*a**5*b**10*x**(7/3) + 4095*a**4*b**11*x**(8/3)/8 + 455*a**3*b**12*x**3/3 + 63*a**2*b**13*x**(10/3)/2 + 45*a*b**14*x**(11/3)/11 + b**15*x**4/4","A",0
2347,1,202,0,4.632087," ","integrate((a+b*x**(1/3))**15/x**3,x)","- \frac{a^{15}}{2 x^{2}} - \frac{9 a^{14} b}{x^{\frac{5}{3}}} - \frac{315 a^{13} b^{2}}{4 x^{\frac{4}{3}}} - \frac{455 a^{12} b^{3}}{x} - \frac{4095 a^{11} b^{4}}{2 x^{\frac{2}{3}}} - \frac{9009 a^{10} b^{5}}{\sqrt[3]{x}} + 5005 a^{9} b^{6} \log{\left(x \right)} + 19305 a^{8} b^{7} \sqrt[3]{x} + \frac{19305 a^{7} b^{8} x^{\frac{2}{3}}}{2} + 5005 a^{6} b^{9} x + \frac{9009 a^{5} b^{10} x^{\frac{4}{3}}}{4} + 819 a^{4} b^{11} x^{\frac{5}{3}} + \frac{455 a^{3} b^{12} x^{2}}{2} + 45 a^{2} b^{13} x^{\frac{7}{3}} + \frac{45 a b^{14} x^{\frac{8}{3}}}{8} + \frac{b^{15} x^{3}}{3}"," ",0,"-a**15/(2*x**2) - 9*a**14*b/x**(5/3) - 315*a**13*b**2/(4*x**(4/3)) - 455*a**12*b**3/x - 4095*a**11*b**4/(2*x**(2/3)) - 9009*a**10*b**5/x**(1/3) + 5005*a**9*b**6*log(x) + 19305*a**8*b**7*x**(1/3) + 19305*a**7*b**8*x**(2/3)/2 + 5005*a**6*b**9*x + 9009*a**5*b**10*x**(4/3)/4 + 819*a**4*b**11*x**(5/3) + 455*a**3*b**12*x**2/2 + 45*a**2*b**13*x**(7/3) + 45*a*b**14*x**(8/3)/8 + b**15*x**3/3","A",0
2348,1,202,0,4.613657," ","integrate((a+b*x**(1/3))**15/x**4,x)","- \frac{a^{15}}{3 x^{3}} - \frac{45 a^{14} b}{8 x^{\frac{8}{3}}} - \frac{45 a^{13} b^{2}}{x^{\frac{7}{3}}} - \frac{455 a^{12} b^{3}}{2 x^{2}} - \frac{819 a^{11} b^{4}}{x^{\frac{5}{3}}} - \frac{9009 a^{10} b^{5}}{4 x^{\frac{4}{3}}} - \frac{5005 a^{9} b^{6}}{x} - \frac{19305 a^{8} b^{7}}{2 x^{\frac{2}{3}}} - \frac{19305 a^{7} b^{8}}{\sqrt[3]{x}} + 5005 a^{6} b^{9} \log{\left(x \right)} + 9009 a^{5} b^{10} \sqrt[3]{x} + \frac{4095 a^{4} b^{11} x^{\frac{2}{3}}}{2} + 455 a^{3} b^{12} x + \frac{315 a^{2} b^{13} x^{\frac{4}{3}}}{4} + 9 a b^{14} x^{\frac{5}{3}} + \frac{b^{15} x^{2}}{2}"," ",0,"-a**15/(3*x**3) - 45*a**14*b/(8*x**(8/3)) - 45*a**13*b**2/x**(7/3) - 455*a**12*b**3/(2*x**2) - 819*a**11*b**4/x**(5/3) - 9009*a**10*b**5/(4*x**(4/3)) - 5005*a**9*b**6/x - 19305*a**8*b**7/(2*x**(2/3)) - 19305*a**7*b**8/x**(1/3) + 5005*a**6*b**9*log(x) + 9009*a**5*b**10*x**(1/3) + 4095*a**4*b**11*x**(2/3)/2 + 455*a**3*b**12*x + 315*a**2*b**13*x**(4/3)/4 + 9*a*b**14*x**(5/3) + b**15*x**2/2","A",0
2349,1,212,0,7.895361," ","integrate((a+b*x**(1/3))**15/x**6,x)","- \frac{a^{15}}{5 x^{5}} - \frac{45 a^{14} b}{14 x^{\frac{14}{3}}} - \frac{315 a^{13} b^{2}}{13 x^{\frac{13}{3}}} - \frac{455 a^{12} b^{3}}{4 x^{4}} - \frac{4095 a^{11} b^{4}}{11 x^{\frac{11}{3}}} - \frac{9009 a^{10} b^{5}}{10 x^{\frac{10}{3}}} - \frac{5005 a^{9} b^{6}}{3 x^{3}} - \frac{19305 a^{8} b^{7}}{8 x^{\frac{8}{3}}} - \frac{19305 a^{7} b^{8}}{7 x^{\frac{7}{3}}} - \frac{5005 a^{6} b^{9}}{2 x^{2}} - \frac{9009 a^{5} b^{10}}{5 x^{\frac{5}{3}}} - \frac{4095 a^{4} b^{11}}{4 x^{\frac{4}{3}}} - \frac{455 a^{3} b^{12}}{x} - \frac{315 a^{2} b^{13}}{2 x^{\frac{2}{3}}} - \frac{45 a b^{14}}{\sqrt[3]{x}} + b^{15} \log{\left(x \right)}"," ",0,"-a**15/(5*x**5) - 45*a**14*b/(14*x**(14/3)) - 315*a**13*b**2/(13*x**(13/3)) - 455*a**12*b**3/(4*x**4) - 4095*a**11*b**4/(11*x**(11/3)) - 9009*a**10*b**5/(10*x**(10/3)) - 5005*a**9*b**6/(3*x**3) - 19305*a**8*b**7/(8*x**(8/3)) - 19305*a**7*b**8/(7*x**(7/3)) - 5005*a**6*b**9/(2*x**2) - 9009*a**5*b**10/(5*x**(5/3)) - 4095*a**4*b**11/(4*x**(4/3)) - 455*a**3*b**12/x - 315*a**2*b**13/(2*x**(2/3)) - 45*a*b**14/x**(1/3) + b**15*log(x)","A",0
2350,1,209,0,10.485052," ","integrate((a+b*x**(1/3))**15/x**7,x)","- \frac{a^{15}}{6 x^{6}} - \frac{45 a^{14} b}{17 x^{\frac{17}{3}}} - \frac{315 a^{13} b^{2}}{16 x^{\frac{16}{3}}} - \frac{91 a^{12} b^{3}}{x^{5}} - \frac{585 a^{11} b^{4}}{2 x^{\frac{14}{3}}} - \frac{693 a^{10} b^{5}}{x^{\frac{13}{3}}} - \frac{5005 a^{9} b^{6}}{4 x^{4}} - \frac{1755 a^{8} b^{7}}{x^{\frac{11}{3}}} - \frac{3861 a^{7} b^{8}}{2 x^{\frac{10}{3}}} - \frac{5005 a^{6} b^{9}}{3 x^{3}} - \frac{9009 a^{5} b^{10}}{8 x^{\frac{8}{3}}} - \frac{585 a^{4} b^{11}}{x^{\frac{7}{3}}} - \frac{455 a^{3} b^{12}}{2 x^{2}} - \frac{63 a^{2} b^{13}}{x^{\frac{5}{3}}} - \frac{45 a b^{14}}{4 x^{\frac{4}{3}}} - \frac{b^{15}}{x}"," ",0,"-a**15/(6*x**6) - 45*a**14*b/(17*x**(17/3)) - 315*a**13*b**2/(16*x**(16/3)) - 91*a**12*b**3/x**5 - 585*a**11*b**4/(2*x**(14/3)) - 693*a**10*b**5/x**(13/3) - 5005*a**9*b**6/(4*x**4) - 1755*a**8*b**7/x**(11/3) - 3861*a**7*b**8/(2*x**(10/3)) - 5005*a**6*b**9/(3*x**3) - 9009*a**5*b**10/(8*x**(8/3)) - 585*a**4*b**11/x**(7/3) - 455*a**3*b**12/(2*x**2) - 63*a**2*b**13/x**(5/3) - 45*a*b**14/(4*x**(4/3)) - b**15/x","B",0
2351,1,216,0,15.179273," ","integrate((a+b*x**(1/3))**15/x**8,x)","- \frac{a^{15}}{7 x^{7}} - \frac{9 a^{14} b}{4 x^{\frac{20}{3}}} - \frac{315 a^{13} b^{2}}{19 x^{\frac{19}{3}}} - \frac{455 a^{12} b^{3}}{6 x^{6}} - \frac{4095 a^{11} b^{4}}{17 x^{\frac{17}{3}}} - \frac{9009 a^{10} b^{5}}{16 x^{\frac{16}{3}}} - \frac{1001 a^{9} b^{6}}{x^{5}} - \frac{19305 a^{8} b^{7}}{14 x^{\frac{14}{3}}} - \frac{1485 a^{7} b^{8}}{x^{\frac{13}{3}}} - \frac{5005 a^{6} b^{9}}{4 x^{4}} - \frac{819 a^{5} b^{10}}{x^{\frac{11}{3}}} - \frac{819 a^{4} b^{11}}{2 x^{\frac{10}{3}}} - \frac{455 a^{3} b^{12}}{3 x^{3}} - \frac{315 a^{2} b^{13}}{8 x^{\frac{8}{3}}} - \frac{45 a b^{14}}{7 x^{\frac{7}{3}}} - \frac{b^{15}}{2 x^{2}}"," ",0,"-a**15/(7*x**7) - 9*a**14*b/(4*x**(20/3)) - 315*a**13*b**2/(19*x**(19/3)) - 455*a**12*b**3/(6*x**6) - 4095*a**11*b**4/(17*x**(17/3)) - 9009*a**10*b**5/(16*x**(16/3)) - 1001*a**9*b**6/x**5 - 19305*a**8*b**7/(14*x**(14/3)) - 1485*a**7*b**8/x**(13/3) - 5005*a**6*b**9/(4*x**4) - 819*a**5*b**10/x**(11/3) - 819*a**4*b**11/(2*x**(10/3)) - 455*a**3*b**12/(3*x**3) - 315*a**2*b**13/(8*x**(8/3)) - 45*a*b**14/(7*x**(7/3)) - b**15/(2*x**2)","A",0
2352,1,216,0,21.796929," ","integrate((a+b*x**(1/3))**15/x**9,x)","- \frac{a^{15}}{8 x^{8}} - \frac{45 a^{14} b}{23 x^{\frac{23}{3}}} - \frac{315 a^{13} b^{2}}{22 x^{\frac{22}{3}}} - \frac{65 a^{12} b^{3}}{x^{7}} - \frac{819 a^{11} b^{4}}{4 x^{\frac{20}{3}}} - \frac{9009 a^{10} b^{5}}{19 x^{\frac{19}{3}}} - \frac{5005 a^{9} b^{6}}{6 x^{6}} - \frac{19305 a^{8} b^{7}}{17 x^{\frac{17}{3}}} - \frac{19305 a^{7} b^{8}}{16 x^{\frac{16}{3}}} - \frac{1001 a^{6} b^{9}}{x^{5}} - \frac{1287 a^{5} b^{10}}{2 x^{\frac{14}{3}}} - \frac{315 a^{4} b^{11}}{x^{\frac{13}{3}}} - \frac{455 a^{3} b^{12}}{4 x^{4}} - \frac{315 a^{2} b^{13}}{11 x^{\frac{11}{3}}} - \frac{9 a b^{14}}{2 x^{\frac{10}{3}}} - \frac{b^{15}}{3 x^{3}}"," ",0,"-a**15/(8*x**8) - 45*a**14*b/(23*x**(23/3)) - 315*a**13*b**2/(22*x**(22/3)) - 65*a**12*b**3/x**7 - 819*a**11*b**4/(4*x**(20/3)) - 9009*a**10*b**5/(19*x**(19/3)) - 5005*a**9*b**6/(6*x**6) - 19305*a**8*b**7/(17*x**(17/3)) - 19305*a**7*b**8/(16*x**(16/3)) - 1001*a**6*b**9/x**5 - 1287*a**5*b**10/(2*x**(14/3)) - 315*a**4*b**11/x**(13/3) - 455*a**3*b**12/(4*x**4) - 315*a**2*b**13/(11*x**(11/3)) - 9*a*b**14/(2*x**(10/3)) - b**15/(3*x**3)","A",0
2353,1,218,0,30.917877," ","integrate((a+b*x**(1/3))**15/x**10,x)","- \frac{a^{15}}{9 x^{9}} - \frac{45 a^{14} b}{26 x^{\frac{26}{3}}} - \frac{63 a^{13} b^{2}}{5 x^{\frac{25}{3}}} - \frac{455 a^{12} b^{3}}{8 x^{8}} - \frac{4095 a^{11} b^{4}}{23 x^{\frac{23}{3}}} - \frac{819 a^{10} b^{5}}{2 x^{\frac{22}{3}}} - \frac{715 a^{9} b^{6}}{x^{7}} - \frac{3861 a^{8} b^{7}}{4 x^{\frac{20}{3}}} - \frac{19305 a^{7} b^{8}}{19 x^{\frac{19}{3}}} - \frac{5005 a^{6} b^{9}}{6 x^{6}} - \frac{9009 a^{5} b^{10}}{17 x^{\frac{17}{3}}} - \frac{4095 a^{4} b^{11}}{16 x^{\frac{16}{3}}} - \frac{91 a^{3} b^{12}}{x^{5}} - \frac{45 a^{2} b^{13}}{2 x^{\frac{14}{3}}} - \frac{45 a b^{14}}{13 x^{\frac{13}{3}}} - \frac{b^{15}}{4 x^{4}}"," ",0,"-a**15/(9*x**9) - 45*a**14*b/(26*x**(26/3)) - 63*a**13*b**2/(5*x**(25/3)) - 455*a**12*b**3/(8*x**8) - 4095*a**11*b**4/(23*x**(23/3)) - 819*a**10*b**5/(2*x**(22/3)) - 715*a**9*b**6/x**7 - 3861*a**8*b**7/(4*x**(20/3)) - 19305*a**7*b**8/(19*x**(19/3)) - 5005*a**6*b**9/(6*x**6) - 9009*a**5*b**10/(17*x**(17/3)) - 4095*a**4*b**11/(16*x**(16/3)) - 91*a**3*b**12/x**5 - 45*a**2*b**13/(2*x**(14/3)) - 45*a*b**14/(13*x**(13/3)) - b**15/(4*x**4)","A",0
2354,1,219,0,42.989992," ","integrate((a+b*x**(1/3))**15/x**11,x)","- \frac{a^{15}}{10 x^{10}} - \frac{45 a^{14} b}{29 x^{\frac{29}{3}}} - \frac{45 a^{13} b^{2}}{4 x^{\frac{28}{3}}} - \frac{455 a^{12} b^{3}}{9 x^{9}} - \frac{315 a^{11} b^{4}}{2 x^{\frac{26}{3}}} - \frac{9009 a^{10} b^{5}}{25 x^{\frac{25}{3}}} - \frac{5005 a^{9} b^{6}}{8 x^{8}} - \frac{19305 a^{8} b^{7}}{23 x^{\frac{23}{3}}} - \frac{1755 a^{7} b^{8}}{2 x^{\frac{22}{3}}} - \frac{715 a^{6} b^{9}}{x^{7}} - \frac{9009 a^{5} b^{10}}{20 x^{\frac{20}{3}}} - \frac{4095 a^{4} b^{11}}{19 x^{\frac{19}{3}}} - \frac{455 a^{3} b^{12}}{6 x^{6}} - \frac{315 a^{2} b^{13}}{17 x^{\frac{17}{3}}} - \frac{45 a b^{14}}{16 x^{\frac{16}{3}}} - \frac{b^{15}}{5 x^{5}}"," ",0,"-a**15/(10*x**10) - 45*a**14*b/(29*x**(29/3)) - 45*a**13*b**2/(4*x**(28/3)) - 455*a**12*b**3/(9*x**9) - 315*a**11*b**4/(2*x**(26/3)) - 9009*a**10*b**5/(25*x**(25/3)) - 5005*a**9*b**6/(8*x**8) - 19305*a**8*b**7/(23*x**(23/3)) - 1755*a**7*b**8/(2*x**(22/3)) - 715*a**6*b**9/x**7 - 9009*a**5*b**10/(20*x**(20/3)) - 4095*a**4*b**11/(19*x**(19/3)) - 455*a**3*b**12/(6*x**6) - 315*a**2*b**13/(17*x**(17/3)) - 45*a*b**14/(16*x**(16/3)) - b**15/(5*x**5)","A",0
2355,1,219,0,57.156150," ","integrate((a+b*x**(1/3))**15/x**12,x)","- \frac{a^{15}}{11 x^{11}} - \frac{45 a^{14} b}{32 x^{\frac{32}{3}}} - \frac{315 a^{13} b^{2}}{31 x^{\frac{31}{3}}} - \frac{91 a^{12} b^{3}}{2 x^{10}} - \frac{4095 a^{11} b^{4}}{29 x^{\frac{29}{3}}} - \frac{1287 a^{10} b^{5}}{4 x^{\frac{28}{3}}} - \frac{5005 a^{9} b^{6}}{9 x^{9}} - \frac{1485 a^{8} b^{7}}{2 x^{\frac{26}{3}}} - \frac{3861 a^{7} b^{8}}{5 x^{\frac{25}{3}}} - \frac{5005 a^{6} b^{9}}{8 x^{8}} - \frac{9009 a^{5} b^{10}}{23 x^{\frac{23}{3}}} - \frac{4095 a^{4} b^{11}}{22 x^{\frac{22}{3}}} - \frac{65 a^{3} b^{12}}{x^{7}} - \frac{63 a^{2} b^{13}}{4 x^{\frac{20}{3}}} - \frac{45 a b^{14}}{19 x^{\frac{19}{3}}} - \frac{b^{15}}{6 x^{6}}"," ",0,"-a**15/(11*x**11) - 45*a**14*b/(32*x**(32/3)) - 315*a**13*b**2/(31*x**(31/3)) - 91*a**12*b**3/(2*x**10) - 4095*a**11*b**4/(29*x**(29/3)) - 1287*a**10*b**5/(4*x**(28/3)) - 5005*a**9*b**6/(9*x**9) - 1485*a**8*b**7/(2*x**(26/3)) - 3861*a**7*b**8/(5*x**(25/3)) - 5005*a**6*b**9/(8*x**8) - 9009*a**5*b**10/(23*x**(23/3)) - 4095*a**4*b**11/(22*x**(22/3)) - 65*a**3*b**12/x**7 - 63*a**2*b**13/(4*x**(20/3)) - 45*a*b**14/(19*x**(19/3)) - b**15/(6*x**6)","A",0
2356,-1,0,0,0.000000," ","integrate(x**3/(a+b*x**(1/3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2357,1,122,0,103.584686," ","integrate(x**2/(a+b*x**(1/3)),x)","\frac{3 a^{8} \log{\left(1 + \frac{b \sqrt[3]{x}}{a} \right)}}{b^{9}} - \frac{3 a^{7} \sqrt[3]{x}}{b^{8}} + \frac{3 a^{6} x^{\frac{2}{3}}}{2 b^{7}} - \frac{a^{5} x}{b^{6}} + \frac{3 a^{4} x^{\frac{4}{3}}}{4 b^{5}} - \frac{3 a^{3} x^{\frac{5}{3}}}{5 b^{4}} + \frac{a^{2} x^{2}}{2 b^{3}} - \frac{3 a x^{\frac{7}{3}}}{7 b^{2}} + \frac{3 x^{\frac{8}{3}}}{8 b}"," ",0,"3*a**8*log(1 + b*x**(1/3)/a)/b**9 - 3*a**7*x**(1/3)/b**8 + 3*a**6*x**(2/3)/(2*b**7) - a**5*x/b**6 + 3*a**4*x**(4/3)/(4*b**5) - 3*a**3*x**(5/3)/(5*b**4) + a**2*x**2/(2*b**3) - 3*a*x**(7/3)/(7*b**2) + 3*x**(8/3)/(8*b)","A",0
2358,1,80,0,8.889051," ","integrate(x/(a+b*x**(1/3)),x)","- \frac{3 a^{5} \log{\left(1 + \frac{b \sqrt[3]{x}}{a} \right)}}{b^{6}} + \frac{3 a^{4} \sqrt[3]{x}}{b^{5}} - \frac{3 a^{3} x^{\frac{2}{3}}}{2 b^{4}} + \frac{a^{2} x}{b^{3}} - \frac{3 a x^{\frac{4}{3}}}{4 b^{2}} + \frac{3 x^{\frac{5}{3}}}{5 b}"," ",0,"-3*a**5*log(1 + b*x**(1/3)/a)/b**6 + 3*a**4*x**(1/3)/b**5 - 3*a**3*x**(2/3)/(2*b**4) + a**2*x/b**3 - 3*a*x**(4/3)/(4*b**2) + 3*x**(5/3)/(5*b)","A",0
2359,1,42,0,0.193509," ","integrate(1/(a+b*x**(1/3)),x)","\begin{cases} \frac{3 a^{2} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{b^{3}} - \frac{3 a \sqrt[3]{x}}{b^{2}} + \frac{3 x^{\frac{2}{3}}}{2 b} & \text{for}\: b \neq 0 \\\frac{x}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*log(a/b + x**(1/3))/b**3 - 3*a*x**(1/3)/b**2 + 3*x**(2/3)/(2*b), Ne(b, 0)), (x/a, True))","A",0
2360,1,37,0,0.626577," ","integrate(1/(a+b*x**(1/3))/x,x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt[3]{x}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \\- \frac{3}{b \sqrt[3]{x}} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a} - \frac{3 \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(1/3), Eq(a, 0) & Eq(b, 0)), (log(x)/a, Eq(b, 0)), (-3/(b*x**(1/3)), Eq(a, 0)), (log(x)/a - 3*log(a/b + x**(1/3))/a, True))","A",0
2361,1,83,0,2.787553," ","integrate(1/(a+b*x**(1/3))/x**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{4}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{3}{4 b x^{\frac{4}{3}}} & \text{for}\: a = 0 \\- \frac{1}{a x} & \text{for}\: b = 0 \\- \frac{1}{a x} + \frac{3 b}{2 a^{2} x^{\frac{2}{3}}} - \frac{3 b^{2}}{a^{3} \sqrt[3]{x}} - \frac{b^{3} \log{\left(x \right)}}{a^{4}} + \frac{3 b^{3} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{a^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(4/3), Eq(a, 0) & Eq(b, 0)), (-3/(4*b*x**(4/3)), Eq(a, 0)), (-1/(a*x), Eq(b, 0)), (-1/(a*x) + 3*b/(2*a**2*x**(2/3)) - 3*b**2/(a**3*x**(1/3)) - b**3*log(x)/a**4 + 3*b**3*log(a/b + x**(1/3))/a**4, True))","A",0
2362,1,129,0,8.702940," ","integrate(1/(a+b*x**(1/3))/x**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{3}{7 b x^{\frac{7}{3}}} & \text{for}\: a = 0 \\- \frac{1}{2 a x^{2}} & \text{for}\: b = 0 \\- \frac{1}{2 a x^{2}} + \frac{3 b}{5 a^{2} x^{\frac{5}{3}}} - \frac{3 b^{2}}{4 a^{3} x^{\frac{4}{3}}} + \frac{b^{3}}{a^{4} x} - \frac{3 b^{4}}{2 a^{5} x^{\frac{2}{3}}} + \frac{3 b^{5}}{a^{6} \sqrt[3]{x}} + \frac{b^{6} \log{\left(x \right)}}{a^{7}} - \frac{3 b^{6} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{a^{7}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/3), Eq(a, 0) & Eq(b, 0)), (-3/(7*b*x**(7/3)), Eq(a, 0)), (-1/(2*a*x**2), Eq(b, 0)), (-1/(2*a*x**2) + 3*b/(5*a**2*x**(5/3)) - 3*b**2/(4*a**3*x**(4/3)) + b**3/(a**4*x) - 3*b**4/(2*a**5*x**(2/3)) + 3*b**5/(a**6*x**(1/3)) + b**6*log(x)/a**7 - 3*b**6*log(a/b + x**(1/3))/a**7, True))","A",0
2363,1,172,0,22.368874," ","integrate(1/(a+b*x**(1/3))/x**4,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{10}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{3}{10 b x^{\frac{10}{3}}} & \text{for}\: a = 0 \\- \frac{1}{3 a x^{3}} & \text{for}\: b = 0 \\- \frac{1}{3 a x^{3}} + \frac{3 b}{8 a^{2} x^{\frac{8}{3}}} - \frac{3 b^{2}}{7 a^{3} x^{\frac{7}{3}}} + \frac{b^{3}}{2 a^{4} x^{2}} - \frac{3 b^{4}}{5 a^{5} x^{\frac{5}{3}}} + \frac{3 b^{5}}{4 a^{6} x^{\frac{4}{3}}} - \frac{b^{6}}{a^{7} x} + \frac{3 b^{7}}{2 a^{8} x^{\frac{2}{3}}} - \frac{3 b^{8}}{a^{9} \sqrt[3]{x}} - \frac{b^{9} \log{\left(x \right)}}{a^{10}} + \frac{3 b^{9} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{a^{10}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(10/3), Eq(a, 0) & Eq(b, 0)), (-3/(10*b*x**(10/3)), Eq(a, 0)), (-1/(3*a*x**3), Eq(b, 0)), (-1/(3*a*x**3) + 3*b/(8*a**2*x**(8/3)) - 3*b**2/(7*a**3*x**(7/3)) + b**3/(2*a**4*x**2) - 3*b**4/(5*a**5*x**(5/3)) + 3*b**5/(4*a**6*x**(4/3)) - b**6/(a**7*x) + 3*b**7/(2*a**8*x**(2/3)) - 3*b**8/(a**9*x**(1/3)) - b**9*log(x)/a**10 + 3*b**9*log(a/b + x**(1/3))/a**10, True))","A",0
2364,1,22,0,0.627207," ","integrate(1/(2+b*x**(1/3))/x,x)","\begin{cases} \frac{\log{\left(x \right)}}{2} - \frac{3 \log{\left(\sqrt[3]{x} + \frac{2}{b} \right)}}{2} & \text{for}\: b \neq 0 \\\frac{\log{\left(x \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/2 - 3*log(x**(1/3) + 2/b)/2, Ne(b, 0)), (log(x)/2, True))","A",0
2365,-1,0,0,0.000000," ","integrate(x**3/(a+b*x**(1/3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2366,1,343,0,56.225082," ","integrate(x**2/(a+b*x**(1/3))**2,x)","- \frac{840 a^{8} x^{\frac{176}{3}} \log{\left(1 + \frac{b \sqrt[3]{x}}{a} \right)}}{35 a b^{9} x^{\frac{176}{3}} + 35 b^{10} x^{59}} - \frac{840 a^{7} b x^{59} \log{\left(1 + \frac{b \sqrt[3]{x}}{a} \right)}}{35 a b^{9} x^{\frac{176}{3}} + 35 b^{10} x^{59}} + \frac{840 a^{7} b x^{59}}{35 a b^{9} x^{\frac{176}{3}} + 35 b^{10} x^{59}} + \frac{420 a^{6} b^{2} x^{\frac{178}{3}}}{35 a b^{9} x^{\frac{176}{3}} + 35 b^{10} x^{59}} - \frac{140 a^{5} b^{3} x^{\frac{179}{3}}}{35 a b^{9} x^{\frac{176}{3}} + 35 b^{10} x^{59}} + \frac{70 a^{4} b^{4} x^{60}}{35 a b^{9} x^{\frac{176}{3}} + 35 b^{10} x^{59}} - \frac{42 a^{3} b^{5} x^{\frac{181}{3}}}{35 a b^{9} x^{\frac{176}{3}} + 35 b^{10} x^{59}} + \frac{28 a^{2} b^{6} x^{\frac{182}{3}}}{35 a b^{9} x^{\frac{176}{3}} + 35 b^{10} x^{59}} - \frac{20 a b^{7} x^{61}}{35 a b^{9} x^{\frac{176}{3}} + 35 b^{10} x^{59}} + \frac{15 b^{8} x^{\frac{184}{3}}}{35 a b^{9} x^{\frac{176}{3}} + 35 b^{10} x^{59}}"," ",0,"-840*a**8*x**(176/3)*log(1 + b*x**(1/3)/a)/(35*a*b**9*x**(176/3) + 35*b**10*x**59) - 840*a**7*b*x**59*log(1 + b*x**(1/3)/a)/(35*a*b**9*x**(176/3) + 35*b**10*x**59) + 840*a**7*b*x**59/(35*a*b**9*x**(176/3) + 35*b**10*x**59) + 420*a**6*b**2*x**(178/3)/(35*a*b**9*x**(176/3) + 35*b**10*x**59) - 140*a**5*b**3*x**(179/3)/(35*a*b**9*x**(176/3) + 35*b**10*x**59) + 70*a**4*b**4*x**60/(35*a*b**9*x**(176/3) + 35*b**10*x**59) - 42*a**3*b**5*x**(181/3)/(35*a*b**9*x**(176/3) + 35*b**10*x**59) + 28*a**2*b**6*x**(182/3)/(35*a*b**9*x**(176/3) + 35*b**10*x**59) - 20*a*b**7*x**61/(35*a*b**9*x**(176/3) + 35*b**10*x**59) + 15*b**8*x**(184/3)/(35*a*b**9*x**(176/3) + 35*b**10*x**59)","B",0
2367,1,243,0,8.520750," ","integrate(x/(a+b*x**(1/3))**2,x)","\frac{60 a^{5} x^{\frac{80}{3}} \log{\left(1 + \frac{b \sqrt[3]{x}}{a} \right)}}{4 a b^{6} x^{\frac{80}{3}} + 4 b^{7} x^{27}} + \frac{60 a^{4} b x^{27} \log{\left(1 + \frac{b \sqrt[3]{x}}{a} \right)}}{4 a b^{6} x^{\frac{80}{3}} + 4 b^{7} x^{27}} - \frac{60 a^{4} b x^{27}}{4 a b^{6} x^{\frac{80}{3}} + 4 b^{7} x^{27}} - \frac{30 a^{3} b^{2} x^{\frac{82}{3}}}{4 a b^{6} x^{\frac{80}{3}} + 4 b^{7} x^{27}} + \frac{10 a^{2} b^{3} x^{\frac{83}{3}}}{4 a b^{6} x^{\frac{80}{3}} + 4 b^{7} x^{27}} - \frac{5 a b^{4} x^{28}}{4 a b^{6} x^{\frac{80}{3}} + 4 b^{7} x^{27}} + \frac{3 b^{5} x^{\frac{85}{3}}}{4 a b^{6} x^{\frac{80}{3}} + 4 b^{7} x^{27}}"," ",0,"60*a**5*x**(80/3)*log(1 + b*x**(1/3)/a)/(4*a*b**6*x**(80/3) + 4*b**7*x**27) + 60*a**4*b*x**27*log(1 + b*x**(1/3)/a)/(4*a*b**6*x**(80/3) + 4*b**7*x**27) - 60*a**4*b*x**27/(4*a*b**6*x**(80/3) + 4*b**7*x**27) - 30*a**3*b**2*x**(82/3)/(4*a*b**6*x**(80/3) + 4*b**7*x**27) + 10*a**2*b**3*x**(83/3)/(4*a*b**6*x**(80/3) + 4*b**7*x**27) - 5*a*b**4*x**28/(4*a*b**6*x**(80/3) + 4*b**7*x**27) + 3*b**5*x**(85/3)/(4*a*b**6*x**(80/3) + 4*b**7*x**27)","B",0
2368,1,109,0,0.450067," ","integrate(1/(a+b*x**(1/3))**2,x)","\begin{cases} - \frac{6 a^{2} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{a b^{3} + b^{4} \sqrt[3]{x}} - \frac{6 a^{2}}{a b^{3} + b^{4} \sqrt[3]{x}} - \frac{6 a b \sqrt[3]{x} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{a b^{3} + b^{4} \sqrt[3]{x}} + \frac{3 b^{2} x^{\frac{2}{3}}}{a b^{3} + b^{4} \sqrt[3]{x}} & \text{for}\: b \neq 0 \\\frac{x}{a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a**2*log(a/b + x**(1/3))/(a*b**3 + b**4*x**(1/3)) - 6*a**2/(a*b**3 + b**4*x**(1/3)) - 6*a*b*x**(1/3)*log(a/b + x**(1/3))/(a*b**3 + b**4*x**(1/3)) + 3*b**2*x**(2/3)/(a*b**3 + b**4*x**(1/3)), Ne(b, 0)), (x/a**2, True))","A",0
2369,1,160,0,1.380793," ","integrate(1/(a+b*x**(1/3))**2/x,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{2}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\log{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \\- \frac{3}{2 b^{2} x^{\frac{2}{3}}} & \text{for}\: a = 0 \\\frac{a x^{\frac{2}{3}} \log{\left(x \right)}}{a^{3} x^{\frac{2}{3}} + a^{2} b x} - \frac{3 a x^{\frac{2}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{a^{3} x^{\frac{2}{3}} + a^{2} b x} + \frac{3 a x^{\frac{2}{3}}}{a^{3} x^{\frac{2}{3}} + a^{2} b x} + \frac{b x \log{\left(x \right)}}{a^{3} x^{\frac{2}{3}} + a^{2} b x} - \frac{3 b x \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{a^{3} x^{\frac{2}{3}} + a^{2} b x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(2/3), Eq(a, 0) & Eq(b, 0)), (log(x)/a**2, Eq(b, 0)), (-3/(2*b**2*x**(2/3)), Eq(a, 0)), (a*x**(2/3)*log(x)/(a**3*x**(2/3) + a**2*b*x) - 3*a*x**(2/3)*log(a/b + x**(1/3))/(a**3*x**(2/3) + a**2*b*x) + 3*a*x**(2/3)/(a**3*x**(2/3) + a**2*b*x) + b*x*log(x)/(a**3*x**(2/3) + a**2*b*x) - 3*b*x*log(a/b + x**(1/3))/(a**3*x**(2/3) + a**2*b*x), True))","A",0
2370,1,272,0,5.574293," ","integrate(1/(a+b*x**(1/3))**2/x**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{a^{2} x} & \text{for}\: b = 0 \\- \frac{3}{5 b^{2} x^{\frac{5}{3}}} & \text{for}\: a = 0 \\- \frac{a^{4} x^{\frac{2}{3}}}{a^{6} x^{\frac{5}{3}} + a^{5} b x^{2}} + \frac{2 a^{3} b x}{a^{6} x^{\frac{5}{3}} + a^{5} b x^{2}} - \frac{6 a^{2} b^{2} x^{\frac{4}{3}}}{a^{6} x^{\frac{5}{3}} + a^{5} b x^{2}} - \frac{4 a b^{3} x^{\frac{5}{3}} \log{\left(x \right)}}{a^{6} x^{\frac{5}{3}} + a^{5} b x^{2}} + \frac{12 a b^{3} x^{\frac{5}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{a^{6} x^{\frac{5}{3}} + a^{5} b x^{2}} - \frac{12 a b^{3} x^{\frac{5}{3}}}{a^{6} x^{\frac{5}{3}} + a^{5} b x^{2}} - \frac{4 b^{4} x^{2} \log{\left(x \right)}}{a^{6} x^{\frac{5}{3}} + a^{5} b x^{2}} + \frac{12 b^{4} x^{2} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{a^{6} x^{\frac{5}{3}} + a^{5} b x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/3), Eq(a, 0) & Eq(b, 0)), (-1/(a**2*x), Eq(b, 0)), (-3/(5*b**2*x**(5/3)), Eq(a, 0)), (-a**4*x**(2/3)/(a**6*x**(5/3) + a**5*b*x**2) + 2*a**3*b*x/(a**6*x**(5/3) + a**5*b*x**2) - 6*a**2*b**2*x**(4/3)/(a**6*x**(5/3) + a**5*b*x**2) - 4*a*b**3*x**(5/3)*log(x)/(a**6*x**(5/3) + a**5*b*x**2) + 12*a*b**3*x**(5/3)*log(a/b + x**(1/3))/(a**6*x**(5/3) + a**5*b*x**2) - 12*a*b**3*x**(5/3)/(a**6*x**(5/3) + a**5*b*x**2) - 4*b**4*x**2*log(x)/(a**6*x**(5/3) + a**5*b*x**2) + 12*b**4*x**2*log(a/b + x**(1/3))/(a**6*x**(5/3) + a**5*b*x**2), True))","A",0
2371,1,405,0,14.130498," ","integrate(1/(a+b*x**(1/3))**2/x**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{8}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{2 a^{2} x^{2}} & \text{for}\: b = 0 \\- \frac{3}{8 b^{2} x^{\frac{8}{3}}} & \text{for}\: a = 0 \\- \frac{10 a^{7} x^{\frac{2}{3}}}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} + \frac{14 a^{6} b x}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} - \frac{21 a^{5} b^{2} x^{\frac{4}{3}}}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} + \frac{35 a^{4} b^{3} x^{\frac{5}{3}}}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} - \frac{70 a^{3} b^{4} x^{2}}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} + \frac{210 a^{2} b^{5} x^{\frac{7}{3}}}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} + \frac{140 a b^{6} x^{\frac{8}{3}} \log{\left(x \right)}}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} - \frac{420 a b^{6} x^{\frac{8}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} + \frac{420 a b^{6} x^{\frac{8}{3}}}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} + \frac{140 b^{7} x^{3} \log{\left(x \right)}}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} - \frac{420 b^{7} x^{3} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{20 a^{9} x^{\frac{8}{3}} + 20 a^{8} b x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(8/3), Eq(a, 0) & Eq(b, 0)), (-1/(2*a**2*x**2), Eq(b, 0)), (-3/(8*b**2*x**(8/3)), Eq(a, 0)), (-10*a**7*x**(2/3)/(20*a**9*x**(8/3) + 20*a**8*b*x**3) + 14*a**6*b*x/(20*a**9*x**(8/3) + 20*a**8*b*x**3) - 21*a**5*b**2*x**(4/3)/(20*a**9*x**(8/3) + 20*a**8*b*x**3) + 35*a**4*b**3*x**(5/3)/(20*a**9*x**(8/3) + 20*a**8*b*x**3) - 70*a**3*b**4*x**2/(20*a**9*x**(8/3) + 20*a**8*b*x**3) + 210*a**2*b**5*x**(7/3)/(20*a**9*x**(8/3) + 20*a**8*b*x**3) + 140*a*b**6*x**(8/3)*log(x)/(20*a**9*x**(8/3) + 20*a**8*b*x**3) - 420*a*b**6*x**(8/3)*log(a/b + x**(1/3))/(20*a**9*x**(8/3) + 20*a**8*b*x**3) + 420*a*b**6*x**(8/3)/(20*a**9*x**(8/3) + 20*a**8*b*x**3) + 140*b**7*x**3*log(x)/(20*a**9*x**(8/3) + 20*a**8*b*x**3) - 420*b**7*x**3*log(a/b + x**(1/3))/(20*a**9*x**(8/3) + 20*a**8*b*x**3), True))","A",0
2372,1,505,0,33.659498," ","integrate(1/(a+b*x**(1/3))**2/x**4,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{11}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{3}{11 b^{2} x^{\frac{11}{3}}} & \text{for}\: a = 0 \\- \frac{1}{3 a^{2} x^{3}} & \text{for}\: b = 0 \\- \frac{28 a^{10} x^{\frac{2}{3}}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} + \frac{35 a^{9} b x}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} - \frac{45 a^{8} b^{2} x^{\frac{4}{3}}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} + \frac{60 a^{7} b^{3} x^{\frac{5}{3}}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} - \frac{84 a^{6} b^{4} x^{2}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} + \frac{126 a^{5} b^{5} x^{\frac{7}{3}}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} - \frac{210 a^{4} b^{6} x^{\frac{8}{3}}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} + \frac{420 a^{3} b^{7} x^{3}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} - \frac{1260 a^{2} b^{8} x^{\frac{10}{3}}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} - \frac{840 a b^{9} x^{\frac{11}{3}} \log{\left(x \right)}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} + \frac{2520 a b^{9} x^{\frac{11}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} - \frac{2520 a b^{9} x^{\frac{11}{3}}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} - \frac{840 b^{10} x^{4} \log{\left(x \right)}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} + \frac{2520 b^{10} x^{4} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{84 a^{12} x^{\frac{11}{3}} + 84 a^{11} b x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(11/3), Eq(a, 0) & Eq(b, 0)), (-3/(11*b**2*x**(11/3)), Eq(a, 0)), (-1/(3*a**2*x**3), Eq(b, 0)), (-28*a**10*x**(2/3)/(84*a**12*x**(11/3) + 84*a**11*b*x**4) + 35*a**9*b*x/(84*a**12*x**(11/3) + 84*a**11*b*x**4) - 45*a**8*b**2*x**(4/3)/(84*a**12*x**(11/3) + 84*a**11*b*x**4) + 60*a**7*b**3*x**(5/3)/(84*a**12*x**(11/3) + 84*a**11*b*x**4) - 84*a**6*b**4*x**2/(84*a**12*x**(11/3) + 84*a**11*b*x**4) + 126*a**5*b**5*x**(7/3)/(84*a**12*x**(11/3) + 84*a**11*b*x**4) - 210*a**4*b**6*x**(8/3)/(84*a**12*x**(11/3) + 84*a**11*b*x**4) + 420*a**3*b**7*x**3/(84*a**12*x**(11/3) + 84*a**11*b*x**4) - 1260*a**2*b**8*x**(10/3)/(84*a**12*x**(11/3) + 84*a**11*b*x**4) - 840*a*b**9*x**(11/3)*log(x)/(84*a**12*x**(11/3) + 84*a**11*b*x**4) + 2520*a*b**9*x**(11/3)*log(a/b + x**(1/3))/(84*a**12*x**(11/3) + 84*a**11*b*x**4) - 2520*a*b**9*x**(11/3)/(84*a**12*x**(11/3) + 84*a**11*b*x**4) - 840*b**10*x**4*log(x)/(84*a**12*x**(11/3) + 84*a**11*b*x**4) + 2520*b**10*x**4*log(a/b + x**(1/3))/(84*a**12*x**(11/3) + 84*a**11*b*x**4), True))","A",0
2373,1,624,0,5.871694," ","integrate(x**3/(a+b*x**(1/3))**3,x)","\begin{cases} - \frac{27720 a^{11} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} - \frac{41580 a^{11}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} - \frac{55440 a^{10} b \sqrt[3]{x} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} - \frac{55440 a^{10} b \sqrt[3]{x}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} - \frac{27720 a^{9} b^{2} x^{\frac{2}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} + \frac{9240 a^{8} b^{3} x}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} - \frac{2310 a^{7} b^{4} x^{\frac{4}{3}}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} + \frac{924 a^{6} b^{5} x^{\frac{5}{3}}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} - \frac{462 a^{5} b^{6} x^{2}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} + \frac{264 a^{4} b^{7} x^{\frac{7}{3}}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} - \frac{165 a^{3} b^{8} x^{\frac{8}{3}}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} + \frac{110 a^{2} b^{9} x^{3}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} - \frac{77 a b^{10} x^{\frac{10}{3}}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} + \frac{56 b^{11} x^{\frac{11}{3}}}{168 a^{2} b^{12} + 336 a b^{13} \sqrt[3]{x} + 168 b^{14} x^{\frac{2}{3}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-27720*a**11*log(a/b + x**(1/3))/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) - 41580*a**11/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) - 55440*a**10*b*x**(1/3)*log(a/b + x**(1/3))/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) - 55440*a**10*b*x**(1/3)/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) - 27720*a**9*b**2*x**(2/3)*log(a/b + x**(1/3))/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) + 9240*a**8*b**3*x/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) - 2310*a**7*b**4*x**(4/3)/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) + 924*a**6*b**5*x**(5/3)/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) - 462*a**5*b**6*x**2/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) + 264*a**4*b**7*x**(7/3)/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) - 165*a**3*b**8*x**(8/3)/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) + 110*a**2*b**9*x**3/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) - 77*a*b**10*x**(10/3)/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)) + 56*b**11*x**(11/3)/(168*a**2*b**12 + 336*a*b**13*x**(1/3) + 168*b**14*x**(2/3)), Ne(b, 0)), (x**4/(4*a**3), True))","A",0
2374,1,493,0,2.248341," ","integrate(x**2/(a+b*x**(1/3))**3,x)","\begin{cases} \frac{840 a^{8} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} + \frac{1260 a^{8}}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} + \frac{1680 a^{7} b \sqrt[3]{x} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} + \frac{1680 a^{7} b \sqrt[3]{x}}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} + \frac{840 a^{6} b^{2} x^{\frac{2}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} - \frac{280 a^{5} b^{3} x}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} + \frac{70 a^{4} b^{4} x^{\frac{4}{3}}}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} - \frac{28 a^{3} b^{5} x^{\frac{5}{3}}}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} + \frac{14 a^{2} b^{6} x^{2}}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} - \frac{8 a b^{7} x^{\frac{7}{3}}}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} + \frac{5 b^{8} x^{\frac{8}{3}}}{10 a^{2} b^{9} + 20 a b^{10} \sqrt[3]{x} + 10 b^{11} x^{\frac{2}{3}}} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((840*a**8*log(a/b + x**(1/3))/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)) + 1260*a**8/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)) + 1680*a**7*b*x**(1/3)*log(a/b + x**(1/3))/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)) + 1680*a**7*b*x**(1/3)/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)) + 840*a**6*b**2*x**(2/3)*log(a/b + x**(1/3))/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)) - 280*a**5*b**3*x/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)) + 70*a**4*b**4*x**(4/3)/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)) - 28*a**3*b**5*x**(5/3)/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)) + 14*a**2*b**6*x**2/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)) - 8*a*b**7*x**(7/3)/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)) + 5*b**8*x**(8/3)/(10*a**2*b**9 + 20*a*b**10*x**(1/3) + 10*b**11*x**(2/3)), Ne(b, 0)), (x**3/(3*a**3), True))","A",0
2375,1,362,0,0.870770," ","integrate(x/(a+b*x**(1/3))**3,x)","\begin{cases} - \frac{60 a^{5} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{2} b^{6} + 4 a b^{7} \sqrt[3]{x} + 2 b^{8} x^{\frac{2}{3}}} - \frac{90 a^{5}}{2 a^{2} b^{6} + 4 a b^{7} \sqrt[3]{x} + 2 b^{8} x^{\frac{2}{3}}} - \frac{120 a^{4} b \sqrt[3]{x} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{2} b^{6} + 4 a b^{7} \sqrt[3]{x} + 2 b^{8} x^{\frac{2}{3}}} - \frac{120 a^{4} b \sqrt[3]{x}}{2 a^{2} b^{6} + 4 a b^{7} \sqrt[3]{x} + 2 b^{8} x^{\frac{2}{3}}} - \frac{60 a^{3} b^{2} x^{\frac{2}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{2} b^{6} + 4 a b^{7} \sqrt[3]{x} + 2 b^{8} x^{\frac{2}{3}}} + \frac{20 a^{2} b^{3} x}{2 a^{2} b^{6} + 4 a b^{7} \sqrt[3]{x} + 2 b^{8} x^{\frac{2}{3}}} - \frac{5 a b^{4} x^{\frac{4}{3}}}{2 a^{2} b^{6} + 4 a b^{7} \sqrt[3]{x} + 2 b^{8} x^{\frac{2}{3}}} + \frac{2 b^{5} x^{\frac{5}{3}}}{2 a^{2} b^{6} + 4 a b^{7} \sqrt[3]{x} + 2 b^{8} x^{\frac{2}{3}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-60*a**5*log(a/b + x**(1/3))/(2*a**2*b**6 + 4*a*b**7*x**(1/3) + 2*b**8*x**(2/3)) - 90*a**5/(2*a**2*b**6 + 4*a*b**7*x**(1/3) + 2*b**8*x**(2/3)) - 120*a**4*b*x**(1/3)*log(a/b + x**(1/3))/(2*a**2*b**6 + 4*a*b**7*x**(1/3) + 2*b**8*x**(2/3)) - 120*a**4*b*x**(1/3)/(2*a**2*b**6 + 4*a*b**7*x**(1/3) + 2*b**8*x**(2/3)) - 60*a**3*b**2*x**(2/3)*log(a/b + x**(1/3))/(2*a**2*b**6 + 4*a*b**7*x**(1/3) + 2*b**8*x**(2/3)) + 20*a**2*b**3*x/(2*a**2*b**6 + 4*a*b**7*x**(1/3) + 2*b**8*x**(2/3)) - 5*a*b**4*x**(4/3)/(2*a**2*b**6 + 4*a*b**7*x**(1/3) + 2*b**8*x**(2/3)) + 2*b**5*x**(5/3)/(2*a**2*b**6 + 4*a*b**7*x**(1/3) + 2*b**8*x**(2/3)), Ne(b, 0)), (x**2/(2*a**3), True))","A",0
2376,1,228,0,0.665601," ","integrate(1/(a+b*x**(1/3))**3,x)","\begin{cases} \frac{6 a^{2} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{2} b^{3} + 4 a b^{4} \sqrt[3]{x} + 2 b^{5} x^{\frac{2}{3}}} + \frac{9 a^{2}}{2 a^{2} b^{3} + 4 a b^{4} \sqrt[3]{x} + 2 b^{5} x^{\frac{2}{3}}} + \frac{12 a b \sqrt[3]{x} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{2} b^{3} + 4 a b^{4} \sqrt[3]{x} + 2 b^{5} x^{\frac{2}{3}}} + \frac{12 a b \sqrt[3]{x}}{2 a^{2} b^{3} + 4 a b^{4} \sqrt[3]{x} + 2 b^{5} x^{\frac{2}{3}}} + \frac{6 b^{2} x^{\frac{2}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{2} b^{3} + 4 a b^{4} \sqrt[3]{x} + 2 b^{5} x^{\frac{2}{3}}} & \text{for}\: b \neq 0 \\\frac{x}{a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*a**2*log(a/b + x**(1/3))/(2*a**2*b**3 + 4*a*b**4*x**(1/3) + 2*b**5*x**(2/3)) + 9*a**2/(2*a**2*b**3 + 4*a*b**4*x**(1/3) + 2*b**5*x**(2/3)) + 12*a*b*x**(1/3)*log(a/b + x**(1/3))/(2*a**2*b**3 + 4*a*b**4*x**(1/3) + 2*b**5*x**(2/3)) + 12*a*b*x**(1/3)/(2*a**2*b**3 + 4*a*b**4*x**(1/3) + 2*b**5*x**(2/3)) + 6*b**2*x**(2/3)*log(a/b + x**(1/3))/(2*a**2*b**3 + 4*a*b**4*x**(1/3) + 2*b**5*x**(2/3)), Ne(b, 0)), (x/a**3, True))","A",0
2377,1,386,0,1.913330," ","integrate(1/(a+b*x**(1/3))**3/x,x)","\begin{cases} \frac{\tilde{\infty}}{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\log{\left(x \right)}}{a^{3}} & \text{for}\: b = 0 \\- \frac{1}{b^{3} x} & \text{for}\: a = 0 \\\frac{2 a^{2} x^{\frac{2}{3}} \log{\left(x \right)}}{2 a^{5} x^{\frac{2}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{4}{3}}} - \frac{6 a^{2} x^{\frac{2}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{5} x^{\frac{2}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{4}{3}}} + \frac{9 a^{2} x^{\frac{2}{3}}}{2 a^{5} x^{\frac{2}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{4}{3}}} + \frac{4 a b x \log{\left(x \right)}}{2 a^{5} x^{\frac{2}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{4}{3}}} - \frac{12 a b x \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{5} x^{\frac{2}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{4}{3}}} + \frac{6 a b x}{2 a^{5} x^{\frac{2}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{4}{3}}} + \frac{2 b^{2} x^{\frac{4}{3}} \log{\left(x \right)}}{2 a^{5} x^{\frac{2}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{4}{3}}} - \frac{6 b^{2} x^{\frac{4}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{5} x^{\frac{2}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{4}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x, Eq(a, 0) & Eq(b, 0)), (log(x)/a**3, Eq(b, 0)), (-1/(b**3*x), Eq(a, 0)), (2*a**2*x**(2/3)*log(x)/(2*a**5*x**(2/3) + 4*a**4*b*x + 2*a**3*b**2*x**(4/3)) - 6*a**2*x**(2/3)*log(a/b + x**(1/3))/(2*a**5*x**(2/3) + 4*a**4*b*x + 2*a**3*b**2*x**(4/3)) + 9*a**2*x**(2/3)/(2*a**5*x**(2/3) + 4*a**4*b*x + 2*a**3*b**2*x**(4/3)) + 4*a*b*x*log(x)/(2*a**5*x**(2/3) + 4*a**4*b*x + 2*a**3*b**2*x**(4/3)) - 12*a*b*x*log(a/b + x**(1/3))/(2*a**5*x**(2/3) + 4*a**4*b*x + 2*a**3*b**2*x**(4/3)) + 6*a*b*x/(2*a**5*x**(2/3) + 4*a**4*b*x + 2*a**3*b**2*x**(4/3)) + 2*b**2*x**(4/3)*log(x)/(2*a**5*x**(2/3) + 4*a**4*b*x + 2*a**3*b**2*x**(4/3)) - 6*b**2*x**(4/3)*log(a/b + x**(1/3))/(2*a**5*x**(2/3) + 4*a**4*b*x + 2*a**3*b**2*x**(4/3)), True))","A",0
2378,1,561,0,4.867361," ","integrate(1/(a+b*x**(1/3))**3/x**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{2}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{a^{3} x} & \text{for}\: b = 0 \\- \frac{1}{2 b^{3} x^{2}} & \text{for}\: a = 0 \\- \frac{2 a^{5} x^{\frac{2}{3}}}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} + \frac{5 a^{4} b x}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} - \frac{20 a^{3} b^{2} x^{\frac{4}{3}}}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} - \frac{20 a^{2} b^{3} x^{\frac{5}{3}} \log{\left(x \right)}}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} + \frac{60 a^{2} b^{3} x^{\frac{5}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} - \frac{90 a^{2} b^{3} x^{\frac{5}{3}}}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} - \frac{40 a b^{4} x^{2} \log{\left(x \right)}}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} + \frac{120 a b^{4} x^{2} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} - \frac{60 a b^{4} x^{2}}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} - \frac{20 b^{5} x^{\frac{7}{3}} \log{\left(x \right)}}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} + \frac{60 b^{5} x^{\frac{7}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{2 a^{8} x^{\frac{5}{3}} + 4 a^{7} b x^{2} + 2 a^{6} b^{2} x^{\frac{7}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**2, Eq(a, 0) & Eq(b, 0)), (-1/(a**3*x), Eq(b, 0)), (-1/(2*b**3*x**2), Eq(a, 0)), (-2*a**5*x**(2/3)/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)) + 5*a**4*b*x/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)) - 20*a**3*b**2*x**(4/3)/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)) - 20*a**2*b**3*x**(5/3)*log(x)/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)) + 60*a**2*b**3*x**(5/3)*log(a/b + x**(1/3))/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)) - 90*a**2*b**3*x**(5/3)/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)) - 40*a*b**4*x**2*log(x)/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)) + 120*a*b**4*x**2*log(a/b + x**(1/3))/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)) - 60*a*b**4*x**2/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)) - 20*b**5*x**(7/3)*log(x)/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)) + 60*b**5*x**(7/3)*log(a/b + x**(1/3))/(2*a**8*x**(5/3) + 4*a**7*b*x**2 + 2*a**6*b**2*x**(7/3)), True))","A",0
2379,1,706,0,11.460433," ","integrate(1/(a+b*x**(1/3))**3/x**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{3}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{2 a^{3} x^{2}} & \text{for}\: b = 0 \\- \frac{1}{3 b^{3} x^{3}} & \text{for}\: a = 0 \\- \frac{5 a^{8} x^{\frac{2}{3}}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} + \frac{8 a^{7} b x}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} - \frac{14 a^{6} b^{2} x^{\frac{4}{3}}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} + \frac{28 a^{5} b^{3} x^{\frac{5}{3}}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} - \frac{70 a^{4} b^{4} x^{2}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} + \frac{280 a^{3} b^{5} x^{\frac{7}{3}}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} + \frac{280 a^{2} b^{6} x^{\frac{8}{3}} \log{\left(x \right)}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} - \frac{840 a^{2} b^{6} x^{\frac{8}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} + \frac{1260 a^{2} b^{6} x^{\frac{8}{3}}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} + \frac{560 a b^{7} x^{3} \log{\left(x \right)}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} - \frac{1680 a b^{7} x^{3} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} + \frac{840 a b^{7} x^{3}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} + \frac{280 b^{8} x^{\frac{10}{3}} \log{\left(x \right)}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} - \frac{840 b^{8} x^{\frac{10}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{10 a^{11} x^{\frac{8}{3}} + 20 a^{10} b x^{3} + 10 a^{9} b^{2} x^{\frac{10}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**3, Eq(a, 0) & Eq(b, 0)), (-1/(2*a**3*x**2), Eq(b, 0)), (-1/(3*b**3*x**3), Eq(a, 0)), (-5*a**8*x**(2/3)/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) + 8*a**7*b*x/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) - 14*a**6*b**2*x**(4/3)/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) + 28*a**5*b**3*x**(5/3)/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) - 70*a**4*b**4*x**2/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) + 280*a**3*b**5*x**(7/3)/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) + 280*a**2*b**6*x**(8/3)*log(x)/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) - 840*a**2*b**6*x**(8/3)*log(a/b + x**(1/3))/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) + 1260*a**2*b**6*x**(8/3)/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) + 560*a*b**7*x**3*log(x)/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) - 1680*a*b**7*x**3*log(a/b + x**(1/3))/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) + 840*a*b**7*x**3/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) + 280*b**8*x**(10/3)*log(x)/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)) - 840*b**8*x**(10/3)*log(a/b + x**(1/3))/(10*a**11*x**(8/3) + 20*a**10*b*x**3 + 10*a**9*b**2*x**(10/3)), True))","A",0
2380,1,847,0,22.572110," ","integrate(1/(a+b*x**(1/3))**3/x**4,x)","\begin{cases} \frac{\tilde{\infty}}{x^{4}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{3 a^{3} x^{3}} & \text{for}\: b = 0 \\- \frac{1}{4 b^{3} x^{4}} & \text{for}\: a = 0 \\- \frac{56 a^{11} x^{\frac{2}{3}}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} + \frac{77 a^{10} b x}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} - \frac{110 a^{9} b^{2} x^{\frac{4}{3}}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} + \frac{165 a^{8} b^{3} x^{\frac{5}{3}}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} - \frac{264 a^{7} b^{4} x^{2}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} + \frac{462 a^{6} b^{5} x^{\frac{7}{3}}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} - \frac{924 a^{5} b^{6} x^{\frac{8}{3}}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} + \frac{2310 a^{4} b^{7} x^{3}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} - \frac{9240 a^{3} b^{8} x^{\frac{10}{3}}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} - \frac{9240 a^{2} b^{9} x^{\frac{11}{3}} \log{\left(x \right)}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} + \frac{27720 a^{2} b^{9} x^{\frac{11}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} - \frac{41580 a^{2} b^{9} x^{\frac{11}{3}}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} - \frac{18480 a b^{10} x^{4} \log{\left(x \right)}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} + \frac{55440 a b^{10} x^{4} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} - \frac{27720 a b^{10} x^{4}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} - \frac{9240 b^{11} x^{\frac{13}{3}} \log{\left(x \right)}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} + \frac{27720 b^{11} x^{\frac{13}{3}} \log{\left(\frac{a}{b} + \sqrt[3]{x} \right)}}{168 a^{14} x^{\frac{11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac{13}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**4, Eq(a, 0) & Eq(b, 0)), (-1/(3*a**3*x**3), Eq(b, 0)), (-1/(4*b**3*x**4), Eq(a, 0)), (-56*a**11*x**(2/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) + 77*a**10*b*x/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 110*a**9*b**2*x**(4/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) + 165*a**8*b**3*x**(5/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 264*a**7*b**4*x**2/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) + 462*a**6*b**5*x**(7/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 924*a**5*b**6*x**(8/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) + 2310*a**4*b**7*x**3/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 9240*a**3*b**8*x**(10/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 9240*a**2*b**9*x**(11/3)*log(x)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) + 27720*a**2*b**9*x**(11/3)*log(a/b + x**(1/3))/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 41580*a**2*b**9*x**(11/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 18480*a*b**10*x**4*log(x)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) + 55440*a*b**10*x**4*log(a/b + x**(1/3))/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 27720*a*b**10*x**4/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 9240*b**11*x**(13/3)*log(x)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) + 27720*b**11*x**(13/3)*log(a/b + x**(1/3))/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)), True))","A",0
2381,1,359,0,1.361518," ","integrate(1/(1+x**(1/3))**(1/2),x)","\frac{6 x^{\frac{14}{3}} \sqrt{\sqrt[3]{x} + 1}}{15 x^{\frac{11}{3}} + 15 x^{\frac{10}{3}} + 5 x^{4} + 5 x^{3}} + \frac{10 x^{\frac{13}{3}} \sqrt{\sqrt[3]{x} + 1}}{15 x^{\frac{11}{3}} + 15 x^{\frac{10}{3}} + 5 x^{4} + 5 x^{3}} + \frac{30 x^{\frac{11}{3}} \sqrt{\sqrt[3]{x} + 1}}{15 x^{\frac{11}{3}} + 15 x^{\frac{10}{3}} + 5 x^{4} + 5 x^{3}} - \frac{48 x^{\frac{11}{3}}}{15 x^{\frac{11}{3}} + 15 x^{\frac{10}{3}} + 5 x^{4} + 5 x^{3}} + \frac{40 x^{\frac{10}{3}} \sqrt{\sqrt[3]{x} + 1}}{15 x^{\frac{11}{3}} + 15 x^{\frac{10}{3}} + 5 x^{4} + 5 x^{3}} - \frac{48 x^{\frac{10}{3}}}{15 x^{\frac{11}{3}} + 15 x^{\frac{10}{3}} + 5 x^{4} + 5 x^{3}} + \frac{10 x^{4} \sqrt{\sqrt[3]{x} + 1}}{15 x^{\frac{11}{3}} + 15 x^{\frac{10}{3}} + 5 x^{4} + 5 x^{3}} - \frac{16 x^{4}}{15 x^{\frac{11}{3}} + 15 x^{\frac{10}{3}} + 5 x^{4} + 5 x^{3}} + \frac{16 x^{3} \sqrt{\sqrt[3]{x} + 1}}{15 x^{\frac{11}{3}} + 15 x^{\frac{10}{3}} + 5 x^{4} + 5 x^{3}} - \frac{16 x^{3}}{15 x^{\frac{11}{3}} + 15 x^{\frac{10}{3}} + 5 x^{4} + 5 x^{3}}"," ",0,"6*x**(14/3)*sqrt(x**(1/3) + 1)/(15*x**(11/3) + 15*x**(10/3) + 5*x**4 + 5*x**3) + 10*x**(13/3)*sqrt(x**(1/3) + 1)/(15*x**(11/3) + 15*x**(10/3) + 5*x**4 + 5*x**3) + 30*x**(11/3)*sqrt(x**(1/3) + 1)/(15*x**(11/3) + 15*x**(10/3) + 5*x**4 + 5*x**3) - 48*x**(11/3)/(15*x**(11/3) + 15*x**(10/3) + 5*x**4 + 5*x**3) + 40*x**(10/3)*sqrt(x**(1/3) + 1)/(15*x**(11/3) + 15*x**(10/3) + 5*x**4 + 5*x**3) - 48*x**(10/3)/(15*x**(11/3) + 15*x**(10/3) + 5*x**4 + 5*x**3) + 10*x**4*sqrt(x**(1/3) + 1)/(15*x**(11/3) + 15*x**(10/3) + 5*x**4 + 5*x**3) - 16*x**4/(15*x**(11/3) + 15*x**(10/3) + 5*x**4 + 5*x**3) + 16*x**3*sqrt(x**(1/3) + 1)/(15*x**(11/3) + 15*x**(10/3) + 5*x**4 + 5*x**3) - 16*x**3/(15*x**(11/3) + 15*x**(10/3) + 5*x**4 + 5*x**3)","B",0
2382,1,20,0,1.365478," ","integrate(1/(1+x**(1/3))/x**(3/2),x)","6 \operatorname{atan}{\left(\sqrt[6]{x} \right)} - \frac{2}{\sqrt{x}} + \frac{6}{\sqrt[6]{x}}"," ",0,"6*atan(x**(1/6)) - 2/sqrt(x) + 6/x**(1/6)","A",0
2383,1,34,0,0.245585," ","integrate(x**(2/3)/(1+x**(1/3)),x)","\frac{3 x^{\frac{4}{3}}}{4} + \frac{3 x^{\frac{2}{3}}}{2} - 3 \sqrt[3]{x} - x + 3 \log{\left(\sqrt[3]{x} + 1 \right)}"," ",0,"3*x**(4/3)/4 + 3*x**(2/3)/2 - 3*x**(1/3) - x + 3*log(x**(1/3) + 1)","A",0
2384,1,14,0,0.173468," ","integrate(1/(1+x**(2/3)),x)","3 \sqrt[3]{x} - 3 \operatorname{atan}{\left(\sqrt[3]{x} \right)}"," ",0,"3*x**(1/3) - 3*atan(x**(1/3))","A",0
2385,1,10,0,0.196099," ","integrate(1/(1+x**(2/3))/x**(1/3),x)","\frac{3 \log{\left(x^{\frac{2}{3}} + 1 \right)}}{2}"," ",0,"3*log(x**(2/3) + 1)/2","A",0
2386,1,7,0,0.292456," ","integrate(1/(1+x**(2/3))/x**(2/3),x)","3 \operatorname{atan}{\left(\sqrt[3]{x} \right)}"," ",0,"3*atan(x**(1/3))","A",0
2387,1,24,0,0.238595," ","integrate((-1+x**(2/3))**(1/2)/x**(1/3),x)","x^{\frac{2}{3}} \sqrt{x^{\frac{2}{3}} - 1} - \sqrt{x^{\frac{2}{3}} - 1}"," ",0,"x**(2/3)*sqrt(x**(2/3) - 1) - sqrt(x**(2/3) - 1)","B",0
2388,1,49,0,1.451907," ","integrate((1+x**(2/3))**(3/2)/x**(1/3),x)","\frac{3 x^{\frac{4}{3}} \sqrt{x^{\frac{2}{3}} + 1}}{5} + \frac{6 x^{\frac{2}{3}} \sqrt{x^{\frac{2}{3}} + 1}}{5} + \frac{3 \sqrt{x^{\frac{2}{3}} + 1}}{5}"," ",0,"3*x**(4/3)*sqrt(x**(2/3) + 1)/5 + 6*x**(2/3)*sqrt(x**(2/3) + 1)/5 + 3*sqrt(x**(2/3) + 1)/5","B",0
2389,1,187,0,1.379629," ","integrate(x**(1/2)/(1+x**(2/3)),x)","\frac{27 x^{\frac{5}{6}} \Gamma\left(\frac{9}{4}\right)}{10 \Gamma\left(\frac{13}{4}\right)} - \frac{27 \sqrt[6]{x} \Gamma\left(\frac{9}{4}\right)}{2 \Gamma\left(\frac{13}{4}\right)} - \frac{27 e^{- \frac{i \pi}{4}} \log{\left(- \sqrt[6]{x} e^{\frac{i \pi}{4}} + 1 \right)} \Gamma\left(\frac{9}{4}\right)}{8 \Gamma\left(\frac{13}{4}\right)} + \frac{27 i e^{- \frac{i \pi}{4}} \log{\left(- \sqrt[6]{x} e^{\frac{3 i \pi}{4}} + 1 \right)} \Gamma\left(\frac{9}{4}\right)}{8 \Gamma\left(\frac{13}{4}\right)} + \frac{27 e^{- \frac{i \pi}{4}} \log{\left(- \sqrt[6]{x} e^{\frac{5 i \pi}{4}} + 1 \right)} \Gamma\left(\frac{9}{4}\right)}{8 \Gamma\left(\frac{13}{4}\right)} - \frac{27 i e^{- \frac{i \pi}{4}} \log{\left(- \sqrt[6]{x} e^{\frac{7 i \pi}{4}} + 1 \right)} \Gamma\left(\frac{9}{4}\right)}{8 \Gamma\left(\frac{13}{4}\right)}"," ",0,"27*x**(5/6)*gamma(9/4)/(10*gamma(13/4)) - 27*x**(1/6)*gamma(9/4)/(2*gamma(13/4)) - 27*exp(-I*pi/4)*log(-x**(1/6)*exp_polar(I*pi/4) + 1)*gamma(9/4)/(8*gamma(13/4)) + 27*I*exp(-I*pi/4)*log(-x**(1/6)*exp_polar(3*I*pi/4) + 1)*gamma(9/4)/(8*gamma(13/4)) + 27*exp(-I*pi/4)*log(-x**(1/6)*exp_polar(5*I*pi/4) + 1)*gamma(9/4)/(8*gamma(13/4)) - 27*I*exp(-I*pi/4)*log(-x**(1/6)*exp_polar(7*I*pi/4) + 1)*gamma(9/4)/(8*gamma(13/4))","C",0
2390,1,462,0,135.826932," ","integrate(x**(1/3)/(-1+x**(5/6)),x)","2 \sqrt{x} + \frac{6 \log{\left(\sqrt[6]{x} - 1 \right)}}{5} - \frac{3 \log{\left(8 \sqrt[6]{x} + 8 \sqrt{5} \sqrt[6]{x} + 16 \sqrt[3]{x} + 16 \right)}}{10} + \frac{3 \sqrt{5} \log{\left(8 \sqrt[6]{x} + 8 \sqrt{5} \sqrt[6]{x} + 16 \sqrt[3]{x} + 16 \right)}}{10} - \frac{3 \sqrt{5} \log{\left(- 8 \sqrt{5} \sqrt[6]{x} + 8 \sqrt[6]{x} + 16 \sqrt[3]{x} + 16 \right)}}{10} - \frac{3 \log{\left(- 8 \sqrt{5} \sqrt[6]{x} + 8 \sqrt[6]{x} + 16 \sqrt[3]{x} + 16 \right)}}{10} - \frac{3 \sqrt{10} \sqrt{5 - \sqrt{5}} \operatorname{atan}{\left(\frac{2 \sqrt{2} \sqrt[6]{x}}{\sqrt{5 - \sqrt{5}}} + \frac{\sqrt{2}}{2 \sqrt{5 - \sqrt{5}}} + \frac{\sqrt{10}}{2 \sqrt{5 - \sqrt{5}}} \right)}}{10} - \frac{3 \sqrt{2} \sqrt{5 - \sqrt{5}} \operatorname{atan}{\left(\frac{2 \sqrt{2} \sqrt[6]{x}}{\sqrt{5 - \sqrt{5}}} + \frac{\sqrt{2}}{2 \sqrt{5 - \sqrt{5}}} + \frac{\sqrt{10}}{2 \sqrt{5 - \sqrt{5}}} \right)}}{10} - \frac{3 \sqrt{2} \sqrt{\sqrt{5} + 5} \operatorname{atan}{\left(\frac{2 \sqrt{2} \sqrt[6]{x}}{\sqrt{\sqrt{5} + 5}} - \frac{\sqrt{10}}{2 \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{2}}{2 \sqrt{\sqrt{5} + 5}} \right)}}{10} + \frac{3 \sqrt{10} \sqrt{\sqrt{5} + 5} \operatorname{atan}{\left(\frac{2 \sqrt{2} \sqrt[6]{x}}{\sqrt{\sqrt{5} + 5}} - \frac{\sqrt{10}}{2 \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{2}}{2 \sqrt{\sqrt{5} + 5}} \right)}}{10}"," ",0,"2*sqrt(x) + 6*log(x**(1/6) - 1)/5 - 3*log(8*x**(1/6) + 8*sqrt(5)*x**(1/6) + 16*x**(1/3) + 16)/10 + 3*sqrt(5)*log(8*x**(1/6) + 8*sqrt(5)*x**(1/6) + 16*x**(1/3) + 16)/10 - 3*sqrt(5)*log(-8*sqrt(5)*x**(1/6) + 8*x**(1/6) + 16*x**(1/3) + 16)/10 - 3*log(-8*sqrt(5)*x**(1/6) + 8*x**(1/6) + 16*x**(1/3) + 16)/10 - 3*sqrt(10)*sqrt(5 - sqrt(5))*atan(2*sqrt(2)*x**(1/6)/sqrt(5 - sqrt(5)) + sqrt(2)/(2*sqrt(5 - sqrt(5))) + sqrt(10)/(2*sqrt(5 - sqrt(5))))/10 - 3*sqrt(2)*sqrt(5 - sqrt(5))*atan(2*sqrt(2)*x**(1/6)/sqrt(5 - sqrt(5)) + sqrt(2)/(2*sqrt(5 - sqrt(5))) + sqrt(10)/(2*sqrt(5 - sqrt(5))))/10 - 3*sqrt(2)*sqrt(sqrt(5) + 5)*atan(2*sqrt(2)*x**(1/6)/sqrt(sqrt(5) + 5) - sqrt(10)/(2*sqrt(sqrt(5) + 5)) + sqrt(2)/(2*sqrt(sqrt(5) + 5)))/10 + 3*sqrt(10)*sqrt(sqrt(5) + 5)*atan(2*sqrt(2)*x**(1/6)/sqrt(sqrt(5) + 5) - sqrt(10)/(2*sqrt(sqrt(5) + 5)) + sqrt(2)/(2*sqrt(sqrt(5) + 5)))/10","B",0
2391,1,165,0,2.959610," ","integrate((3-1/x**(1/2))**(1/2),x)","\begin{cases} \frac{3 x^{\frac{5}{4}}}{\sqrt{3 \sqrt{x} - 1}} - \frac{3 x^{\frac{3}{4}}}{2 \sqrt{3 \sqrt{x} - 1}} + \frac{\sqrt[4]{x}}{6 \sqrt{3 \sqrt{x} - 1}} - \frac{\sqrt{3} \operatorname{acosh}{\left(\sqrt{3} \sqrt[4]{x} \right)}}{18} & \text{for}\: 3 \left|{\sqrt{x}}\right| > 1 \\- \frac{3 i x^{\frac{5}{4}}}{\sqrt{1 - 3 \sqrt{x}}} + \frac{3 i x^{\frac{3}{4}}}{2 \sqrt{1 - 3 \sqrt{x}}} - \frac{i \sqrt[4]{x}}{6 \sqrt{1 - 3 \sqrt{x}}} + \frac{\sqrt{3} i \operatorname{asin}{\left(\sqrt{3} \sqrt[4]{x} \right)}}{18} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x**(5/4)/sqrt(3*sqrt(x) - 1) - 3*x**(3/4)/(2*sqrt(3*sqrt(x) - 1)) + x**(1/4)/(6*sqrt(3*sqrt(x) - 1)) - sqrt(3)*acosh(sqrt(3)*x**(1/4))/18, 3*Abs(sqrt(x)) > 1), (-3*I*x**(5/4)/sqrt(1 - 3*sqrt(x)) + 3*I*x**(3/4)/(2*sqrt(1 - 3*sqrt(x))) - I*x**(1/4)/(6*sqrt(1 - 3*sqrt(x))) + sqrt(3)*I*asin(sqrt(3)*x**(1/4))/18, True))","A",0
2392,1,60,0,3.237668," ","integrate(1/(1+1/x**(1/2))**(1/2),x)","\frac{x^{\frac{5}{4}}}{\sqrt{\sqrt{x} + 1}} - \frac{x^{\frac{3}{4}}}{2 \sqrt{\sqrt{x} + 1}} - \frac{3 \sqrt[4]{x}}{2 \sqrt{\sqrt{x} + 1}} + \frac{3 \operatorname{asinh}{\left(\sqrt[4]{x} \right)}}{2}"," ",0,"x**(5/4)/sqrt(sqrt(x) + 1) - x**(3/4)/(2*sqrt(sqrt(x) + 1)) - 3*x**(1/4)/(2*sqrt(sqrt(x) + 1)) + 3*asinh(x**(1/4))/2","A",0
2393,1,46,0,4.317553," ","integrate((a+b/x**(3/2))**(2/3),x)","- \frac{2 a^{\frac{2}{3}} x \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{2}{3} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b e^{i \pi}}{a x^{\frac{3}{2}}}} \right)}}{3 \Gamma\left(\frac{1}{3}\right)}"," ",0,"-2*a**(2/3)*x*gamma(-2/3)*hyper((-2/3, -2/3), (1/3,), b*exp_polar(I*pi)/(a*x**(3/2)))/(3*gamma(1/3))","C",0
2394,1,15,0,2.268727," ","integrate((a+b/x**(1/3))*x**4,x)","\frac{a x^{5}}{5} + \frac{3 b x^{\frac{14}{3}}}{14}"," ",0,"a*x**5/5 + 3*b*x**(14/3)/14","A",0
2395,1,15,0,1.243200," ","integrate((a+b/x**(1/3))*x**3,x)","\frac{a x^{4}}{4} + \frac{3 b x^{\frac{11}{3}}}{11}"," ",0,"a*x**4/4 + 3*b*x**(11/3)/11","A",0
2396,1,15,0,0.550712," ","integrate((a+b/x**(1/3))*x**2,x)","\frac{a x^{3}}{3} + \frac{3 b x^{\frac{8}{3}}}{8}"," ",0,"a*x**3/3 + 3*b*x**(8/3)/8","A",0
2397,1,15,0,0.237190," ","integrate((a+b/x**(1/3))*x,x)","\frac{a x^{2}}{2} + \frac{3 b x^{\frac{5}{3}}}{5}"," ",0,"a*x**2/2 + 3*b*x**(5/3)/5","A",0
2398,1,12,0,0.082736," ","integrate(a+b/x**(1/3),x)","a x + \frac{3 b x^{\frac{2}{3}}}{2}"," ",0,"a*x + 3*b*x**(2/3)/2","A",0
2399,1,12,0,0.398916," ","integrate((a+b/x**(1/3))/x,x)","a \log{\left(x \right)} - \frac{3 b}{\sqrt[3]{x}}"," ",0,"a*log(x) - 3*b/x**(1/3)","A",0
2400,1,14,0,0.737214," ","integrate((a+b/x**(1/3))/x**2,x)","- \frac{a}{x} - \frac{3 b}{4 x^{\frac{4}{3}}}"," ",0,"-a/x - 3*b/(4*x**(4/3))","A",0
2401,1,17,0,1.322562," ","integrate((a+b/x**(1/3))/x**3,x)","- \frac{a}{2 x^{2}} - \frac{3 b}{7 x^{\frac{7}{3}}}"," ",0,"-a/(2*x**2) - 3*b/(7*x**(7/3))","A",0
2402,1,17,0,2.402330," ","integrate((a+b/x**(1/3))/x**4,x)","- \frac{a}{3 x^{3}} - \frac{3 b}{10 x^{\frac{10}{3}}}"," ",0,"-a/(3*x**3) - 3*b/(10*x**(10/3))","A",0
2403,1,31,0,3.171834," ","integrate((a+b/x**(1/3))**2*x**4,x)","\frac{a^{2} x^{5}}{5} + \frac{3 a b x^{\frac{14}{3}}}{7} + \frac{3 b^{2} x^{\frac{13}{3}}}{13}"," ",0,"a**2*x**5/5 + 3*a*b*x**(14/3)/7 + 3*b**2*x**(13/3)/13","A",0
2404,1,31,0,1.786563," ","integrate((a+b/x**(1/3))**2*x**3,x)","\frac{a^{2} x^{4}}{4} + \frac{6 a b x^{\frac{11}{3}}}{11} + \frac{3 b^{2} x^{\frac{10}{3}}}{10}"," ",0,"a**2*x**4/4 + 6*a*b*x**(11/3)/11 + 3*b**2*x**(10/3)/10","A",0
2405,1,31,0,0.894812," ","integrate((a+b/x**(1/3))**2*x**2,x)","\frac{a^{2} x^{3}}{3} + \frac{3 a b x^{\frac{8}{3}}}{4} + \frac{3 b^{2} x^{\frac{7}{3}}}{7}"," ",0,"a**2*x**3/3 + 3*a*b*x**(8/3)/4 + 3*b**2*x**(7/3)/7","A",0
2406,1,31,0,0.402468," ","integrate((a+b/x**(1/3))**2*x,x)","\frac{a^{2} x^{2}}{2} + \frac{6 a b x^{\frac{5}{3}}}{5} + \frac{3 b^{2} x^{\frac{4}{3}}}{4}"," ",0,"a**2*x**2/2 + 6*a*b*x**(5/3)/5 + 3*b**2*x**(4/3)/4","A",0
2407,1,24,0,0.186800," ","integrate((a+b/x**(1/3))**2,x)","a^{2} x + 3 a b x^{\frac{2}{3}} + 3 b^{2} \sqrt[3]{x}"," ",0,"a**2*x + 3*a*b*x**(2/3) + 3*b**2*x**(1/3)","A",0
2408,1,27,0,0.510150," ","integrate((a+b/x**(1/3))**2/x,x)","a^{2} \log{\left(x \right)} - \frac{6 a b}{\sqrt[3]{x}} - \frac{3 b^{2}}{2 x^{\frac{2}{3}}}"," ",0,"a**2*log(x) - 6*a*b/x**(1/3) - 3*b**2/(2*x**(2/3))","A",0
2409,1,29,0,0.955395," ","integrate((a+b/x**(1/3))**2/x**2,x)","- \frac{a^{2}}{x} - \frac{3 a b}{2 x^{\frac{4}{3}}} - \frac{3 b^{2}}{5 x^{\frac{5}{3}}}"," ",0,"-a**2/x - 3*a*b/(2*x**(4/3)) - 3*b**2/(5*x**(5/3))","A",0
2410,1,32,0,1.848225," ","integrate((a+b/x**(1/3))**2/x**3,x)","- \frac{a^{2}}{2 x^{2}} - \frac{6 a b}{7 x^{\frac{7}{3}}} - \frac{3 b^{2}}{8 x^{\frac{8}{3}}}"," ",0,"-a**2/(2*x**2) - 6*a*b/(7*x**(7/3)) - 3*b**2/(8*x**(8/3))","A",0
2411,1,32,0,2.977402," ","integrate((a+b/x**(1/3))**2/x**4,x)","- \frac{a^{2}}{3 x^{3}} - \frac{3 a b}{5 x^{\frac{10}{3}}} - \frac{3 b^{2}}{11 x^{\frac{11}{3}}}"," ",0,"-a**2/(3*x**3) - 3*a*b/(5*x**(10/3)) - 3*b**2/(11*x**(11/3))","A",0
2412,1,42,0,3.961389," ","integrate((a+b/x**(1/3))**3*x**4,x)","\frac{a^{3} x^{5}}{5} + \frac{9 a^{2} b x^{\frac{14}{3}}}{14} + \frac{9 a b^{2} x^{\frac{13}{3}}}{13} + \frac{b^{3} x^{4}}{4}"," ",0,"a**3*x**5/5 + 9*a**2*b*x**(14/3)/14 + 9*a*b**2*x**(13/3)/13 + b**3*x**4/4","A",0
2413,1,42,0,2.275128," ","integrate((a+b/x**(1/3))**3*x**3,x)","\frac{a^{3} x^{4}}{4} + \frac{9 a^{2} b x^{\frac{11}{3}}}{11} + \frac{9 a b^{2} x^{\frac{10}{3}}}{10} + \frac{b^{3} x^{3}}{3}"," ",0,"a**3*x**4/4 + 9*a**2*b*x**(11/3)/11 + 9*a*b**2*x**(10/3)/10 + b**3*x**3/3","A",0
2414,1,42,0,1.218369," ","integrate((a+b/x**(1/3))**3*x**2,x)","\frac{a^{3} x^{3}}{3} + \frac{9 a^{2} b x^{\frac{8}{3}}}{8} + \frac{9 a b^{2} x^{\frac{7}{3}}}{7} + \frac{b^{3} x^{2}}{2}"," ",0,"a**3*x**3/3 + 9*a**2*b*x**(8/3)/8 + 9*a*b**2*x**(7/3)/7 + b**3*x**2/2","A",0
2415,1,39,0,0.560129," ","integrate((a+b/x**(1/3))**3*x,x)","\frac{a^{3} x^{2}}{2} + \frac{9 a^{2} b x^{\frac{5}{3}}}{5} + \frac{9 a b^{2} x^{\frac{4}{3}}}{4} + b^{3} x"," ",0,"a**3*x**2/2 + 9*a**2*b*x**(5/3)/5 + 9*a*b**2*x**(4/3)/4 + b**3*x","A",0
2416,1,36,0,0.257457," ","integrate((a+b/x**(1/3))**3,x)","a^{3} x + \frac{9 a^{2} b x^{\frac{2}{3}}}{2} + 9 a b^{2} \sqrt[3]{x} + b^{3} \log{\left(x \right)}"," ",0,"a**3*x + 9*a**2*b*x**(2/3)/2 + 9*a*b**2*x**(1/3) + b**3*log(x)","A",0
2417,1,36,0,0.657200," ","integrate((a+b/x**(1/3))**3/x,x)","a^{3} \log{\left(x \right)} - \frac{9 a^{2} b}{\sqrt[3]{x}} - \frac{9 a b^{2}}{2 x^{\frac{2}{3}}} - \frac{b^{3}}{x}"," ",0,"a**3*log(x) - 9*a**2*b/x**(1/3) - 9*a*b**2/(2*x**(2/3)) - b**3/x","A",0
2418,1,41,0,1.184200," ","integrate((a+b/x**(1/3))**3/x**2,x)","- \frac{a^{3}}{x} - \frac{9 a^{2} b}{4 x^{\frac{4}{3}}} - \frac{9 a b^{2}}{5 x^{\frac{5}{3}}} - \frac{b^{3}}{2 x^{2}}"," ",0,"-a**3/x - 9*a**2*b/(4*x**(4/3)) - 9*a*b**2/(5*x**(5/3)) - b**3/(2*x**2)","A",0
2419,1,44,0,2.038119," ","integrate((a+b/x**(1/3))**3/x**3,x)","- \frac{a^{3}}{2 x^{2}} - \frac{9 a^{2} b}{7 x^{\frac{7}{3}}} - \frac{9 a b^{2}}{8 x^{\frac{8}{3}}} - \frac{b^{3}}{3 x^{3}}"," ",0,"-a**3/(2*x**2) - 9*a**2*b/(7*x**(7/3)) - 9*a*b**2/(8*x**(8/3)) - b**3/(3*x**3)","A",0
2420,1,44,0,3.469728," ","integrate((a+b/x**(1/3))**3/x**4,x)","- \frac{a^{3}}{3 x^{3}} - \frac{9 a^{2} b}{10 x^{\frac{10}{3}}} - \frac{9 a b^{2}}{11 x^{\frac{11}{3}}} - \frac{b^{3}}{4 x^{4}}"," ",0,"-a**3/(3*x**3) - 9*a**2*b/(10*x**(10/3)) - 9*a*b**2/(11*x**(11/3)) - b**3/(4*x**4)","A",0
2421,1,143,0,4.141513," ","integrate(x**2/(a+b/x**(1/3)),x)","\begin{cases} \frac{x^{3}}{3 a} - \frac{3 b x^{\frac{8}{3}}}{8 a^{2}} + \frac{3 b^{2} x^{\frac{7}{3}}}{7 a^{3}} - \frac{b^{3} x^{2}}{2 a^{4}} + \frac{3 b^{4} x^{\frac{5}{3}}}{5 a^{5}} - \frac{3 b^{5} x^{\frac{4}{3}}}{4 a^{6}} + \frac{b^{6} x}{a^{7}} - \frac{3 b^{7} x^{\frac{2}{3}}}{2 a^{8}} + \frac{3 b^{8} \sqrt[3]{x}}{a^{9}} - \frac{3 b^{9} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{a^{10}} & \text{for}\: a \neq 0 \\\frac{3 x^{\frac{10}{3}}}{10 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**3/(3*a) - 3*b*x**(8/3)/(8*a**2) + 3*b**2*x**(7/3)/(7*a**3) - b**3*x**2/(2*a**4) + 3*b**4*x**(5/3)/(5*a**5) - 3*b**5*x**(4/3)/(4*a**6) + b**6*x/a**7 - 3*b**7*x**(2/3)/(2*a**8) + 3*b**8*x**(1/3)/a**9 - 3*b**9*log(x**(1/3) + b/a)/a**10, Ne(a, 0)), (3*x**(10/3)/(10*b), True))","A",0
2422,1,100,0,1.261597," ","integrate(x/(a+b/x**(1/3)),x)","\begin{cases} \frac{x^{2}}{2 a} - \frac{3 b x^{\frac{5}{3}}}{5 a^{2}} + \frac{3 b^{2} x^{\frac{4}{3}}}{4 a^{3}} - \frac{b^{3} x}{a^{4}} + \frac{3 b^{4} x^{\frac{2}{3}}}{2 a^{5}} - \frac{3 b^{5} \sqrt[3]{x}}{a^{6}} + \frac{3 b^{6} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{a^{7}} & \text{for}\: a \neq 0 \\\frac{3 x^{\frac{7}{3}}}{7 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2/(2*a) - 3*b*x**(5/3)/(5*a**2) + 3*b**2*x**(4/3)/(4*a**3) - b**3*x/a**4 + 3*b**4*x**(2/3)/(2*a**5) - 3*b**5*x**(1/3)/a**6 + 3*b**6*log(x**(1/3) + b/a)/a**7, Ne(a, 0)), (3*x**(7/3)/(7*b), True))","A",0
2423,1,58,0,0.410692," ","integrate(1/(a+b/x**(1/3)),x)","\begin{cases} \frac{x}{a} - \frac{3 b x^{\frac{2}{3}}}{2 a^{2}} + \frac{3 b^{2} \sqrt[3]{x}}{a^{3}} - \frac{3 b^{3} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{a^{4}} & \text{for}\: a \neq 0 \\\frac{3 x^{\frac{4}{3}}}{4 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a - 3*b*x**(2/3)/(2*a**2) + 3*b**2*x**(1/3)/a**3 - 3*b**3*log(x**(1/3) + b/a)/a**4, Ne(a, 0)), (3*x**(4/3)/(4*b), True))","A",0
2424,1,20,0,0.630848," ","integrate(1/(a+b/x**(1/3))/x,x)","\begin{cases} \frac{3 \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{a} & \text{for}\: a \neq 0 \\\frac{3 \sqrt[3]{x}}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*log(x**(1/3) + b/a)/a, Ne(a, 0)), (3*x**(1/3)/b, True))","A",0
2425,1,73,0,1.815062," ","integrate(1/(a+b/x**(1/3))/x**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{2}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{a x} & \text{for}\: b = 0 \\- \frac{3}{2 b x^{\frac{2}{3}}} & \text{for}\: a = 0 \\\frac{a^{2} \log{\left(x \right)}}{b^{3}} - \frac{3 a^{2} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{b^{3}} + \frac{3 a}{b^{2} \sqrt[3]{x}} - \frac{3}{2 b x^{\frac{2}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(2/3), Eq(a, 0) & Eq(b, 0)), (-1/(a*x), Eq(b, 0)), (-3/(2*b*x**(2/3)), Eq(a, 0)), (a**2*log(x)/b**3 - 3*a**2*log(x**(1/3) + b/a)/b**3 + 3*a/(b**2*x**(1/3)) - 3/(2*b*x**(2/3)), True))","A",0
2426,1,116,0,5.504439," ","integrate(1/(a+b/x**(1/3))/x**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{2 a x^{2}} & \text{for}\: b = 0 \\- \frac{3}{5 b x^{\frac{5}{3}}} & \text{for}\: a = 0 \\- \frac{a^{5} \log{\left(x \right)}}{b^{6}} + \frac{3 a^{5} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{b^{6}} - \frac{3 a^{4}}{b^{5} \sqrt[3]{x}} + \frac{3 a^{3}}{2 b^{4} x^{\frac{2}{3}}} - \frac{a^{2}}{b^{3} x} + \frac{3 a}{4 b^{2} x^{\frac{4}{3}}} - \frac{3}{5 b x^{\frac{5}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/3), Eq(a, 0) & Eq(b, 0)), (-1/(2*a*x**2), Eq(b, 0)), (-3/(5*b*x**(5/3)), Eq(a, 0)), (-a**5*log(x)/b**6 + 3*a**5*log(x**(1/3) + b/a)/b**6 - 3*a**4/(b**5*x**(1/3)) + 3*a**3/(2*b**4*x**(2/3)) - a**2/(b**3*x) + 3*a/(4*b**2*x**(4/3)) - 3/(5*b*x**(5/3)), True))","A",0
2427,1,158,0,13.975515," ","integrate(1/(a+b/x**(1/3))/x**4,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{8}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{3 a x^{3}} & \text{for}\: b = 0 \\- \frac{3}{8 b x^{\frac{8}{3}}} & \text{for}\: a = 0 \\\frac{a^{8} \log{\left(x \right)}}{b^{9}} - \frac{3 a^{8} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{b^{9}} + \frac{3 a^{7}}{b^{8} \sqrt[3]{x}} - \frac{3 a^{6}}{2 b^{7} x^{\frac{2}{3}}} + \frac{a^{5}}{b^{6} x} - \frac{3 a^{4}}{4 b^{5} x^{\frac{4}{3}}} + \frac{3 a^{3}}{5 b^{4} x^{\frac{5}{3}}} - \frac{a^{2}}{2 b^{3} x^{2}} + \frac{3 a}{7 b^{2} x^{\frac{7}{3}}} - \frac{3}{8 b x^{\frac{8}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(8/3), Eq(a, 0) & Eq(b, 0)), (-1/(3*a*x**3), Eq(b, 0)), (-3/(8*b*x**(8/3)), Eq(a, 0)), (a**8*log(x)/b**9 - 3*a**8*log(x**(1/3) + b/a)/b**9 + 3*a**7/(b**8*x**(1/3)) - 3*a**6/(2*b**7*x**(2/3)) + a**5/(b**6*x) - 3*a**4/(4*b**5*x**(4/3)) + 3*a**3/(5*b**4*x**(5/3)) - a**2/(2*b**3*x**2) + 3*a/(7*b**2*x**(7/3)) - 3/(8*b*x**(8/3)), True))","A",0
2428,1,201,0,31.455950," ","integrate(1/(a+b/x**(1/3))/x**5,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{11}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{4 a x^{4}} & \text{for}\: b = 0 \\- \frac{3}{11 b x^{\frac{11}{3}}} & \text{for}\: a = 0 \\- \frac{a^{11} \log{\left(x \right)}}{b^{12}} + \frac{3 a^{11} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{b^{12}} - \frac{3 a^{10}}{b^{11} \sqrt[3]{x}} + \frac{3 a^{9}}{2 b^{10} x^{\frac{2}{3}}} - \frac{a^{8}}{b^{9} x} + \frac{3 a^{7}}{4 b^{8} x^{\frac{4}{3}}} - \frac{3 a^{6}}{5 b^{7} x^{\frac{5}{3}}} + \frac{a^{5}}{2 b^{6} x^{2}} - \frac{3 a^{4}}{7 b^{5} x^{\frac{7}{3}}} + \frac{3 a^{3}}{8 b^{4} x^{\frac{8}{3}}} - \frac{a^{2}}{3 b^{3} x^{3}} + \frac{3 a}{10 b^{2} x^{\frac{10}{3}}} - \frac{3}{11 b x^{\frac{11}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(11/3), Eq(a, 0) & Eq(b, 0)), (-1/(4*a*x**4), Eq(b, 0)), (-3/(11*b*x**(11/3)), Eq(a, 0)), (-a**11*log(x)/b**12 + 3*a**11*log(x**(1/3) + b/a)/b**12 - 3*a**10/(b**11*x**(1/3)) + 3*a**9/(2*b**10*x**(2/3)) - a**8/(b**9*x) + 3*a**7/(4*b**8*x**(4/3)) - 3*a**6/(5*b**7*x**(5/3)) + a**5/(2*b**6*x**2) - 3*a**4/(7*b**5*x**(7/3)) + 3*a**3/(8*b**4*x**(8/3)) - a**2/(3*b**3*x**3) + 3*a/(10*b**2*x**(10/3)) - 3/(11*b*x**(11/3)), True))","A",0
2429,1,367,0,7.047342," ","integrate(x**2/(a+b/x**(1/3))**2,x)","\begin{cases} \frac{28 a^{10} x^{\frac{10}{3}}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} - \frac{35 a^{9} b x^{3}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} + \frac{45 a^{8} b^{2} x^{\frac{8}{3}}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} - \frac{60 a^{7} b^{3} x^{\frac{7}{3}}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} + \frac{84 a^{6} b^{4} x^{2}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} - \frac{126 a^{5} b^{5} x^{\frac{5}{3}}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} + \frac{210 a^{4} b^{6} x^{\frac{4}{3}}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} - \frac{420 a^{3} b^{7} x}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} + \frac{1260 a^{2} b^{8} x^{\frac{2}{3}}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} - \frac{2520 a b^{9} \sqrt[3]{x} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} - \frac{2520 b^{10} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} - \frac{2520 b^{10}}{84 a^{12} \sqrt[3]{x} + 84 a^{11} b} & \text{for}\: a \neq 0 \\\frac{3 x^{\frac{11}{3}}}{11 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((28*a**10*x**(10/3)/(84*a**12*x**(1/3) + 84*a**11*b) - 35*a**9*b*x**3/(84*a**12*x**(1/3) + 84*a**11*b) + 45*a**8*b**2*x**(8/3)/(84*a**12*x**(1/3) + 84*a**11*b) - 60*a**7*b**3*x**(7/3)/(84*a**12*x**(1/3) + 84*a**11*b) + 84*a**6*b**4*x**2/(84*a**12*x**(1/3) + 84*a**11*b) - 126*a**5*b**5*x**(5/3)/(84*a**12*x**(1/3) + 84*a**11*b) + 210*a**4*b**6*x**(4/3)/(84*a**12*x**(1/3) + 84*a**11*b) - 420*a**3*b**7*x/(84*a**12*x**(1/3) + 84*a**11*b) + 1260*a**2*b**8*x**(2/3)/(84*a**12*x**(1/3) + 84*a**11*b) - 2520*a*b**9*x**(1/3)*log(x**(1/3) + b/a)/(84*a**12*x**(1/3) + 84*a**11*b) - 2520*b**10*log(x**(1/3) + b/a)/(84*a**12*x**(1/3) + 84*a**11*b) - 2520*b**10/(84*a**12*x**(1/3) + 84*a**11*b), Ne(a, 0)), (3*x**(11/3)/(11*b**2), True))","A",0
2430,1,277,0,2.195667," ","integrate(x/(a+b/x**(1/3))**2,x)","\begin{cases} \frac{10 a^{7} x^{\frac{7}{3}}}{20 a^{9} \sqrt[3]{x} + 20 a^{8} b} - \frac{14 a^{6} b x^{2}}{20 a^{9} \sqrt[3]{x} + 20 a^{8} b} + \frac{21 a^{5} b^{2} x^{\frac{5}{3}}}{20 a^{9} \sqrt[3]{x} + 20 a^{8} b} - \frac{35 a^{4} b^{3} x^{\frac{4}{3}}}{20 a^{9} \sqrt[3]{x} + 20 a^{8} b} + \frac{70 a^{3} b^{4} x}{20 a^{9} \sqrt[3]{x} + 20 a^{8} b} - \frac{210 a^{2} b^{5} x^{\frac{2}{3}}}{20 a^{9} \sqrt[3]{x} + 20 a^{8} b} + \frac{420 a b^{6} \sqrt[3]{x} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{20 a^{9} \sqrt[3]{x} + 20 a^{8} b} + \frac{420 b^{7} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{20 a^{9} \sqrt[3]{x} + 20 a^{8} b} + \frac{420 b^{7}}{20 a^{9} \sqrt[3]{x} + 20 a^{8} b} & \text{for}\: a \neq 0 \\\frac{3 x^{\frac{8}{3}}}{8 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((10*a**7*x**(7/3)/(20*a**9*x**(1/3) + 20*a**8*b) - 14*a**6*b*x**2/(20*a**9*x**(1/3) + 20*a**8*b) + 21*a**5*b**2*x**(5/3)/(20*a**9*x**(1/3) + 20*a**8*b) - 35*a**4*b**3*x**(4/3)/(20*a**9*x**(1/3) + 20*a**8*b) + 70*a**3*b**4*x/(20*a**9*x**(1/3) + 20*a**8*b) - 210*a**2*b**5*x**(2/3)/(20*a**9*x**(1/3) + 20*a**8*b) + 420*a*b**6*x**(1/3)*log(x**(1/3) + b/a)/(20*a**9*x**(1/3) + 20*a**8*b) + 420*b**7*log(x**(1/3) + b/a)/(20*a**9*x**(1/3) + 20*a**8*b) + 420*b**7/(20*a**9*x**(1/3) + 20*a**8*b), Ne(a, 0)), (3*x**(8/3)/(8*b**2), True))","A",0
2431,1,165,0,0.669125," ","integrate(1/(a+b/x**(1/3))**2,x)","\begin{cases} \frac{a^{4} x^{\frac{4}{3}}}{a^{6} \sqrt[3]{x} + a^{5} b} - \frac{2 a^{3} b x}{a^{6} \sqrt[3]{x} + a^{5} b} + \frac{6 a^{2} b^{2} x^{\frac{2}{3}}}{a^{6} \sqrt[3]{x} + a^{5} b} - \frac{12 a b^{3} \sqrt[3]{x} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{a^{6} \sqrt[3]{x} + a^{5} b} - \frac{12 b^{4} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{a^{6} \sqrt[3]{x} + a^{5} b} - \frac{12 b^{4}}{a^{6} \sqrt[3]{x} + a^{5} b} & \text{for}\: a \neq 0 \\\frac{3 x^{\frac{5}{3}}}{5 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x**(4/3)/(a**6*x**(1/3) + a**5*b) - 2*a**3*b*x/(a**6*x**(1/3) + a**5*b) + 6*a**2*b**2*x**(2/3)/(a**6*x**(1/3) + a**5*b) - 12*a*b**3*x**(1/3)*log(x**(1/3) + b/a)/(a**6*x**(1/3) + a**5*b) - 12*b**4*log(x**(1/3) + b/a)/(a**6*x**(1/3) + a**5*b) - 12*b**4/(a**6*x**(1/3) + a**5*b), Ne(a, 0)), (3*x**(5/3)/(5*b**2), True))","A",0
2432,1,99,0,1.080893," ","integrate(1/(a+b/x**(1/3))**2/x,x)","\begin{cases} \frac{3 a x \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{a^{3} x + a^{2} b x^{\frac{2}{3}}} + \frac{3 b x^{\frac{2}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{a^{3} x + a^{2} b x^{\frac{2}{3}}} + \frac{3 b x^{\frac{2}{3}}}{a^{3} x + a^{2} b x^{\frac{2}{3}}} & \text{for}\: a \neq 0 \\\frac{3 x^{\frac{2}{3}}}{2 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*x*log(x**(1/3) + b/a)/(a**3*x + a**2*b*x**(2/3)) + 3*b*x**(2/3)*log(x**(1/3) + b/a)/(a**3*x + a**2*b*x**(2/3)) + 3*b*x**(2/3)/(a**3*x + a**2*b*x**(2/3)), Ne(a, 0)), (3*x**(2/3)/(2*b**2), True))","A",0
2433,1,211,0,2.792757," ","integrate(1/(a+b/x**(1/3))**2/x**2,x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt[3]{x}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{a^{2} x} & \text{for}\: b = 0 \\- \frac{3}{b^{2} \sqrt[3]{x}} & \text{for}\: a = 0 \\- \frac{2 a^{2} x^{2} \log{\left(x \right)}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} + \frac{6 a^{2} x^{2} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} - \frac{2 a b x^{\frac{5}{3}} \log{\left(x \right)}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} + \frac{6 a b x^{\frac{5}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} - \frac{6 a b x^{\frac{5}{3}}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} - \frac{3 b^{2} x^{\frac{4}{3}}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(1/3), Eq(a, 0) & Eq(b, 0)), (-1/(a**2*x), Eq(b, 0)), (-3/(b**2*x**(1/3)), Eq(a, 0)), (-2*a**2*x**2*log(x)/(a*b**3*x**2 + b**4*x**(5/3)) + 6*a**2*x**2*log(x**(1/3) + b/a)/(a*b**3*x**2 + b**4*x**(5/3)) - 2*a*b*x**(5/3)*log(x)/(a*b**3*x**2 + b**4*x**(5/3)) + 6*a*b*x**(5/3)*log(x**(1/3) + b/a)/(a*b**3*x**2 + b**4*x**(5/3)) - 6*a*b*x**(5/3)/(a*b**3*x**2 + b**4*x**(5/3)) - 3*b**2*x**(4/3)/(a*b**3*x**2 + b**4*x**(5/3)), True))","A",0
2434,1,340,0,7.657778," ","integrate(1/(a+b/x**(1/3))**2/x**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{4}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{2 a^{2} x^{2}} & \text{for}\: b = 0 \\- \frac{3}{4 b^{2} x^{\frac{4}{3}}} & \text{for}\: a = 0 \\\frac{20 a^{5} x^{3} \log{\left(x \right)}}{4 a b^{6} x^{3} + 4 b^{7} x^{\frac{8}{3}}} - \frac{60 a^{5} x^{3} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{4 a b^{6} x^{3} + 4 b^{7} x^{\frac{8}{3}}} + \frac{20 a^{4} b x^{\frac{8}{3}} \log{\left(x \right)}}{4 a b^{6} x^{3} + 4 b^{7} x^{\frac{8}{3}}} - \frac{60 a^{4} b x^{\frac{8}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{4 a b^{6} x^{3} + 4 b^{7} x^{\frac{8}{3}}} + \frac{60 a^{4} b x^{\frac{8}{3}}}{4 a b^{6} x^{3} + 4 b^{7} x^{\frac{8}{3}}} + \frac{30 a^{3} b^{2} x^{\frac{7}{3}}}{4 a b^{6} x^{3} + 4 b^{7} x^{\frac{8}{3}}} - \frac{10 a^{2} b^{3} x^{2}}{4 a b^{6} x^{3} + 4 b^{7} x^{\frac{8}{3}}} + \frac{5 a b^{4} x^{\frac{5}{3}}}{4 a b^{6} x^{3} + 4 b^{7} x^{\frac{8}{3}}} - \frac{3 b^{5} x^{\frac{4}{3}}}{4 a b^{6} x^{3} + 4 b^{7} x^{\frac{8}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(4/3), Eq(a, 0) & Eq(b, 0)), (-1/(2*a**2*x**2), Eq(b, 0)), (-3/(4*b**2*x**(4/3)), Eq(a, 0)), (20*a**5*x**3*log(x)/(4*a*b**6*x**3 + 4*b**7*x**(8/3)) - 60*a**5*x**3*log(x**(1/3) + b/a)/(4*a*b**6*x**3 + 4*b**7*x**(8/3)) + 20*a**4*b*x**(8/3)*log(x)/(4*a*b**6*x**3 + 4*b**7*x**(8/3)) - 60*a**4*b*x**(8/3)*log(x**(1/3) + b/a)/(4*a*b**6*x**3 + 4*b**7*x**(8/3)) + 60*a**4*b*x**(8/3)/(4*a*b**6*x**3 + 4*b**7*x**(8/3)) + 30*a**3*b**2*x**(7/3)/(4*a*b**6*x**3 + 4*b**7*x**(8/3)) - 10*a**2*b**3*x**2/(4*a*b**6*x**3 + 4*b**7*x**(8/3)) + 5*a*b**4*x**(5/3)/(4*a*b**6*x**3 + 4*b**7*x**(8/3)) - 3*b**5*x**(4/3)/(4*a*b**6*x**3 + 4*b**7*x**(8/3)), True))","A",0
2435,1,440,0,18.162271," ","integrate(1/(a+b/x**(1/3))**2/x**4,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{3}{7 b^{2} x^{\frac{7}{3}}} & \text{for}\: a = 0 \\- \frac{1}{3 a^{2} x^{3}} & \text{for}\: b = 0 \\- \frac{280 a^{8} x^{4} \log{\left(x \right)}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} + \frac{840 a^{8} x^{4} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} - \frac{280 a^{7} b x^{\frac{11}{3}} \log{\left(x \right)}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} + \frac{840 a^{7} b x^{\frac{11}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} - \frac{840 a^{7} b x^{\frac{11}{3}}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} - \frac{420 a^{6} b^{2} x^{\frac{10}{3}}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} + \frac{140 a^{5} b^{3} x^{3}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} - \frac{70 a^{4} b^{4} x^{\frac{8}{3}}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} + \frac{42 a^{3} b^{5} x^{\frac{7}{3}}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} - \frac{28 a^{2} b^{6} x^{2}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} + \frac{20 a b^{7} x^{\frac{5}{3}}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} - \frac{15 b^{8} x^{\frac{4}{3}}}{35 a b^{9} x^{4} + 35 b^{10} x^{\frac{11}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/3), Eq(a, 0) & Eq(b, 0)), (-3/(7*b**2*x**(7/3)), Eq(a, 0)), (-1/(3*a**2*x**3), Eq(b, 0)), (-280*a**8*x**4*log(x)/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) + 840*a**8*x**4*log(x**(1/3) + b/a)/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) - 280*a**7*b*x**(11/3)*log(x)/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) + 840*a**7*b*x**(11/3)*log(x**(1/3) + b/a)/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) - 840*a**7*b*x**(11/3)/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) - 420*a**6*b**2*x**(10/3)/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) + 140*a**5*b**3*x**3/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) - 70*a**4*b**4*x**(8/3)/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) + 42*a**3*b**5*x**(7/3)/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) - 28*a**2*b**6*x**2/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) + 20*a*b**7*x**(5/3)/(35*a*b**9*x**4 + 35*b**10*x**(11/3)) - 15*b**8*x**(4/3)/(35*a*b**9*x**4 + 35*b**10*x**(11/3)), True))","A",0
2436,1,541,0,39.254649," ","integrate(1/(a+b/x**(1/3))**2/x**5,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{10}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{3}{10 b^{2} x^{\frac{10}{3}}} & \text{for}\: a = 0 \\- \frac{1}{4 a^{2} x^{4}} & \text{for}\: b = 0 \\\frac{9240 a^{11} x^{5} \log{\left(x \right)}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} - \frac{27720 a^{11} x^{5} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} + \frac{9240 a^{10} b x^{\frac{14}{3}} \log{\left(x \right)}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} - \frac{27720 a^{10} b x^{\frac{14}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} + \frac{27720 a^{10} b x^{\frac{14}{3}}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} + \frac{13860 a^{9} b^{2} x^{\frac{13}{3}}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} - \frac{4620 a^{8} b^{3} x^{4}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} + \frac{2310 a^{7} b^{4} x^{\frac{11}{3}}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} - \frac{1386 a^{6} b^{5} x^{\frac{10}{3}}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} + \frac{924 a^{5} b^{6} x^{3}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} - \frac{660 a^{4} b^{7} x^{\frac{8}{3}}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} + \frac{495 a^{3} b^{8} x^{\frac{7}{3}}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} - \frac{385 a^{2} b^{9} x^{2}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} + \frac{308 a b^{10} x^{\frac{5}{3}}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} - \frac{252 b^{11} x^{\frac{4}{3}}}{840 a b^{12} x^{5} + 840 b^{13} x^{\frac{14}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(10/3), Eq(a, 0) & Eq(b, 0)), (-3/(10*b**2*x**(10/3)), Eq(a, 0)), (-1/(4*a**2*x**4), Eq(b, 0)), (9240*a**11*x**5*log(x)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) - 27720*a**11*x**5*log(x**(1/3) + b/a)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) + 9240*a**10*b*x**(14/3)*log(x)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) - 27720*a**10*b*x**(14/3)*log(x**(1/3) + b/a)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) + 27720*a**10*b*x**(14/3)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) + 13860*a**9*b**2*x**(13/3)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) - 4620*a**8*b**3*x**4/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) + 2310*a**7*b**4*x**(11/3)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) - 1386*a**6*b**5*x**(10/3)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) + 924*a**5*b**6*x**3/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) - 660*a**4*b**7*x**(8/3)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) + 495*a**3*b**8*x**(7/3)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) - 385*a**2*b**9*x**2/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) + 308*a*b**10*x**(5/3)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)) - 252*b**11*x**(4/3)/(840*a*b**12*x**5 + 840*b**13*x**(14/3)), True))","A",0
2437,1,624,0,6.311549," ","integrate(x**2/(a+b/x**(1/3))**3,x)","\begin{cases} \frac{56 a^{11} x^{\frac{11}{3}}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} - \frac{77 a^{10} b x^{\frac{10}{3}}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} + \frac{110 a^{9} b^{2} x^{3}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} - \frac{165 a^{8} b^{3} x^{\frac{8}{3}}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} + \frac{264 a^{7} b^{4} x^{\frac{7}{3}}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} - \frac{462 a^{6} b^{5} x^{2}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} + \frac{924 a^{5} b^{6} x^{\frac{5}{3}}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} - \frac{2310 a^{4} b^{7} x^{\frac{4}{3}}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} + \frac{9240 a^{3} b^{8} x}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} - \frac{27720 a^{2} b^{9} x^{\frac{2}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} - \frac{55440 a b^{10} \sqrt[3]{x} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} - \frac{55440 a b^{10} \sqrt[3]{x}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} - \frac{27720 b^{11} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} - \frac{41580 b^{11}}{168 a^{14} x^{\frac{2}{3}} + 336 a^{13} b \sqrt[3]{x} + 168 a^{12} b^{2}} & \text{for}\: a \neq 0 \\\frac{x^{4}}{4 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((56*a**11*x**(11/3)/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) - 77*a**10*b*x**(10/3)/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) + 110*a**9*b**2*x**3/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) - 165*a**8*b**3*x**(8/3)/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) + 264*a**7*b**4*x**(7/3)/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) - 462*a**6*b**5*x**2/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) + 924*a**5*b**6*x**(5/3)/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) - 2310*a**4*b**7*x**(4/3)/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) + 9240*a**3*b**8*x/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) - 27720*a**2*b**9*x**(2/3)*log(x**(1/3) + b/a)/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) - 55440*a*b**10*x**(1/3)*log(x**(1/3) + b/a)/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) - 55440*a*b**10*x**(1/3)/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) - 27720*b**11*log(x**(1/3) + b/a)/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2) - 41580*b**11/(168*a**14*x**(2/3) + 336*a**13*b*x**(1/3) + 168*a**12*b**2), Ne(a, 0)), (x**4/(4*b**3), True))","A",0
2438,1,493,0,2.233171," ","integrate(x/(a+b/x**(1/3))**3,x)","\begin{cases} \frac{5 a^{8} x^{\frac{8}{3}}}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} - \frac{8 a^{7} b x^{\frac{7}{3}}}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} + \frac{14 a^{6} b^{2} x^{2}}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} - \frac{28 a^{5} b^{3} x^{\frac{5}{3}}}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} + \frac{70 a^{4} b^{4} x^{\frac{4}{3}}}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} - \frac{280 a^{3} b^{5} x}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} + \frac{840 a^{2} b^{6} x^{\frac{2}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} + \frac{1680 a b^{7} \sqrt[3]{x} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} + \frac{1680 a b^{7} \sqrt[3]{x}}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} + \frac{840 b^{8} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} + \frac{1260 b^{8}}{10 a^{11} x^{\frac{2}{3}} + 20 a^{10} b \sqrt[3]{x} + 10 a^{9} b^{2}} & \text{for}\: a \neq 0 \\\frac{x^{3}}{3 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**8*x**(8/3)/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2) - 8*a**7*b*x**(7/3)/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2) + 14*a**6*b**2*x**2/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2) - 28*a**5*b**3*x**(5/3)/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2) + 70*a**4*b**4*x**(4/3)/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2) - 280*a**3*b**5*x/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2) + 840*a**2*b**6*x**(2/3)*log(x**(1/3) + b/a)/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2) + 1680*a*b**7*x**(1/3)*log(x**(1/3) + b/a)/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2) + 1680*a*b**7*x**(1/3)/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2) + 840*b**8*log(x**(1/3) + b/a)/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2) + 1260*b**8/(10*a**11*x**(2/3) + 20*a**10*b*x**(1/3) + 10*a**9*b**2), Ne(a, 0)), (x**3/(3*b**3), True))","A",0
2439,1,362,0,0.895391," ","integrate(1/(a+b/x**(1/3))**3,x)","\begin{cases} \frac{2 a^{5} x^{\frac{5}{3}}}{2 a^{8} x^{\frac{2}{3}} + 4 a^{7} b \sqrt[3]{x} + 2 a^{6} b^{2}} - \frac{5 a^{4} b x^{\frac{4}{3}}}{2 a^{8} x^{\frac{2}{3}} + 4 a^{7} b \sqrt[3]{x} + 2 a^{6} b^{2}} + \frac{20 a^{3} b^{2} x}{2 a^{8} x^{\frac{2}{3}} + 4 a^{7} b \sqrt[3]{x} + 2 a^{6} b^{2}} - \frac{60 a^{2} b^{3} x^{\frac{2}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{8} x^{\frac{2}{3}} + 4 a^{7} b \sqrt[3]{x} + 2 a^{6} b^{2}} - \frac{120 a b^{4} \sqrt[3]{x} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{8} x^{\frac{2}{3}} + 4 a^{7} b \sqrt[3]{x} + 2 a^{6} b^{2}} - \frac{120 a b^{4} \sqrt[3]{x}}{2 a^{8} x^{\frac{2}{3}} + 4 a^{7} b \sqrt[3]{x} + 2 a^{6} b^{2}} - \frac{60 b^{5} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{8} x^{\frac{2}{3}} + 4 a^{7} b \sqrt[3]{x} + 2 a^{6} b^{2}} - \frac{90 b^{5}}{2 a^{8} x^{\frac{2}{3}} + 4 a^{7} b \sqrt[3]{x} + 2 a^{6} b^{2}} & \text{for}\: a \neq 0 \\\frac{x^{2}}{2 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**5*x**(5/3)/(2*a**8*x**(2/3) + 4*a**7*b*x**(1/3) + 2*a**6*b**2) - 5*a**4*b*x**(4/3)/(2*a**8*x**(2/3) + 4*a**7*b*x**(1/3) + 2*a**6*b**2) + 20*a**3*b**2*x/(2*a**8*x**(2/3) + 4*a**7*b*x**(1/3) + 2*a**6*b**2) - 60*a**2*b**3*x**(2/3)*log(x**(1/3) + b/a)/(2*a**8*x**(2/3) + 4*a**7*b*x**(1/3) + 2*a**6*b**2) - 120*a*b**4*x**(1/3)*log(x**(1/3) + b/a)/(2*a**8*x**(2/3) + 4*a**7*b*x**(1/3) + 2*a**6*b**2) - 120*a*b**4*x**(1/3)/(2*a**8*x**(2/3) + 4*a**7*b*x**(1/3) + 2*a**6*b**2) - 60*b**5*log(x**(1/3) + b/a)/(2*a**8*x**(2/3) + 4*a**7*b*x**(1/3) + 2*a**6*b**2) - 90*b**5/(2*a**8*x**(2/3) + 4*a**7*b*x**(1/3) + 2*a**6*b**2), Ne(a, 0)), (x**2/(2*b**3), True))","A",0
2440,1,240,0,1.893476," ","integrate(1/(a+b/x**(1/3))**3/x,x)","\begin{cases} \frac{6 a^{2} x^{\frac{4}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{5} x^{\frac{4}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{2}{3}}} + \frac{12 a b x \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{5} x^{\frac{4}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{2}{3}}} + \frac{12 a b x}{2 a^{5} x^{\frac{4}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{2}{3}}} + \frac{6 b^{2} x^{\frac{2}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{5} x^{\frac{4}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{2}{3}}} + \frac{9 b^{2} x^{\frac{2}{3}}}{2 a^{5} x^{\frac{4}{3}} + 4 a^{4} b x + 2 a^{3} b^{2} x^{\frac{2}{3}}} & \text{for}\: a \neq 0 \\\frac{x}{b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*a**2*x**(4/3)*log(x**(1/3) + b/a)/(2*a**5*x**(4/3) + 4*a**4*b*x + 2*a**3*b**2*x**(2/3)) + 12*a*b*x*log(x**(1/3) + b/a)/(2*a**5*x**(4/3) + 4*a**4*b*x + 2*a**3*b**2*x**(2/3)) + 12*a*b*x/(2*a**5*x**(4/3) + 4*a**4*b*x + 2*a**3*b**2*x**(2/3)) + 6*b**2*x**(2/3)*log(x**(1/3) + b/a)/(2*a**5*x**(4/3) + 4*a**4*b*x + 2*a**3*b**2*x**(2/3)) + 9*b**2*x**(2/3)/(2*a**5*x**(4/3) + 4*a**4*b*x + 2*a**3*b**2*x**(2/3)), Ne(a, 0)), (x/b**3, True))","A",0
2441,1,406,0,4.625973," ","integrate(1/(a+b/x**(1/3))**3/x**2,x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\log{\left(x \right)}}{b^{3}} & \text{for}\: a = 0 \\- \frac{1}{a^{3} x} & \text{for}\: b = 0 \\\frac{2 a^{2} x^{\frac{7}{3}} \log{\left(x \right)}}{2 a^{2} b^{3} x^{\frac{7}{3}} + 4 a b^{4} x^{2} + 2 b^{5} x^{\frac{5}{3}}} - \frac{6 a^{2} x^{\frac{7}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{2} b^{3} x^{\frac{7}{3}} + 4 a b^{4} x^{2} + 2 b^{5} x^{\frac{5}{3}}} + \frac{4 a b x^{2} \log{\left(x \right)}}{2 a^{2} b^{3} x^{\frac{7}{3}} + 4 a b^{4} x^{2} + 2 b^{5} x^{\frac{5}{3}}} - \frac{12 a b x^{2} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{2} b^{3} x^{\frac{7}{3}} + 4 a b^{4} x^{2} + 2 b^{5} x^{\frac{5}{3}}} + \frac{6 a b x^{2}}{2 a^{2} b^{3} x^{\frac{7}{3}} + 4 a b^{4} x^{2} + 2 b^{5} x^{\frac{5}{3}}} + \frac{2 b^{2} x^{\frac{5}{3}} \log{\left(x \right)}}{2 a^{2} b^{3} x^{\frac{7}{3}} + 4 a b^{4} x^{2} + 2 b^{5} x^{\frac{5}{3}}} - \frac{6 b^{2} x^{\frac{5}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{2} b^{3} x^{\frac{7}{3}} + 4 a b^{4} x^{2} + 2 b^{5} x^{\frac{5}{3}}} + \frac{9 b^{2} x^{\frac{5}{3}}}{2 a^{2} b^{3} x^{\frac{7}{3}} + 4 a b^{4} x^{2} + 2 b^{5} x^{\frac{5}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0)), (log(x)/b**3, Eq(a, 0)), (-1/(a**3*x), Eq(b, 0)), (2*a**2*x**(7/3)*log(x)/(2*a**2*b**3*x**(7/3) + 4*a*b**4*x**2 + 2*b**5*x**(5/3)) - 6*a**2*x**(7/3)*log(x**(1/3) + b/a)/(2*a**2*b**3*x**(7/3) + 4*a*b**4*x**2 + 2*b**5*x**(5/3)) + 4*a*b*x**2*log(x)/(2*a**2*b**3*x**(7/3) + 4*a*b**4*x**2 + 2*b**5*x**(5/3)) - 12*a*b*x**2*log(x**(1/3) + b/a)/(2*a**2*b**3*x**(7/3) + 4*a*b**4*x**2 + 2*b**5*x**(5/3)) + 6*a*b*x**2/(2*a**2*b**3*x**(7/3) + 4*a*b**4*x**2 + 2*b**5*x**(5/3)) + 2*b**2*x**(5/3)*log(x)/(2*a**2*b**3*x**(7/3) + 4*a*b**4*x**2 + 2*b**5*x**(5/3)) - 6*b**2*x**(5/3)*log(x**(1/3) + b/a)/(2*a**2*b**3*x**(7/3) + 4*a*b**4*x**2 + 2*b**5*x**(5/3)) + 9*b**2*x**(5/3)/(2*a**2*b**3*x**(7/3) + 4*a*b**4*x**2 + 2*b**5*x**(5/3)), True))","A",0
2442,1,561,0,11.104750," ","integrate(1/(a+b/x**(1/3))**3/x**3,x)","\begin{cases} \frac{\tilde{\infty}}{x} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{b^{3} x} & \text{for}\: a = 0 \\- \frac{1}{2 a^{3} x^{2}} & \text{for}\: b = 0 \\- \frac{20 a^{5} x^{\frac{10}{3}} \log{\left(x \right)}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} + \frac{60 a^{5} x^{\frac{10}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} - \frac{40 a^{4} b x^{3} \log{\left(x \right)}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} + \frac{120 a^{4} b x^{3} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} - \frac{60 a^{4} b x^{3}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} - \frac{20 a^{3} b^{2} x^{\frac{8}{3}} \log{\left(x \right)}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} + \frac{60 a^{3} b^{2} x^{\frac{8}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} - \frac{90 a^{3} b^{2} x^{\frac{8}{3}}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} - \frac{20 a^{2} b^{3} x^{\frac{7}{3}}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} + \frac{5 a b^{4} x^{2}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} - \frac{2 b^{5} x^{\frac{5}{3}}}{2 a^{2} b^{6} x^{\frac{10}{3}} + 4 a b^{7} x^{3} + 2 b^{8} x^{\frac{8}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x, Eq(a, 0) & Eq(b, 0)), (-1/(b**3*x), Eq(a, 0)), (-1/(2*a**3*x**2), Eq(b, 0)), (-20*a**5*x**(10/3)*log(x)/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)) + 60*a**5*x**(10/3)*log(x**(1/3) + b/a)/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)) - 40*a**4*b*x**3*log(x)/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)) + 120*a**4*b*x**3*log(x**(1/3) + b/a)/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)) - 60*a**4*b*x**3/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)) - 20*a**3*b**2*x**(8/3)*log(x)/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)) + 60*a**3*b**2*x**(8/3)*log(x**(1/3) + b/a)/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)) - 90*a**3*b**2*x**(8/3)/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)) - 20*a**2*b**3*x**(7/3)/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)) + 5*a*b**4*x**2/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)) - 2*b**5*x**(5/3)/(2*a**2*b**6*x**(10/3) + 4*a*b**7*x**3 + 2*b**8*x**(8/3)), True))","A",0
2443,1,707,0,22.226056," ","integrate(1/(a+b/x**(1/3))**3/x**4,x)","\begin{cases} \frac{\tilde{\infty}}{x^{2}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{2 b^{3} x^{2}} & \text{for}\: a = 0 \\- \frac{1}{3 a^{3} x^{3}} & \text{for}\: b = 0 \\\frac{280 a^{8} x^{\frac{13}{3}} \log{\left(x \right)}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} - \frac{840 a^{8} x^{\frac{13}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} + \frac{560 a^{7} b x^{4} \log{\left(x \right)}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} - \frac{1680 a^{7} b x^{4} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} + \frac{840 a^{7} b x^{4}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} + \frac{280 a^{6} b^{2} x^{\frac{11}{3}} \log{\left(x \right)}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} - \frac{840 a^{6} b^{2} x^{\frac{11}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} + \frac{1260 a^{6} b^{2} x^{\frac{11}{3}}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} + \frac{280 a^{5} b^{3} x^{\frac{10}{3}}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} - \frac{70 a^{4} b^{4} x^{3}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} + \frac{28 a^{3} b^{5} x^{\frac{8}{3}}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} - \frac{14 a^{2} b^{6} x^{\frac{7}{3}}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} + \frac{8 a b^{7} x^{2}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} - \frac{5 b^{8} x^{\frac{5}{3}}}{10 a^{2} b^{9} x^{\frac{13}{3}} + 20 a b^{10} x^{4} + 10 b^{11} x^{\frac{11}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**2, Eq(a, 0) & Eq(b, 0)), (-1/(2*b**3*x**2), Eq(a, 0)), (-1/(3*a**3*x**3), Eq(b, 0)), (280*a**8*x**(13/3)*log(x)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) - 840*a**8*x**(13/3)*log(x**(1/3) + b/a)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) + 560*a**7*b*x**4*log(x)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) - 1680*a**7*b*x**4*log(x**(1/3) + b/a)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) + 840*a**7*b*x**4/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) + 280*a**6*b**2*x**(11/3)*log(x)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) - 840*a**6*b**2*x**(11/3)*log(x**(1/3) + b/a)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) + 1260*a**6*b**2*x**(11/3)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) + 280*a**5*b**3*x**(10/3)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) - 70*a**4*b**4*x**3/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) + 28*a**3*b**5*x**(8/3)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) - 14*a**2*b**6*x**(7/3)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) + 8*a*b**7*x**2/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)) - 5*b**8*x**(5/3)/(10*a**2*b**9*x**(13/3) + 20*a*b**10*x**4 + 10*b**11*x**(11/3)), True))","A",0
2444,1,848,0,40.814493," ","integrate(1/(a+b/x**(1/3))**3/x**5,x)","\begin{cases} \frac{\tilde{\infty}}{x^{3}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{3 b^{3} x^{3}} & \text{for}\: a = 0 \\- \frac{1}{4 a^{3} x^{4}} & \text{for}\: b = 0 \\- \frac{9240 a^{11} x^{\frac{16}{3}} \log{\left(x \right)}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} + \frac{27720 a^{11} x^{\frac{16}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} - \frac{18480 a^{10} b x^{5} \log{\left(x \right)}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} + \frac{55440 a^{10} b x^{5} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} - \frac{27720 a^{10} b x^{5}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} - \frac{9240 a^{9} b^{2} x^{\frac{14}{3}} \log{\left(x \right)}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} + \frac{27720 a^{9} b^{2} x^{\frac{14}{3}} \log{\left(\sqrt[3]{x} + \frac{b}{a} \right)}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} - \frac{41580 a^{9} b^{2} x^{\frac{14}{3}}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} - \frac{9240 a^{8} b^{3} x^{\frac{13}{3}}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} + \frac{2310 a^{7} b^{4} x^{4}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} - \frac{924 a^{6} b^{5} x^{\frac{11}{3}}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} + \frac{462 a^{5} b^{6} x^{\frac{10}{3}}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} - \frac{264 a^{4} b^{7} x^{3}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} + \frac{165 a^{3} b^{8} x^{\frac{8}{3}}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} - \frac{110 a^{2} b^{9} x^{\frac{7}{3}}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} + \frac{77 a b^{10} x^{2}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} - \frac{56 b^{11} x^{\frac{5}{3}}}{168 a^{2} b^{12} x^{\frac{16}{3}} + 336 a b^{13} x^{5} + 168 b^{14} x^{\frac{14}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**3, Eq(a, 0) & Eq(b, 0)), (-1/(3*b**3*x**3), Eq(a, 0)), (-1/(4*a**3*x**4), Eq(b, 0)), (-9240*a**11*x**(16/3)*log(x)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) + 27720*a**11*x**(16/3)*log(x**(1/3) + b/a)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) - 18480*a**10*b*x**5*log(x)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) + 55440*a**10*b*x**5*log(x**(1/3) + b/a)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) - 27720*a**10*b*x**5/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) - 9240*a**9*b**2*x**(14/3)*log(x)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) + 27720*a**9*b**2*x**(14/3)*log(x**(1/3) + b/a)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) - 41580*a**9*b**2*x**(14/3)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) - 9240*a**8*b**3*x**(13/3)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) + 2310*a**7*b**4*x**4/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) - 924*a**6*b**5*x**(11/3)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) + 462*a**5*b**6*x**(10/3)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) - 264*a**4*b**7*x**3/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) + 165*a**3*b**8*x**(8/3)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) - 110*a**2*b**9*x**(7/3)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) + 77*a*b**10*x**2/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)) - 56*b**11*x**(5/3)/(168*a**2*b**12*x**(16/3) + 336*a*b**13*x**5 + 168*b**14*x**(14/3)), True))","A",0
2445,1,34,0,0.148652," ","integrate(1/(1+b/x**(1/3)),x)","- 3 b^{3} \log{\left(b + \sqrt[3]{x} \right)} + 3 b^{2} \sqrt[3]{x} - \frac{3 b x^{\frac{2}{3}}}{2} + x"," ",0,"-3*b**3*log(b + x**(1/3)) + 3*b**2*x**(1/3) - 3*b*x**(2/3)/2 + x","A",0
2446,1,31,0,1.900820," ","integrate(x**(2/3)*(1+x**(5/3))**(2/3),x)","\frac{9 x^{\frac{5}{3}} \left(x^{\frac{5}{3}} + 1\right)^{\frac{2}{3}}}{25} + \frac{9 \left(x^{\frac{5}{3}} + 1\right)^{\frac{2}{3}}}{25}"," ",0,"9*x**(5/3)*(x**(5/3) + 1)**(2/3)/25 + 9*(x**(5/3) + 1)**(2/3)/25","B",0
2447,-1,0,0,0.000000," ","integrate(x**(7/3)*(a**(10/3)-x**(10/3))**(19/7),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2448,1,41,0,4.079299," ","integrate(1/(1+x**(1/5)),x)","\frac{5 x^{\frac{4}{5}}}{4} - \frac{5 x^{\frac{3}{5}}}{3} + \frac{5 x^{\frac{2}{5}}}{2} - 5 \sqrt[5]{x} + 5 \log{\left(\sqrt[5]{x} + 1 \right)}"," ",0,"5*x**(4/5)/4 - 5*x**(3/5)/3 + 5*x**(2/5)/2 - 5*x**(1/5) + 5*log(x**(1/5) + 1)","A",0
2449,1,12,0,0.639866," ","integrate(1/x**(1/5)/(1+x**(4/5))**(1/2),x)","\frac{5 \sqrt{x^{\frac{4}{5}} + 1}}{2}"," ",0,"5*sqrt(x**(4/5) + 1)/2","A",0
2450,1,78,0,8.203967," ","integrate((a+b/x**(3/5))**(2/3),x)","- \frac{5 b^{\frac{2}{3}} x^{\frac{3}{5}} \left(\frac{a x^{\frac{3}{5}}}{b} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{5}{3}\right)}{3 \Gamma\left(- \frac{2}{3}\right)} - \frac{5 b^{\frac{5}{3}} \left(\frac{a x^{\frac{3}{5}}}{b} + 1\right)^{\frac{2}{3}} \Gamma\left(- \frac{5}{3}\right)}{3 a \Gamma\left(- \frac{2}{3}\right)}"," ",0,"-5*b**(2/3)*x**(3/5)*(a*x**(3/5)/b + 1)**(2/3)*gamma(-5/3)/(3*gamma(-2/3)) - 5*b**(5/3)*(a*x**(3/5)/b + 1)**(2/3)*gamma(-5/3)/(3*a*gamma(-2/3))","B",0
2451,1,51,0,0.496125," ","integrate(x**3*(a+b*x**n),x)","\begin{cases} \frac{a n x^{4}}{4 n + 16} + \frac{4 a x^{4}}{4 n + 16} + \frac{4 b x^{4} x^{n}}{4 n + 16} & \text{for}\: n \neq -4 \\\frac{a x^{4}}{4} + b \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*n*x**4/(4*n + 16) + 4*a*x**4/(4*n + 16) + 4*b*x**4*x**n/(4*n + 16), Ne(n, -4)), (a*x**4/4 + b*log(x), True))","A",0
2452,1,51,0,0.373949," ","integrate(x**2*(a+b*x**n),x)","\begin{cases} \frac{a n x^{3}}{3 n + 9} + \frac{3 a x^{3}}{3 n + 9} + \frac{3 b x^{3} x^{n}}{3 n + 9} & \text{for}\: n \neq -3 \\\frac{a x^{3}}{3} + b \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*n*x**3/(3*n + 9) + 3*a*x**3/(3*n + 9) + 3*b*x**3*x**n/(3*n + 9), Ne(n, -3)), (a*x**3/3 + b*log(x), True))","A",0
2453,1,51,0,0.287948," ","integrate(x*(a+b*x**n),x)","\begin{cases} \frac{a n x^{2}}{2 n + 4} + \frac{2 a x^{2}}{2 n + 4} + \frac{2 b x^{2} x^{n}}{2 n + 4} & \text{for}\: n \neq -2 \\\frac{a x^{2}}{2} + b \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*n*x**2/(2*n + 4) + 2*a*x**2/(2*n + 4) + 2*b*x**2*x**n/(2*n + 4), Ne(n, -2)), (a*x**2/2 + b*log(x), True))","A",0
2454,1,17,0,0.062493," ","integrate(a+b*x**n,x)","a x + b \left(\begin{cases} \frac{x^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((x**(n + 1)/(n + 1), Ne(n, -1)), (log(x), True))","A",0
2455,1,17,0,0.196903," ","integrate((a+b*x**n)/x,x)","\begin{cases} a \log{\left(x \right)} + \frac{b x^{n}}{n} & \text{for}\: n \neq 0 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*log(x) + b*x**n/n, Ne(n, 0)), ((a + b)*log(x), True))","A",0
2456,1,32,0,0.428286," ","integrate((a+b*x**n)/x**2,x)","\begin{cases} - \frac{a n}{n x - x} + \frac{a}{n x - x} + \frac{b x^{n}}{n x - x} & \text{for}\: n \neq 1 \\- \frac{a}{x} + b \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*n/(n*x - x) + a/(n*x - x) + b*x**n/(n*x - x), Ne(n, 1)), (-a/x + b*log(x), True))","A",0
2457,1,60,0,0.569759," ","integrate((a+b*x**n)/x**3,x)","\begin{cases} - \frac{a n}{2 n x^{2} - 4 x^{2}} + \frac{2 a}{2 n x^{2} - 4 x^{2}} + \frac{2 b x^{n}}{2 n x^{2} - 4 x^{2}} & \text{for}\: n \neq 2 \\- \frac{a}{2 x^{2}} + b \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*n/(2*n*x**2 - 4*x**2) + 2*a/(2*n*x**2 - 4*x**2) + 2*b*x**n/(2*n*x**2 - 4*x**2), Ne(n, 2)), (-a/(2*x**2) + b*log(x), True))","A",0
2458,1,202,0,0.967640," ","integrate(x**3*(a+b*x**n)**2,x)","\begin{cases} \frac{a^{2} x^{4}}{4} + 2 a b \log{\left(x \right)} - \frac{b^{2}}{4 x^{4}} & \text{for}\: n = -4 \\\frac{a^{2} x^{4}}{4} + a b x^{2} + b^{2} \log{\left(x \right)} & \text{for}\: n = -2 \\\frac{a^{2} n^{2} x^{4}}{4 n^{2} + 24 n + 32} + \frac{6 a^{2} n x^{4}}{4 n^{2} + 24 n + 32} + \frac{8 a^{2} x^{4}}{4 n^{2} + 24 n + 32} + \frac{8 a b n x^{4} x^{n}}{4 n^{2} + 24 n + 32} + \frac{16 a b x^{4} x^{n}}{4 n^{2} + 24 n + 32} + \frac{2 b^{2} n x^{4} x^{2 n}}{4 n^{2} + 24 n + 32} + \frac{8 b^{2} x^{4} x^{2 n}}{4 n^{2} + 24 n + 32} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**4/4 + 2*a*b*log(x) - b**2/(4*x**4), Eq(n, -4)), (a**2*x**4/4 + a*b*x**2 + b**2*log(x), Eq(n, -2)), (a**2*n**2*x**4/(4*n**2 + 24*n + 32) + 6*a**2*n*x**4/(4*n**2 + 24*n + 32) + 8*a**2*x**4/(4*n**2 + 24*n + 32) + 8*a*b*n*x**4*x**n/(4*n**2 + 24*n + 32) + 16*a*b*x**4*x**n/(4*n**2 + 24*n + 32) + 2*b**2*n*x**4*x**(2*n)/(4*n**2 + 24*n + 32) + 8*b**2*x**4*x**(2*n)/(4*n**2 + 24*n + 32), True))","A",0
2459,1,211,0,1.922932," ","integrate(x**2*(a+b*x**n)**2,x)","\begin{cases} \frac{a^{2} x^{3}}{3} + 2 a b \log{\left(x \right)} - \frac{b^{2}}{3 x^{3}} & \text{for}\: n = -3 \\\frac{a^{2} x^{3}}{3} + \frac{4 a b x^{\frac{3}{2}}}{3} + b^{2} \log{\left(x \right)} & \text{for}\: n = - \frac{3}{2} \\\frac{2 a^{2} n^{2} x^{3}}{6 n^{2} + 27 n + 27} + \frac{9 a^{2} n x^{3}}{6 n^{2} + 27 n + 27} + \frac{9 a^{2} x^{3}}{6 n^{2} + 27 n + 27} + \frac{12 a b n x^{3} x^{n}}{6 n^{2} + 27 n + 27} + \frac{18 a b x^{3} x^{n}}{6 n^{2} + 27 n + 27} + \frac{3 b^{2} n x^{3} x^{2 n}}{6 n^{2} + 27 n + 27} + \frac{9 b^{2} x^{3} x^{2 n}}{6 n^{2} + 27 n + 27} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**3/3 + 2*a*b*log(x) - b**2/(3*x**3), Eq(n, -3)), (a**2*x**3/3 + 4*a*b*x**(3/2)/3 + b**2*log(x), Eq(n, -3/2)), (2*a**2*n**2*x**3/(6*n**2 + 27*n + 27) + 9*a**2*n*x**3/(6*n**2 + 27*n + 27) + 9*a**2*x**3/(6*n**2 + 27*n + 27) + 12*a*b*n*x**3*x**n/(6*n**2 + 27*n + 27) + 18*a*b*x**3*x**n/(6*n**2 + 27*n + 27) + 3*b**2*n*x**3*x**(2*n)/(6*n**2 + 27*n + 27) + 9*b**2*x**3*x**(2*n)/(6*n**2 + 27*n + 27), True))","A",0
2460,1,201,0,0.527255," ","integrate(x*(a+b*x**n)**2,x)","\begin{cases} \frac{a^{2} x^{2}}{2} + 2 a b \log{\left(x \right)} - \frac{b^{2}}{2 x^{2}} & \text{for}\: n = -2 \\\frac{a^{2} x^{2}}{2} + 2 a b x + b^{2} \log{\left(x \right)} & \text{for}\: n = -1 \\\frac{a^{2} n^{2} x^{2}}{2 n^{2} + 6 n + 4} + \frac{3 a^{2} n x^{2}}{2 n^{2} + 6 n + 4} + \frac{2 a^{2} x^{2}}{2 n^{2} + 6 n + 4} + \frac{4 a b n x^{2} x^{n}}{2 n^{2} + 6 n + 4} + \frac{4 a b x^{2} x^{n}}{2 n^{2} + 6 n + 4} + \frac{b^{2} n x^{2} x^{2 n}}{2 n^{2} + 6 n + 4} + \frac{2 b^{2} x^{2} x^{2 n}}{2 n^{2} + 6 n + 4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**2/2 + 2*a*b*log(x) - b**2/(2*x**2), Eq(n, -2)), (a**2*x**2/2 + 2*a*b*x + b**2*log(x), Eq(n, -1)), (a**2*n**2*x**2/(2*n**2 + 6*n + 4) + 3*a**2*n*x**2/(2*n**2 + 6*n + 4) + 2*a**2*x**2/(2*n**2 + 6*n + 4) + 4*a*b*n*x**2*x**n/(2*n**2 + 6*n + 4) + 4*a*b*x**2*x**n/(2*n**2 + 6*n + 4) + b**2*n*x**2*x**(2*n)/(2*n**2 + 6*n + 4) + 2*b**2*x**2*x**(2*n)/(2*n**2 + 6*n + 4), True))","A",0
2461,1,182,0,0.466315," ","integrate((a+b*x**n)**2,x)","\begin{cases} a^{2} x + 2 a b \log{\left(x \right)} - \frac{b^{2}}{x} & \text{for}\: n = -1 \\a^{2} x + 4 a b \sqrt{x} + b^{2} \log{\left(x \right)} & \text{for}\: n = - \frac{1}{2} \\\frac{2 a^{2} n^{2} x}{2 n^{2} + 3 n + 1} + \frac{3 a^{2} n x}{2 n^{2} + 3 n + 1} + \frac{a^{2} x}{2 n^{2} + 3 n + 1} + \frac{4 a b n x x^{n}}{2 n^{2} + 3 n + 1} + \frac{2 a b x x^{n}}{2 n^{2} + 3 n + 1} + \frac{b^{2} n x x^{2 n}}{2 n^{2} + 3 n + 1} + \frac{b^{2} x x^{2 n}}{2 n^{2} + 3 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*log(x) - b**2/x, Eq(n, -1)), (a**2*x + 4*a*b*sqrt(x) + b**2*log(x), Eq(n, -1/2)), (2*a**2*n**2*x/(2*n**2 + 3*n + 1) + 3*a**2*n*x/(2*n**2 + 3*n + 1) + a**2*x/(2*n**2 + 3*n + 1) + 4*a*b*n*x*x**n/(2*n**2 + 3*n + 1) + 2*a*b*x*x**n/(2*n**2 + 3*n + 1) + b**2*n*x*x**(2*n)/(2*n**2 + 3*n + 1) + b**2*x*x**(2*n)/(2*n**2 + 3*n + 1), True))","A",0
2462,1,36,0,0.278948," ","integrate((a+b*x**n)**2/x,x)","\begin{cases} a^{2} \log{\left(x \right)} + \frac{2 a b x^{n}}{n} + \frac{b^{2} x^{2 n}}{2 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*log(x) + 2*a*b*x**n/n + b**2*x**(2*n)/(2*n), Ne(n, 0)), ((a + b)**2*log(x), True))","A",0
2463,1,190,0,0.751654," ","integrate((a+b*x**n)**2/x**2,x)","\begin{cases} - \frac{a^{2}}{x} - \frac{4 a b}{\sqrt{x}} + b^{2} \log{\left(x \right)} & \text{for}\: n = \frac{1}{2} \\- \frac{a^{2}}{x} + 2 a b \log{\left(x \right)} + b^{2} x & \text{for}\: n = 1 \\- \frac{2 a^{2} n^{2}}{2 n^{2} x - 3 n x + x} + \frac{3 a^{2} n}{2 n^{2} x - 3 n x + x} - \frac{a^{2}}{2 n^{2} x - 3 n x + x} + \frac{4 a b n x^{n}}{2 n^{2} x - 3 n x + x} - \frac{2 a b x^{n}}{2 n^{2} x - 3 n x + x} + \frac{b^{2} n x^{2 n}}{2 n^{2} x - 3 n x + x} - \frac{b^{2} x^{2 n}}{2 n^{2} x - 3 n x + x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/x - 4*a*b/sqrt(x) + b**2*log(x), Eq(n, 1/2)), (-a**2/x + 2*a*b*log(x) + b**2*x, Eq(n, 1)), (-2*a**2*n**2/(2*n**2*x - 3*n*x + x) + 3*a**2*n/(2*n**2*x - 3*n*x + x) - a**2/(2*n**2*x - 3*n*x + x) + 4*a*b*n*x**n/(2*n**2*x - 3*n*x + x) - 2*a*b*x**n/(2*n**2*x - 3*n*x + x) + b**2*n*x**(2*n)/(2*n**2*x - 3*n*x + x) - b**2*x**(2*n)/(2*n**2*x - 3*n*x + x), True))","A",0
2464,1,245,0,0.723761," ","integrate((a+b*x**n)**2/x**3,x)","\begin{cases} - \frac{a^{2}}{2 x^{2}} - \frac{2 a b}{x} + b^{2} \log{\left(x \right)} & \text{for}\: n = 1 \\- \frac{a^{2}}{2 x^{2}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{2}}{2} & \text{for}\: n = 2 \\- \frac{a^{2} n^{2}}{2 n^{2} x^{2} - 6 n x^{2} + 4 x^{2}} + \frac{3 a^{2} n}{2 n^{2} x^{2} - 6 n x^{2} + 4 x^{2}} - \frac{2 a^{2}}{2 n^{2} x^{2} - 6 n x^{2} + 4 x^{2}} + \frac{4 a b n x^{n}}{2 n^{2} x^{2} - 6 n x^{2} + 4 x^{2}} - \frac{4 a b x^{n}}{2 n^{2} x^{2} - 6 n x^{2} + 4 x^{2}} + \frac{b^{2} n x^{2 n}}{2 n^{2} x^{2} - 6 n x^{2} + 4 x^{2}} - \frac{2 b^{2} x^{2 n}}{2 n^{2} x^{2} - 6 n x^{2} + 4 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(2*x**2) - 2*a*b/x + b**2*log(x), Eq(n, 1)), (-a**2/(2*x**2) + 2*a*b*log(x) + b**2*x**2/2, Eq(n, 2)), (-a**2*n**2/(2*n**2*x**2 - 6*n*x**2 + 4*x**2) + 3*a**2*n/(2*n**2*x**2 - 6*n*x**2 + 4*x**2) - 2*a**2/(2*n**2*x**2 - 6*n*x**2 + 4*x**2) + 4*a*b*n*x**n/(2*n**2*x**2 - 6*n*x**2 + 4*x**2) - 4*a*b*x**n/(2*n**2*x**2 - 6*n*x**2 + 4*x**2) + b**2*n*x**(2*n)/(2*n**2*x**2 - 6*n*x**2 + 4*x**2) - 2*b**2*x**(2*n)/(2*n**2*x**2 - 6*n*x**2 + 4*x**2), True))","A",0
2465,1,507,0,10.032369," ","integrate(x**3*(a+b*x**n)**3,x)","\begin{cases} \frac{a^{3} x^{4}}{4} + 3 a^{2} b \log{\left(x \right)} - \frac{3 a b^{2}}{4 x^{4}} - \frac{b^{3}}{8 x^{8}} & \text{for}\: n = -4 \\\frac{a^{3} x^{4}}{4} + \frac{3 a^{2} b x^{2}}{2} + 3 a b^{2} \log{\left(x \right)} - \frac{b^{3}}{2 x^{2}} & \text{for}\: n = -2 \\\frac{a^{3} x^{4}}{4} + \frac{9 a^{2} b x^{\frac{8}{3}}}{8} + \frac{9 a b^{2} x^{\frac{4}{3}}}{4} + b^{3} \log{\left(x \right)} & \text{for}\: n = - \frac{4}{3} \\\frac{3 a^{3} n^{3} x^{4}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{22 a^{3} n^{2} x^{4}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{48 a^{3} n x^{4}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{32 a^{3} x^{4}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{36 a^{2} b n^{2} x^{4} x^{n}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{120 a^{2} b n x^{4} x^{n}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{96 a^{2} b x^{4} x^{n}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{18 a b^{2} n^{2} x^{4} x^{2 n}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{96 a b^{2} n x^{4} x^{2 n}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{96 a b^{2} x^{4} x^{2 n}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{4 b^{3} n^{2} x^{4} x^{3 n}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{24 b^{3} n x^{4} x^{3 n}}{12 n^{3} + 88 n^{2} + 192 n + 128} + \frac{32 b^{3} x^{4} x^{3 n}}{12 n^{3} + 88 n^{2} + 192 n + 128} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x**4/4 + 3*a**2*b*log(x) - 3*a*b**2/(4*x**4) - b**3/(8*x**8), Eq(n, -4)), (a**3*x**4/4 + 3*a**2*b*x**2/2 + 3*a*b**2*log(x) - b**3/(2*x**2), Eq(n, -2)), (a**3*x**4/4 + 9*a**2*b*x**(8/3)/8 + 9*a*b**2*x**(4/3)/4 + b**3*log(x), Eq(n, -4/3)), (3*a**3*n**3*x**4/(12*n**3 + 88*n**2 + 192*n + 128) + 22*a**3*n**2*x**4/(12*n**3 + 88*n**2 + 192*n + 128) + 48*a**3*n*x**4/(12*n**3 + 88*n**2 + 192*n + 128) + 32*a**3*x**4/(12*n**3 + 88*n**2 + 192*n + 128) + 36*a**2*b*n**2*x**4*x**n/(12*n**3 + 88*n**2 + 192*n + 128) + 120*a**2*b*n*x**4*x**n/(12*n**3 + 88*n**2 + 192*n + 128) + 96*a**2*b*x**4*x**n/(12*n**3 + 88*n**2 + 192*n + 128) + 18*a*b**2*n**2*x**4*x**(2*n)/(12*n**3 + 88*n**2 + 192*n + 128) + 96*a*b**2*n*x**4*x**(2*n)/(12*n**3 + 88*n**2 + 192*n + 128) + 96*a*b**2*x**4*x**(2*n)/(12*n**3 + 88*n**2 + 192*n + 128) + 4*b**3*n**2*x**4*x**(3*n)/(12*n**3 + 88*n**2 + 192*n + 128) + 24*b**3*n*x**4*x**(3*n)/(12*n**3 + 88*n**2 + 192*n + 128) + 32*b**3*x**4*x**(3*n)/(12*n**3 + 88*n**2 + 192*n + 128), True))","A",0
2466,1,500,0,3.275574," ","integrate(x**2*(a+b*x**n)**3,x)","\begin{cases} \frac{a^{3} x^{3}}{3} + 3 a^{2} b \log{\left(x \right)} - \frac{a b^{2}}{x^{3}} - \frac{b^{3}}{6 x^{6}} & \text{for}\: n = -3 \\\frac{a^{3} x^{3}}{3} + 2 a^{2} b x^{\frac{3}{2}} + 3 a b^{2} \log{\left(x \right)} - \frac{2 b^{3}}{3 x^{\frac{3}{2}}} & \text{for}\: n = - \frac{3}{2} \\\frac{a^{3} x^{3}}{3} + \frac{3 a^{2} b x^{2}}{2} + 3 a b^{2} x + b^{3} \log{\left(x \right)} & \text{for}\: n = -1 \\\frac{2 a^{3} n^{3} x^{3}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{11 a^{3} n^{2} x^{3}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{18 a^{3} n x^{3}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{9 a^{3} x^{3}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{18 a^{2} b n^{2} x^{3} x^{n}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{45 a^{2} b n x^{3} x^{n}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{27 a^{2} b x^{3} x^{n}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{9 a b^{2} n^{2} x^{3} x^{2 n}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{36 a b^{2} n x^{3} x^{2 n}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{27 a b^{2} x^{3} x^{2 n}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{2 b^{3} n^{2} x^{3} x^{3 n}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{9 b^{3} n x^{3} x^{3 n}}{6 n^{3} + 33 n^{2} + 54 n + 27} + \frac{9 b^{3} x^{3} x^{3 n}}{6 n^{3} + 33 n^{2} + 54 n + 27} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x**3/3 + 3*a**2*b*log(x) - a*b**2/x**3 - b**3/(6*x**6), Eq(n, -3)), (a**3*x**3/3 + 2*a**2*b*x**(3/2) + 3*a*b**2*log(x) - 2*b**3/(3*x**(3/2)), Eq(n, -3/2)), (a**3*x**3/3 + 3*a**2*b*x**2/2 + 3*a*b**2*x + b**3*log(x), Eq(n, -1)), (2*a**3*n**3*x**3/(6*n**3 + 33*n**2 + 54*n + 27) + 11*a**3*n**2*x**3/(6*n**3 + 33*n**2 + 54*n + 27) + 18*a**3*n*x**3/(6*n**3 + 33*n**2 + 54*n + 27) + 9*a**3*x**3/(6*n**3 + 33*n**2 + 54*n + 27) + 18*a**2*b*n**2*x**3*x**n/(6*n**3 + 33*n**2 + 54*n + 27) + 45*a**2*b*n*x**3*x**n/(6*n**3 + 33*n**2 + 54*n + 27) + 27*a**2*b*x**3*x**n/(6*n**3 + 33*n**2 + 54*n + 27) + 9*a*b**2*n**2*x**3*x**(2*n)/(6*n**3 + 33*n**2 + 54*n + 27) + 36*a*b**2*n*x**3*x**(2*n)/(6*n**3 + 33*n**2 + 54*n + 27) + 27*a*b**2*x**3*x**(2*n)/(6*n**3 + 33*n**2 + 54*n + 27) + 2*b**3*n**2*x**3*x**(3*n)/(6*n**3 + 33*n**2 + 54*n + 27) + 9*b**3*n*x**3*x**(3*n)/(6*n**3 + 33*n**2 + 54*n + 27) + 9*b**3*x**3*x**(3*n)/(6*n**3 + 33*n**2 + 54*n + 27), True))","A",0
2467,1,500,0,1.777820," ","integrate(x*(a+b*x**n)**3,x)","\begin{cases} \frac{a^{3} x^{2}}{2} + 3 a^{2} b \log{\left(x \right)} - \frac{3 a b^{2}}{2 x^{2}} - \frac{b^{3}}{4 x^{4}} & \text{for}\: n = -2 \\\frac{a^{3} x^{2}}{2} + 3 a^{2} b x + 3 a b^{2} \log{\left(x \right)} - \frac{b^{3}}{x} & \text{for}\: n = -1 \\\frac{a^{3} x^{2}}{2} + \frac{9 a^{2} b x^{\frac{4}{3}}}{4} + \frac{9 a b^{2} x^{\frac{2}{3}}}{2} + b^{3} \log{\left(x \right)} & \text{for}\: n = - \frac{2}{3} \\\frac{3 a^{3} n^{3} x^{2}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{11 a^{3} n^{2} x^{2}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{12 a^{3} n x^{2}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{4 a^{3} x^{2}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{18 a^{2} b n^{2} x^{2} x^{n}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{30 a^{2} b n x^{2} x^{n}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{12 a^{2} b x^{2} x^{n}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{9 a b^{2} n^{2} x^{2} x^{2 n}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{24 a b^{2} n x^{2} x^{2 n}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{12 a b^{2} x^{2} x^{2 n}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{2 b^{3} n^{2} x^{2} x^{3 n}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{6 b^{3} n x^{2} x^{3 n}}{6 n^{3} + 22 n^{2} + 24 n + 8} + \frac{4 b^{3} x^{2} x^{3 n}}{6 n^{3} + 22 n^{2} + 24 n + 8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x**2/2 + 3*a**2*b*log(x) - 3*a*b**2/(2*x**2) - b**3/(4*x**4), Eq(n, -2)), (a**3*x**2/2 + 3*a**2*b*x + 3*a*b**2*log(x) - b**3/x, Eq(n, -1)), (a**3*x**2/2 + 9*a**2*b*x**(4/3)/4 + 9*a*b**2*x**(2/3)/2 + b**3*log(x), Eq(n, -2/3)), (3*a**3*n**3*x**2/(6*n**3 + 22*n**2 + 24*n + 8) + 11*a**3*n**2*x**2/(6*n**3 + 22*n**2 + 24*n + 8) + 12*a**3*n*x**2/(6*n**3 + 22*n**2 + 24*n + 8) + 4*a**3*x**2/(6*n**3 + 22*n**2 + 24*n + 8) + 18*a**2*b*n**2*x**2*x**n/(6*n**3 + 22*n**2 + 24*n + 8) + 30*a**2*b*n*x**2*x**n/(6*n**3 + 22*n**2 + 24*n + 8) + 12*a**2*b*x**2*x**n/(6*n**3 + 22*n**2 + 24*n + 8) + 9*a*b**2*n**2*x**2*x**(2*n)/(6*n**3 + 22*n**2 + 24*n + 8) + 24*a*b**2*n*x**2*x**(2*n)/(6*n**3 + 22*n**2 + 24*n + 8) + 12*a*b**2*x**2*x**(2*n)/(6*n**3 + 22*n**2 + 24*n + 8) + 2*b**3*n**2*x**2*x**(3*n)/(6*n**3 + 22*n**2 + 24*n + 8) + 6*b**3*n*x**2*x**(3*n)/(6*n**3 + 22*n**2 + 24*n + 8) + 4*b**3*x**2*x**(3*n)/(6*n**3 + 22*n**2 + 24*n + 8), True))","A",0
2468,1,469,0,0.820316," ","integrate((a+b*x**n)**3,x)","\begin{cases} a^{3} x + 3 a^{2} b \log{\left(x \right)} - \frac{3 a b^{2}}{x} - \frac{b^{3}}{2 x^{2}} & \text{for}\: n = -1 \\a^{3} x + 6 a^{2} b \sqrt{x} + 3 a b^{2} \log{\left(x \right)} - \frac{2 b^{3}}{\sqrt{x}} & \text{for}\: n = - \frac{1}{2} \\a^{3} x + \frac{9 a^{2} b x^{\frac{2}{3}}}{2} + 9 a b^{2} \sqrt[3]{x} + b^{3} \log{\left(x \right)} & \text{for}\: n = - \frac{1}{3} \\\frac{6 a^{3} n^{3} x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{11 a^{3} n^{2} x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{6 a^{3} n x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{a^{3} x}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{18 a^{2} b n^{2} x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{15 a^{2} b n x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{3 a^{2} b x x^{n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{9 a b^{2} n^{2} x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{12 a b^{2} n x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{3 a b^{2} x x^{2 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{2 b^{3} n^{2} x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{3 b^{3} n x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} + \frac{b^{3} x x^{3 n}}{6 n^{3} + 11 n^{2} + 6 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*log(x) - 3*a*b**2/x - b**3/(2*x**2), Eq(n, -1)), (a**3*x + 6*a**2*b*sqrt(x) + 3*a*b**2*log(x) - 2*b**3/sqrt(x), Eq(n, -1/2)), (a**3*x + 9*a**2*b*x**(2/3)/2 + 9*a*b**2*x**(1/3) + b**3*log(x), Eq(n, -1/3)), (6*a**3*n**3*x/(6*n**3 + 11*n**2 + 6*n + 1) + 11*a**3*n**2*x/(6*n**3 + 11*n**2 + 6*n + 1) + 6*a**3*n*x/(6*n**3 + 11*n**2 + 6*n + 1) + a**3*x/(6*n**3 + 11*n**2 + 6*n + 1) + 18*a**2*b*n**2*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 15*a**2*b*n*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 3*a**2*b*x*x**n/(6*n**3 + 11*n**2 + 6*n + 1) + 9*a*b**2*n**2*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 12*a*b**2*n*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 3*a*b**2*x*x**(2*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 2*b**3*n**2*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1) + 3*b**3*n*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1) + b**3*x*x**(3*n)/(6*n**3 + 11*n**2 + 6*n + 1), True))","A",0
2469,1,53,0,0.423470," ","integrate((a+b*x**n)**3/x,x)","\begin{cases} a^{3} \log{\left(x \right)} + \frac{3 a^{2} b x^{n}}{n} + \frac{3 a b^{2} x^{2 n}}{2 n} + \frac{b^{3} x^{3 n}}{3 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*log(x) + 3*a**2*b*x**n/n + 3*a*b**2*x**(2*n)/(2*n) + b**3*x**(3*n)/(3*n), Ne(n, 0)), ((a + b)**3*log(x), True))","A",0
2470,1,508,0,1.286557," ","integrate((a+b*x**n)**3/x**2,x)","\begin{cases} - \frac{a^{3}}{x} - \frac{9 a^{2} b}{2 x^{\frac{2}{3}}} - \frac{9 a b^{2}}{\sqrt[3]{x}} + b^{3} \log{\left(x \right)} & \text{for}\: n = \frac{1}{3} \\- \frac{a^{3}}{x} - \frac{6 a^{2} b}{\sqrt{x}} + 3 a b^{2} \log{\left(x \right)} + 2 b^{3} \sqrt{x} & \text{for}\: n = \frac{1}{2} \\- \frac{a^{3}}{x} + 3 a^{2} b \log{\left(x \right)} + 3 a b^{2} x + \frac{b^{3} x^{2}}{2} & \text{for}\: n = 1 \\- \frac{6 a^{3} n^{3}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} + \frac{11 a^{3} n^{2}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} - \frac{6 a^{3} n}{6 n^{3} x - 11 n^{2} x + 6 n x - x} + \frac{a^{3}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} + \frac{18 a^{2} b n^{2} x^{n}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} - \frac{15 a^{2} b n x^{n}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} + \frac{3 a^{2} b x^{n}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} + \frac{9 a b^{2} n^{2} x^{2 n}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} - \frac{12 a b^{2} n x^{2 n}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} + \frac{3 a b^{2} x^{2 n}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} + \frac{2 b^{3} n^{2} x^{3 n}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} - \frac{3 b^{3} n x^{3 n}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} + \frac{b^{3} x^{3 n}}{6 n^{3} x - 11 n^{2} x + 6 n x - x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3/x - 9*a**2*b/(2*x**(2/3)) - 9*a*b**2/x**(1/3) + b**3*log(x), Eq(n, 1/3)), (-a**3/x - 6*a**2*b/sqrt(x) + 3*a*b**2*log(x) + 2*b**3*sqrt(x), Eq(n, 1/2)), (-a**3/x + 3*a**2*b*log(x) + 3*a*b**2*x + b**3*x**2/2, Eq(n, 1)), (-6*a**3*n**3/(6*n**3*x - 11*n**2*x + 6*n*x - x) + 11*a**3*n**2/(6*n**3*x - 11*n**2*x + 6*n*x - x) - 6*a**3*n/(6*n**3*x - 11*n**2*x + 6*n*x - x) + a**3/(6*n**3*x - 11*n**2*x + 6*n*x - x) + 18*a**2*b*n**2*x**n/(6*n**3*x - 11*n**2*x + 6*n*x - x) - 15*a**2*b*n*x**n/(6*n**3*x - 11*n**2*x + 6*n*x - x) + 3*a**2*b*x**n/(6*n**3*x - 11*n**2*x + 6*n*x - x) + 9*a*b**2*n**2*x**(2*n)/(6*n**3*x - 11*n**2*x + 6*n*x - x) - 12*a*b**2*n*x**(2*n)/(6*n**3*x - 11*n**2*x + 6*n*x - x) + 3*a*b**2*x**(2*n)/(6*n**3*x - 11*n**2*x + 6*n*x - x) + 2*b**3*n**2*x**(3*n)/(6*n**3*x - 11*n**2*x + 6*n*x - x) - 3*b**3*n*x**(3*n)/(6*n**3*x - 11*n**2*x + 6*n*x - x) + b**3*x**(3*n)/(6*n**3*x - 11*n**2*x + 6*n*x - x), True))","A",0
2471,1,627,0,1.723095," ","integrate((a+b*x**n)**3/x**3,x)","\begin{cases} - \frac{a^{3}}{2 x^{2}} - \frac{9 a^{2} b}{4 x^{\frac{4}{3}}} - \frac{9 a b^{2}}{2 x^{\frac{2}{3}}} + b^{3} \log{\left(x \right)} & \text{for}\: n = \frac{2}{3} \\- \frac{a^{3}}{2 x^{2}} - \frac{3 a^{2} b}{x} + 3 a b^{2} \log{\left(x \right)} + b^{3} x & \text{for}\: n = 1 \\- \frac{a^{3}}{2 x^{2}} + 3 a^{2} b \log{\left(x \right)} + \frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} x^{4}}{4} & \text{for}\: n = 2 \\- \frac{3 a^{3} n^{3}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} + \frac{11 a^{3} n^{2}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} - \frac{12 a^{3} n}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} + \frac{4 a^{3}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} + \frac{18 a^{2} b n^{2} x^{n}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} - \frac{30 a^{2} b n x^{n}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} + \frac{12 a^{2} b x^{n}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} + \frac{9 a b^{2} n^{2} x^{2 n}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} - \frac{24 a b^{2} n x^{2 n}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} + \frac{12 a b^{2} x^{2 n}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} + \frac{2 b^{3} n^{2} x^{3 n}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} - \frac{6 b^{3} n x^{3 n}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} + \frac{4 b^{3} x^{3 n}}{6 n^{3} x^{2} - 22 n^{2} x^{2} + 24 n x^{2} - 8 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3/(2*x**2) - 9*a**2*b/(4*x**(4/3)) - 9*a*b**2/(2*x**(2/3)) + b**3*log(x), Eq(n, 2/3)), (-a**3/(2*x**2) - 3*a**2*b/x + 3*a*b**2*log(x) + b**3*x, Eq(n, 1)), (-a**3/(2*x**2) + 3*a**2*b*log(x) + 3*a*b**2*x**2/2 + b**3*x**4/4, Eq(n, 2)), (-3*a**3*n**3/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) + 11*a**3*n**2/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) - 12*a**3*n/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) + 4*a**3/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) + 18*a**2*b*n**2*x**n/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) - 30*a**2*b*n*x**n/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) + 12*a**2*b*x**n/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) + 9*a*b**2*n**2*x**(2*n)/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) - 24*a*b**2*n*x**(2*n)/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) + 12*a*b**2*x**(2*n)/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) + 2*b**3*n**2*x**(3*n)/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) - 6*b**3*n*x**(3*n)/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2) + 4*b**3*x**(3*n)/(6*n**3*x**2 - 22*n**2*x**2 + 24*n*x**2 - 8*x**2), True))","A",0
2472,1,36,0,0.834568," ","integrate(x/(a+b*x**n),x)","\frac{2 x^{2} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a n^{2} \Gamma\left(1 + \frac{2}{n}\right)}"," ",0,"2*x**2*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a*n**2*gamma(1 + 2/n))","C",0
2473,1,32,0,0.797337," ","integrate(1/(a+b*x**n),x)","\frac{x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a n^{2} \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*n**2*gamma(1 + 1/n))","C",0
2474,1,41,0,0.740439," ","integrate(1/x/(a+b*x**n),x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \\- \frac{x^{- n}}{b n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{n} \right)}}{a n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (log(x)/a, Eq(b, 0)), (-x**(-n)/(b*n), Eq(a, 0)), (log(x)/(a + b), Eq(n, 0)), (log(x)/a - log(a/b + x**n)/(a*n), True))","A",0
2475,1,39,0,0.916044," ","integrate(1/x**2/(a+b*x**n),x)","- \frac{\Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a n^{2} x \Gamma\left(1 - \frac{1}{n}\right)}"," ",0,"-lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a*n**2*x*gamma(1 - 1/n))","C",0
2476,1,44,0,1.003023," ","integrate(1/x**3/(a+b*x**n),x)","- \frac{2 \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a n^{2} x^{2} \Gamma\left(1 - \frac{2}{n}\right)}"," ",0,"-2*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a*n**2*x**2*gamma(1 - 2/n))","C",0
2477,1,274,0,1.221423," ","integrate(x/(a+b*x**n)**2,x)","\frac{2 n x^{2} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{2}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{2}{n}\right)\right)} + \frac{2 n x^{2} \Gamma\left(\frac{2}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{2}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{2}{n}\right)\right)} - \frac{4 x^{2} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{2}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{2}{n}\right)\right)} + \frac{2 b n x^{2} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(1 + \frac{2}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{2}{n}\right)\right)} - \frac{4 b x^{2} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(1 + \frac{2}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{2}{n}\right)\right)}"," ",0,"2*n*x**2*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a*(a*n**3*gamma(1 + 2/n) + b*n**3*x**n*gamma(1 + 2/n))) + 2*n*x**2*gamma(2/n)/(a*(a*n**3*gamma(1 + 2/n) + b*n**3*x**n*gamma(1 + 2/n))) - 4*x**2*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a*(a*n**3*gamma(1 + 2/n) + b*n**3*x**n*gamma(1 + 2/n))) + 2*b*n*x**2*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**2*(a*n**3*gamma(1 + 2/n) + b*n**3*x**n*gamma(1 + 2/n))) - 4*b*x**2*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**2*(a*n**3*gamma(1 + 2/n) + b*n**3*x**n*gamma(1 + 2/n)))","C",0
2478,1,257,0,1.164182," ","integrate(1/(a+b*x**n)**2,x)","\frac{n x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{n x \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{b n x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{b x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)}"," ",0,"n*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) + n*x*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) - x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) + b*n*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) - b*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n)))","C",0
2479,1,160,0,1.554064," ","integrate(1/x/(a+b*x**n)**2,x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\- \frac{x^{- 2 n}}{2 b^{2} n} & \text{for}\: a = 0 \\\tilde{\infty} \log{\left(x \right)} & \text{for}\: b = - a x^{- n} \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{2}} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \\\frac{a n \log{\left(x \right)}}{a^{3} n + a^{2} b n x^{n}} - \frac{a \log{\left(\frac{a}{b} + x^{n} \right)}}{a^{3} n + a^{2} b n x^{n}} + \frac{a}{a^{3} n + a^{2} b n x^{n}} + \frac{b n x^{n} \log{\left(x \right)}}{a^{3} n + a^{2} b n x^{n}} - \frac{b x^{n} \log{\left(\frac{a}{b} + x^{n} \right)}}{a^{3} n + a^{2} b n x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (-x**(-2*n)/(2*b**2*n), Eq(a, 0)), (zoo*log(x), Eq(b, -a*x**(-n))), (log(x)/(a + b)**2, Eq(n, 0)), (log(x)/a**2, Eq(b, 0)), (a*n*log(x)/(a**3*n + a**2*b*n*x**n) - a*log(a/b + x**n)/(a**3*n + a**2*b*n*x**n) + a/(a**3*n + a**2*b*n*x**n) + b*n*x**n*log(x)/(a**3*n + a**2*b*n*x**n) - b*x**n*log(a/b + x**n)/(a**3*n + a**2*b*n*x**n), True))","A",0
2480,1,289,0,1.499485," ","integrate(1/x**2/(a+b*x**n)**2,x)","- \frac{n \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a \left(a n^{3} x \Gamma\left(1 - \frac{1}{n}\right) + b n^{3} x x^{n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{n \Gamma\left(- \frac{1}{n}\right)}{a \left(a n^{3} x \Gamma\left(1 - \frac{1}{n}\right) + b n^{3} x x^{n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{\Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a \left(a n^{3} x \Gamma\left(1 - \frac{1}{n}\right) + b n^{3} x x^{n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{b n x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a^{2} \left(a n^{3} x \Gamma\left(1 - \frac{1}{n}\right) + b n^{3} x x^{n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{b x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a^{2} \left(a n^{3} x \Gamma\left(1 - \frac{1}{n}\right) + b n^{3} x x^{n} \Gamma\left(1 - \frac{1}{n}\right)\right)}"," ",0,"-n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a*(a*n**3*x*gamma(1 - 1/n) + b*n**3*x*x**n*gamma(1 - 1/n))) - n*gamma(-1/n)/(a*(a*n**3*x*gamma(1 - 1/n) + b*n**3*x*x**n*gamma(1 - 1/n))) - lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a*(a*n**3*x*gamma(1 - 1/n) + b*n**3*x*x**n*gamma(1 - 1/n))) - b*n*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a**2*(a*n**3*x*gamma(1 - 1/n) + b*n**3*x*x**n*gamma(1 - 1/n))) - b*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a**2*(a*n**3*x*gamma(1 - 1/n) + b*n**3*x*x**n*gamma(1 - 1/n)))","C",0
2481,1,321,0,1.727349," ","integrate(1/x**3/(a+b*x**n)**2,x)","- \frac{2 n \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a \left(a n^{3} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + b n^{3} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{2 n \Gamma\left(- \frac{2}{n}\right)}{a \left(a n^{3} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + b n^{3} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{4 \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a \left(a n^{3} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + b n^{3} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{2 b n x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{2} \left(a n^{3} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + b n^{3} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{4 b x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{2} \left(a n^{3} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + b n^{3} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right)\right)}"," ",0,"-2*n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a*(a*n**3*x**2*gamma(1 - 2/n) + b*n**3*x**2*x**n*gamma(1 - 2/n))) - 2*n*gamma(-2/n)/(a*(a*n**3*x**2*gamma(1 - 2/n) + b*n**3*x**2*x**n*gamma(1 - 2/n))) - 4*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a*(a*n**3*x**2*gamma(1 - 2/n) + b*n**3*x**2*x**n*gamma(1 - 2/n))) - 2*b*n*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**2*(a*n**3*x**2*gamma(1 - 2/n) + b*n**3*x**2*x**n*gamma(1 - 2/n))) - 4*b*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**2*(a*n**3*x**2*gamma(1 - 2/n) + b*n**3*x**2*x**n*gamma(1 - 2/n)))","C",0
2482,1,1930,0,1.773546," ","integrate(x/(a+b*x**n)**3,x)","\frac{2 a n^{2} x^{2} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)} + \frac{3 a n^{2} x^{2} \Gamma\left(\frac{2}{n}\right)}{a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)} - \frac{6 a n x^{2} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)} - \frac{2 a n x^{2} \Gamma\left(\frac{2}{n}\right)}{a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)} + \frac{4 a x^{2} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)} + \frac{6 b n^{2} x^{2} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)} + \frac{5 b n^{2} x^{2} x^{n} \Gamma\left(\frac{2}{n}\right)}{a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)} - \frac{18 b n x^{2} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)} - \frac{4 b n x^{2} x^{n} \Gamma\left(\frac{2}{n}\right)}{a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)} + \frac{12 b x^{2} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)} + \frac{6 b^{2} n^{2} x^{2} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a \left(a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)\right)} + \frac{2 b^{2} n^{2} x^{2} x^{2 n} \Gamma\left(\frac{2}{n}\right)}{a \left(a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)\right)} - \frac{18 b^{2} n x^{2} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a \left(a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)\right)} - \frac{2 b^{2} n x^{2} x^{2 n} \Gamma\left(\frac{2}{n}\right)}{a \left(a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)\right)} + \frac{12 b^{2} x^{2} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a \left(a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)\right)} + \frac{2 b^{3} n^{2} x^{2} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{2} \left(a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)\right)} - \frac{6 b^{3} n x^{2} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{2} \left(a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)\right)} + \frac{4 b^{3} x^{2} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2}{n}\right) \Gamma\left(\frac{2}{n}\right)}{a^{2} \left(a^{4} n^{4} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{2}{n}\right) + a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{2}{n}\right)\right)}"," ",0,"2*a*n**2*x**2*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)) + 3*a*n**2*x**2*gamma(2/n)/(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)) - 6*a*n*x**2*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)) - 2*a*n*x**2*gamma(2/n)/(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)) + 4*a*x**2*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)) + 6*b*n**2*x**2*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)) + 5*b*n**2*x**2*x**n*gamma(2/n)/(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)) - 18*b*n*x**2*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)) - 4*b*n*x**2*x**n*gamma(2/n)/(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)) + 12*b*x**2*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)) + 6*b**2*n**2*x**2*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a*(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n))) + 2*b**2*n**2*x**2*x**(2*n)*gamma(2/n)/(a*(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n))) - 18*b**2*n*x**2*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a*(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n))) - 2*b**2*n*x**2*x**(2*n)*gamma(2/n)/(a*(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n))) + 12*b**2*x**2*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a*(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n))) + 2*b**3*n**2*x**2*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**2*(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n))) - 6*b**3*n*x**2*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**2*(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n))) + 4*b**3*x**2*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2/n)*gamma(2/n)/(a**2*(a**4*n**4*gamma(1 + 2/n) + 3*a**3*b*n**4*x**n*gamma(1 + 2/n) + 3*a**2*b**2*n**4*x**(2*n)*gamma(1 + 2/n) + a*b**3*n**4*x**(3*n)*gamma(1 + 2/n)))","C",0
2483,1,1953,0,1.707600," ","integrate(1/(a+b*x**n)**3,x)","\frac{2 a n^{2} x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{3 a n^{2} x \Gamma\left(\frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} - \frac{3 a n x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} - \frac{a n x \Gamma\left(\frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{a x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{6 b n^{2} x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{5 b n^{2} x x^{n} \Gamma\left(\frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} - \frac{9 b n x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} - \frac{2 b n x x^{n} \Gamma\left(\frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{3 b x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)} + \frac{6 b^{2} n^{2} x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{2 b^{2} n^{2} x x^{2 n} \Gamma\left(\frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{9 b^{2} n x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{b^{2} n x x^{2 n} \Gamma\left(\frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{3 b^{2} x x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{2 b^{3} n^{2} x x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{3 b^{3} n x x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{b^{3} x x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(1 + \frac{1}{n}\right)\right)}"," ",0,"2*a*n**2*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)) + 3*a*n**2*x*gamma(1/n)/(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)) - 3*a*n*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)) - a*n*x*gamma(1/n)/(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)) + a*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)) + 6*b*n**2*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)) + 5*b*n**2*x*x**n*gamma(1/n)/(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)) - 9*b*n*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)) - 2*b*n*x*x**n*gamma(1/n)/(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)) + 3*b*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)) + 6*b**2*n**2*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n))) + 2*b**2*n**2*x*x**(2*n)*gamma(1/n)/(a*(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n))) - 9*b**2*n*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n))) - b**2*n*x*x**(2*n)*gamma(1/n)/(a*(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n))) + 3*b**2*x*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n))) + 2*b**3*n**2*x*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n))) - 3*b**3*n*x*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n))) + b**3*x*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(2*a**4*n**4*gamma(1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(1 + 1/n)))","C",0
2484,1,406,0,2.797685," ","integrate(1/x/(a+b*x**n)**3,x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\- \frac{x^{- 3 n}}{3 b^{3} n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{3}} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{a^{3}} & \text{for}\: b = 0 \\\frac{2 a^{2} n \log{\left(x \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} - \frac{2 a^{2} \log{\left(\frac{a}{b} + x^{n} \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} + \frac{3 a^{2}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} + \frac{4 a b n x^{n} \log{\left(x \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} - \frac{4 a b x^{n} \log{\left(\frac{a}{b} + x^{n} \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} + \frac{2 a b x^{n}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} + \frac{2 b^{2} n x^{2 n} \log{\left(x \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} - \frac{2 b^{2} x^{2 n} \log{\left(\frac{a}{b} + x^{n} \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (-x**(-3*n)/(3*b**3*n), Eq(a, 0)), (log(x)/(a + b)**3, Eq(n, 0)), (log(x)/a**3, Eq(b, 0)), (2*a**2*n*log(x)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) - 2*a**2*log(a/b + x**n)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) + 3*a**2/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) + 4*a*b*n*x**n*log(x)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) - 4*a*b*x**n*log(a/b + x**n)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) + 2*a*b*x**n/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) + 2*b**2*n*x**(2*n)*log(x)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) - 2*b**2*x**(2*n)*log(a/b + x**n)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)), True))","A",0
2485,1,2118,0,2.377844," ","integrate(1/x**2/(a+b*x**n)**3,x)","- \frac{2 a n^{2} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)} - \frac{3 a n^{2} \Gamma\left(- \frac{1}{n}\right)}{2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)} - \frac{3 a n \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)} - \frac{a n \Gamma\left(- \frac{1}{n}\right)}{2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)} - \frac{a \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)} - \frac{6 b n^{2} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)} - \frac{5 b n^{2} x^{n} \Gamma\left(- \frac{1}{n}\right)}{2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)} - \frac{9 b n x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)} - \frac{2 b n x^{n} \Gamma\left(- \frac{1}{n}\right)}{2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)} - \frac{3 b x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)} - \frac{6 b^{2} n^{2} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{2 b^{2} n^{2} x^{2 n} \Gamma\left(- \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{9 b^{2} n x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{b^{2} n x^{2 n} \Gamma\left(- \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{3 b^{2} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{2 b^{3} n^{2} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{3 b^{3} n x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)\right)} - \frac{b^{3} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} x \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{3} b n^{4} x x^{n} \Gamma\left(1 - \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x x^{2 n} \Gamma\left(1 - \frac{1}{n}\right) + 2 a b^{3} n^{4} x x^{3 n} \Gamma\left(1 - \frac{1}{n}\right)\right)}"," ",0,"-2*a*n**2*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)) - 3*a*n**2*gamma(-1/n)/(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)) - 3*a*n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)) - a*n*gamma(-1/n)/(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)) - a*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)) - 6*b*n**2*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)) - 5*b*n**2*x**n*gamma(-1/n)/(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)) - 9*b*n*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)) - 2*b*n*x**n*gamma(-1/n)/(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)) - 3*b*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)) - 6*b**2*n**2*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a*(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n))) - 2*b**2*n**2*x**(2*n)*gamma(-1/n)/(a*(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n))) - 9*b**2*n*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a*(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n))) - b**2*n*x**(2*n)*gamma(-1/n)/(a*(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n))) - 3*b**2*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a*(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n))) - 2*b**3*n**2*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a**2*(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n))) - 3*b**3*n*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a**2*(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n))) - b**3*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, exp_polar(I*pi)/n)*gamma(-1/n)/(a**2*(2*a**4*n**4*x*gamma(1 - 1/n) + 6*a**3*b*n**4*x*x**n*gamma(1 - 1/n) + 6*a**2*b**2*n**4*x*x**(2*n)*gamma(1 - 1/n) + 2*a*b**3*n**4*x*x**(3*n)*gamma(1 - 1/n)))","C",0
2486,1,2207,0,2.795767," ","integrate(1/x**3/(a+b*x**n)**3,x)","- \frac{2 a n^{2} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)} - \frac{3 a n^{2} \Gamma\left(- \frac{2}{n}\right)}{a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)} - \frac{6 a n \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)} - \frac{2 a n \Gamma\left(- \frac{2}{n}\right)}{a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)} - \frac{4 a \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)} - \frac{6 b n^{2} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)} - \frac{5 b n^{2} x^{n} \Gamma\left(- \frac{2}{n}\right)}{a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)} - \frac{18 b n x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)} - \frac{4 b n x^{n} \Gamma\left(- \frac{2}{n}\right)}{a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)} - \frac{12 b x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)} - \frac{6 b^{2} n^{2} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a \left(a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{2 b^{2} n^{2} x^{2 n} \Gamma\left(- \frac{2}{n}\right)}{a \left(a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{18 b^{2} n x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a \left(a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{2 b^{2} n x^{2 n} \Gamma\left(- \frac{2}{n}\right)}{a \left(a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{12 b^{2} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a \left(a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{2 b^{3} n^{2} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{2} \left(a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{6 b^{3} n x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{2} \left(a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)\right)} - \frac{4 b^{3} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{2 e^{i \pi}}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{a^{2} \left(a^{4} n^{4} x^{2} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{3} b n^{4} x^{2} x^{n} \Gamma\left(1 - \frac{2}{n}\right) + 3 a^{2} b^{2} n^{4} x^{2} x^{2 n} \Gamma\left(1 - \frac{2}{n}\right) + a b^{3} n^{4} x^{2} x^{3 n} \Gamma\left(1 - \frac{2}{n}\right)\right)}"," ",0,"-2*a*n**2*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)) - 3*a*n**2*gamma(-2/n)/(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)) - 6*a*n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)) - 2*a*n*gamma(-2/n)/(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)) - 4*a*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)) - 6*b*n**2*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)) - 5*b*n**2*x**n*gamma(-2/n)/(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)) - 18*b*n*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)) - 4*b*n*x**n*gamma(-2/n)/(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)) - 12*b*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)) - 6*b**2*n**2*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a*(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n))) - 2*b**2*n**2*x**(2*n)*gamma(-2/n)/(a*(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n))) - 18*b**2*n*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a*(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n))) - 2*b**2*n*x**(2*n)*gamma(-2/n)/(a*(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n))) - 12*b**2*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a*(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n))) - 2*b**3*n**2*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**2*(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n))) - 6*b**3*n*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**2*(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n))) - 4*b**3*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 2*exp_polar(I*pi)/n)*gamma(-2/n)/(a**2*(a**4*n**4*x**2*gamma(1 - 2/n) + 3*a**3*b*n**4*x**2*x**n*gamma(1 - 2/n) + 3*a**2*b**2*n**4*x**2*x**(2*n)*gamma(1 - 2/n) + a*b**3*n**4*x**2*x**(3*n)*gamma(1 - 2/n)))","C",0
2487,1,42,0,1.255761," ","integrate(x*(a+b*x**n)**(1/2),x)","\frac{\sqrt{a} x^{2} \Gamma\left(\frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{n} \\ 1 + \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{2}{n}\right)}"," ",0,"sqrt(a)*x**2*gamma(2/n)*hyper((-1/2, 2/n), (1 + 2/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 2/n))","C",0
2488,1,41,0,1.147462," ","integrate((a+b*x**n)**(1/2),x)","\frac{\sqrt{a} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"sqrt(a)*x*gamma(1/n)*hyper((-1/2, 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
2489,1,76,0,1.707034," ","integrate((a+b*x**n)**(1/2)/x,x)","- \frac{2 \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a} x^{- \frac{n}{2}}}{\sqrt{b}} \right)}}{n} + \frac{2 a x^{- \frac{n}{2}}}{\sqrt{b} n \sqrt{\frac{a x^{- n}}{b} + 1}} + \frac{2 \sqrt{b} x^{\frac{n}{2}}}{n \sqrt{\frac{a x^{- n}}{b} + 1}}"," ",0,"-2*sqrt(a)*asinh(sqrt(a)*x**(-n/2)/sqrt(b))/n + 2*a*x**(-n/2)/(sqrt(b)*n*sqrt(a*x**(-n)/b + 1)) + 2*sqrt(b)*x**(n/2)/(n*sqrt(a*x**(-n)/b + 1))","B",0
2490,1,44,0,1.246590," ","integrate((a+b*x**n)**(1/2)/x**2,x)","\frac{\sqrt{a} \Gamma\left(- \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{n} \\ 1 - \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n x \Gamma\left(1 - \frac{1}{n}\right)}"," ",0,"sqrt(a)*gamma(-1/n)*hyper((-1/2, -1/n), (1 - 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*x*gamma(1 - 1/n))","C",0
2491,1,46,0,1.430075," ","integrate((a+b*x**n)**(1/2)/x**3,x)","\frac{\sqrt{a} \Gamma\left(- \frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{2}{n} \\ 1 - \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n x^{2} \Gamma\left(1 - \frac{2}{n}\right)}"," ",0,"sqrt(a)*gamma(-2/n)*hyper((-1/2, -2/n), (1 - 2/n,), b*x**n*exp_polar(I*pi)/a)/(n*x**2*gamma(1 - 2/n))","C",0
2492,1,42,0,2.399120," ","integrate(x*(a+b*x**n)**(3/2),x)","\frac{a^{\frac{3}{2}} x^{2} \Gamma\left(\frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{2}{n} \\ 1 + \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{2}{n}\right)}"," ",0,"a**(3/2)*x**2*gamma(2/n)*hyper((-3/2, 2/n), (1 + 2/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 2/n))","C",0
2493,1,41,0,1.915064," ","integrate((a+b*x**n)**(3/2),x)","\frac{a^{\frac{3}{2}} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a**(3/2)*x*gamma(1/n)*hyper((-3/2, 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
2494,1,87,0,3.021023," ","integrate((a+b*x**n)**(3/2)/x,x)","\frac{8 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{n}}{a}}}{3 n} + \frac{a^{\frac{3}{2}} \log{\left(\frac{b x^{n}}{a} \right)}}{n} - \frac{2 a^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{b x^{n}}{a}} + 1 \right)}}{n} + \frac{2 \sqrt{a} b x^{n} \sqrt{1 + \frac{b x^{n}}{a}}}{3 n}"," ",0,"8*a**(3/2)*sqrt(1 + b*x**n/a)/(3*n) + a**(3/2)*log(b*x**n/a)/n - 2*a**(3/2)*log(sqrt(1 + b*x**n/a) + 1)/n + 2*sqrt(a)*b*x**n*sqrt(1 + b*x**n/a)/(3*n)","A",0
2495,1,44,0,1.959142," ","integrate((a+b*x**n)**(3/2)/x**2,x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{n} \\ 1 - \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n x \Gamma\left(1 - \frac{1}{n}\right)}"," ",0,"a**(3/2)*gamma(-1/n)*hyper((-3/2, -1/n), (1 - 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*x*gamma(1 - 1/n))","C",0
2496,1,46,0,1.988727," ","integrate((a+b*x**n)**(3/2)/x**3,x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{2}{n} \\ 1 - \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n x^{2} \Gamma\left(1 - \frac{2}{n}\right)}"," ",0,"a**(3/2)*gamma(-2/n)*hyper((-3/2, -2/n), (1 - 2/n,), b*x**n*exp_polar(I*pi)/a)/(n*x**2*gamma(1 - 2/n))","C",0
2497,1,42,0,6.902476," ","integrate(x*(a+b*x**n)**(5/2),x)","\frac{a^{\frac{5}{2}} x^{2} \Gamma\left(\frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{2}{n} \\ 1 + \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{2}{n}\right)}"," ",0,"a**(5/2)*x**2*gamma(2/n)*hyper((-5/2, 2/n), (1 + 2/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 2/n))","C",0
2498,1,41,0,5.244204," ","integrate((a+b*x**n)**(5/2),x)","\frac{a^{\frac{5}{2}} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a**(5/2)*x*gamma(1/n)*hyper((-5/2, 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
2499,1,117,0,7.983362," ","integrate((a+b*x**n)**(5/2)/x,x)","\frac{46 a^{\frac{5}{2}} \sqrt{1 + \frac{b x^{n}}{a}}}{15 n} + \frac{a^{\frac{5}{2}} \log{\left(\frac{b x^{n}}{a} \right)}}{n} - \frac{2 a^{\frac{5}{2}} \log{\left(\sqrt{1 + \frac{b x^{n}}{a}} + 1 \right)}}{n} + \frac{22 a^{\frac{3}{2}} b x^{n} \sqrt{1 + \frac{b x^{n}}{a}}}{15 n} + \frac{2 \sqrt{a} b^{2} x^{2 n} \sqrt{1 + \frac{b x^{n}}{a}}}{5 n}"," ",0,"46*a**(5/2)*sqrt(1 + b*x**n/a)/(15*n) + a**(5/2)*log(b*x**n/a)/n - 2*a**(5/2)*log(sqrt(1 + b*x**n/a) + 1)/n + 22*a**(3/2)*b*x**n*sqrt(1 + b*x**n/a)/(15*n) + 2*sqrt(a)*b**2*x**(2*n)*sqrt(1 + b*x**n/a)/(5*n)","A",0
2500,1,44,0,5.343890," ","integrate((a+b*x**n)**(5/2)/x**2,x)","\frac{a^{\frac{5}{2}} \Gamma\left(- \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{1}{n} \\ 1 - \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n x \Gamma\left(1 - \frac{1}{n}\right)}"," ",0,"a**(5/2)*gamma(-1/n)*hyper((-5/2, -1/n), (1 - 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*x*gamma(1 - 1/n))","C",0
2501,1,46,0,5.359919," ","integrate((a+b*x**n)**(5/2)/x**3,x)","\frac{a^{\frac{5}{2}} \Gamma\left(- \frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{2}{n} \\ 1 - \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n x^{2} \Gamma\left(1 - \frac{2}{n}\right)}"," ",0,"a**(5/2)*gamma(-2/n)*hyper((-5/2, -2/n), (1 - 2/n,), b*x**n*exp_polar(I*pi)/a)/(n*x**2*gamma(1 - 2/n))","C",0
2502,1,41,0,1.120872," ","integrate(x/(a+b*x**n)**(1/2),x)","\frac{x^{2} \Gamma\left(\frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{n} \\ 1 + \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(1 + \frac{2}{n}\right)}"," ",0,"x**2*gamma(2/n)*hyper((1/2, 2/n), (1 + 2/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(1 + 2/n))","C",0
2503,1,39,0,1.086918," ","integrate(1/(a+b*x**n)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"x*gamma(1/n)*hyper((1/2, 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(1 + 1/n))","C",0
2504,1,26,0,1.326513," ","integrate(1/x/(a+b*x**n)**(1/2),x)","- \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{a} x^{- \frac{n}{2}}}{\sqrt{b}} \right)}}{\sqrt{a} n}"," ",0,"-2*asinh(sqrt(a)*x**(-n/2)/sqrt(b))/(sqrt(a)*n)","A",0
2505,1,42,0,1.333685," ","integrate(1/x**2/(a+b*x**n)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - \frac{1}{n} \\ 1 - \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n x \Gamma\left(1 - \frac{1}{n}\right)}"," ",0,"gamma(-1/n)*hyper((1/2, -1/n), (1 - 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*x*gamma(1 - 1/n))","C",0
2506,1,44,0,1.582376," ","integrate(1/x**3/(a+b*x**n)**(1/2),x)","\frac{\Gamma\left(- \frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - \frac{2}{n} \\ 1 - \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n x^{2} \Gamma\left(1 - \frac{2}{n}\right)}"," ",0,"gamma(-2/n)*hyper((1/2, -2/n), (1 - 2/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*x**2*gamma(1 - 2/n))","C",0
2507,1,41,0,1.413783," ","integrate(x/(a+b*x**n)**(3/2),x)","\frac{x^{2} \Gamma\left(\frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{2}{n} \\ 1 + \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{a^{\frac{3}{2}} n \Gamma\left(1 + \frac{2}{n}\right)}"," ",0,"x**2*gamma(2/n)*hyper((3/2, 2/n), (1 + 2/n,), b*x**n*exp_polar(I*pi)/a)/(a**(3/2)*n*gamma(1 + 2/n))","C",0
2508,1,39,0,1.365713," ","integrate(1/(a+b*x**n)**(3/2),x)","\frac{x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{a^{\frac{3}{2}} n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"x*gamma(1/n)*hyper((3/2, 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(a**(3/2)*n*gamma(1 + 1/n))","C",0
2509,1,184,0,2.490807," ","integrate(1/x/(a+b*x**n)**(3/2),x)","\frac{2 a^{3} \sqrt{1 + \frac{b x^{n}}{a}}}{a^{\frac{9}{2}} n + a^{\frac{7}{2}} b n x^{n}} + \frac{a^{3} \log{\left(\frac{b x^{n}}{a} \right)}}{a^{\frac{9}{2}} n + a^{\frac{7}{2}} b n x^{n}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{n}}{a}} + 1 \right)}}{a^{\frac{9}{2}} n + a^{\frac{7}{2}} b n x^{n}} + \frac{a^{2} b x^{n} \log{\left(\frac{b x^{n}}{a} \right)}}{a^{\frac{9}{2}} n + a^{\frac{7}{2}} b n x^{n}} - \frac{2 a^{2} b x^{n} \log{\left(\sqrt{1 + \frac{b x^{n}}{a}} + 1 \right)}}{a^{\frac{9}{2}} n + a^{\frac{7}{2}} b n x^{n}}"," ",0,"2*a**3*sqrt(1 + b*x**n/a)/(a**(9/2)*n + a**(7/2)*b*n*x**n) + a**3*log(b*x**n/a)/(a**(9/2)*n + a**(7/2)*b*n*x**n) - 2*a**3*log(sqrt(1 + b*x**n/a) + 1)/(a**(9/2)*n + a**(7/2)*b*n*x**n) + a**2*b*x**n*log(b*x**n/a)/(a**(9/2)*n + a**(7/2)*b*n*x**n) - 2*a**2*b*x**n*log(sqrt(1 + b*x**n/a) + 1)/(a**(9/2)*n + a**(7/2)*b*n*x**n)","B",0
2510,1,42,0,1.913175," ","integrate(1/x**2/(a+b*x**n)**(3/2),x)","\frac{\Gamma\left(- \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - \frac{1}{n} \\ 1 - \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{a^{\frac{3}{2}} n x \Gamma\left(1 - \frac{1}{n}\right)}"," ",0,"gamma(-1/n)*hyper((3/2, -1/n), (1 - 1/n,), b*x**n*exp_polar(I*pi)/a)/(a**(3/2)*n*x*gamma(1 - 1/n))","C",0
2511,1,44,0,2.399458," ","integrate(1/x**3/(a+b*x**n)**(3/2),x)","\frac{\Gamma\left(- \frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - \frac{2}{n} \\ 1 - \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{a^{\frac{3}{2}} n x^{2} \Gamma\left(1 - \frac{2}{n}\right)}"," ",0,"gamma(-2/n)*hyper((3/2, -2/n), (1 - 2/n,), b*x**n*exp_polar(I*pi)/a)/(a**(3/2)*n*x**2*gamma(1 - 2/n))","C",0
2512,1,41,0,2.453475," ","integrate(x/(a+b*x**n)**(5/2),x)","\frac{x^{2} \Gamma\left(\frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, \frac{2}{n} \\ 1 + \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{a^{\frac{5}{2}} n \Gamma\left(1 + \frac{2}{n}\right)}"," ",0,"x**2*gamma(2/n)*hyper((5/2, 2/n), (1 + 2/n,), b*x**n*exp_polar(I*pi)/a)/(a**(5/2)*n*gamma(1 + 2/n))","C",0
2513,1,39,0,2.372913," ","integrate(1/(a+b*x**n)**(5/2),x)","\frac{x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{a^{\frac{5}{2}} n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"x*gamma(1/n)*hyper((5/2, 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(a**(5/2)*n*gamma(1 + 1/n))","C",0
2514,1,860,0,5.322465," ","integrate(1/x/(a+b*x**n)**(5/2),x)","\frac{8 a^{7} \sqrt{1 + \frac{b x^{n}}{a}}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}} + \frac{3 a^{7} \log{\left(\frac{b x^{n}}{a} \right)}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}} - \frac{6 a^{7} \log{\left(\sqrt{1 + \frac{b x^{n}}{a}} + 1 \right)}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}} + \frac{14 a^{6} b x^{n} \sqrt{1 + \frac{b x^{n}}{a}}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}} + \frac{9 a^{6} b x^{n} \log{\left(\frac{b x^{n}}{a} \right)}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}} - \frac{18 a^{6} b x^{n} \log{\left(\sqrt{1 + \frac{b x^{n}}{a}} + 1 \right)}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}} + \frac{6 a^{5} b^{2} x^{2 n} \sqrt{1 + \frac{b x^{n}}{a}}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}} + \frac{9 a^{5} b^{2} x^{2 n} \log{\left(\frac{b x^{n}}{a} \right)}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}} - \frac{18 a^{5} b^{2} x^{2 n} \log{\left(\sqrt{1 + \frac{b x^{n}}{a}} + 1 \right)}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}} + \frac{3 a^{4} b^{3} x^{3 n} \log{\left(\frac{b x^{n}}{a} \right)}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}} - \frac{6 a^{4} b^{3} x^{3 n} \log{\left(\sqrt{1 + \frac{b x^{n}}{a}} + 1 \right)}}{3 a^{\frac{19}{2}} n + 9 a^{\frac{17}{2}} b n x^{n} + 9 a^{\frac{15}{2}} b^{2} n x^{2 n} + 3 a^{\frac{13}{2}} b^{3} n x^{3 n}}"," ",0,"8*a**7*sqrt(1 + b*x**n/a)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n)) + 3*a**7*log(b*x**n/a)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n)) - 6*a**7*log(sqrt(1 + b*x**n/a) + 1)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n)) + 14*a**6*b*x**n*sqrt(1 + b*x**n/a)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n)) + 9*a**6*b*x**n*log(b*x**n/a)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n)) - 18*a**6*b*x**n*log(sqrt(1 + b*x**n/a) + 1)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n)) + 6*a**5*b**2*x**(2*n)*sqrt(1 + b*x**n/a)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n)) + 9*a**5*b**2*x**(2*n)*log(b*x**n/a)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n)) - 18*a**5*b**2*x**(2*n)*log(sqrt(1 + b*x**n/a) + 1)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n)) + 3*a**4*b**3*x**(3*n)*log(b*x**n/a)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n)) - 6*a**4*b**3*x**(3*n)*log(sqrt(1 + b*x**n/a) + 1)/(3*a**(19/2)*n + 9*a**(17/2)*b*n*x**n + 9*a**(15/2)*b**2*n*x**(2*n) + 3*a**(13/2)*b**3*n*x**(3*n))","B",0
2515,1,42,0,3.998754," ","integrate(1/x**2/(a+b*x**n)**(5/2),x)","\frac{\Gamma\left(- \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - \frac{1}{n} \\ 1 - \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{a^{\frac{5}{2}} n x \Gamma\left(1 - \frac{1}{n}\right)}"," ",0,"gamma(-1/n)*hyper((5/2, -1/n), (1 - 1/n,), b*x**n*exp_polar(I*pi)/a)/(a**(5/2)*n*x*gamma(1 - 1/n))","C",0
2516,1,44,0,5.225739," ","integrate(1/x**3/(a+b*x**n)**(5/2),x)","\frac{\Gamma\left(- \frac{2}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - \frac{2}{n} \\ 1 - \frac{2}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{a^{\frac{5}{2}} n x^{2} \Gamma\left(1 - \frac{2}{n}\right)}"," ",0,"gamma(-2/n)*hyper((5/2, -2/n), (1 - 2/n,), b*x**n*exp_polar(I*pi)/a)/(a**(5/2)*n*x**2*gamma(1 - 2/n))","C",0
2517,1,46,0,1.338971," ","integrate((a+b*x**n)**(1/3)/x,x)","- \frac{\sqrt[3]{b} x^{\frac{n}{3}} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{a x^{- n} e^{i \pi}}{b}} \right)}}{n \Gamma\left(\frac{2}{3}\right)}"," ",0,"-b**(1/3)*x**(n/3)*gamma(-1/3)*hyper((-1/3, -1/3), (2/3,), a*x**(-n)*exp_polar(I*pi)/b)/(n*gamma(2/3))","C",0
2518,1,26,0,4.850564," ","integrate(x**(-1+4*n)*(a+b*x**n),x)","\begin{cases} \frac{a x^{4 n}}{4 n} + \frac{b x^{5 n}}{5 n} & \text{for}\: n \neq 0 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**(4*n)/(4*n) + b*x**(5*n)/(5*n), Ne(n, 0)), ((a + b)*log(x), True))","A",0
2519,1,26,0,4.696307," ","integrate(x**(-1+3*n)*(a+b*x**n),x)","\begin{cases} \frac{a x^{3 n}}{3 n} + \frac{b x^{4 n}}{4 n} & \text{for}\: n \neq 0 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**(3*n)/(3*n) + b*x**(4*n)/(4*n), Ne(n, 0)), ((a + b)*log(x), True))","A",0
2520,1,26,0,4.744788," ","integrate(x**(-1+2*n)*(a+b*x**n),x)","\begin{cases} \frac{a x^{2 n}}{2 n} + \frac{b x^{3 n}}{3 n} & \text{for}\: n \neq 0 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**(2*n)/(2*n) + b*x**(3*n)/(3*n), Ne(n, 0)), ((a + b)*log(x), True))","A",0
2521,1,22,0,1.587792," ","integrate(x**(-1+n)*(a+b*x**n),x)","\begin{cases} \frac{a x^{n}}{n} + \frac{b x^{2 n}}{2 n} & \text{for}\: n \neq 0 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**n/n + b*x**(2*n)/(2*n), Ne(n, 0)), ((a + b)*log(x), True))","A",0
2522,1,17,0,0.203131," ","integrate((a+b*x**n)/x,x)","\begin{cases} a \log{\left(x \right)} + \frac{b x^{n}}{n} & \text{for}\: n \neq 0 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*log(x) + b*x**n/n, Ne(n, 0)), ((a + b)*log(x), True))","A",0
2523,1,107,0,12.856368," ","integrate(x**(-1-n)*(a+b*x**n),x)","\begin{cases} a x + b \log{\left(x \right)} & \text{for}\: n = -1 \\\left(a + b\right) \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{a n}{n^{2} x^{n} + n x^{n}} - \frac{a}{n^{2} x^{n} + n x^{n}} + \frac{b n^{2} x^{n} \log{\left(x \right)}}{n^{2} x^{n} + n x^{n}} + \frac{b n x^{n} \log{\left(x \right)}}{n^{2} x^{n} + n x^{n}} + \frac{b n x^{n}}{n^{2} x^{n} + n x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x + b*log(x), Eq(n, -1)), ((a + b)*log(x), Eq(n, 0)), (-a*n/(n**2*x**n + n*x**n) - a/(n**2*x**n + n*x**n) + b*n**2*x**n*log(x)/(n**2*x**n + n*x**n) + b*n*x**n*log(x)/(n**2*x**n + n*x**n) + b*n*x**n/(n**2*x**n + n*x**n), True))","A",0
2524,1,24,0,4.946457," ","integrate(x**(-1-2*n)*(a+b*x**n),x)","\begin{cases} - \frac{a x^{- 2 n}}{2 n} - \frac{b x^{- n}}{n} & \text{for}\: n \neq 0 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*x**(-2*n)/(2*n) - b*x**(-n)/n, Ne(n, 0)), ((a + b)*log(x), True))","A",0
2525,1,27,0,4.944042," ","integrate(x**(-1-3*n)*(a+b*x**n),x)","\begin{cases} - \frac{a x^{- 3 n}}{3 n} - \frac{b x^{- 2 n}}{2 n} & \text{for}\: n \neq 0 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*x**(-3*n)/(3*n) - b*x**(-2*n)/(2*n), Ne(n, 0)), ((a + b)*log(x), True))","A",0
2526,1,27,0,4.949092," ","integrate(x**(-1-4*n)*(a+b*x**n),x)","\begin{cases} - \frac{a x^{- 4 n}}{4 n} - \frac{b x^{- 3 n}}{3 n} & \text{for}\: n \neq 0 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*x**(-4*n)/(4*n) - b*x**(-3*n)/(3*n), Ne(n, 0)), ((a + b)*log(x), True))","A",0
2527,1,27,0,5.039501," ","integrate(x**(-1-5*n)*(a+b*x**n),x)","\begin{cases} - \frac{a x^{- 5 n}}{5 n} - \frac{b x^{- 4 n}}{4 n} & \text{for}\: n \neq 0 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*x**(-5*n)/(5*n) - b*x**(-4*n)/(4*n), Ne(n, 0)), ((a + b)*log(x), True))","A",0
2528,1,44,0,11.973401," ","integrate(x**(-1+4*n)*(a+b*x**n)**2,x)","\begin{cases} \frac{a^{2} x^{4 n}}{4 n} + \frac{2 a b x^{5 n}}{5 n} + \frac{b^{2} x^{6 n}}{6 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**(4*n)/(4*n) + 2*a*b*x**(5*n)/(5*n) + b**2*x**(6*n)/(6*n), Ne(n, 0)), ((a + b)**2*log(x), True))","A",0
2529,1,42,0,11.757723," ","integrate(x**(-1+3*n)*(a+b*x**n)**2,x)","\begin{cases} \frac{a^{2} x^{3 n}}{3 n} + \frac{a b x^{4 n}}{2 n} + \frac{b^{2} x^{5 n}}{5 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**(3*n)/(3*n) + a*b*x**(4*n)/(2*n) + b**2*x**(5*n)/(5*n), Ne(n, 0)), ((a + b)**2*log(x), True))","A",0
2530,1,44,0,11.697677," ","integrate(x**(-1+2*n)*(a+b*x**n)**2,x)","\begin{cases} \frac{a^{2} x^{2 n}}{2 n} + \frac{2 a b x^{3 n}}{3 n} + \frac{b^{2} x^{4 n}}{4 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**(2*n)/(2*n) + 2*a*b*x**(3*n)/(3*n) + b**2*x**(4*n)/(4*n), Ne(n, 0)), ((a + b)**2*log(x), True))","A",0
2531,1,37,0,3.145116," ","integrate(x**(-1+n)*(a+b*x**n)**2,x)","\begin{cases} \frac{a^{2} x^{n}}{n} + \frac{a b x^{2 n}}{n} + \frac{b^{2} x^{3 n}}{3 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**n/n + a*b*x**(2*n)/n + b**2*x**(3*n)/(3*n), Ne(n, 0)), ((a + b)**2*log(x), True))","A",0
2532,1,36,0,0.285324," ","integrate((a+b*x**n)**2/x,x)","\begin{cases} a^{2} \log{\left(x \right)} + \frac{2 a b x^{n}}{n} + \frac{b^{2} x^{2 n}}{2 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*log(x) + 2*a*b*x**n/n + b**2*x**(2*n)/(2*n), Ne(n, 0)), ((a + b)**2*log(x), True))","A",0
2533,1,175,0,28.502869," ","integrate(x**(-1-n)*(a+b*x**n)**2,x)","\begin{cases} a^{2} x + 2 a b \log{\left(x \right)} - \frac{b^{2}}{x} & \text{for}\: n = -1 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{a^{2} n}{n^{2} x^{n} + n x^{n}} - \frac{a^{2}}{n^{2} x^{n} + n x^{n}} + \frac{2 a b n^{2} x^{n} \log{\left(x \right)}}{n^{2} x^{n} + n x^{n}} + \frac{2 a b n x^{n} \log{\left(x \right)}}{n^{2} x^{n} + n x^{n}} + \frac{2 a b n x^{n}}{n^{2} x^{n} + n x^{n}} + \frac{b^{2} n x^{2 n}}{n^{2} x^{n} + n x^{n}} + \frac{b^{2} x^{2 n}}{n^{2} x^{n} + n x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*log(x) - b**2/x, Eq(n, -1)), ((a + b)**2*log(x), Eq(n, 0)), (-a**2*n/(n**2*x**n + n*x**n) - a**2/(n**2*x**n + n*x**n) + 2*a*b*n**2*x**n*log(x)/(n**2*x**n + n*x**n) + 2*a*b*n*x**n*log(x)/(n**2*x**n + n*x**n) + 2*a*b*n*x**n/(n**2*x**n + n*x**n) + b**2*n*x**(2*n)/(n**2*x**n + n*x**n) + b**2*x**(2*n)/(n**2*x**n + n*x**n), True))","A",0
2534,1,235,0,57.237214," ","integrate(x**(-1-2*n)*(a+b*x**n)**2,x)","\begin{cases} a^{2} x + 4 a b \sqrt{x} + b^{2} \log{\left(x \right)} & \text{for}\: n = - \frac{1}{2} \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{2 a^{2} n}{4 n^{2} x^{2 n} + 2 n x^{2 n}} - \frac{a^{2}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} - \frac{8 a b n x^{n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} - \frac{4 a b x^{n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{4 b^{2} n^{2} x^{2 n} \log{\left(x \right)}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{2 b^{2} n x^{2 n} \log{\left(x \right)}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{2 b^{2} n x^{2 n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 4*a*b*sqrt(x) + b**2*log(x), Eq(n, -1/2)), ((a + b)**2*log(x), Eq(n, 0)), (-2*a**2*n/(4*n**2*x**(2*n) + 2*n*x**(2*n)) - a**2/(4*n**2*x**(2*n) + 2*n*x**(2*n)) - 8*a*b*n*x**n/(4*n**2*x**(2*n) + 2*n*x**(2*n)) - 4*a*b*x**n/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 4*b**2*n**2*x**(2*n)*log(x)/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 2*b**2*n*x**(2*n)*log(x)/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 2*b**2*n*x**(2*n)/(4*n**2*x**(2*n) + 2*n*x**(2*n)), True))","A",0
2535,1,39,0,11.445652," ","integrate(x**(-1-3*n)*(a+b*x**n)**2,x)","\begin{cases} - \frac{a^{2} x^{- 3 n}}{3 n} - \frac{a b x^{- 2 n}}{n} - \frac{b^{2} x^{- n}}{n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**(-3*n)/(3*n) - a*b*x**(-2*n)/n - b**2*x**(-n)/n, Ne(n, 0)), ((a + b)**2*log(x), True))","A",0
2536,1,46,0,11.468507," ","integrate(x**(-1-4*n)*(a+b*x**n)**2,x)","\begin{cases} - \frac{a^{2} x^{- 4 n}}{4 n} - \frac{2 a b x^{- 3 n}}{3 n} - \frac{b^{2} x^{- 2 n}}{2 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**(-4*n)/(4*n) - 2*a*b*x**(-3*n)/(3*n) - b**2*x**(-2*n)/(2*n), Ne(n, 0)), ((a + b)**2*log(x), True))","A",0
2537,1,44,0,11.329295," ","integrate(x**(-1-5*n)*(a+b*x**n)**2,x)","\begin{cases} - \frac{a^{2} x^{- 5 n}}{5 n} - \frac{a b x^{- 4 n}}{2 n} - \frac{b^{2} x^{- 3 n}}{3 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**(-5*n)/(5*n) - a*b*x**(-4*n)/(2*n) - b**2*x**(-3*n)/(3*n), Ne(n, 0)), ((a + b)**2*log(x), True))","A",0
2538,1,46,0,11.683913," ","integrate(x**(-1-6*n)*(a+b*x**n)**2,x)","\begin{cases} - \frac{a^{2} x^{- 6 n}}{6 n} - \frac{2 a b x^{- 5 n}}{5 n} - \frac{b^{2} x^{- 4 n}}{4 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**(-6*n)/(6*n) - 2*a*b*x**(-5*n)/(5*n) - b**2*x**(-4*n)/(4*n), Ne(n, 0)), ((a + b)**2*log(x), True))","A",0
2539,1,60,0,26.845794," ","integrate(x**(-1+4*n)*(a+b*x**n)**3,x)","\begin{cases} \frac{a^{3} x^{4 n}}{4 n} + \frac{3 a^{2} b x^{5 n}}{5 n} + \frac{a b^{2} x^{6 n}}{2 n} + \frac{b^{3} x^{7 n}}{7 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x**(4*n)/(4*n) + 3*a**2*b*x**(5*n)/(5*n) + a*b**2*x**(6*n)/(2*n) + b**3*x**(7*n)/(7*n), Ne(n, 0)), ((a + b)**3*log(x), True))","A",0
2540,1,61,0,26.439339," ","integrate(x**(-1+3*n)*(a+b*x**n)**3,x)","\begin{cases} \frac{a^{3} x^{3 n}}{3 n} + \frac{3 a^{2} b x^{4 n}}{4 n} + \frac{3 a b^{2} x^{5 n}}{5 n} + \frac{b^{3} x^{6 n}}{6 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x**(3*n)/(3*n) + 3*a**2*b*x**(4*n)/(4*n) + 3*a*b**2*x**(5*n)/(5*n) + b**3*x**(6*n)/(6*n), Ne(n, 0)), ((a + b)**3*log(x), True))","A",0
2541,1,58,0,26.600482," ","integrate(x**(-1+2*n)*(a+b*x**n)**3,x)","\begin{cases} \frac{a^{3} x^{2 n}}{2 n} + \frac{a^{2} b x^{3 n}}{n} + \frac{3 a b^{2} x^{4 n}}{4 n} + \frac{b^{3} x^{5 n}}{5 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x**(2*n)/(2*n) + a**2*b*x**(3*n)/n + 3*a*b**2*x**(4*n)/(4*n) + b**3*x**(5*n)/(5*n), Ne(n, 0)), ((a + b)**3*log(x), True))","A",0
2542,1,54,0,5.480584," ","integrate(x**(-1+n)*(a+b*x**n)**3,x)","\begin{cases} \frac{a^{3} x^{n}}{n} + \frac{3 a^{2} b x^{2 n}}{2 n} + \frac{a b^{2} x^{3 n}}{n} + \frac{b^{3} x^{4 n}}{4 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x**n/n + 3*a**2*b*x**(2*n)/(2*n) + a*b**2*x**(3*n)/n + b**3*x**(4*n)/(4*n), Ne(n, 0)), ((a + b)**3*log(x), True))","A",0
2543,1,53,0,0.445126," ","integrate((a+b*x**n)**3/x,x)","\begin{cases} a^{3} \log{\left(x \right)} + \frac{3 a^{2} b x^{n}}{n} + \frac{3 a b^{2} x^{2 n}}{2 n} + \frac{b^{3} x^{3 n}}{3 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*log(x) + 3*a**2*b*x**n/n + 3*a*b**2*x**(2*n)/(2*n) + b**3*x**(3*n)/(3*n), Ne(n, 0)), ((a + b)**3*log(x), True))","A",0
2544,1,277,0,61.805285," ","integrate(x**(-1-n)*(a+b*x**n)**3,x)","\begin{cases} a^{3} x + 3 a^{2} b \log{\left(x \right)} - \frac{3 a b^{2}}{x} - \frac{b^{3}}{2 x^{2}} & \text{for}\: n = -1 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{2 a^{3} n}{2 n^{2} x^{n} + 2 n x^{n}} - \frac{2 a^{3}}{2 n^{2} x^{n} + 2 n x^{n}} + \frac{6 a^{2} b n^{2} x^{n} \log{\left(x \right)}}{2 n^{2} x^{n} + 2 n x^{n}} + \frac{6 a^{2} b n x^{n} \log{\left(x \right)}}{2 n^{2} x^{n} + 2 n x^{n}} + \frac{6 a^{2} b n x^{n}}{2 n^{2} x^{n} + 2 n x^{n}} + \frac{6 a b^{2} n x^{2 n}}{2 n^{2} x^{n} + 2 n x^{n}} + \frac{6 a b^{2} x^{2 n}}{2 n^{2} x^{n} + 2 n x^{n}} + \frac{b^{3} n x^{3 n}}{2 n^{2} x^{n} + 2 n x^{n}} + \frac{b^{3} x^{3 n}}{2 n^{2} x^{n} + 2 n x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*log(x) - 3*a*b**2/x - b**3/(2*x**2), Eq(n, -1)), ((a + b)**3*log(x), Eq(n, 0)), (-2*a**3*n/(2*n**2*x**n + 2*n*x**n) - 2*a**3/(2*n**2*x**n + 2*n*x**n) + 6*a**2*b*n**2*x**n*log(x)/(2*n**2*x**n + 2*n*x**n) + 6*a**2*b*n*x**n*log(x)/(2*n**2*x**n + 2*n*x**n) + 6*a**2*b*n*x**n/(2*n**2*x**n + 2*n*x**n) + 6*a*b**2*n*x**(2*n)/(2*n**2*x**n + 2*n*x**n) + 6*a*b**2*x**(2*n)/(2*n**2*x**n + 2*n*x**n) + b**3*n*x**(3*n)/(2*n**2*x**n + 2*n*x**n) + b**3*x**(3*n)/(2*n**2*x**n + 2*n*x**n), True))","A",0
2545,1,318,0,117.454139," ","integrate(x**(-1-2*n)*(a+b*x**n)**3,x)","\begin{cases} a^{3} x + 6 a^{2} b \sqrt{x} + 3 a b^{2} \log{\left(x \right)} - \frac{2 b^{3}}{\sqrt{x}} & \text{for}\: n = - \frac{1}{2} \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{2 a^{3} n}{4 n^{2} x^{2 n} + 2 n x^{2 n}} - \frac{a^{3}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} - \frac{12 a^{2} b n x^{n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} - \frac{6 a^{2} b x^{n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{12 a b^{2} n^{2} x^{2 n} \log{\left(x \right)}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{6 a b^{2} n x^{2 n} \log{\left(x \right)}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{6 a b^{2} n x^{2 n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{4 b^{3} n x^{3 n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{2 b^{3} x^{3 n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 6*a**2*b*sqrt(x) + 3*a*b**2*log(x) - 2*b**3/sqrt(x), Eq(n, -1/2)), ((a + b)**3*log(x), Eq(n, 0)), (-2*a**3*n/(4*n**2*x**(2*n) + 2*n*x**(2*n)) - a**3/(4*n**2*x**(2*n) + 2*n*x**(2*n)) - 12*a**2*b*n*x**n/(4*n**2*x**(2*n) + 2*n*x**(2*n)) - 6*a**2*b*x**n/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 12*a*b**2*n**2*x**(2*n)*log(x)/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 6*a*b**2*n*x**(2*n)*log(x)/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 6*a*b**2*n*x**(2*n)/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 4*b**3*n*x**(3*n)/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 2*b**3*x**(3*n)/(4*n**2*x**(2*n) + 2*n*x**(2*n)), True))","A",0
2546,-1,0,0,0.000000," ","integrate(x**(-1-3*n)*(a+b*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2547,1,56,0,26.982409," ","integrate(x**(-1-4*n)*(a+b*x**n)**3,x)","\begin{cases} - \frac{a^{3} x^{- 4 n}}{4 n} - \frac{a^{2} b x^{- 3 n}}{n} - \frac{3 a b^{2} x^{- 2 n}}{2 n} - \frac{b^{3} x^{- n}}{n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*x**(-4*n)/(4*n) - a**2*b*x**(-3*n)/n - 3*a*b**2*x**(-2*n)/(2*n) - b**3*x**(-n)/n, Ne(n, 0)), ((a + b)**3*log(x), True))","A",0
2548,1,60,0,26.465765," ","integrate(x**(-1-5*n)*(a+b*x**n)**3,x)","\begin{cases} - \frac{a^{3} x^{- 5 n}}{5 n} - \frac{3 a^{2} b x^{- 4 n}}{4 n} - \frac{a b^{2} x^{- 3 n}}{n} - \frac{b^{3} x^{- 2 n}}{2 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*x**(-5*n)/(5*n) - 3*a**2*b*x**(-4*n)/(4*n) - a*b**2*x**(-3*n)/n - b**3*x**(-2*n)/(2*n), Ne(n, 0)), ((a + b)**3*log(x), True))","A",0
2549,1,63,0,26.874403," ","integrate(x**(-1-6*n)*(a+b*x**n)**3,x)","\begin{cases} - \frac{a^{3} x^{- 6 n}}{6 n} - \frac{3 a^{2} b x^{- 5 n}}{5 n} - \frac{3 a b^{2} x^{- 4 n}}{4 n} - \frac{b^{3} x^{- 3 n}}{3 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*x**(-6*n)/(6*n) - 3*a**2*b*x**(-5*n)/(5*n) - 3*a*b**2*x**(-4*n)/(4*n) - b**3*x**(-3*n)/(3*n), Ne(n, 0)), ((a + b)**3*log(x), True))","A",0
2550,1,61,0,27.125807," ","integrate(x**(-1-7*n)*(a+b*x**n)**3,x)","\begin{cases} - \frac{a^{3} x^{- 7 n}}{7 n} - \frac{a^{2} b x^{- 6 n}}{2 n} - \frac{3 a b^{2} x^{- 5 n}}{5 n} - \frac{b^{3} x^{- 4 n}}{4 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{3} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*x**(-7*n)/(7*n) - a**2*b*x**(-6*n)/(2*n) - 3*a*b**2*x**(-5*n)/(5*n) - b**3*x**(-4*n)/(4*n), Ne(n, 0)), ((a + b)**3*log(x), True))","A",0
2551,1,92,0,117.296731," ","integrate(x**(-1+4*n)*(a+b*x**n)**5,x)","\begin{cases} \frac{a^{5} x^{4 n}}{4 n} + \frac{a^{4} b x^{5 n}}{n} + \frac{5 a^{3} b^{2} x^{6 n}}{3 n} + \frac{10 a^{2} b^{3} x^{7 n}}{7 n} + \frac{5 a b^{4} x^{8 n}}{8 n} + \frac{b^{5} x^{9 n}}{9 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{5} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**5*x**(4*n)/(4*n) + a**4*b*x**(5*n)/n + 5*a**3*b**2*x**(6*n)/(3*n) + 10*a**2*b**3*x**(7*n)/(7*n) + 5*a*b**4*x**(8*n)/(8*n) + b**5*x**(9*n)/(9*n), Ne(n, 0)), ((a + b)**5*log(x), True))","A",0
2552,1,94,0,117.785283," ","integrate(x**(-1+3*n)*(a+b*x**n)**5,x)","\begin{cases} \frac{a^{5} x^{3 n}}{3 n} + \frac{5 a^{4} b x^{4 n}}{4 n} + \frac{2 a^{3} b^{2} x^{5 n}}{n} + \frac{5 a^{2} b^{3} x^{6 n}}{3 n} + \frac{5 a b^{4} x^{7 n}}{7 n} + \frac{b^{5} x^{8 n}}{8 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{5} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**5*x**(3*n)/(3*n) + 5*a**4*b*x**(4*n)/(4*n) + 2*a**3*b**2*x**(5*n)/n + 5*a**2*b**3*x**(6*n)/(3*n) + 5*a*b**4*x**(7*n)/(7*n) + b**5*x**(8*n)/(8*n), Ne(n, 0)), ((a + b)**5*log(x), True))","A",0
2553,1,94,0,117.652978," ","integrate(x**(-1+2*n)*(a+b*x**n)**5,x)","\begin{cases} \frac{a^{5} x^{2 n}}{2 n} + \frac{5 a^{4} b x^{3 n}}{3 n} + \frac{5 a^{3} b^{2} x^{4 n}}{2 n} + \frac{2 a^{2} b^{3} x^{5 n}}{n} + \frac{5 a b^{4} x^{6 n}}{6 n} + \frac{b^{5} x^{7 n}}{7 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{5} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**5*x**(2*n)/(2*n) + 5*a**4*b*x**(3*n)/(3*n) + 5*a**3*b**2*x**(4*n)/(2*n) + 2*a**2*b**3*x**(5*n)/n + 5*a*b**4*x**(6*n)/(6*n) + b**5*x**(7*n)/(7*n), Ne(n, 0)), ((a + b)**5*log(x), True))","A",0
2554,1,88,0,15.828610," ","integrate(x**(-1+n)*(a+b*x**n)**5,x)","\begin{cases} \frac{a^{5} x^{n}}{n} + \frac{5 a^{4} b x^{2 n}}{2 n} + \frac{10 a^{3} b^{2} x^{3 n}}{3 n} + \frac{5 a^{2} b^{3} x^{4 n}}{2 n} + \frac{a b^{4} x^{5 n}}{n} + \frac{b^{5} x^{6 n}}{6 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{5} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**5*x**n/n + 5*a**4*b*x**(2*n)/(2*n) + 10*a**3*b**2*x**(3*n)/(3*n) + 5*a**2*b**3*x**(4*n)/(2*n) + a*b**4*x**(5*n)/n + b**5*x**(6*n)/(6*n), Ne(n, 0)), ((a + b)**5*log(x), True))","A",0
2555,1,85,0,0.944309," ","integrate((a+b*x**n)**5/x,x)","\begin{cases} a^{5} \log{\left(x \right)} + \frac{5 a^{4} b x^{n}}{n} + \frac{5 a^{3} b^{2} x^{2 n}}{n} + \frac{10 a^{2} b^{3} x^{3 n}}{3 n} + \frac{5 a b^{4} x^{4 n}}{4 n} + \frac{b^{5} x^{5 n}}{5 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{5} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**5*log(x) + 5*a**4*b*x**n/n + 5*a**3*b**2*x**(2*n)/n + 10*a**2*b**3*x**(3*n)/(3*n) + 5*a*b**4*x**(4*n)/(4*n) + b**5*x**(5*n)/(5*n), Ne(n, 0)), ((a + b)**5*log(x), True))","A",0
2556,-1,0,0,0.000000," ","integrate(x**(-1-n)*(a+b*x**n)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2557,-1,0,0,0.000000," ","integrate(x**(-1-2*n)*(a+b*x**n)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2558,-1,0,0,0.000000," ","integrate(x**(-1-3*n)*(a+b*x**n)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2559,-1,0,0,0.000000," ","integrate(x**(-1-4*n)*(a+b*x**n)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2560,-1,0,0,0.000000," ","integrate(x**(-1-5*n)*(a+b*x**n)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2561,1,90,0,124.556281," ","integrate(x**(-1-6*n)*(a+b*x**n)**5,x)","\begin{cases} - \frac{a^{5} x^{- 6 n}}{6 n} - \frac{a^{4} b x^{- 5 n}}{n} - \frac{5 a^{3} b^{2} x^{- 4 n}}{2 n} - \frac{10 a^{2} b^{3} x^{- 3 n}}{3 n} - \frac{5 a b^{4} x^{- 2 n}}{2 n} - \frac{b^{5} x^{- n}}{n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{5} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**5*x**(-6*n)/(6*n) - a**4*b*x**(-5*n)/n - 5*a**3*b**2*x**(-4*n)/(2*n) - 10*a**2*b**3*x**(-3*n)/(3*n) - 5*a*b**4*x**(-2*n)/(2*n) - b**5*x**(-n)/n, Ne(n, 0)), ((a + b)**5*log(x), True))","A",0
2562,-1,0,0,0.000000," ","integrate(x**(-1-7*n)*(a+b*x**n)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2563,-1,0,0,0.000000," ","integrate(x**(-1-8*n)*(a+b*x**n)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2564,1,94,0,124.330114," ","integrate(x**(-1-9*n)*(a+b*x**n)**5,x)","\begin{cases} - \frac{a^{5} x^{- 9 n}}{9 n} - \frac{5 a^{4} b x^{- 8 n}}{8 n} - \frac{10 a^{3} b^{2} x^{- 7 n}}{7 n} - \frac{5 a^{2} b^{3} x^{- 6 n}}{3 n} - \frac{a b^{4} x^{- 5 n}}{n} - \frac{b^{5} x^{- 4 n}}{4 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{5} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**5*x**(-9*n)/(9*n) - 5*a**4*b*x**(-8*n)/(8*n) - 10*a**3*b**2*x**(-7*n)/(7*n) - 5*a**2*b**3*x**(-6*n)/(3*n) - a*b**4*x**(-5*n)/n - b**5*x**(-4*n)/(4*n), Ne(n, 0)), ((a + b)**5*log(x), True))","A",0
2565,1,97,0,118.317124," ","integrate(x**(-1-10*n)*(a+b*x**n)**5,x)","\begin{cases} - \frac{a^{5} x^{- 10 n}}{10 n} - \frac{5 a^{4} b x^{- 9 n}}{9 n} - \frac{5 a^{3} b^{2} x^{- 8 n}}{4 n} - \frac{10 a^{2} b^{3} x^{- 7 n}}{7 n} - \frac{5 a b^{4} x^{- 6 n}}{6 n} - \frac{b^{5} x^{- 5 n}}{5 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{5} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**5*x**(-10*n)/(10*n) - 5*a**4*b*x**(-9*n)/(9*n) - 5*a**3*b**2*x**(-8*n)/(4*n) - 10*a**2*b**3*x**(-7*n)/(7*n) - 5*a*b**4*x**(-6*n)/(6*n) - b**5*x**(-5*n)/(5*n), Ne(n, 0)), ((a + b)**5*log(x), True))","A",0
2566,-1,0,0,0.000000," ","integrate(x**(-1+9*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2567,-1,0,0,0.000000," ","integrate(x**(-1+8*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2568,-1,0,0,0.000000," ","integrate(x**(-1+7*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2569,-1,0,0,0.000000," ","integrate(x**(-1+6*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2570,-1,0,0,0.000000," ","integrate(x**(-1+5*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2571,-1,0,0,0.000000," ","integrate(x**(-1+4*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2572,-1,0,0,0.000000," ","integrate(x**(-1+3*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2573,-1,0,0,0.000000," ","integrate(x**(-1+2*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2574,1,133,0,64.514266," ","integrate(x**(-1+n)*(a+b*x**n)**8,x)","\begin{cases} \frac{a^{8} x^{n}}{n} + \frac{4 a^{7} b x^{2 n}}{n} + \frac{28 a^{6} b^{2} x^{3 n}}{3 n} + \frac{14 a^{5} b^{3} x^{4 n}}{n} + \frac{14 a^{4} b^{4} x^{5 n}}{n} + \frac{28 a^{3} b^{5} x^{6 n}}{3 n} + \frac{4 a^{2} b^{6} x^{7 n}}{n} + \frac{a b^{7} x^{8 n}}{n} + \frac{b^{8} x^{9 n}}{9 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{8} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**8*x**n/n + 4*a**7*b*x**(2*n)/n + 28*a**6*b**2*x**(3*n)/(3*n) + 14*a**5*b**3*x**(4*n)/n + 14*a**4*b**4*x**(5*n)/n + 28*a**3*b**5*x**(6*n)/(3*n) + 4*a**2*b**6*x**(7*n)/n + a*b**7*x**(8*n)/n + b**8*x**(9*n)/(9*n), Ne(n, 0)), ((a + b)**8*log(x), True))","A",0
2575,1,136,0,4.052189," ","integrate((a+b*x**n)**8/x,x)","\begin{cases} a^{8} \log{\left(x \right)} + \frac{8 a^{7} b x^{n}}{n} + \frac{14 a^{6} b^{2} x^{2 n}}{n} + \frac{56 a^{5} b^{3} x^{3 n}}{3 n} + \frac{35 a^{4} b^{4} x^{4 n}}{2 n} + \frac{56 a^{3} b^{5} x^{5 n}}{5 n} + \frac{14 a^{2} b^{6} x^{6 n}}{3 n} + \frac{8 a b^{7} x^{7 n}}{7 n} + \frac{b^{8} x^{8 n}}{8 n} & \text{for}\: n \neq 0 \\\left(a + b\right)^{8} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**8*log(x) + 8*a**7*b*x**n/n + 14*a**6*b**2*x**(2*n)/n + 56*a**5*b**3*x**(3*n)/(3*n) + 35*a**4*b**4*x**(4*n)/(2*n) + 56*a**3*b**5*x**(5*n)/(5*n) + 14*a**2*b**6*x**(6*n)/(3*n) + 8*a*b**7*x**(7*n)/(7*n) + b**8*x**(8*n)/(8*n), Ne(n, 0)), ((a + b)**8*log(x), True))","A",0
2576,-1,0,0,0.000000," ","integrate(x**(-1-n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2577,-1,0,0,0.000000," ","integrate(x**(-1-2*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2578,-1,0,0,0.000000," ","integrate(x**(-1-3*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2579,-1,0,0,0.000000," ","integrate(x**(-1-4*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2580,-1,0,0,0.000000," ","integrate(x**(-1-5*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2581,-1,0,0,0.000000," ","integrate(x**(-1-6*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2582,-1,0,0,0.000000," ","integrate(x**(-1-7*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2583,-1,0,0,0.000000," ","integrate(x**(-1-8*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2584,-1,0,0,0.000000," ","integrate(x**(-1-9*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2585,-1,0,0,0.000000," ","integrate(x**(-1-10*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2586,-1,0,0,0.000000," ","integrate(x**(-1-11*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2587,-1,0,0,0.000000," ","integrate(x**(-1-12*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2588,-1,0,0,0.000000," ","integrate(x**(-1-13*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2589,-1,0,0,0.000000," ","integrate(x**(-1-14*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2590,-1,0,0,0.000000," ","integrate(x**(-1-15*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2591,-1,0,0,0.000000," ","integrate(x**(-1+n)*(a+b*x**n)**16,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2592,1,160,0,0.106868," ","integrate(x**12*(b*x**13+a)**12,x)","\frac{a^{12} x^{13}}{13} + \frac{6 a^{11} b x^{26}}{13} + \frac{22 a^{10} b^{2} x^{39}}{13} + \frac{55 a^{9} b^{3} x^{52}}{13} + \frac{99 a^{8} b^{4} x^{65}}{13} + \frac{132 a^{7} b^{5} x^{78}}{13} + \frac{132 a^{6} b^{6} x^{91}}{13} + \frac{99 a^{5} b^{7} x^{104}}{13} + \frac{55 a^{4} b^{8} x^{117}}{13} + \frac{22 a^{3} b^{9} x^{130}}{13} + \frac{6 a^{2} b^{10} x^{143}}{13} + \frac{a b^{11} x^{156}}{13} + \frac{b^{12} x^{169}}{169}"," ",0,"a**12*x**13/13 + 6*a**11*b*x**26/13 + 22*a**10*b**2*x**39/13 + 55*a**9*b**3*x**52/13 + 99*a**8*b**4*x**65/13 + 132*a**7*b**5*x**78/13 + 132*a**6*b**6*x**91/13 + 99*a**5*b**7*x**104/13 + 55*a**4*b**8*x**117/13 + 22*a**3*b**9*x**130/13 + 6*a**2*b**10*x**143/13 + a*b**11*x**156/13 + b**12*x**169/169","B",0
2593,1,160,0,0.110283," ","integrate(x**24*(b*x**25+a)**12,x)","\frac{a^{12} x^{25}}{25} + \frac{6 a^{11} b x^{50}}{25} + \frac{22 a^{10} b^{2} x^{75}}{25} + \frac{11 a^{9} b^{3} x^{100}}{5} + \frac{99 a^{8} b^{4} x^{125}}{25} + \frac{132 a^{7} b^{5} x^{150}}{25} + \frac{132 a^{6} b^{6} x^{175}}{25} + \frac{99 a^{5} b^{7} x^{200}}{25} + \frac{11 a^{4} b^{8} x^{225}}{5} + \frac{22 a^{3} b^{9} x^{250}}{25} + \frac{6 a^{2} b^{10} x^{275}}{25} + \frac{a b^{11} x^{300}}{25} + \frac{b^{12} x^{325}}{325}"," ",0,"a**12*x**25/25 + 6*a**11*b*x**50/25 + 22*a**10*b**2*x**75/25 + 11*a**9*b**3*x**100/5 + 99*a**8*b**4*x**125/25 + 132*a**7*b**5*x**150/25 + 132*a**6*b**6*x**175/25 + 99*a**5*b**7*x**200/25 + 11*a**4*b**8*x**225/5 + 22*a**3*b**9*x**250/25 + 6*a**2*b**10*x**275/25 + a*b**11*x**300/25 + b**12*x**325/325","B",0
2594,1,160,0,0.113168," ","integrate(x**36*(b*x**37+a)**12,x)","\frac{a^{12} x^{37}}{37} + \frac{6 a^{11} b x^{74}}{37} + \frac{22 a^{10} b^{2} x^{111}}{37} + \frac{55 a^{9} b^{3} x^{148}}{37} + \frac{99 a^{8} b^{4} x^{185}}{37} + \frac{132 a^{7} b^{5} x^{222}}{37} + \frac{132 a^{6} b^{6} x^{259}}{37} + \frac{99 a^{5} b^{7} x^{296}}{37} + \frac{55 a^{4} b^{8} x^{333}}{37} + \frac{22 a^{3} b^{9} x^{370}}{37} + \frac{6 a^{2} b^{10} x^{407}}{37} + \frac{a b^{11} x^{444}}{37} + \frac{b^{12} x^{481}}{481}"," ",0,"a**12*x**37/37 + 6*a**11*b*x**74/37 + 22*a**10*b**2*x**111/37 + 55*a**9*b**3*x**148/37 + 99*a**8*b**4*x**185/37 + 132*a**7*b**5*x**222/37 + 132*a**6*b**6*x**259/37 + 99*a**5*b**7*x**296/37 + 55*a**4*b**8*x**333/37 + 22*a**3*b**9*x**370/37 + 6*a**2*b**10*x**407/37 + a*b**11*x**444/37 + b**12*x**481/481","B",0
2595,1,284,0,159.992089," ","integrate(x**(12*m)*(a+b*x**(1+12*m))**12,x)","\begin{cases} \frac{13 a^{12} x x^{12 m}}{156 m + 13} + \frac{78 a^{11} b x^{2} x^{24 m}}{156 m + 13} + \frac{286 a^{10} b^{2} x^{3} x^{36 m}}{156 m + 13} + \frac{715 a^{9} b^{3} x^{4} x^{48 m}}{156 m + 13} + \frac{1287 a^{8} b^{4} x^{5} x^{60 m}}{156 m + 13} + \frac{1716 a^{7} b^{5} x^{6} x^{72 m}}{156 m + 13} + \frac{1716 a^{6} b^{6} x^{7} x^{84 m}}{156 m + 13} + \frac{1287 a^{5} b^{7} x^{8} x^{96 m}}{156 m + 13} + \frac{715 a^{4} b^{8} x^{9} x^{108 m}}{156 m + 13} + \frac{286 a^{3} b^{9} x^{10} x^{120 m}}{156 m + 13} + \frac{78 a^{2} b^{10} x^{11} x^{132 m}}{156 m + 13} + \frac{13 a b^{11} x^{12} x^{144 m}}{156 m + 13} + \frac{b^{12} x^{13} x^{156 m}}{156 m + 13} & \text{for}\: m \neq - \frac{1}{12} \\\left(a + b\right)^{12} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((13*a**12*x*x**(12*m)/(156*m + 13) + 78*a**11*b*x**2*x**(24*m)/(156*m + 13) + 286*a**10*b**2*x**3*x**(36*m)/(156*m + 13) + 715*a**9*b**3*x**4*x**(48*m)/(156*m + 13) + 1287*a**8*b**4*x**5*x**(60*m)/(156*m + 13) + 1716*a**7*b**5*x**6*x**(72*m)/(156*m + 13) + 1716*a**6*b**6*x**7*x**(84*m)/(156*m + 13) + 1287*a**5*b**7*x**8*x**(96*m)/(156*m + 13) + 715*a**4*b**8*x**9*x**(108*m)/(156*m + 13) + 286*a**3*b**9*x**10*x**(120*m)/(156*m + 13) + 78*a**2*b**10*x**11*x**(132*m)/(156*m + 13) + 13*a*b**11*x**12*x**(144*m)/(156*m + 13) + b**12*x**13*x**(156*m)/(156*m + 13), Ne(m, -1/12)), ((a + b)**12*log(x), True))","A",0
2596,1,284,0,161.660781," ","integrate(x**(12*m)*(a+b*x**(1+12*m))**12,x)","\begin{cases} \frac{13 a^{12} x x^{12 m}}{156 m + 13} + \frac{78 a^{11} b x^{2} x^{24 m}}{156 m + 13} + \frac{286 a^{10} b^{2} x^{3} x^{36 m}}{156 m + 13} + \frac{715 a^{9} b^{3} x^{4} x^{48 m}}{156 m + 13} + \frac{1287 a^{8} b^{4} x^{5} x^{60 m}}{156 m + 13} + \frac{1716 a^{7} b^{5} x^{6} x^{72 m}}{156 m + 13} + \frac{1716 a^{6} b^{6} x^{7} x^{84 m}}{156 m + 13} + \frac{1287 a^{5} b^{7} x^{8} x^{96 m}}{156 m + 13} + \frac{715 a^{4} b^{8} x^{9} x^{108 m}}{156 m + 13} + \frac{286 a^{3} b^{9} x^{10} x^{120 m}}{156 m + 13} + \frac{78 a^{2} b^{10} x^{11} x^{132 m}}{156 m + 13} + \frac{13 a b^{11} x^{12} x^{144 m}}{156 m + 13} + \frac{b^{12} x^{13} x^{156 m}}{156 m + 13} & \text{for}\: m \neq - \frac{1}{12} \\\left(a + b\right)^{12} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((13*a**12*x*x**(12*m)/(156*m + 13) + 78*a**11*b*x**2*x**(24*m)/(156*m + 13) + 286*a**10*b**2*x**3*x**(36*m)/(156*m + 13) + 715*a**9*b**3*x**4*x**(48*m)/(156*m + 13) + 1287*a**8*b**4*x**5*x**(60*m)/(156*m + 13) + 1716*a**7*b**5*x**6*x**(72*m)/(156*m + 13) + 1716*a**6*b**6*x**7*x**(84*m)/(156*m + 13) + 1287*a**5*b**7*x**8*x**(96*m)/(156*m + 13) + 715*a**4*b**8*x**9*x**(108*m)/(156*m + 13) + 286*a**3*b**9*x**10*x**(120*m)/(156*m + 13) + 78*a**2*b**10*x**11*x**(132*m)/(156*m + 13) + 13*a*b**11*x**12*x**(144*m)/(156*m + 13) + b**12*x**13*x**(156*m)/(156*m + 13), Ne(m, -1/12)), ((a + b)**12*log(x), True))","A",0
2597,1,87,0,95.403011," ","integrate(x**(-1+5*n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{5 n}}{5 a n} & \text{for}\: b = 0 \\\frac{a^{4} \log{\left(\frac{a}{b} + x^{n} \right)}}{b^{5} n} - \frac{a^{3} x^{n}}{b^{4} n} + \frac{a^{2} x^{2 n}}{2 b^{3} n} - \frac{a x^{3 n}}{3 b^{2} n} + \frac{x^{4 n}}{4 b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**(5*n)/(5*a*n), Eq(b, 0)), (a**4*log(a/b + x**n)/(b**5*n) - a**3*x**n/(b**4*n) + a**2*x**(2*n)/(2*b**3*n) - a*x**(3*n)/(3*b**2*n) + x**(4*n)/(4*b*n), True))","A",0
2598,1,71,0,45.920794," ","integrate(x**(-1+4*n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{4 n}}{4 a n} & \text{for}\: b = 0 \\- \frac{a^{3} \log{\left(\frac{a}{b} + x^{n} \right)}}{b^{4} n} + \frac{a^{2} x^{n}}{b^{3} n} - \frac{a x^{2 n}}{2 b^{2} n} + \frac{x^{3 n}}{3 b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**(4*n)/(4*a*n), Eq(b, 0)), (-a**3*log(a/b + x**n)/(b**4*n) + a**2*x**n/(b**3*n) - a*x**(2*n)/(2*b**2*n) + x**(3*n)/(3*b*n), True))","A",0
2599,1,56,0,25.359905," ","integrate(x**(-1+3*n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{3 n}}{3 a n} & \text{for}\: b = 0 \\\frac{a^{2} \log{\left(\frac{a}{b} + x^{n} \right)}}{b^{3} n} - \frac{a x^{n}}{b^{2} n} + \frac{x^{2 n}}{2 b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**(3*n)/(3*a*n), Eq(b, 0)), (a**2*log(a/b + x**n)/(b**3*n) - a*x**n/(b**2*n) + x**(2*n)/(2*b*n), True))","A",0
2600,1,41,0,12.228298," ","integrate(x**(-1+2*n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{2 n}}{2 a n} & \text{for}\: b = 0 \\- \frac{a \log{\left(\frac{a}{b} + x^{n} \right)}}{b^{2} n} + \frac{x^{n}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**(2*n)/(2*a*n), Eq(b, 0)), (-a*log(a/b + x**n)/(b**2*n) + x**n/(b*n), True))","A",0
2601,1,27,0,2.541781," ","integrate(x**(-1+n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{n}}{a n} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + x^{n} \right)}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**n/(a*n), Eq(b, 0)), (log(a/b + x**n)/(b*n), True))","A",0
2602,1,41,0,0.735621," ","integrate(1/x/(a+b*x**n),x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \\- \frac{x^{- n}}{b n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{n} \right)}}{a n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (log(x)/a, Eq(b, 0)), (-x**(-n)/(b*n), Eq(a, 0)), (log(x)/(a + b), Eq(n, 0)), (log(x)/a - log(a/b + x**n)/(a*n), True))","A",0
2603,1,48,0,21.081024," ","integrate(x**(-1-n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{b} & \text{for}\: a = 0 \wedge n = 0 \\- \frac{x^{- 2 n}}{2 b n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\- \frac{x^{- n}}{a n} + \frac{b \log{\left(x^{- n} + \frac{b}{a} \right)}}{a^{2} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/b, Eq(a, 0) & Eq(n, 0)), (-x**(-2*n)/(2*b*n), Eq(a, 0)), (log(x)/(a + b), Eq(n, 0)), (-x**(-n)/(a*n) + b*log(x**(-n) + b/a)/(a**2*n), True))","A",0
2604,1,85,0,141.581567," ","integrate(x**(-1-2*n)/(a+b*x**n),x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\- \frac{x^{- 3 n}}{3 b n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\- \frac{x^{- 2 n}}{2 a n} & \text{for}\: b = 0 \\- \frac{x^{- 2 n}}{2 a n} + \frac{b x^{- n}}{a^{2} n} + \frac{b^{2} \log{\left(x \right)}}{a^{3}} - \frac{b^{2} \log{\left(\frac{a}{b} + x^{n} \right)}}{a^{3} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (-x**(-3*n)/(3*b*n), Eq(a, 0)), (log(x)/(a + b), Eq(n, 0)), (-x**(-2*n)/(2*a*n), Eq(b, 0)), (-x**(-2*n)/(2*a*n) + b*x**(-n)/(a**2*n) + b**2*log(x)/a**3 - b**2*log(a/b + x**n)/(a**3*n), True))","A",0
2605,-1,0,0,0.000000," ","integrate(x**(-1-3*n)/(a+b*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2606,1,87,0,95.823407," ","integrate(x**(-1+5*n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{5 n}}{5 a n} & \text{for}\: b = 0 \\\frac{a^{4} \log{\left(\frac{a}{b} + x^{n} \right)}}{b^{5} n} - \frac{a^{3} x^{n}}{b^{4} n} + \frac{a^{2} x^{2 n}}{2 b^{3} n} - \frac{a x^{3 n}}{3 b^{2} n} + \frac{x^{4 n}}{4 b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**(5*n)/(5*a*n), Eq(b, 0)), (a**4*log(a/b + x**n)/(b**5*n) - a**3*x**n/(b**4*n) + a**2*x**(2*n)/(2*b**3*n) - a*x**(3*n)/(3*b**2*n) + x**(4*n)/(4*b*n), True))","A",0
2607,1,71,0,48.257619," ","integrate(x**(-1+4*n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{4 n}}{4 a n} & \text{for}\: b = 0 \\- \frac{a^{3} \log{\left(\frac{a}{b} + x^{n} \right)}}{b^{4} n} + \frac{a^{2} x^{n}}{b^{3} n} - \frac{a x^{2 n}}{2 b^{2} n} + \frac{x^{3 n}}{3 b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**(4*n)/(4*a*n), Eq(b, 0)), (-a**3*log(a/b + x**n)/(b**4*n) + a**2*x**n/(b**3*n) - a*x**(2*n)/(2*b**2*n) + x**(3*n)/(3*b*n), True))","A",0
2608,1,56,0,26.720621," ","integrate(x**(-1+3*n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{3 n}}{3 a n} & \text{for}\: b = 0 \\\frac{a^{2} \log{\left(\frac{a}{b} + x^{n} \right)}}{b^{3} n} - \frac{a x^{n}}{b^{2} n} + \frac{x^{2 n}}{2 b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**(3*n)/(3*a*n), Eq(b, 0)), (a**2*log(a/b + x**n)/(b**3*n) - a*x**n/(b**2*n) + x**(2*n)/(2*b*n), True))","A",0
2609,1,41,0,13.293917," ","integrate(x**(-1+2*n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{2 n}}{2 a n} & \text{for}\: b = 0 \\- \frac{a \log{\left(\frac{a}{b} + x^{n} \right)}}{b^{2} n} + \frac{x^{n}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**(2*n)/(2*a*n), Eq(b, 0)), (-a*log(a/b + x**n)/(b**2*n) + x**n/(b*n), True))","A",0
2610,1,27,0,2.702059," ","integrate(x**(-1+n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{n}}{a n} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + x^{n} \right)}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**n/(a*n), Eq(b, 0)), (log(a/b + x**n)/(b*n), True))","A",0
2611,1,41,0,0.743900," ","integrate(1/x/(a+b*x**n),x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \\- \frac{x^{- n}}{b n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{n} \right)}}{a n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (log(x)/a, Eq(b, 0)), (-x**(-n)/(b*n), Eq(a, 0)), (log(x)/(a + b), Eq(n, 0)), (log(x)/a - log(a/b + x**n)/(a*n), True))","A",0
2612,1,48,0,22.379745," ","integrate(x**(-1-n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{b} & \text{for}\: a = 0 \wedge n = 0 \\- \frac{x^{- 2 n}}{2 b n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\- \frac{x^{- n}}{a n} + \frac{b \log{\left(x^{- n} + \frac{b}{a} \right)}}{a^{2} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/b, Eq(a, 0) & Eq(n, 0)), (-x**(-2*n)/(2*b*n), Eq(a, 0)), (log(x)/(a + b), Eq(n, 0)), (-x**(-n)/(a*n) + b*log(x**(-n) + b/a)/(a**2*n), True))","A",0
2613,1,85,0,145.963952," ","integrate(x**(-1-2*n)/(a+b*x**n),x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\- \frac{x^{- 3 n}}{3 b n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\- \frac{x^{- 2 n}}{2 a n} & \text{for}\: b = 0 \\- \frac{x^{- 2 n}}{2 a n} + \frac{b x^{- n}}{a^{2} n} + \frac{b^{2} \log{\left(x \right)}}{a^{3}} - \frac{b^{2} \log{\left(\frac{a}{b} + x^{n} \right)}}{a^{3} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (-x**(-3*n)/(3*b*n), Eq(a, 0)), (log(x)/(a + b), Eq(n, 0)), (-x**(-2*n)/(2*a*n), Eq(b, 0)), (-x**(-2*n)/(2*a*n) + b*x**(-n)/(a**2*n) + b**2*log(x)/a**3 - b**2*log(a/b + x**n)/(a**3*n), True))","A",0
2614,-1,0,0,0.000000," ","integrate(x**(-1-3*n)/(a+b*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2615,1,78,0,76.518037," ","integrate(x**(-1+5*n)/(2+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{2} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{b + 2} & \text{for}\: n = 0 \\\frac{x^{5 n}}{10 n} & \text{for}\: b = 0 \\\frac{x^{4 n}}{4 b n} - \frac{2 x^{3 n}}{3 b^{2} n} + \frac{2 x^{2 n}}{b^{3} n} - \frac{8 x^{n}}{b^{4} n} + \frac{16 \log{\left(x^{n} + \frac{2}{b} \right)}}{b^{5} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/2, Eq(b, 0) & Eq(n, 0)), (log(x)/(b + 2), Eq(n, 0)), (x**(5*n)/(10*n), Eq(b, 0)), (x**(4*n)/(4*b*n) - 2*x**(3*n)/(3*b**2*n) + 2*x**(2*n)/(b**3*n) - 8*x**n/(b**4*n) + 16*log(x**n + 2/b)/(b**5*n), True))","A",0
2616,1,63,0,36.356119," ","integrate(x**(-1+4*n)/(2+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{2} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{b + 2} & \text{for}\: n = 0 \\\frac{x^{4 n}}{8 n} & \text{for}\: b = 0 \\\frac{x^{3 n}}{3 b n} - \frac{x^{2 n}}{b^{2} n} + \frac{4 x^{n}}{b^{3} n} - \frac{8 \log{\left(x^{n} + \frac{2}{b} \right)}}{b^{4} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/2, Eq(b, 0) & Eq(n, 0)), (log(x)/(b + 2), Eq(n, 0)), (x**(4*n)/(8*n), Eq(b, 0)), (x**(3*n)/(3*b*n) - x**(2*n)/(b**2*n) + 4*x**n/(b**3*n) - 8*log(x**n + 2/b)/(b**4*n), True))","A",0
2617,1,53,0,19.572208," ","integrate(x**(-1+3*n)/(2+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{2} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{b + 2} & \text{for}\: n = 0 \\\frac{x^{3 n}}{6 n} & \text{for}\: b = 0 \\\frac{x^{2 n}}{2 b n} - \frac{2 x^{n}}{b^{2} n} + \frac{4 \log{\left(x^{n} + \frac{2}{b} \right)}}{b^{3} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/2, Eq(b, 0) & Eq(n, 0)), (log(x)/(b + 2), Eq(n, 0)), (x**(3*n)/(6*n), Eq(b, 0)), (x**(2*n)/(2*b*n) - 2*x**n/(b**2*n) + 4*log(x**n + 2/b)/(b**3*n), True))","A",0
2618,1,39,0,9.717461," ","integrate(x**(-1+2*n)/(2+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{2} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{b + 2} & \text{for}\: n = 0 \\\frac{x^{2 n}}{4 n} & \text{for}\: b = 0 \\\frac{x^{n}}{b n} - \frac{2 \log{\left(x^{n} + \frac{2}{b} \right)}}{b^{2} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/2, Eq(b, 0) & Eq(n, 0)), (log(x)/(b + 2), Eq(n, 0)), (x**(2*n)/(4*n), Eq(b, 0)), (x**n/(b*n) - 2*log(x**n + 2/b)/(b**2*n), True))","A",0
2619,1,27,0,2.379780," ","integrate(x**(-1+n)/(2+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{2} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{b + 2} & \text{for}\: n = 0 \\\frac{x^{n}}{2 n} & \text{for}\: b = 0 \\\frac{\log{\left(x^{n} + \frac{2}{b} \right)}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/2, Eq(b, 0) & Eq(n, 0)), (log(x)/(b + 2), Eq(n, 0)), (x**n/(2*n), Eq(b, 0)), (log(x**n + 2/b)/(b*n), True))","A",0
2620,1,29,0,0.585663," ","integrate(1/x/(2+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{2} & \text{for}\: b = 0 \wedge \left(b = 0 \vee n = 0\right) \\\frac{\log{\left(x \right)}}{b + 2} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{2} - \frac{\log{\left(x^{n} + \frac{2}{b} \right)}}{2 n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/2, Eq(b, 0) & (Eq(b, 0) | Eq(n, 0))), (log(x)/(b + 2), Eq(n, 0)), (log(x)/2 - log(x**n + 2/b)/(2*n), True))","A",0
2621,1,29,0,18.256567," ","integrate(x**(-1-n)/(2+b*x**n),x)","\begin{cases} \frac{b \log{\left(\frac{b}{2} + x^{- n} \right)}}{4 n} - \frac{x^{- n}}{2 n} & \text{for}\: n \neq 0 \\\frac{\log{\left(x \right)}}{b + 2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b*log(b/2 + x**(-n))/(4*n) - x**(-n)/(2*n), Ne(n, 0)), (log(x)/(b + 2), True))","A",0
2622,1,63,0,132.457597," ","integrate(x**(-1-2*n)/(2+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{2} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{b + 2} & \text{for}\: n = 0 \\- \frac{x^{- 2 n}}{4 n} & \text{for}\: b = 0 \\\frac{b^{2} \log{\left(x \right)}}{8} - \frac{b^{2} \log{\left(x^{n} + \frac{2}{b} \right)}}{8 n} + \frac{b x^{- n}}{4 n} - \frac{x^{- 2 n}}{4 n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/2, Eq(b, 0) & Eq(n, 0)), (log(x)/(b + 2), Eq(n, 0)), (-x**(-2*n)/(4*n), Eq(b, 0)), (b**2*log(x)/8 - b**2*log(x**n + 2/b)/(8*n) + b*x**(-n)/(4*n) - x**(-2*n)/(4*n), True))","A",0
2623,-1,0,0,0.000000," ","integrate(x**(-1-3*n)/(2+b*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2624,-2,0,0,0.000000," ","integrate(x**(-1+4*n)/(a+b*x**n)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2625,1,129,0,157.495543," ","integrate(x**(-1+3*n)/(a+b*x**n)**2,x)","\begin{cases} \frac{\log{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \wedge n = 0 \\\frac{x^{3 n}}{3 a^{2} n} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{2}} & \text{for}\: n = 0 \\- \frac{2 a^{2} \log{\left(\frac{a}{b} + x^{n} \right)}}{a b^{3} n + b^{4} n x^{n}} - \frac{2 a^{2}}{a b^{3} n + b^{4} n x^{n}} - \frac{2 a b x^{n} \log{\left(\frac{a}{b} + x^{n} \right)}}{a b^{3} n + b^{4} n x^{n}} + \frac{b^{2} x^{2 n}}{a b^{3} n + b^{4} n x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a**2, Eq(b, 0) & Eq(n, 0)), (x**(3*n)/(3*a**2*n), Eq(b, 0)), (log(x)/(a + b)**2, Eq(n, 0)), (-2*a**2*log(a/b + x**n)/(a*b**3*n + b**4*n*x**n) - 2*a**2/(a*b**3*n + b**4*n*x**n) - 2*a*b*x**n*log(a/b + x**n)/(a*b**3*n + b**4*n*x**n) + b**2*x**(2*n)/(a*b**3*n + b**4*n*x**n), True))","A",0
2626,1,95,0,99.174237," ","integrate(x**(-1+2*n)/(a+b*x**n)**2,x)","\begin{cases} \frac{\log{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \wedge n = 0 \\\frac{x^{2 n}}{2 a^{2} n} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{2}} & \text{for}\: n = 0 \\\frac{a \log{\left(\frac{a}{b} + x^{n} \right)}}{a b^{2} n + b^{3} n x^{n}} + \frac{a}{a b^{2} n + b^{3} n x^{n}} + \frac{b x^{n} \log{\left(\frac{a}{b} + x^{n} \right)}}{a b^{2} n + b^{3} n x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a**2, Eq(b, 0) & Eq(n, 0)), (x**(2*n)/(2*a**2*n), Eq(b, 0)), (log(x)/(a + b)**2, Eq(n, 0)), (a*log(a/b + x**n)/(a*b**2*n + b**3*n*x**n) + a/(a*b**2*n + b**3*n*x**n) + b*x**n*log(a/b + x**n)/(a*b**2*n + b**3*n*x**n), True))","A",0
2627,1,37,0,9.896439," ","integrate(x**(-1+n)/(a+b*x**n)**2,x)","\begin{cases} \frac{\log{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \wedge n = 0 \\\frac{x^{n}}{a^{2} n} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{2}} & \text{for}\: n = 0 \\- \frac{1}{a b n + b^{2} n x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a**2, Eq(b, 0) & Eq(n, 0)), (x**n/(a**2*n), Eq(b, 0)), (log(x)/(a + b)**2, Eq(n, 0)), (-1/(a*b*n + b**2*n*x**n), True))","A",0
2628,1,160,0,1.451464," ","integrate(1/x/(a+b*x**n)**2,x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\- \frac{x^{- 2 n}}{2 b^{2} n} & \text{for}\: a = 0 \\\tilde{\infty} \log{\left(x \right)} & \text{for}\: b = - a x^{- n} \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{2}} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \\\frac{a n \log{\left(x \right)}}{a^{3} n + a^{2} b n x^{n}} - \frac{a \log{\left(\frac{a}{b} + x^{n} \right)}}{a^{3} n + a^{2} b n x^{n}} + \frac{a}{a^{3} n + a^{2} b n x^{n}} + \frac{b n x^{n} \log{\left(x \right)}}{a^{3} n + a^{2} b n x^{n}} - \frac{b x^{n} \log{\left(\frac{a}{b} + x^{n} \right)}}{a^{3} n + a^{2} b n x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (-x**(-2*n)/(2*b**2*n), Eq(a, 0)), (zoo*log(x), Eq(b, -a*x**(-n))), (log(x)/(a + b)**2, Eq(n, 0)), (log(x)/a**2, Eq(b, 0)), (a*n*log(x)/(a**3*n + a**2*b*n*x**n) - a*log(a/b + x**n)/(a**3*n + a**2*b*n*x**n) + a/(a**3*n + a**2*b*n*x**n) + b*n*x**n*log(x)/(a**3*n + a**2*b*n*x**n) - b*x**n*log(a/b + x**n)/(a**3*n + a**2*b*n*x**n), True))","A",0
2629,1,172,0,125.743326," ","integrate(x**(-1-n)/(a+b*x**n)**2,x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\- \frac{x^{- 3 n}}{3 b^{2} n} & \text{for}\: a = 0 \\\frac{\tilde{\infty} x^{- n}}{n} & \text{for}\: b = - a x^{- n} \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{2}} & \text{for}\: n = 0 \\- \frac{a^{2}}{a^{4} n x^{n} + a^{3} b n x^{2 n}} + \frac{2 a b x^{n} \log{\left(x^{- n} + \frac{b}{a} \right)}}{a^{4} n x^{n} + a^{3} b n x^{2 n}} + \frac{2 b^{2} x^{2 n} \log{\left(x^{- n} + \frac{b}{a} \right)}}{a^{4} n x^{n} + a^{3} b n x^{2 n}} + \frac{2 b^{2} x^{2 n}}{a^{4} n x^{n} + a^{3} b n x^{2 n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (-x**(-3*n)/(3*b**2*n), Eq(a, 0)), (zoo*x**(-n)/n, Eq(b, -a*x**(-n))), (log(x)/(a + b)**2, Eq(n, 0)), (-a**2/(a**4*n*x**n + a**3*b*n*x**(2*n)) + 2*a*b*x**n*log(x**(-n) + b/a)/(a**4*n*x**n + a**3*b*n*x**(2*n)) + 2*b**2*x**(2*n)*log(x**(-n) + b/a)/(a**4*n*x**n + a**3*b*n*x**(2*n)) + 2*b**2*x**(2*n)/(a**4*n*x**n + a**3*b*n*x**(2*n)), True))","A",0
2630,-1,0,0,0.000000," ","integrate(x**(-1-2*n)/(a+b*x**n)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2631,-1,0,0,0.000000," ","integrate(x**(-1-3*n)/(a+b*x**n)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2632,-2,0,0,0.000000," ","integrate(x**(-1+4*n)/(a+b*x**n)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2633,-2,0,0,0.000000," ","integrate(x**(-1+3*n)/(a+b*x**n)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2634,1,61,0,158.688602," ","integrate(x**(-1+2*n)/(a+b*x**n)**3,x)","\begin{cases} \frac{\log{\left(x \right)}}{b^{3}} & \text{for}\: a = 0 \wedge n = 0 \\- \frac{x^{- n}}{b^{3} n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{3}} & \text{for}\: n = 0 \\\frac{x^{2 n}}{2 a^{3} n + 4 a^{2} b n x^{n} + 2 a b^{2} n x^{2 n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/b**3, Eq(a, 0) & Eq(n, 0)), (-x**(-n)/(b**3*n), Eq(a, 0)), (log(x)/(a + b)**3, Eq(n, 0)), (x**(2*n)/(2*a**3*n + 4*a**2*b*n*x**n + 2*a*b**2*n*x**(2*n)), True))","A",0
2635,1,56,0,30.215331," ","integrate(x**(-1+n)/(a+b*x**n)**3,x)","\begin{cases} \frac{\log{\left(x \right)}}{a^{3}} & \text{for}\: b = 0 \wedge n = 0 \\\frac{x^{n}}{a^{3} n} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{3}} & \text{for}\: n = 0 \\- \frac{1}{2 a^{2} b n + 4 a b^{2} n x^{n} + 2 b^{3} n x^{2 n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a**3, Eq(b, 0) & Eq(n, 0)), (x**n/(a**3*n), Eq(b, 0)), (log(x)/(a + b)**3, Eq(n, 0)), (-1/(2*a**2*b*n + 4*a*b**2*n*x**n + 2*b**3*n*x**(2*n)), True))","A",0
2636,1,406,0,2.671327," ","integrate(1/x/(a+b*x**n)**3,x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\- \frac{x^{- 3 n}}{3 b^{3} n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{3}} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{a^{3}} & \text{for}\: b = 0 \\\frac{2 a^{2} n \log{\left(x \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} - \frac{2 a^{2} \log{\left(\frac{a}{b} + x^{n} \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} + \frac{3 a^{2}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} + \frac{4 a b n x^{n} \log{\left(x \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} - \frac{4 a b x^{n} \log{\left(\frac{a}{b} + x^{n} \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} + \frac{2 a b x^{n}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} + \frac{2 b^{2} n x^{2 n} \log{\left(x \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} - \frac{2 b^{2} x^{2 n} \log{\left(\frac{a}{b} + x^{n} \right)}}{2 a^{5} n + 4 a^{4} b n x^{n} + 2 a^{3} b^{2} n x^{2 n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (-x**(-3*n)/(3*b**3*n), Eq(a, 0)), (log(x)/(a + b)**3, Eq(n, 0)), (log(x)/a**3, Eq(b, 0)), (2*a**2*n*log(x)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) - 2*a**2*log(a/b + x**n)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) + 3*a**2/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) + 4*a*b*n*x**n*log(x)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) - 4*a*b*x**n*log(a/b + x**n)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) + 2*a*b*x**n/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) + 2*b**2*n*x**(2*n)*log(x)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)) - 2*b**2*x**(2*n)*log(a/b + x**n)/(2*a**5*n + 4*a**4*b*n*x**n + 2*a**3*b**2*n*x**(2*n)), True))","A",0
2637,-2,0,0,0.000000," ","integrate(x**(-1-n)/(a+b*x**n)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2638,-1,0,0,0.000000," ","integrate(x**(-1-2*n)/(a+b*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2639,-1,0,0,0.000000," ","integrate(x**(-1-1/2*n)/(a+b*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2640,1,192,0,5.469959," ","integrate(x**(-1-2/3*n)/(a+b*x**n),x)","\frac{x^{- \frac{2 n}{3}} \Gamma\left(- \frac{2}{3}\right)}{a n \Gamma\left(\frac{1}{3}\right)} - \frac{2 b^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{2}{3}\right)}{3 a^{\frac{5}{3}} n \Gamma\left(\frac{1}{3}\right)} + \frac{2 b^{\frac{2}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{2}{3}\right)}{3 a^{\frac{5}{3}} n \Gamma\left(\frac{1}{3}\right)} - \frac{2 b^{\frac{2}{3}} e^{\frac{i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{2}{3}\right)}{3 a^{\frac{5}{3}} n \Gamma\left(\frac{1}{3}\right)}"," ",0,"x**(-2*n/3)*gamma(-2/3)/(a*n*gamma(1/3)) - 2*b**(2/3)*exp(-I*pi/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(-2/3)/(3*a**(5/3)*n*gamma(1/3)) + 2*b**(2/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(I*pi)/a**(1/3))*gamma(-2/3)/(3*a**(5/3)*n*gamma(1/3)) - 2*b**(2/3)*exp(I*pi/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(-2/3)/(3*a**(5/3)*n*gamma(1/3))","C",0
2641,1,267,0,5.728131," ","integrate(x**(-1-3/4*n)/(a+b*x**n),x)","\frac{x^{- \frac{3 n}{4}} \Gamma\left(- \frac{3}{4}\right)}{a n \Gamma\left(\frac{1}{4}\right)} - \frac{3 b^{\frac{3}{4}} e^{- \frac{i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{3}{4}\right)}{4 a^{\frac{7}{4}} n \Gamma\left(\frac{1}{4}\right)} + \frac{3 i b^{\frac{3}{4}} e^{- \frac{i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{3 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{3}{4}\right)}{4 a^{\frac{7}{4}} n \Gamma\left(\frac{1}{4}\right)} + \frac{3 b^{\frac{3}{4}} e^{- \frac{i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{5 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{3}{4}\right)}{4 a^{\frac{7}{4}} n \Gamma\left(\frac{1}{4}\right)} - \frac{3 i b^{\frac{3}{4}} e^{- \frac{i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{7 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{3}{4}\right)}{4 a^{\frac{7}{4}} n \Gamma\left(\frac{1}{4}\right)}"," ",0,"x**(-3*n/4)*gamma(-3/4)/(a*n*gamma(1/4)) - 3*b**(3/4)*exp(-I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(I*pi/4)/a**(1/4))*gamma(-3/4)/(4*a**(7/4)*n*gamma(1/4)) + 3*I*b**(3/4)*exp(-I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(3*I*pi/4)/a**(1/4))*gamma(-3/4)/(4*a**(7/4)*n*gamma(1/4)) + 3*b**(3/4)*exp(-I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(5*I*pi/4)/a**(1/4))*gamma(-3/4)/(4*a**(7/4)*n*gamma(1/4)) - 3*I*b**(3/4)*exp(-I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(7*I*pi/4)/a**(1/4))*gamma(-3/4)/(4*a**(7/4)*n*gamma(1/4))","C",0
2642,1,48,0,25.358835," ","integrate(x**(-1-n)/(a+b*x**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{b} & \text{for}\: a = 0 \wedge n = 0 \\- \frac{x^{- 2 n}}{2 b n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\- \frac{x^{- n}}{a n} + \frac{b \log{\left(x^{- n} + \frac{b}{a} \right)}}{a^{2} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/b, Eq(a, 0) & Eq(n, 0)), (-x**(-2*n)/(2*b*n), Eq(a, 0)), (log(x)/(a + b), Eq(n, 0)), (-x**(-n)/(a*n) + b*log(x**(-n) + b/a)/(a**2*n), True))","A",0
2643,-1,0,0,0.000000," ","integrate(x**(-1-1/2*n)/(a+b*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2644,-1,0,0,0.000000," ","integrate(x**(-1-1/3*n)/(a+b*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2645,-1,0,0,0.000000," ","integrate(x**(-1-1/4*n)/(a+b*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2646,1,56,0,4.656259," ","integrate(x**(-1-3/2*n)/(a+b*x**n),x)","- \frac{2 x^{- \frac{3 n}{2}}}{3 a n} + \frac{2 b x^{- \frac{n}{2}}}{a^{2} n} + \frac{2 b^{\frac{3}{2}} \operatorname{atan}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{a^{\frac{5}{2}} n}"," ",0,"-2*x**(-3*n/2)/(3*a*n) + 2*b*x**(-n/2)/(a**2*n) + 2*b**(3/2)*atan(sqrt(b)*x**(n/2)/sqrt(a))/(a**(5/2)*n)","A",0
2647,1,230,0,4.341057," ","integrate(x**(-1-4/3*n)/(a+b*x**n),x)","\frac{x^{- \frac{4 n}{3}} \Gamma\left(- \frac{4}{3}\right)}{a n \Gamma\left(- \frac{1}{3}\right)} - \frac{4 b x^{- \frac{n}{3}} \Gamma\left(- \frac{4}{3}\right)}{a^{2} n \Gamma\left(- \frac{1}{3}\right)} + \frac{4 b^{\frac{4}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{4}{3}\right)}{3 a^{\frac{7}{3}} n \Gamma\left(- \frac{1}{3}\right)} + \frac{4 b^{\frac{4}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{4}{3}\right)}{3 a^{\frac{7}{3}} n \Gamma\left(- \frac{1}{3}\right)} + \frac{4 b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{4}{3}\right)}{3 a^{\frac{7}{3}} n \Gamma\left(- \frac{1}{3}\right)}"," ",0,"x**(-4*n/3)*gamma(-4/3)/(a*n*gamma(-1/3)) - 4*b*x**(-n/3)*gamma(-4/3)/(a**2*n*gamma(-1/3)) + 4*b**(4/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(-4/3)/(3*a**(7/3)*n*gamma(-1/3)) + 4*b**(4/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(I*pi)/a**(1/3))*gamma(-4/3)/(3*a**(7/3)*n*gamma(-1/3)) + 4*b**(4/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(-4/3)/(3*a**(7/3)*n*gamma(-1/3))","C",0
2648,1,309,0,4.749132," ","integrate(x**(-1-5/4*n)/(a+b*x**n),x)","\frac{x^{- \frac{5 n}{4}} \Gamma\left(- \frac{5}{4}\right)}{a n \Gamma\left(- \frac{1}{4}\right)} - \frac{5 b x^{- \frac{n}{4}} \Gamma\left(- \frac{5}{4}\right)}{a^{2} n \Gamma\left(- \frac{1}{4}\right)} + \frac{5 b^{\frac{5}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{5}{4}\right)}{4 a^{\frac{9}{4}} n \Gamma\left(- \frac{1}{4}\right)} + \frac{5 i b^{\frac{5}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{3 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{5}{4}\right)}{4 a^{\frac{9}{4}} n \Gamma\left(- \frac{1}{4}\right)} - \frac{5 b^{\frac{5}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{5 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{5}{4}\right)}{4 a^{\frac{9}{4}} n \Gamma\left(- \frac{1}{4}\right)} - \frac{5 i b^{\frac{5}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{7 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{5}{4}\right)}{4 a^{\frac{9}{4}} n \Gamma\left(- \frac{1}{4}\right)}"," ",0,"x**(-5*n/4)*gamma(-5/4)/(a*n*gamma(-1/4)) - 5*b*x**(-n/4)*gamma(-5/4)/(a**2*n*gamma(-1/4)) + 5*b**(5/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(I*pi/4)/a**(1/4))*gamma(-5/4)/(4*a**(9/4)*n*gamma(-1/4)) + 5*I*b**(5/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(3*I*pi/4)/a**(1/4))*gamma(-5/4)/(4*a**(9/4)*n*gamma(-1/4)) - 5*b**(5/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(5*I*pi/4)/a**(1/4))*gamma(-5/4)/(4*a**(9/4)*n*gamma(-1/4)) - 5*I*b**(5/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(7*I*pi/4)/a**(1/4))*gamma(-5/4)/(4*a**(9/4)*n*gamma(-1/4))","C",0
2649,1,2572,0,36.971732," ","integrate(x**(-1+4*n)*(a+b*x**n)**(1/2),x)","- \frac{32 a^{\frac{29}{2}} b^{\frac{23}{2}} x^{\frac{23 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} - \frac{176 a^{\frac{27}{2}} b^{\frac{25}{2}} x^{\frac{25 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} - \frac{396 a^{\frac{25}{2}} b^{\frac{27}{2}} x^{\frac{27 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} - \frac{462 a^{\frac{23}{2}} b^{\frac{29}{2}} x^{\frac{29 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} - \frac{210 a^{\frac{21}{2}} b^{\frac{31}{2}} x^{\frac{31 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{378 a^{\frac{19}{2}} b^{\frac{33}{2}} x^{\frac{33 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{1134 a^{\frac{17}{2}} b^{\frac{35}{2}} x^{\frac{35 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{1494 a^{\frac{15}{2}} b^{\frac{37}{2}} x^{\frac{37 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{1098 a^{\frac{13}{2}} b^{\frac{39}{2}} x^{\frac{39 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{430 a^{\frac{11}{2}} b^{\frac{41}{2}} x^{\frac{41 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{70 a^{\frac{9}{2}} b^{\frac{43}{2}} x^{\frac{43 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{32 a^{15} b^{11} x^{11 n}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{192 a^{14} b^{12} x^{12 n}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{480 a^{13} b^{13} x^{13 n}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{640 a^{12} b^{14} x^{14 n}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{480 a^{11} b^{15} x^{15 n}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{192 a^{10} b^{16} x^{16 n}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}} + \frac{32 a^{9} b^{17} x^{17 n}}{315 a^{\frac{21}{2}} b^{15} n x^{11 n} + 1890 a^{\frac{19}{2}} b^{16} n x^{12 n} + 4725 a^{\frac{17}{2}} b^{17} n x^{13 n} + 6300 a^{\frac{15}{2}} b^{18} n x^{14 n} + 4725 a^{\frac{13}{2}} b^{19} n x^{15 n} + 1890 a^{\frac{11}{2}} b^{20} n x^{16 n} + 315 a^{\frac{9}{2}} b^{21} n x^{17 n}}"," ",0,"-32*a**(29/2)*b**(23/2)*x**(23*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) - 176*a**(27/2)*b**(25/2)*x**(25*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) - 396*a**(25/2)*b**(27/2)*x**(27*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) - 462*a**(23/2)*b**(29/2)*x**(29*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) - 210*a**(21/2)*b**(31/2)*x**(31*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 378*a**(19/2)*b**(33/2)*x**(33*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 1134*a**(17/2)*b**(35/2)*x**(35*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 1494*a**(15/2)*b**(37/2)*x**(37*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 1098*a**(13/2)*b**(39/2)*x**(39*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 430*a**(11/2)*b**(41/2)*x**(41*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 70*a**(9/2)*b**(43/2)*x**(43*n/2)*sqrt(a*x**(-n)/b + 1)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 32*a**15*b**11*x**(11*n)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 192*a**14*b**12*x**(12*n)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 480*a**13*b**13*x**(13*n)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 640*a**12*b**14*x**(14*n)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 480*a**11*b**15*x**(15*n)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 192*a**10*b**16*x**(16*n)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n)) + 32*a**9*b**17*x**(17*n)/(315*a**(21/2)*b**15*n*x**(11*n) + 1890*a**(19/2)*b**16*n*x**(12*n) + 4725*a**(17/2)*b**17*n*x**(13*n) + 6300*a**(15/2)*b**18*n*x**(14*n) + 4725*a**(13/2)*b**19*n*x**(15*n) + 1890*a**(11/2)*b**20*n*x**(16*n) + 315*a**(9/2)*b**21*n*x**(17*n))","B",0
2650,1,1015,0,21.957811," ","integrate(x**(-1+3*n)*(a+b*x**n)**(1/2),x)","\frac{16 a^{\frac{19}{2}} b^{\frac{9}{2}} x^{\frac{9 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}} + \frac{40 a^{\frac{17}{2}} b^{\frac{11}{2}} x^{\frac{11 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}} + \frac{30 a^{\frac{15}{2}} b^{\frac{13}{2}} x^{\frac{13 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}} + \frac{40 a^{\frac{13}{2}} b^{\frac{15}{2}} x^{\frac{15 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}} + \frac{100 a^{\frac{11}{2}} b^{\frac{17}{2}} x^{\frac{17 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}} + \frac{96 a^{\frac{9}{2}} b^{\frac{19}{2}} x^{\frac{19 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}} + \frac{30 a^{\frac{7}{2}} b^{\frac{21}{2}} x^{\frac{21 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}} - \frac{16 a^{10} b^{4} x^{4 n}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}} - \frac{48 a^{9} b^{5} x^{5 n}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}} - \frac{48 a^{8} b^{6} x^{6 n}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}} - \frac{16 a^{7} b^{7} x^{7 n}}{105 a^{\frac{13}{2}} b^{7} n x^{4 n} + 315 a^{\frac{11}{2}} b^{8} n x^{5 n} + 315 a^{\frac{9}{2}} b^{9} n x^{6 n} + 105 a^{\frac{7}{2}} b^{10} n x^{7 n}}"," ",0,"16*a**(19/2)*b**(9/2)*x**(9*n/2)*sqrt(a*x**(-n)/b + 1)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n)) + 40*a**(17/2)*b**(11/2)*x**(11*n/2)*sqrt(a*x**(-n)/b + 1)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n)) + 30*a**(15/2)*b**(13/2)*x**(13*n/2)*sqrt(a*x**(-n)/b + 1)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n)) + 40*a**(13/2)*b**(15/2)*x**(15*n/2)*sqrt(a*x**(-n)/b + 1)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n)) + 100*a**(11/2)*b**(17/2)*x**(17*n/2)*sqrt(a*x**(-n)/b + 1)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n)) + 96*a**(9/2)*b**(19/2)*x**(19*n/2)*sqrt(a*x**(-n)/b + 1)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n)) + 30*a**(7/2)*b**(21/2)*x**(21*n/2)*sqrt(a*x**(-n)/b + 1)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n)) - 16*a**10*b**4*x**(4*n)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n)) - 48*a**9*b**5*x**(5*n)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n)) - 48*a**8*b**6*x**(6*n)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n)) - 16*a**7*b**7*x**(7*n)/(105*a**(13/2)*b**7*n*x**(4*n) + 315*a**(11/2)*b**8*n*x**(5*n) + 315*a**(9/2)*b**9*n*x**(6*n) + 105*a**(7/2)*b**10*n*x**(7*n))","B",0
2651,1,338,0,13.986360," ","integrate(x**(-1+2*n)*(a+b*x**n)**(1/2),x)","- \frac{4 a^{\frac{11}{2}} b^{\frac{3}{2}} x^{\frac{3 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} n x^{n} + 15 a^{\frac{5}{2}} b^{4} n x^{2 n}} - \frac{2 a^{\frac{9}{2}} b^{\frac{5}{2}} x^{\frac{5 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} n x^{n} + 15 a^{\frac{5}{2}} b^{4} n x^{2 n}} + \frac{8 a^{\frac{7}{2}} b^{\frac{7}{2}} x^{\frac{7 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} n x^{n} + 15 a^{\frac{5}{2}} b^{4} n x^{2 n}} + \frac{6 a^{\frac{5}{2}} b^{\frac{9}{2}} x^{\frac{9 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{\frac{7}{2}} b^{3} n x^{n} + 15 a^{\frac{5}{2}} b^{4} n x^{2 n}} + \frac{4 a^{6} b x^{n}}{15 a^{\frac{7}{2}} b^{3} n x^{n} + 15 a^{\frac{5}{2}} b^{4} n x^{2 n}} + \frac{4 a^{5} b^{2} x^{2 n}}{15 a^{\frac{7}{2}} b^{3} n x^{n} + 15 a^{\frac{5}{2}} b^{4} n x^{2 n}}"," ",0,"-4*a**(11/2)*b**(3/2)*x**(3*n/2)*sqrt(a*x**(-n)/b + 1)/(15*a**(7/2)*b**3*n*x**n + 15*a**(5/2)*b**4*n*x**(2*n)) - 2*a**(9/2)*b**(5/2)*x**(5*n/2)*sqrt(a*x**(-n)/b + 1)/(15*a**(7/2)*b**3*n*x**n + 15*a**(5/2)*b**4*n*x**(2*n)) + 8*a**(7/2)*b**(7/2)*x**(7*n/2)*sqrt(a*x**(-n)/b + 1)/(15*a**(7/2)*b**3*n*x**n + 15*a**(5/2)*b**4*n*x**(2*n)) + 6*a**(5/2)*b**(9/2)*x**(9*n/2)*sqrt(a*x**(-n)/b + 1)/(15*a**(7/2)*b**3*n*x**n + 15*a**(5/2)*b**4*n*x**(2*n)) + 4*a**6*b*x**n/(15*a**(7/2)*b**3*n*x**n + 15*a**(5/2)*b**4*n*x**(2*n)) + 4*a**5*b**2*x**(2*n)/(15*a**(7/2)*b**3*n*x**n + 15*a**(5/2)*b**4*n*x**(2*n))","B",0
2652,1,48,0,2.661009," ","integrate(x**(-1+n)*(a+b*x**n)**(1/2),x)","\frac{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{n}}{a}}}{3 b n} + \frac{2 \sqrt{a} x^{n} \sqrt{1 + \frac{b x^{n}}{a}}}{3 n}"," ",0,"2*a**(3/2)*sqrt(1 + b*x**n/a)/(3*b*n) + 2*sqrt(a)*x**n*sqrt(1 + b*x**n/a)/(3*n)","B",0
2653,1,76,0,1.663712," ","integrate((a+b*x**n)**(1/2)/x,x)","- \frac{2 \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a} x^{- \frac{n}{2}}}{\sqrt{b}} \right)}}{n} + \frac{2 a x^{- \frac{n}{2}}}{\sqrt{b} n \sqrt{\frac{a x^{- n}}{b} + 1}} + \frac{2 \sqrt{b} x^{\frac{n}{2}}}{n \sqrt{\frac{a x^{- n}}{b} + 1}}"," ",0,"-2*sqrt(a)*asinh(sqrt(a)*x**(-n/2)/sqrt(b))/n + 2*a*x**(-n/2)/(sqrt(b)*n*sqrt(a*x**(-n)/b + 1)) + 2*sqrt(b)*x**(n/2)/(n*sqrt(a*x**(-n)/b + 1))","B",0
2654,1,49,0,25.075257," ","integrate(x**(-1-n)*(a+b*x**n)**(1/2),x)","- \frac{\sqrt{b} x^{- \frac{n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{n} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} x^{- \frac{n}{2}}}{\sqrt{b}} \right)}}{\sqrt{a} n}"," ",0,"-sqrt(b)*x**(-n/2)*sqrt(a*x**(-n)/b + 1)/n - b*asinh(sqrt(a)*x**(-n/2)/sqrt(b))/(sqrt(a)*n)","A",0
2655,1,112,0,54.197243," ","integrate(x**(-1-2*n)*(a+b*x**n)**(1/2),x)","- \frac{a x^{- \frac{5 n}{2}}}{2 \sqrt{b} n \sqrt{\frac{a x^{- n}}{b} + 1}} - \frac{3 \sqrt{b} x^{- \frac{3 n}{2}}}{4 n \sqrt{\frac{a x^{- n}}{b} + 1}} - \frac{b^{\frac{3}{2}} x^{- \frac{n}{2}}}{4 a n \sqrt{\frac{a x^{- n}}{b} + 1}} + \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x^{- \frac{n}{2}}}{\sqrt{b}} \right)}}{4 a^{\frac{3}{2}} n}"," ",0,"-a*x**(-5*n/2)/(2*sqrt(b)*n*sqrt(a*x**(-n)/b + 1)) - 3*sqrt(b)*x**(-3*n/2)/(4*n*sqrt(a*x**(-n)/b + 1)) - b**(3/2)*x**(-n/2)/(4*a*n*sqrt(a*x**(-n)/b + 1)) + b**2*asinh(sqrt(a)*x**(-n/2)/sqrt(b))/(4*a**(3/2)*n)","A",0
2656,-1,0,0,0.000000," ","integrate(x**(-1-3*n)*(a+b*x**n)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2657,-1,0,0,0.000000," ","integrate(x**(-1-4*n)*(a+b*x**n)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2658,1,2422,0,28.397611," ","integrate(x**(-1+4*n)/(a+b*x**n)**(1/2),x)","- \frac{32 a^{\frac{25}{2}} b^{\frac{23}{2}} x^{\frac{23 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} - \frac{176 a^{\frac{23}{2}} b^{\frac{25}{2}} x^{\frac{25 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} - \frac{396 a^{\frac{21}{2}} b^{\frac{27}{2}} x^{\frac{27 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} - \frac{462 a^{\frac{19}{2}} b^{\frac{29}{2}} x^{\frac{29 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} - \frac{280 a^{\frac{17}{2}} b^{\frac{31}{2}} x^{\frac{31 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} - \frac{42 a^{\frac{15}{2}} b^{\frac{33}{2}} x^{\frac{33 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{84 a^{\frac{13}{2}} b^{\frac{35}{2}} x^{\frac{35 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{94 a^{\frac{11}{2}} b^{\frac{37}{2}} x^{\frac{37 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{48 a^{\frac{9}{2}} b^{\frac{39}{2}} x^{\frac{39 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{10 a^{\frac{7}{2}} b^{\frac{41}{2}} x^{\frac{41 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{32 a^{13} b^{11} x^{11 n}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{192 a^{12} b^{12} x^{12 n}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{480 a^{11} b^{13} x^{13 n}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{640 a^{10} b^{14} x^{14 n}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{480 a^{9} b^{15} x^{15 n}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{192 a^{8} b^{16} x^{16 n}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}} + \frac{32 a^{7} b^{17} x^{17 n}}{35 a^{\frac{19}{2}} b^{15} n x^{11 n} + 210 a^{\frac{17}{2}} b^{16} n x^{12 n} + 525 a^{\frac{15}{2}} b^{17} n x^{13 n} + 700 a^{\frac{13}{2}} b^{18} n x^{14 n} + 525 a^{\frac{11}{2}} b^{19} n x^{15 n} + 210 a^{\frac{9}{2}} b^{20} n x^{16 n} + 35 a^{\frac{7}{2}} b^{21} n x^{17 n}}"," ",0,"-32*a**(25/2)*b**(23/2)*x**(23*n/2)*sqrt(a*x**(-n)/b + 1)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) - 176*a**(23/2)*b**(25/2)*x**(25*n/2)*sqrt(a*x**(-n)/b + 1)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) - 396*a**(21/2)*b**(27/2)*x**(27*n/2)*sqrt(a*x**(-n)/b + 1)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) - 462*a**(19/2)*b**(29/2)*x**(29*n/2)*sqrt(a*x**(-n)/b + 1)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) - 280*a**(17/2)*b**(31/2)*x**(31*n/2)*sqrt(a*x**(-n)/b + 1)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) - 42*a**(15/2)*b**(33/2)*x**(33*n/2)*sqrt(a*x**(-n)/b + 1)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 84*a**(13/2)*b**(35/2)*x**(35*n/2)*sqrt(a*x**(-n)/b + 1)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 94*a**(11/2)*b**(37/2)*x**(37*n/2)*sqrt(a*x**(-n)/b + 1)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 48*a**(9/2)*b**(39/2)*x**(39*n/2)*sqrt(a*x**(-n)/b + 1)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 10*a**(7/2)*b**(41/2)*x**(41*n/2)*sqrt(a*x**(-n)/b + 1)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 32*a**13*b**11*x**(11*n)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 192*a**12*b**12*x**(12*n)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 480*a**11*b**13*x**(13*n)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 640*a**10*b**14*x**(14*n)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 480*a**9*b**15*x**(15*n)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 192*a**8*b**16*x**(16*n)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n)) + 32*a**7*b**17*x**(17*n)/(35*a**(19/2)*b**15*n*x**(11*n) + 210*a**(17/2)*b**16*n*x**(12*n) + 525*a**(15/2)*b**17*n*x**(13*n) + 700*a**(13/2)*b**18*n*x**(14*n) + 525*a**(11/2)*b**19*n*x**(15*n) + 210*a**(9/2)*b**20*n*x**(16*n) + 35*a**(7/2)*b**21*n*x**(17*n))","B",0
2659,1,916,0,16.534204," ","integrate(x**(-1+3*n)/(a+b*x**n)**(1/2),x)","\frac{16 a^{\frac{15}{2}} b^{\frac{9}{2}} x^{\frac{9 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} n x^{4 n} + 45 a^{\frac{9}{2}} b^{8} n x^{5 n} + 45 a^{\frac{7}{2}} b^{9} n x^{6 n} + 15 a^{\frac{5}{2}} b^{10} n x^{7 n}} + \frac{40 a^{\frac{13}{2}} b^{\frac{11}{2}} x^{\frac{11 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} n x^{4 n} + 45 a^{\frac{9}{2}} b^{8} n x^{5 n} + 45 a^{\frac{7}{2}} b^{9} n x^{6 n} + 15 a^{\frac{5}{2}} b^{10} n x^{7 n}} + \frac{30 a^{\frac{11}{2}} b^{\frac{13}{2}} x^{\frac{13 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} n x^{4 n} + 45 a^{\frac{9}{2}} b^{8} n x^{5 n} + 45 a^{\frac{7}{2}} b^{9} n x^{6 n} + 15 a^{\frac{5}{2}} b^{10} n x^{7 n}} + \frac{10 a^{\frac{9}{2}} b^{\frac{15}{2}} x^{\frac{15 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} n x^{4 n} + 45 a^{\frac{9}{2}} b^{8} n x^{5 n} + 45 a^{\frac{7}{2}} b^{9} n x^{6 n} + 15 a^{\frac{5}{2}} b^{10} n x^{7 n}} + \frac{10 a^{\frac{7}{2}} b^{\frac{17}{2}} x^{\frac{17 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} n x^{4 n} + 45 a^{\frac{9}{2}} b^{8} n x^{5 n} + 45 a^{\frac{7}{2}} b^{9} n x^{6 n} + 15 a^{\frac{5}{2}} b^{10} n x^{7 n}} + \frac{6 a^{\frac{5}{2}} b^{\frac{19}{2}} x^{\frac{19 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{\frac{11}{2}} b^{7} n x^{4 n} + 45 a^{\frac{9}{2}} b^{8} n x^{5 n} + 45 a^{\frac{7}{2}} b^{9} n x^{6 n} + 15 a^{\frac{5}{2}} b^{10} n x^{7 n}} - \frac{16 a^{8} b^{4} x^{4 n}}{15 a^{\frac{11}{2}} b^{7} n x^{4 n} + 45 a^{\frac{9}{2}} b^{8} n x^{5 n} + 45 a^{\frac{7}{2}} b^{9} n x^{6 n} + 15 a^{\frac{5}{2}} b^{10} n x^{7 n}} - \frac{48 a^{7} b^{5} x^{5 n}}{15 a^{\frac{11}{2}} b^{7} n x^{4 n} + 45 a^{\frac{9}{2}} b^{8} n x^{5 n} + 45 a^{\frac{7}{2}} b^{9} n x^{6 n} + 15 a^{\frac{5}{2}} b^{10} n x^{7 n}} - \frac{48 a^{6} b^{6} x^{6 n}}{15 a^{\frac{11}{2}} b^{7} n x^{4 n} + 45 a^{\frac{9}{2}} b^{8} n x^{5 n} + 45 a^{\frac{7}{2}} b^{9} n x^{6 n} + 15 a^{\frac{5}{2}} b^{10} n x^{7 n}} - \frac{16 a^{5} b^{7} x^{7 n}}{15 a^{\frac{11}{2}} b^{7} n x^{4 n} + 45 a^{\frac{9}{2}} b^{8} n x^{5 n} + 45 a^{\frac{7}{2}} b^{9} n x^{6 n} + 15 a^{\frac{5}{2}} b^{10} n x^{7 n}}"," ",0,"16*a**(15/2)*b**(9/2)*x**(9*n/2)*sqrt(a*x**(-n)/b + 1)/(15*a**(11/2)*b**7*n*x**(4*n) + 45*a**(9/2)*b**8*n*x**(5*n) + 45*a**(7/2)*b**9*n*x**(6*n) + 15*a**(5/2)*b**10*n*x**(7*n)) + 40*a**(13/2)*b**(11/2)*x**(11*n/2)*sqrt(a*x**(-n)/b + 1)/(15*a**(11/2)*b**7*n*x**(4*n) + 45*a**(9/2)*b**8*n*x**(5*n) + 45*a**(7/2)*b**9*n*x**(6*n) + 15*a**(5/2)*b**10*n*x**(7*n)) + 30*a**(11/2)*b**(13/2)*x**(13*n/2)*sqrt(a*x**(-n)/b + 1)/(15*a**(11/2)*b**7*n*x**(4*n) + 45*a**(9/2)*b**8*n*x**(5*n) + 45*a**(7/2)*b**9*n*x**(6*n) + 15*a**(5/2)*b**10*n*x**(7*n)) + 10*a**(9/2)*b**(15/2)*x**(15*n/2)*sqrt(a*x**(-n)/b + 1)/(15*a**(11/2)*b**7*n*x**(4*n) + 45*a**(9/2)*b**8*n*x**(5*n) + 45*a**(7/2)*b**9*n*x**(6*n) + 15*a**(5/2)*b**10*n*x**(7*n)) + 10*a**(7/2)*b**(17/2)*x**(17*n/2)*sqrt(a*x**(-n)/b + 1)/(15*a**(11/2)*b**7*n*x**(4*n) + 45*a**(9/2)*b**8*n*x**(5*n) + 45*a**(7/2)*b**9*n*x**(6*n) + 15*a**(5/2)*b**10*n*x**(7*n)) + 6*a**(5/2)*b**(19/2)*x**(19*n/2)*sqrt(a*x**(-n)/b + 1)/(15*a**(11/2)*b**7*n*x**(4*n) + 45*a**(9/2)*b**8*n*x**(5*n) + 45*a**(7/2)*b**9*n*x**(6*n) + 15*a**(5/2)*b**10*n*x**(7*n)) - 16*a**8*b**4*x**(4*n)/(15*a**(11/2)*b**7*n*x**(4*n) + 45*a**(9/2)*b**8*n*x**(5*n) + 45*a**(7/2)*b**9*n*x**(6*n) + 15*a**(5/2)*b**10*n*x**(7*n)) - 48*a**7*b**5*x**(5*n)/(15*a**(11/2)*b**7*n*x**(4*n) + 45*a**(9/2)*b**8*n*x**(5*n) + 45*a**(7/2)*b**9*n*x**(6*n) + 15*a**(5/2)*b**10*n*x**(7*n)) - 48*a**6*b**6*x**(6*n)/(15*a**(11/2)*b**7*n*x**(4*n) + 45*a**(9/2)*b**8*n*x**(5*n) + 45*a**(7/2)*b**9*n*x**(6*n) + 15*a**(5/2)*b**10*n*x**(7*n)) - 16*a**5*b**7*x**(7*n)/(15*a**(11/2)*b**7*n*x**(4*n) + 45*a**(9/2)*b**8*n*x**(5*n) + 45*a**(7/2)*b**9*n*x**(6*n) + 15*a**(5/2)*b**10*n*x**(7*n))","B",0
2660,1,275,0,9.484772," ","integrate(x**(-1+2*n)/(a+b*x**n)**(1/2),x)","- \frac{4 a^{\frac{7}{2}} b^{\frac{3}{2}} x^{\frac{3 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} n x^{n} + 3 a^{\frac{3}{2}} b^{4} n x^{2 n}} - \frac{2 a^{\frac{5}{2}} b^{\frac{5}{2}} x^{\frac{5 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} n x^{n} + 3 a^{\frac{3}{2}} b^{4} n x^{2 n}} + \frac{2 a^{\frac{3}{2}} b^{\frac{7}{2}} x^{\frac{7 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{3 a^{\frac{5}{2}} b^{3} n x^{n} + 3 a^{\frac{3}{2}} b^{4} n x^{2 n}} + \frac{4 a^{4} b x^{n}}{3 a^{\frac{5}{2}} b^{3} n x^{n} + 3 a^{\frac{3}{2}} b^{4} n x^{2 n}} + \frac{4 a^{3} b^{2} x^{2 n}}{3 a^{\frac{5}{2}} b^{3} n x^{n} + 3 a^{\frac{3}{2}} b^{4} n x^{2 n}}"," ",0,"-4*a**(7/2)*b**(3/2)*x**(3*n/2)*sqrt(a*x**(-n)/b + 1)/(3*a**(5/2)*b**3*n*x**n + 3*a**(3/2)*b**4*n*x**(2*n)) - 2*a**(5/2)*b**(5/2)*x**(5*n/2)*sqrt(a*x**(-n)/b + 1)/(3*a**(5/2)*b**3*n*x**n + 3*a**(3/2)*b**4*n*x**(2*n)) + 2*a**(3/2)*b**(7/2)*x**(7*n/2)*sqrt(a*x**(-n)/b + 1)/(3*a**(5/2)*b**3*n*x**n + 3*a**(3/2)*b**4*n*x**(2*n)) + 4*a**4*b*x**n/(3*a**(5/2)*b**3*n*x**n + 3*a**(3/2)*b**4*n*x**(2*n)) + 4*a**3*b**2*x**(2*n)/(3*a**(5/2)*b**3*n*x**n + 3*a**(3/2)*b**4*n*x**(2*n))","B",0
2661,1,41,0,7.714685," ","integrate(x**(-1+n)/(a+b*x**n)**(1/2),x)","\begin{cases} \frac{\log{\left(x \right)}}{\sqrt{a}} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{\sqrt{a + b}} & \text{for}\: n = 0 \\\frac{x^{n}}{\sqrt{a} n} & \text{for}\: b = 0 \\\frac{2 \sqrt{a + b x^{n}}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/sqrt(a), Eq(b, 0) & Eq(n, 0)), (log(x)/sqrt(a + b), Eq(n, 0)), (x**n/(sqrt(a)*n), Eq(b, 0)), (2*sqrt(a + b*x**n)/(b*n), True))","A",0
2662,1,26,0,1.695918," ","integrate(1/x/(a+b*x**n)**(1/2),x)","- \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{a} x^{- \frac{n}{2}}}{\sqrt{b}} \right)}}{\sqrt{a} n}"," ",0,"-2*asinh(sqrt(a)*x**(-n/2)/sqrt(b))/(sqrt(a)*n)","A",0
2663,1,49,0,39.241244," ","integrate(x**(-1-n)/(a+b*x**n)**(1/2),x)","- \frac{\sqrt{b} x^{- \frac{n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{a n} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a} x^{- \frac{n}{2}}}{\sqrt{b}} \right)}}{a^{\frac{3}{2}} n}"," ",0,"-sqrt(b)*x**(-n/2)*sqrt(a*x**(-n)/b + 1)/(a*n) + b*asinh(sqrt(a)*x**(-n/2)/sqrt(b))/(a**(3/2)*n)","A",0
2664,1,117,0,85.035102," ","integrate(x**(-1-2*n)/(a+b*x**n)**(1/2),x)","- \frac{x^{- \frac{5 n}{2}}}{2 \sqrt{b} n \sqrt{\frac{a x^{- n}}{b} + 1}} + \frac{\sqrt{b} x^{- \frac{3 n}{2}}}{4 a n \sqrt{\frac{a x^{- n}}{b} + 1}} + \frac{3 b^{\frac{3}{2}} x^{- \frac{n}{2}}}{4 a^{2} n \sqrt{\frac{a x^{- n}}{b} + 1}} - \frac{3 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a} x^{- \frac{n}{2}}}{\sqrt{b}} \right)}}{4 a^{\frac{5}{2}} n}"," ",0,"-x**(-5*n/2)/(2*sqrt(b)*n*sqrt(a*x**(-n)/b + 1)) + sqrt(b)*x**(-3*n/2)/(4*a*n*sqrt(a*x**(-n)/b + 1)) + 3*b**(3/2)*x**(-n/2)/(4*a**2*n*sqrt(a*x**(-n)/b + 1)) - 3*b**2*asinh(sqrt(a)*x**(-n/2)/sqrt(b))/(4*a**(5/2)*n)","A",0
2665,-1,0,0,0.000000," ","integrate(x**(-1-3*n)/(a+b*x**n)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2666,-1,0,0,0.000000," ","integrate(x**(-1-4*n)/(a+b*x**n)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2667,-1,0,0,0.000000," ","integrate(x**m*(a+b*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2668,1,1280,0,59.344018," ","integrate(x**m*(a+b*x**n)**2,x)","\begin{cases} \left(a + b\right)^{2} \log{\left(x \right)} & \text{for}\: m = -1 \wedge n = 0 \\a^{2} \log{\left(x \right)} + \frac{2 a b x^{n}}{n} + \frac{b^{2} x^{2 n}}{2 n} & \text{for}\: m = -1 \\- \frac{2 a^{2} n}{4 n^{2} x^{2 n} + 2 n x^{2 n}} - \frac{a^{2}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} - \frac{8 a b n x^{n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} - \frac{4 a b x^{n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{4 b^{2} n^{2} x^{2 n} \log{\left(x \right)}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{2 b^{2} n x^{2 n} \log{\left(x \right)}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} + \frac{2 b^{2} n x^{2 n}}{4 n^{2} x^{2 n} + 2 n x^{2 n}} & \text{for}\: m = - 2 n - 1 \\- \frac{a^{2} n}{n^{2} x^{n} + n x^{n}} - \frac{a^{2}}{n^{2} x^{n} + n x^{n}} + \frac{2 a b n^{2} x^{n} \log{\left(x \right)}}{n^{2} x^{n} + n x^{n}} + \frac{2 a b n x^{n} \log{\left(x \right)}}{n^{2} x^{n} + n x^{n}} + \frac{2 a b n x^{n}}{n^{2} x^{n} + n x^{n}} + \frac{b^{2} n x^{2 n}}{n^{2} x^{n} + n x^{n}} + \frac{b^{2} x^{2 n}}{n^{2} x^{n} + n x^{n}} & \text{for}\: m = - n - 1 \\\frac{a^{2} 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^{2} 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^{2} 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^{2} 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^{2} 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^{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{2 a b 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{4 a b 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{4 a b 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{4 a b 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 a b 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^{2} 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{b^{2} 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 b^{2} 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{b^{2} 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{b^{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} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a + b)**2*log(x), Eq(m, -1) & Eq(n, 0)), (a**2*log(x) + 2*a*b*x**n/n + b**2*x**(2*n)/(2*n), Eq(m, -1)), (-2*a**2*n/(4*n**2*x**(2*n) + 2*n*x**(2*n)) - a**2/(4*n**2*x**(2*n) + 2*n*x**(2*n)) - 8*a*b*n*x**n/(4*n**2*x**(2*n) + 2*n*x**(2*n)) - 4*a*b*x**n/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 4*b**2*n**2*x**(2*n)*log(x)/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 2*b**2*n*x**(2*n)*log(x)/(4*n**2*x**(2*n) + 2*n*x**(2*n)) + 2*b**2*n*x**(2*n)/(4*n**2*x**(2*n) + 2*n*x**(2*n)), Eq(m, -2*n - 1)), (-a**2*n/(n**2*x**n + n*x**n) - a**2/(n**2*x**n + n*x**n) + 2*a*b*n**2*x**n*log(x)/(n**2*x**n + n*x**n) + 2*a*b*n*x**n*log(x)/(n**2*x**n + n*x**n) + 2*a*b*n*x**n/(n**2*x**n + n*x**n) + b**2*n*x**(2*n)/(n**2*x**n + n*x**n) + b**2*x**(2*n)/(n**2*x**n + n*x**n), Eq(m, -n - 1)), (a**2*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**2*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**2*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**2*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**2*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**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) + 2*a*b*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) + 4*a*b*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) + 4*a*b*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) + 4*a*b*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*a*b*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**2*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) + b**2*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*b**2*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) + b**2*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) + b**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), True))","A",0
2669,1,175,0,3.420619," ","integrate(x**m*(a+b*x**n),x)","\begin{cases} \left(a + b\right) \log{\left(x \right)} & \text{for}\: m = -1 \wedge n = 0 \\a \log{\left(x \right)} + \frac{b x^{n}}{n} & \text{for}\: m = -1 \\\frac{a m x x^{m}}{m^{2} + m} + \frac{b m^{2} \log{\left(x \right)}}{m^{2} + m} + \frac{b m \log{\left(x \right)}}{m^{2} + m} & \text{for}\: n = - m - 1 \\\frac{a m x x^{m}}{m^{2} + m n + 2 m + n + 1} + \frac{a n x x^{m}}{m^{2} + m n + 2 m + n + 1} + \frac{a x x^{m}}{m^{2} + m n + 2 m + n + 1} + \frac{b m x x^{m} x^{n}}{m^{2} + m n + 2 m + n + 1} + \frac{b x x^{m} x^{n}}{m^{2} + m n + 2 m + n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a + b)*log(x), Eq(m, -1) & Eq(n, 0)), (a*log(x) + b*x**n/n, Eq(m, -1)), (a*m*x*x**m/(m**2 + m) + b*m**2*log(x)/(m**2 + m) + b*m*log(x)/(m**2 + m), Eq(n, -m - 1)), (a*m*x*x**m/(m**2 + m*n + 2*m + n + 1) + a*n*x*x**m/(m**2 + m*n + 2*m + n + 1) + a*x*x**m/(m**2 + m*n + 2*m + n + 1) + b*m*x*x**m*x**n/(m**2 + m*n + 2*m + n + 1) + b*x*x**m*x**n/(m**2 + m*n + 2*m + n + 1), True))","A",0
2670,1,95,0,1.169160," ","integrate(x**m/(a+b*x**n),x)","\frac{m x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a n^{2} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a n^{2} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}"," ",0,"m*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*n**2*gamma(m/n + 1 + 1/n)) + x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*n**2*gamma(m/n + 1 + 1/n))","C",0
2671,1,840,0,2.150719," ","integrate(x**m/(a+b*x**n)**2,x)","- \frac{m^{2} x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{m n x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{m n x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{2 m x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{n x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{n x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{b m^{2} x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{b m n x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{2 b m x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{b n x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{b x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)}"," ",0,"-m**2*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) + m*n*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) + m*n*x*x**m*gamma(m/n + 1/n)/(a*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) - 2*m*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) + n*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) + n*x*x**m*gamma(m/n + 1/n)/(a*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) - x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) - b*m**2*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) + b*m*n*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) - 2*b*m*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) + b*n*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n))) - b*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(a*n**3*gamma(m/n + 1 + 1/n) + b*n**3*x**n*gamma(m/n + 1 + 1/n)))","C",0
2672,1,6803,0,4.753034," ","integrate(x**m/(a+b*x**n)**3,x)","\frac{a m^{3} x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{3 a m^{2} n x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{a m^{2} n x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{3 a m^{2} x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{2 a m n^{2} x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{3 a m n^{2} x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{6 a m n x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{2 a m n x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{3 a m x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{2 a n^{2} x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{3 a n^{2} x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{3 a n x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{a n x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{a x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{3 b m^{3} x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{9 b m^{2} n x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{2 b m^{2} n x x^{m} x^{n} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{9 b m^{2} x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{6 b m n^{2} x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{5 b m n^{2} x x^{m} x^{n} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{18 b m n x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{4 b m n x x^{m} x^{n} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{9 b m x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{6 b n^{2} x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{5 b n^{2} x x^{m} x^{n} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{9 b n x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} - \frac{2 b n x x^{m} x^{n} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{3 b x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{3 b^{2} m^{3} x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{9 b^{2} m^{2} n x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{b^{2} m^{2} n x x^{m} x^{2 n} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{9 b^{2} m^{2} x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{6 b^{2} m n^{2} x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{2 b^{2} m n^{2} x x^{m} x^{2 n} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{18 b^{2} m n x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{2 b^{2} m n x x^{m} x^{2 n} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{9 b^{2} m x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{6 b^{2} n^{2} x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{2 b^{2} n^{2} x x^{m} x^{2 n} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{9 b^{2} n x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{b^{2} n x x^{m} x^{2 n} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{3 b^{2} x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{b^{3} m^{3} x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{3 b^{3} m^{2} n x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{3 b^{3} m^{2} x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{2 b^{3} m n^{2} x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{6 b^{3} m n x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{3 b^{3} m x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{2 b^{3} n^{2} x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} - \frac{3 b^{3} n x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)} + \frac{b^{3} x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a^{2} \left(2 a^{4} n^{4} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{3} b n^{4} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 6 a^{2} b^{2} n^{4} x^{2 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) + 2 a b^{3} n^{4} x^{3 n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)\right)}"," ",0,"a*m**3*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - 3*a*m**2*n*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - a*m**2*n*x*x**m*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 3*a*m**2*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 2*a*m*n**2*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 3*a*m*n**2*x*x**m*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - 6*a*m*n*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - 2*a*m*n*x*x**m*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 3*a*m*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 2*a*n**2*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 3*a*n**2*x*x**m*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - 3*a*n*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - a*n*x*x**m*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + a*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 3*b*m**3*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - 9*b*m**2*n*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - 2*b*m**2*n*x*x**m*x**n*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 9*b*m**2*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 6*b*m*n**2*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 5*b*m*n**2*x*x**m*x**n*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - 18*b*m*n*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - 4*b*m*n*x*x**m*x**n*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 9*b*m*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 6*b*n**2*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 5*b*n**2*x*x**m*x**n*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - 9*b*n*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) - 2*b*n*x*x**m*x**n*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 3*b*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)) + 3*b**2*m**3*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) - 9*b**2*m**2*n*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) - b**2*m**2*n*x*x**m*x**(2*n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 9*b**2*m**2*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 6*b**2*m*n**2*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 2*b**2*m*n**2*x*x**m*x**(2*n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) - 18*b**2*m*n*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) - 2*b**2*m*n*x*x**m*x**(2*n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 9*b**2*m*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 6*b**2*n**2*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 2*b**2*n**2*x*x**m*x**(2*n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) - 9*b**2*n*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) - b**2*n*x*x**m*x**(2*n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 3*b**2*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + b**3*m**3*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) - 3*b**3*m**2*n*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 3*b**3*m**2*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 2*b**3*m*n**2*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) - 6*b**3*m*n*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 3*b**3*m*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + 2*b**3*n**2*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) - 3*b**3*n*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n))) + b**3*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a**2*(2*a**4*n**4*gamma(m/n + 1 + 1/n) + 6*a**3*b*n**4*x**n*gamma(m/n + 1 + 1/n) + 6*a**2*b**2*n**4*x**(2*n)*gamma(m/n + 1 + 1/n) + 2*a*b**3*n**4*x**(3*n)*gamma(m/n + 1 + 1/n)))","C",0
2673,1,58,0,15.810160," ","integrate(x**m*(a+b*x**n)**(3/2),x)","\frac{a^{\frac{3}{2}} x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{m}{n} + \frac{1}{n} \\ \frac{m}{n} + 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}"," ",0,"a**(3/2)*x*x**m*gamma(m/n + 1/n)*hyper((-3/2, m/n + 1/n), (m/n + 1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(m/n + 1 + 1/n))","C",0
2674,1,58,0,2.043495," ","integrate(x**m*(a+b*x**n)**(1/2),x)","\frac{\sqrt{a} x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{n} + \frac{1}{n} \\ \frac{m}{n} + 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}"," ",0,"sqrt(a)*x*x**m*gamma(m/n + 1/n)*hyper((-1/2, m/n + 1/n), (m/n + 1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(m/n + 1 + 1/n))","C",0
2675,1,56,0,1.556209," ","integrate(x**m/(a+b*x**n)**(1/2),x)","\frac{x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} + \frac{1}{n} \\ \frac{m}{n} + 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}"," ",0,"x*x**m*gamma(m/n + 1/n)*hyper((1/2, m/n + 1/n), (m/n + 1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 1 + 1/n))","C",0
2676,1,56,0,2.962721," ","integrate(x**m/(a+b*x**n)**(3/2),x)","\frac{x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{n} + \frac{1}{n} \\ \frac{m}{n} + 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{a^{\frac{3}{2}} n \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}"," ",0,"x*x**m*gamma(m/n + 1/n)*hyper((3/2, m/n + 1/n), (m/n + 1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(a**(3/2)*n*gamma(m/n + 1 + 1/n))","C",0
2677,1,56,0,15.544450," ","integrate(x**m/(a+b*x**n)**(5/2),x)","\frac{x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, \frac{m}{n} + \frac{1}{n} \\ \frac{m}{n} + 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{a^{\frac{5}{2}} n \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}"," ",0,"x*x**m*gamma(m/n + 1/n)*hyper((5/2, m/n + 1/n), (m/n + 1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(a**(5/2)*n*gamma(m/n + 1 + 1/n))","C",0
2678,1,49,0,29.263362," ","integrate(x**(3+2*n)/(a+b*x**n)**(1/2),x)","\frac{x^{4} x^{2 n} \Gamma\left(2 + \frac{4}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, 2 + \frac{4}{n} \\ 3 + \frac{4}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(3 + \frac{4}{n}\right)}"," ",0,"x**4*x**(2*n)*gamma(2 + 4/n)*hyper((1/2, 2 + 4/n), (3 + 4/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(3 + 4/n))","C",0
2679,1,48,0,4.291491," ","integrate(x**(3+n)/(a+b*x**n)**(1/2),x)","\frac{x^{4} x^{n} \Gamma\left(1 + \frac{4}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, 1 + \frac{4}{n} \\ 2 + \frac{4}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(2 + \frac{4}{n}\right)}"," ",0,"x**4*x**n*gamma(1 + 4/n)*hyper((1/2, 1 + 4/n), (2 + 4/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(2 + 4/n))","C",0
2680,1,44,0,40.982930," ","integrate(x**(3-n)/(a+b*x**n)**(1/2),x)","\frac{x^{4} x^{- n} \Gamma\left(-1 + \frac{4}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, -1 + \frac{4}{n} \\ \frac{4}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{4}{n}\right)}"," ",0,"x**4*x**(-n)*gamma(-1 + 4/n)*hyper((1/2, -1 + 4/n), (4/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(4/n))","C",0
2681,1,49,0,37.274244," ","integrate(x**(3-2*n)/(a+b*x**n)**(1/2),x)","\frac{x^{4} x^{- 2 n} \Gamma\left(-2 + \frac{4}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, -2 + \frac{4}{n} \\ -1 + \frac{4}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(-1 + \frac{4}{n}\right)}"," ",0,"x**4*x**(-2*n)*gamma(-2 + 4/n)*hyper((1/2, -2 + 4/n), (-1 + 4/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(-1 + 4/n))","C",0
2682,1,65,0,3.285884," ","integrate(x**(m+2*n)/(a+b*x**n)**(1/2),x)","\frac{x x^{m} x^{2 n} \Gamma\left(\frac{m}{n} + 2 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} + 2 + \frac{1}{n} \\ \frac{m}{n} + 3 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 3 + \frac{1}{n}\right)}"," ",0,"x*x**m*x**(2*n)*gamma(m/n + 2 + 1/n)*hyper((1/2, m/n + 2 + 1/n), (m/n + 3 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 3 + 1/n))","C",0
2683,1,63,0,4.495716," ","integrate(x**(m+n)/(a+b*x**n)**(1/2),x)","\frac{x x^{m} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} + 1 + \frac{1}{n} \\ \frac{m}{n} + 2 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 2 + \frac{1}{n}\right)}"," ",0,"x*x**m*x**n*gamma(m/n + 1 + 1/n)*hyper((1/2, m/n + 1 + 1/n), (m/n + 2 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 2 + 1/n))","C",0
2684,1,60,0,9.555135," ","integrate(x**(m-n)/(a+b*x**n)**(1/2),x)","\frac{x x^{m} x^{- n} \Gamma\left(\frac{m}{n} - 1 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} - 1 + \frac{1}{n} \\ \frac{m}{n} + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}"," ",0,"x*x**m*x**(-n)*gamma(m/n - 1 + 1/n)*hyper((1/2, m/n - 1 + 1/n), (m/n + 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 1/n))","C",0
2685,1,65,0,16.600499," ","integrate(x**(m-2*n)/(a+b*x**n)**(1/2),x)","\frac{x x^{m} x^{- 2 n} \Gamma\left(\frac{m}{n} - 2 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} - 2 + \frac{1}{n} \\ \frac{m}{n} - 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} - 1 + \frac{1}{n}\right)}"," ",0,"x*x**m*x**(-2*n)*gamma(m/n - 2 + 1/n)*hyper((1/2, m/n - 2 + 1/n), (m/n - 1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n - 1 + 1/n))","C",0
2686,1,94,0,64.200292," ","integrate(-1/2*b*n*x**(-1+m+n)/(a+b*x**n)**(3/2)+m*x**(-1+m)/(a+b*x**n)**(1/2),x)","\frac{m x^{m} \Gamma\left(\frac{m}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} \\ \frac{m}{n} + 1 \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 1\right)} - \frac{b x^{m} x^{n} \Gamma\left(\frac{m}{n} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{n} + 1 \\ \frac{m}{n} + 2 \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{m}{n} + 2\right)}"," ",0,"m*x**m*gamma(m/n)*hyper((1/2, m/n), (m/n + 1,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 1)) - b*x**m*x**n*gamma(m/n + 1)*hyper((3/2, m/n + 1), (m/n + 2,), b*x**n*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(m/n + 2))","C",0
2687,1,148,0,16.506188," ","integrate(x**(-1+7/2*n)/(a+b*x**n)**(1/2),x)","\frac{5 a^{\frac{5}{2}} x^{\frac{n}{2}}}{8 b^{3} n \sqrt{1 + \frac{b x^{n}}{a}}} + \frac{5 a^{\frac{3}{2}} x^{\frac{3 n}{2}}}{24 b^{2} n \sqrt{1 + \frac{b x^{n}}{a}}} - \frac{\sqrt{a} x^{\frac{5 n}{2}}}{12 b n \sqrt{1 + \frac{b x^{n}}{a}}} - \frac{5 a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{8 b^{\frac{7}{2}} n} + \frac{x^{\frac{7 n}{2}}}{3 \sqrt{a} n \sqrt{1 + \frac{b x^{n}}{a}}}"," ",0,"5*a**(5/2)*x**(n/2)/(8*b**3*n*sqrt(1 + b*x**n/a)) + 5*a**(3/2)*x**(3*n/2)/(24*b**2*n*sqrt(1 + b*x**n/a)) - sqrt(a)*x**(5*n/2)/(12*b*n*sqrt(1 + b*x**n/a)) - 5*a**3*asinh(sqrt(b)*x**(n/2)/sqrt(a))/(8*b**(7/2)*n) + x**(7*n/2)/(3*sqrt(a)*n*sqrt(1 + b*x**n/a))","A",0
2688,1,116,0,12.737180," ","integrate(x**(-1+5/2*n)/(a+b*x**n)**(1/2),x)","- \frac{3 a^{\frac{3}{2}} x^{\frac{n}{2}}}{4 b^{2} n \sqrt{1 + \frac{b x^{n}}{a}}} - \frac{\sqrt{a} x^{\frac{3 n}{2}}}{4 b n \sqrt{1 + \frac{b x^{n}}{a}}} + \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{4 b^{\frac{5}{2}} n} + \frac{x^{\frac{5 n}{2}}}{2 \sqrt{a} n \sqrt{1 + \frac{b x^{n}}{a}}}"," ",0,"-3*a**(3/2)*x**(n/2)/(4*b**2*n*sqrt(1 + b*x**n/a)) - sqrt(a)*x**(3*n/2)/(4*b*n*sqrt(1 + b*x**n/a)) + 3*a**2*asinh(sqrt(b)*x**(n/2)/sqrt(a))/(4*b**(5/2)*n) + x**(5*n/2)/(2*sqrt(a)*n*sqrt(1 + b*x**n/a))","A",0
2689,1,49,0,9.863250," ","integrate(x**(-1+3/2*n)/(a+b*x**n)**(1/2),x)","\frac{\sqrt{a} x^{\frac{n}{2}} \sqrt{1 + \frac{b x^{n}}{a}}}{b n} - \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{b^{\frac{3}{2}} n}"," ",0,"sqrt(a)*x**(n/2)*sqrt(1 + b*x**n/a)/(b*n) - a*asinh(sqrt(b)*x**(n/2)/sqrt(a))/(b**(3/2)*n)","A",0
2690,1,24,0,8.138196," ","integrate(x**(-1+1/2*n)/(a+b*x**n)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{\sqrt{b} n}"," ",0,"2*asinh(sqrt(b)*x**(n/2)/sqrt(a))/(sqrt(b)*n)","A",0
2691,1,22,0,34.932810," ","integrate(x**(-1-1/2*n)/(a+b*x**n)**(1/2),x)","- \frac{2 \sqrt{b} \sqrt{\frac{a x^{- n}}{b} + 1}}{a n}"," ",0,"-2*sqrt(b)*sqrt(a*x**(-n)/b + 1)/(a*n)","A",0
2692,1,51,0,5.960316," ","integrate(x**(-1-3/2*n)/(a+b*x**n)**(1/2),x)","- \frac{2 \sqrt{b} x^{- n} \sqrt{\frac{a x^{- n}}{b} + 1}}{3 a n} + \frac{4 b^{\frac{3}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{3 a^{2} n}"," ",0,"-2*sqrt(b)*x**(-n)*sqrt(a*x**(-n)/b + 1)/(3*a*n) + 4*b**(3/2)*sqrt(a*x**(-n)/b + 1)/(3*a**2*n)","A",0
2693,1,354,0,6.249630," ","integrate(x**(-1-5/2*n)/(a+b*x**n)**(1/2),x)","- \frac{6 a^{4} b^{\frac{9}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{5} b^{4} n x^{2 n} + 30 a^{4} b^{5} n x^{3 n} + 15 a^{3} b^{6} n x^{4 n}} - \frac{4 a^{3} b^{\frac{11}{2}} x^{n} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{5} b^{4} n x^{2 n} + 30 a^{4} b^{5} n x^{3 n} + 15 a^{3} b^{6} n x^{4 n}} - \frac{6 a^{2} b^{\frac{13}{2}} x^{2 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{5} b^{4} n x^{2 n} + 30 a^{4} b^{5} n x^{3 n} + 15 a^{3} b^{6} n x^{4 n}} - \frac{24 a b^{\frac{15}{2}} x^{3 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{5} b^{4} n x^{2 n} + 30 a^{4} b^{5} n x^{3 n} + 15 a^{3} b^{6} n x^{4 n}} - \frac{16 b^{\frac{17}{2}} x^{4 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{15 a^{5} b^{4} n x^{2 n} + 30 a^{4} b^{5} n x^{3 n} + 15 a^{3} b^{6} n x^{4 n}}"," ",0,"-6*a**4*b**(9/2)*sqrt(a*x**(-n)/b + 1)/(15*a**5*b**4*n*x**(2*n) + 30*a**4*b**5*n*x**(3*n) + 15*a**3*b**6*n*x**(4*n)) - 4*a**3*b**(11/2)*x**n*sqrt(a*x**(-n)/b + 1)/(15*a**5*b**4*n*x**(2*n) + 30*a**4*b**5*n*x**(3*n) + 15*a**3*b**6*n*x**(4*n)) - 6*a**2*b**(13/2)*x**(2*n)*sqrt(a*x**(-n)/b + 1)/(15*a**5*b**4*n*x**(2*n) + 30*a**4*b**5*n*x**(3*n) + 15*a**3*b**6*n*x**(4*n)) - 24*a*b**(15/2)*x**(3*n)*sqrt(a*x**(-n)/b + 1)/(15*a**5*b**4*n*x**(2*n) + 30*a**4*b**5*n*x**(3*n) + 15*a**3*b**6*n*x**(4*n)) - 16*b**(17/2)*x**(4*n)*sqrt(a*x**(-n)/b + 1)/(15*a**5*b**4*n*x**(2*n) + 30*a**4*b**5*n*x**(3*n) + 15*a**3*b**6*n*x**(4*n))","B",0
2694,1,605,0,6.513055," ","integrate(x**(-1-7/2*n)/(a+b*x**n)**(1/2),x)","- \frac{10 a^{6} b^{\frac{19}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}} - \frac{18 a^{5} b^{\frac{21}{2}} x^{n} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}} - \frac{10 a^{4} b^{\frac{23}{2}} x^{2 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}} + \frac{10 a^{3} b^{\frac{25}{2}} x^{3 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}} + \frac{60 a^{2} b^{\frac{27}{2}} x^{4 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}} + \frac{80 a b^{\frac{29}{2}} x^{5 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}} + \frac{32 b^{\frac{31}{2}} x^{6 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}}"," ",0,"-10*a**6*b**(19/2)*sqrt(a*x**(-n)/b + 1)/(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n)) - 18*a**5*b**(21/2)*x**n*sqrt(a*x**(-n)/b + 1)/(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n)) - 10*a**4*b**(23/2)*x**(2*n)*sqrt(a*x**(-n)/b + 1)/(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n)) + 10*a**3*b**(25/2)*x**(3*n)*sqrt(a*x**(-n)/b + 1)/(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n)) + 60*a**2*b**(27/2)*x**(4*n)*sqrt(a*x**(-n)/b + 1)/(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n)) + 80*a*b**(29/2)*x**(5*n)*sqrt(a*x**(-n)/b + 1)/(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n)) + 32*b**(31/2)*x**(6*n)*sqrt(a*x**(-n)/b + 1)/(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n))","B",0
2695,1,94,0,7.844818," ","integrate(x**m/(a+b*x**(-2+m))**(1/2),x)","\frac{x x^{m} \Gamma\left(\frac{m}{m - 2} + \frac{1}{m - 2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{m - 2} + \frac{1}{m - 2} \\ \frac{m}{m - 2} + 1 + \frac{1}{m - 2} \end{matrix}\middle| {\frac{b x^{m} e^{i \pi}}{a x^{2}}} \right)}}{\sqrt{a} m \Gamma\left(\frac{m}{m - 2} + 1 + \frac{1}{m - 2}\right) - 2 \sqrt{a} \Gamma\left(\frac{m}{m - 2} + 1 + \frac{1}{m - 2}\right)}"," ",0,"x*x**m*gamma(m/(m - 2) + 1/(m - 2))*hyper((1/2, m/(m - 2) + 1/(m - 2)), (m/(m - 2) + 1 + 1/(m - 2),), b*x**m*exp_polar(I*pi)/(a*x**2))/(sqrt(a)*m*gamma(m/(m - 2) + 1 + 1/(m - 2)) - 2*sqrt(a)*gamma(m/(m - 2) + 1 + 1/(m - 2)))","C",0
2696,1,95,0,17.103522," ","integrate(x**m/(a+b*x**(2-m))**(1/2),x)","- \frac{x x^{m} \Gamma\left(\frac{m}{2 - m} + \frac{1}{2 - m}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2 - m} + \frac{1}{2 - m} \\ \frac{m}{2 - m} + 1 + \frac{1}{2 - m} \end{matrix}\middle| {\frac{b x^{2} x^{- m} e^{i \pi}}{a}} \right)}}{\sqrt{a} m \Gamma\left(\frac{m}{2 - m} + 1 + \frac{1}{2 - m}\right) - 2 \sqrt{a} \Gamma\left(\frac{m}{2 - m} + 1 + \frac{1}{2 - m}\right)}"," ",0,"-x*x**m*gamma(m/(2 - m) + 1/(2 - m))*hyper((1/2, m/(2 - m) + 1/(2 - m)), (m/(2 - m) + 1 + 1/(2 - m),), b*x**2*x**(-m)*exp_polar(I*pi)/a)/(sqrt(a)*m*gamma(m/(2 - m) + 1 + 1/(2 - m)) - 2*sqrt(a)*gamma(m/(2 - m) + 1 + 1/(2 - m)))","C",0
2697,1,170,0,25.957572," ","integrate(6*a*x**2/b/(4+m)/(a+b*x**(-2+m))**(1/2)+x**m/(a+b*x**(-2+m))**(1/2),x)","\frac{6 a x^{3} \Gamma\left(\frac{3}{m - 2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{m - 2} \\ 1 + \frac{3}{m - 2} \end{matrix}\middle| {\frac{b x^{m} e^{i \pi}}{a x^{2}}} \right)}}{b \left(m + 4\right) \left(\sqrt{a} m \Gamma\left(1 + \frac{3}{m - 2}\right) - 2 \sqrt{a} \Gamma\left(1 + \frac{3}{m - 2}\right)\right)} + \frac{x x^{m} \Gamma\left(\frac{m}{m - 2} + \frac{1}{m - 2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{m - 2} + \frac{1}{m - 2} \\ \frac{m}{m - 2} + 1 + \frac{1}{m - 2} \end{matrix}\middle| {\frac{b x^{m} e^{i \pi}}{a x^{2}}} \right)}}{\sqrt{a} m \Gamma\left(\frac{m}{m - 2} + 1 + \frac{1}{m - 2}\right) - 2 \sqrt{a} \Gamma\left(\frac{m}{m - 2} + 1 + \frac{1}{m - 2}\right)}"," ",0,"6*a*x**3*gamma(3/(m - 2))*hyper((1/2, 3/(m - 2)), (1 + 3/(m - 2),), b*x**m*exp_polar(I*pi)/(a*x**2))/(b*(m + 4)*(sqrt(a)*m*gamma(1 + 3/(m - 2)) - 2*sqrt(a)*gamma(1 + 3/(m - 2)))) + x*x**m*gamma(m/(m - 2) + 1/(m - 2))*hyper((1/2, m/(m - 2) + 1/(m - 2)), (m/(m - 2) + 1 + 1/(m - 2),), b*x**m*exp_polar(I*pi)/(a*x**2))/(sqrt(a)*m*gamma(m/(m - 2) + 1 + 1/(m - 2)) - 2*sqrt(a)*gamma(m/(m - 2) + 1 + 1/(m - 2)))","C",0
2698,1,100,0,101.859107," ","integrate(1/2*x**(-1+m)*(2*a*m+b*(2*m-n)*x**n)/(a+b*x**n)**(3/2),x)","\frac{m x^{m} \Gamma\left(\frac{m}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{n} \\ \frac{m}{n} + 1 \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 1\right)} + \frac{b x^{m} x^{n} \left(2 m - n\right) \Gamma\left(\frac{m}{n} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{n} + 1 \\ \frac{m}{n} + 2 \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} n \Gamma\left(\frac{m}{n} + 2\right)}"," ",0,"m*x**m*gamma(m/n)*hyper((3/2, m/n), (m/n + 1,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 1)) + b*x**m*x**n*(2*m - n)*gamma(m/n + 1)*hyper((3/2, m/n + 1), (m/n + 2,), b*x**n*exp_polar(I*pi)/a)/(2*a**(3/2)*n*gamma(m/n + 2))","C",0
2699,1,94,0,47.509106," ","integrate(-1/2*b*n*x**(-1+m+n)/(a+b*x**n)**(3/2)+m*x**(-1+m)/(a+b*x**n)**(1/2),x)","\frac{m x^{m} \Gamma\left(\frac{m}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} \\ \frac{m}{n} + 1 \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 1\right)} - \frac{b x^{m} x^{n} \Gamma\left(\frac{m}{n} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{n} + 1 \\ \frac{m}{n} + 2 \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{m}{n} + 2\right)}"," ",0,"m*x**m*gamma(m/n)*hyper((1/2, m/n), (m/n + 1,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 1)) - b*x**m*x**n*gamma(m/n + 1)*hyper((3/2, m/n + 1), (m/n + 2,), b*x**n*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(m/n + 2))","C",0
2700,1,117,0,2.481642," ","integrate(x**m/(a+b*x**(3+3*m))**(1/3),x)","\frac{x x^{m} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{m}{3 m + 3} + 1 + \frac{1}{3 m + 3} \end{matrix}\middle| {\frac{b x^{3} x^{3 m} e^{i \pi}}{a}} \right)}}{3 a^{\frac{m}{3 m + 3}} a^{\frac{1}{3 m + 3}} m \Gamma\left(\frac{m}{3 m + 3} + 1 + \frac{1}{3 m + 3}\right) + 3 a^{\frac{m}{3 m + 3}} a^{\frac{1}{3 m + 3}} \Gamma\left(\frac{m}{3 m + 3} + 1 + \frac{1}{3 m + 3}\right)}"," ",0,"x*x**m*gamma(1/3)*hyper((1/3, 1/3), (m/(3*m + 3) + 1 + 1/(3*m + 3),), b*x**3*x**(3*m)*exp_polar(I*pi)/a)/(3*a**(m/(3*m + 3))*a**(1/(3*m + 3))*m*gamma(m/(3*m + 3) + 1 + 1/(3*m + 3)) + 3*a**(m/(3*m + 3))*a**(1/(3*m + 3))*gamma(m/(3*m + 3) + 1 + 1/(3*m + 3)))","C",0
2701,-1,0,0,0.000000," ","integrate(x**m*(a+b/(x**(3/2+3/2*m)))**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2702,1,39,0,7.813806," ","integrate(x**(-1+1/3*n)/(a+b*x**n)**(1/3),x)","\frac{x^{\frac{n}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt[3]{a} n \Gamma\left(\frac{4}{3}\right)}"," ",0,"x**(n/3)*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**n*exp_polar(I*pi)/a)/(a**(1/3)*n*gamma(4/3))","C",0
2703,1,46,0,123.911281," ","integrate(x**(-1-2/3*n)*(a+b*x**n)**(2/3),x)","\frac{a^{\frac{2}{3}} x^{- \frac{2 n}{3}} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{2}{3} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(\frac{1}{3}\right)}"," ",0,"a**(2/3)*x**(-2*n/3)*gamma(-2/3)*hyper((-2/3, -2/3), (1/3,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1/3))","C",0
2704,1,54,0,10.683178," ","integrate(x**m*(a+b*x**n)**p,x)","\frac{a^{p} x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{n} + \frac{1}{n} \\ \frac{m}{n} + 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}"," ",0,"a**p*x*x**m*gamma(m/n + 1/n)*hyper((-p, m/n + 1/n), (m/n + 1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(m/n + 1 + 1/n))","C",0
2705,-1,0,0,0.000000," ","integrate((a+b*x**n)**(-4-1/n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2706,-1,0,0,0.000000," ","integrate((a+b*x**n)**(-3-1/n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2707,-1,0,0,0.000000," ","integrate((a+b*x**n)**(-2-1/n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2708,1,211,0,28.866703," ","integrate((a+b*x**n)**(-1-1/n),x)","\begin{cases} - \frac{b^{- \frac{1}{n}} x x^{- n} \left(x^{n}\right)^{- \frac{1}{n}}}{b n} & \text{for}\: a = 0 \\0^{-1 - \frac{1}{n}} x & \text{for}\: a = - b x^{n} \\x \left(0^{n}\right)^{-1 - \frac{1}{n}} & \text{for}\: a = 0^{n} - b x^{n} \\\frac{a^{2} x}{a^{3} \left(a + b x^{n}\right)^{\frac{1}{n}} + 2 a^{2} b x^{n} \left(a + b x^{n}\right)^{\frac{1}{n}} + a b^{2} x^{2 n} \left(a + b x^{n}\right)^{\frac{1}{n}}} + \frac{a b x x^{n}}{a^{3} \left(a + b x^{n}\right)^{\frac{1}{n}} + 2 a^{2} b x^{n} \left(a + b x^{n}\right)^{\frac{1}{n}} + a b^{2} x^{2 n} \left(a + b x^{n}\right)^{\frac{1}{n}}} + \frac{b x x^{n}}{a^{2} \left(a + b x^{n}\right)^{\frac{1}{n}} + a b x^{n} \left(a + b x^{n}\right)^{\frac{1}{n}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-b**(-1/n)*x*x**(-n)*(x**n)**(-1/n)/(b*n), Eq(a, 0)), (0**(-1 - 1/n)*x, Eq(a, -b*x**n)), (x*(0**n)**(-1 - 1/n), Eq(a, 0**n - b*x**n)), (a**2*x/(a**3*(a + b*x**n)**(1/n) + 2*a**2*b*x**n*(a + b*x**n)**(1/n) + a*b**2*x**(2*n)*(a + b*x**n)**(1/n)) + a*b*x*x**n/(a**3*(a + b*x**n)**(1/n) + 2*a**2*b*x**n*(a + b*x**n)**(1/n) + a*b**2*x**(2*n)*(a + b*x**n)**(1/n)) + b*x*x**n/(a**2*(a + b*x**n)**(1/n) + a*b*x**n*(a + b*x**n)**(1/n)), True))","A",0
2709,1,39,0,10.711050," ","integrate(1/((a+b*x**n)**(1/n)),x)","\frac{a^{- \frac{1}{n}} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a**(-1/n)*x*gamma(1/n)*hyper((1/n, 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
2710,1,42,0,7.410178," ","integrate((a+b*x**n)**(1-1/n),x)","\frac{a a^{- \frac{1}{n}} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, -1 + \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a*a**(-1/n)*x*gamma(1/n)*hyper((1/n, -1 + 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
2711,1,44,0,90.915574," ","integrate((a+b*x**n)**(2-1/n),x)","\frac{a^{2} a^{- \frac{1}{n}} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, -2 + \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a**2*a**(-1/n)*x*gamma(1/n)*hyper((1/n, -2 + 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
2712,0,0,0,0.000000," ","integrate(x**m*(b*x**n)**p,x)","\begin{cases} \frac{b^{p} x x^{m} \left(x^{n}\right)^{p}}{m + n p + 1} & \text{for}\: m \neq - n p - 1 \\\int x^{- n p - 1} \left(b x^{n}\right)^{p}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x*x**m*(x**n)**p/(m + n*p + 1), Ne(m, -n*p - 1)), (Integral(x**(-n*p - 1)*(b*x**n)**p, x), True))","F",0
2713,0,0,0,0.000000," ","integrate(x**2*(b*x**n)**p,x)","\begin{cases} \frac{b^{p} x^{3} \left(x^{n}\right)^{p}}{n p + 3} & \text{for}\: n \neq - \frac{3}{p} \\\int x^{2} \left(b x^{- \frac{3}{p}}\right)^{p}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x**3*(x**n)**p/(n*p + 3), Ne(n, -3/p)), (Integral(x**2*(b*x**(-3/p))**p, x), True))","F",0
2714,0,0,0,0.000000," ","integrate(x*(b*x**n)**p,x)","\begin{cases} \frac{b^{p} x^{2} \left(x^{n}\right)^{p}}{n p + 2} & \text{for}\: n \neq - \frac{2}{p} \\\int x \left(b x^{- \frac{2}{p}}\right)^{p}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x**2*(x**n)**p/(n*p + 2), Ne(n, -2/p)), (Integral(x*(b*x**(-2/p))**p, x), True))","F",0
2715,0,0,0,0.000000," ","integrate((b*x**n)**p,x)","\begin{cases} \frac{b^{p} x \left(x^{n}\right)^{p}}{n p + 1} & \text{for}\: n \neq - \frac{1}{p} \\\int \left(b x^{- \frac{1}{p}}\right)^{p}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*x*(x**n)**p/(n*p + 1), Ne(n, -1/p)), (Integral((b*x**(-1/p))**p, x), True))","F",0
2716,1,22,0,0.303028," ","integrate((b*x**n)**p/x,x)","\begin{cases} \log{\left(x \right)} & \text{for}\: p = 0 \wedge \left(n = 0 \vee p = 0\right) \\b^{p} \log{\left(x \right)} & \text{for}\: n = 0 \\\frac{b^{p} \left(x^{n}\right)^{p}}{n p} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x), Eq(p, 0) & (Eq(n, 0) | Eq(p, 0))), (b**p*log(x), Eq(n, 0)), (b**p*(x**n)**p/(n*p), True))","A",0
2717,0,0,0,0.000000," ","integrate((b*x**n)**p/x**2,x)","\begin{cases} \frac{b^{p} \left(x^{n}\right)^{p}}{n p x - x} & \text{for}\: n \neq \frac{1}{p} \\\int \frac{\left(b x^{\frac{1}{p}}\right)^{p}}{x^{2}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*(x**n)**p/(n*p*x - x), Ne(n, 1/p)), (Integral((b*x**(1/p))**p/x**2, x), True))","F",0
2718,0,0,0,0.000000," ","integrate((b*x**n)**p/x**3,x)","\begin{cases} \frac{b^{p} \left(x^{n}\right)^{p}}{n p x^{2} - 2 x^{2}} & \text{for}\: n \neq \frac{2}{p} \\\int \frac{\left(b x^{\frac{2}{p}}\right)^{p}}{x^{3}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*(x**n)**p/(n*p*x**2 - 2*x**2), Ne(n, 2/p)), (Integral((b*x**(2/p))**p/x**3, x), True))","F",0
2719,0,0,0,0.000000," ","integrate((b*x**n)**p/x**4,x)","\begin{cases} \frac{b^{p} \left(x^{n}\right)^{p}}{n p x^{3} - 3 x^{3}} & \text{for}\: n \neq \frac{3}{p} \\\int \frac{\left(b x^{\frac{3}{p}}\right)^{p}}{x^{4}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**p*(x**n)**p/(n*p*x**3 - 3*x**3), Ne(n, 3/p)), (Integral((b*x**(3/p))**p/x**4, x), True))","F",0
2720,1,75,0,46.606997," ","integrate(x**(-1+n)*(a+b*x**n)**p,x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \wedge p = -1 \\\frac{a^{p} x^{n}}{n} & \text{for}\: b = 0 \\\left(a + b\right)^{p} \log{\left(x \right)} & \text{for}\: n = 0 \\\frac{\log{\left(\frac{a}{b} + x^{n} \right)}}{b n} & \text{for}\: p = -1 \\\frac{a \left(a + b x^{n}\right)^{p}}{b n p + b n} + \frac{b x^{n} \left(a + b x^{n}\right)^{p}}{b n p + b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0) & Eq(p, -1)), (a**p*x**n/n, Eq(b, 0)), ((a + b)**p*log(x), Eq(n, 0)), (log(a/b + x**n)/(b*n), Eq(p, -1)), (a*(a + b*x**n)**p/(b*n*p + b*n) + b*x**n*(a + b*x**n)**p/(b*n*p + b*n), True))","A",0
2721,-1,0,0,0.000000," ","integrate(x**(-1+2*n)*(a+b*x**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2722,-2,0,0,0.000000," ","integrate(x**(-1+3*n)*(a+b*x**n)**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2723,-1,0,0,0.000000," ","integrate(x**(-1+4*n)*(a+b*x**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2724,-2,0,0,0.000000," ","integrate(x**(-n*p-n-1)*(a+b*x**n)**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2725,-1,0,0,0.000000," ","integrate(x**(-1-9*n)*(a+b*x**n)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2726,-1,0,0,0.000000," ","integrate(x**(-4-3*p)*(b*x**3+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2727,1,97,0,1.647634," ","integrate((b*x**3+a)**8/x**28,x)","\frac{- a^{8} - 9 a^{7} b x^{3} - 36 a^{6} b^{2} x^{6} - 84 a^{5} b^{3} x^{9} - 126 a^{4} b^{4} x^{12} - 126 a^{3} b^{5} x^{15} - 84 a^{2} b^{6} x^{18} - 36 a b^{7} x^{21} - 9 b^{8} x^{24}}{27 x^{27}}"," ",0,"(-a**8 - 9*a**7*b*x**3 - 36*a**6*b**2*x**6 - 84*a**5*b**3*x**9 - 126*a**4*b**4*x**12 - 126*a**3*b**5*x**15 - 84*a**2*b**6*x**18 - 36*a*b**7*x**21 - 9*b**8*x**24)/(27*x**27)","B",0
2728,1,41,0,0.995900," ","integrate(1/x/(a+b*x**n),x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \\- \frac{x^{- n}}{b n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{n} \right)}}{a n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (log(x)/a, Eq(b, 0)), (-x**(-n)/(b*n), Eq(a, 0)), (log(x)/(a + b), Eq(n, 0)), (log(x)/a - log(a/b + x**n)/(a*n), True))","A",0
2729,1,15,0,0.324671," ","integrate(1/x/(b*x**3+a),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
2730,-1,0,0,0.000000," ","integrate(1/((a+b*x**n)**((1+4*n)/n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2731,-1,0,0,0.000000," ","integrate(1/((a+b*x**n)**((1+3*n)/n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2732,-1,0,0,0.000000," ","integrate(1/((a+b*x**n)**((1+2*n)/n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2733,-1,0,0,0.000000," ","integrate(1/((a+b*x**n)**((1+n)/n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2734,1,39,0,11.536207," ","integrate(1/((a+b*x**n)**(1/n)),x)","\frac{a^{- \frac{1}{n}} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a**(-1/n)*x*gamma(1/n)*hyper((1/n, 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
2735,1,42,0,12.215106," ","integrate(1/((a+b*x**n)**((1-n)/n)),x)","\frac{a a^{- \frac{1}{n}} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, -1 + \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a*a**(-1/n)*x*gamma(1/n)*hyper((1/n, -1 + 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
2736,1,44,0,109.599102," ","integrate(1/((a+b*x**n)**((1-2*n)/n)),x)","\frac{a^{2} a^{- \frac{1}{n}} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, -2 + \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a**2*a**(-1/n)*x*gamma(1/n)*hyper((1/n, -2 + 1/n), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
2737,1,39,0,1.302227," ","integrate(1/x/(a+b/(x**n)),x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \\\frac{x^{n}}{b n} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{a} + \frac{\log{\left(\frac{a}{b} + x^{- n} \right)}}{a n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (log(x)/a, Eq(b, 0)), (x**n/(b*n), Eq(a, 0)), (log(x)/(a + b), Eq(n, 0)), (log(x)/a + log(a/b + x**(-n))/(a*n), True))","A",0
2738,1,37,0,1.460481," ","integrate(x**m/(a+b*x**(1+m)),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge m = -1 \\\frac{x x^{m}}{a \left(m + 1\right)} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: m = -1 \\\frac{\log{\left(\frac{a}{b} + x x^{m} \right)}}{b m + b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(m, -1)), (x*x**m/(a*(m + 1)), Eq(b, 0)), (log(x)/(a + b), Eq(m, -1)), (log(a/b + x*x**m)/(b*m + b), True))","A",0
2739,1,100,0,134.228835," ","integrate(x**m*(a+b*x**(1+m))**n,x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge m = -1 \wedge n = -1 \\\frac{a^{n} x x^{m}}{m + 1} & \text{for}\: b = 0 \\\left(a + b\right)^{n} \log{\left(x \right)} & \text{for}\: m = -1 \\\frac{\log{\left(\frac{a}{b} + x x^{m} \right)}}{b m + b} & \text{for}\: n = -1 \\\frac{a \left(a + b x x^{m}\right)^{n}}{b m n + b m + b n + b} + \frac{b x x^{m} \left(a + b x x^{m}\right)^{n}}{b m n + b m + b n + b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(m, -1) & Eq(n, -1)), (a**n*x*x**m/(m + 1), Eq(b, 0)), ((a + b)**n*log(x), Eq(m, -1)), (log(a/b + x*x**m)/(b*m + b), Eq(n, -1)), (a*(a + b*x*x**m)**n/(b*m*n + b*m + b*n + b) + b*x*x**m*(a + b*x*x**m)**n/(b*m*n + b*m + b*n + b), True))","A",0
2740,-1,0,0,0.000000," ","integrate(x**m*(a+b*x**(2+2*m))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2741,1,61,0,113.141982," ","integrate(x**m*(a+b*x**(2+2*m))**2,x)","\begin{cases} \frac{15 a^{2} x x^{m}}{15 m + 15} + \frac{10 a b x^{3} x^{3 m}}{15 m + 15} + \frac{3 b^{2} x^{5} x^{5 m}}{15 m + 15} & \text{for}\: m \neq -1 \\\left(a + b\right)^{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*a**2*x*x**m/(15*m + 15) + 10*a*b*x**3*x**(3*m)/(15*m + 15) + 3*b**2*x**5*x**(5*m)/(15*m + 15), Ne(m, -1)), ((a + b)**2*log(x), True))","A",0
2742,1,36,0,9.913256," ","integrate(x**m*(a+b*x**(2+2*m)),x)","\begin{cases} \frac{3 a x x^{m}}{3 m + 3} + \frac{b x^{3} x^{3 m}}{3 m + 3} & \text{for}\: m \neq -1 \\\left(a + b\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*x*x**m/(3*m + 3) + b*x**3*x**(3*m)/(3*m + 3), Ne(m, -1)), ((a + b)*log(x), True))","A",0
2743,1,197,0,2.569587," ","integrate(x**m/(a+b*x**(2+2*m)),x)","\frac{i \sqrt{\pi} a^{- \frac{m}{2 m + 2}} a^{- \frac{1}{2 m + 2}} \log{\left(1 - \frac{\sqrt{b} x x^{m} e^{\frac{i \pi}{2}}}{\sqrt{a}} \right)}}{4 \sqrt{b} m \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) + 4 \sqrt{b} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right)} - \frac{i \sqrt{\pi} a^{- \frac{m}{2 m + 2}} a^{- \frac{1}{2 m + 2}} \log{\left(1 - \frac{\sqrt{b} x x^{m} e^{\frac{3 i \pi}{2}}}{\sqrt{a}} \right)}}{4 \sqrt{b} m \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) + 4 \sqrt{b} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right)}"," ",0,"I*sqrt(pi)*a**(-m/(2*m + 2))*a**(-1/(2*m + 2))*log(1 - sqrt(b)*x*x**m*exp_polar(I*pi/2)/sqrt(a))/(4*sqrt(b)*m*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) + 4*sqrt(b)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2))) - I*sqrt(pi)*a**(-m/(2*m + 2))*a**(-1/(2*m + 2))*log(1 - sqrt(b)*x*x**m*exp_polar(3*I*pi/2)/sqrt(a))/(4*sqrt(b)*m*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) + 4*sqrt(b)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)))","C",0
2744,1,865,0,8.622809," ","integrate(x**m/(a+b*x**(2+2*m))**2,x)","- \frac{i \sqrt{\pi} a^{- \frac{m}{2 m + 2}} a^{- \frac{1}{2 m + 2}} \log{\left(1 - \frac{\sqrt{b} x x^{m} e^{\frac{i \pi}{2}}}{\sqrt{a}} \right)}}{- 8 a \sqrt{b} m \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 a \sqrt{b} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 b^{\frac{3}{2}} m x^{2} x^{2 m} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 b^{\frac{3}{2}} x^{2} x^{2 m} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right)} + \frac{i \sqrt{\pi} a^{- \frac{m}{2 m + 2}} a^{- \frac{1}{2 m + 2}} \log{\left(1 - \frac{\sqrt{b} x x^{m} e^{\frac{3 i \pi}{2}}}{\sqrt{a}} \right)}}{- 8 a \sqrt{b} m \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 a \sqrt{b} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 b^{\frac{3}{2}} m x^{2} x^{2 m} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 b^{\frac{3}{2}} x^{2} x^{2 m} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right)} - \frac{i \sqrt{\pi} a^{- \frac{m}{2 m + 2}} a^{- \frac{1}{2 m + 2}} b x^{2} x^{2 m} \log{\left(1 - \frac{\sqrt{b} x x^{m} e^{\frac{i \pi}{2}}}{\sqrt{a}} \right)}}{a \left(- 8 a \sqrt{b} m \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 a \sqrt{b} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 b^{\frac{3}{2}} m x^{2} x^{2 m} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 b^{\frac{3}{2}} x^{2} x^{2 m} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right)\right)} + \frac{i \sqrt{\pi} a^{- \frac{m}{2 m + 2}} a^{- \frac{1}{2 m + 2}} b x^{2} x^{2 m} \log{\left(1 - \frac{\sqrt{b} x x^{m} e^{\frac{3 i \pi}{2}}}{\sqrt{a}} \right)}}{a \left(- 8 a \sqrt{b} m \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 a \sqrt{b} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 b^{\frac{3}{2}} m x^{2} x^{2 m} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 b^{\frac{3}{2}} x^{2} x^{2 m} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right)\right)} - \frac{2 \sqrt{\pi} a^{- \frac{m}{2 m + 2}} a^{- \frac{1}{2 m + 2}} \sqrt{b} x x^{m}}{\sqrt{a} \left(- 8 a \sqrt{b} m \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 a \sqrt{b} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 b^{\frac{3}{2}} m x^{2} x^{2 m} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) - 8 b^{\frac{3}{2}} x^{2} x^{2 m} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right)\right)}"," ",0,"-I*sqrt(pi)*a**(-m/(2*m + 2))*a**(-1/(2*m + 2))*log(1 - sqrt(b)*x*x**m*exp_polar(I*pi/2)/sqrt(a))/(-8*a*sqrt(b)*m*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*a*sqrt(b)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*b**(3/2)*m*x**2*x**(2*m)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*b**(3/2)*x**2*x**(2*m)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2))) + I*sqrt(pi)*a**(-m/(2*m + 2))*a**(-1/(2*m + 2))*log(1 - sqrt(b)*x*x**m*exp_polar(3*I*pi/2)/sqrt(a))/(-8*a*sqrt(b)*m*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*a*sqrt(b)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*b**(3/2)*m*x**2*x**(2*m)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*b**(3/2)*x**2*x**(2*m)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2))) - I*sqrt(pi)*a**(-m/(2*m + 2))*a**(-1/(2*m + 2))*b*x**2*x**(2*m)*log(1 - sqrt(b)*x*x**m*exp_polar(I*pi/2)/sqrt(a))/(a*(-8*a*sqrt(b)*m*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*a*sqrt(b)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*b**(3/2)*m*x**2*x**(2*m)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*b**(3/2)*x**2*x**(2*m)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)))) + I*sqrt(pi)*a**(-m/(2*m + 2))*a**(-1/(2*m + 2))*b*x**2*x**(2*m)*log(1 - sqrt(b)*x*x**m*exp_polar(3*I*pi/2)/sqrt(a))/(a*(-8*a*sqrt(b)*m*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*a*sqrt(b)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*b**(3/2)*m*x**2*x**(2*m)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*b**(3/2)*x**2*x**(2*m)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)))) - 2*sqrt(pi)*a**(-m/(2*m + 2))*a**(-1/(2*m + 2))*sqrt(b)*x*x**m/(sqrt(a)*(-8*a*sqrt(b)*m*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*a*sqrt(b)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*b**(3/2)*m*x**2*x**(2*m)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) - 8*b**(3/2)*x**2*x**(2*m)*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2))))","C",0
2745,-1,0,0,0.000000," ","integrate(x**m/(a+b*x**(2+2*m))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2746,-1,0,0,0.000000," ","integrate(x**m*(a+b*x**(2+2*m))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2747,-1,0,0,0.000000," ","integrate(x**m*(a+b*x**(2+2*m))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2748,1,121,0,9.589061," ","integrate(x**m*(a+b*x**(2+2*m))**(1/2),x)","\frac{\sqrt{\pi} a x x^{m} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{2} \\ \frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2} \end{matrix}\middle| {\frac{b x^{2} x^{2 m} e^{i \pi}}{a}} \right)}}{2 a^{\frac{m}{2 m + 2}} a^{\frac{1}{2 m + 2}} m \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) + 2 a^{\frac{m}{2 m + 2}} a^{\frac{1}{2 m + 2}} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right)}"," ",0,"sqrt(pi)*a*x*x**m*hyper((-1/2, 1/2), (m/(2*m + 2) + 1 + 1/(2*m + 2),), b*x**2*x**(2*m)*exp_polar(I*pi)/a)/(2*a**(m/(2*m + 2))*a**(1/(2*m + 2))*m*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) + 2*a**(m/(2*m + 2))*a**(1/(2*m + 2))*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)))","C",0
2749,1,117,0,3.422562," ","integrate(x**m/(a+b*x**(2+2*m))**(1/2),x)","\frac{\sqrt{\pi} x x^{m} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2} \end{matrix}\middle| {\frac{b x^{2} x^{2 m} e^{i \pi}}{a}} \right)}}{2 a^{\frac{m}{2 m + 2}} a^{\frac{1}{2 m + 2}} m \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) + 2 a^{\frac{m}{2 m + 2}} a^{\frac{1}{2 m + 2}} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right)}"," ",0,"sqrt(pi)*x*x**m*hyper((1/2, 1/2), (m/(2*m + 2) + 1 + 1/(2*m + 2),), b*x**2*x**(2*m)*exp_polar(I*pi)/a)/(2*a**(m/(2*m + 2))*a**(1/(2*m + 2))*m*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) + 2*a**(m/(2*m + 2))*a**(1/(2*m + 2))*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)))","C",0
2750,1,121,0,21.632546," ","integrate(x**m/(a+b*x**(2+2*m))**(3/2),x)","\frac{\sqrt{\pi} x x^{m} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{1}{2} \\ \frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2} \end{matrix}\middle| {\frac{b x^{2} x^{2 m} e^{i \pi}}{a}} \right)}}{2 a a^{\frac{m}{2 m + 2}} a^{\frac{1}{2 m + 2}} m \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right) + 2 a a^{\frac{m}{2 m + 2}} a^{\frac{1}{2 m + 2}} \Gamma\left(\frac{m}{2 m + 2} + 1 + \frac{1}{2 m + 2}\right)}"," ",0,"sqrt(pi)*x*x**m*hyper((3/2, 1/2), (m/(2*m + 2) + 1 + 1/(2*m + 2),), b*x**2*x**(2*m)*exp_polar(I*pi)/a)/(2*a*a**(m/(2*m + 2))*a**(1/(2*m + 2))*m*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)) + 2*a*a**(m/(2*m + 2))*a**(1/(2*m + 2))*gamma(m/(2*m + 2) + 1 + 1/(2*m + 2)))","C",0
2751,-1,0,0,0.000000," ","integrate(x**m/(a+b*x**(2+2*m))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2752,-1,0,0,0.000000," ","integrate(x**m/(a+b*x**(2+2*m))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2753,1,48,0,4.445450," ","integrate(x**n*(1+x**(1+n))**(1/2),x)","\begin{cases} \frac{2 x x^{n} \sqrt{x x^{n} + 1}}{3 n + 3} + \frac{2 \sqrt{x x^{n} + 1}}{3 n + 3} & \text{for}\: n \neq -1 \\\sqrt{2} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x*x**n*sqrt(x*x**n + 1)/(3*n + 3) + 2*sqrt(x*x**n + 1)/(3*n + 3), Ne(n, -1)), (sqrt(2)*log(x), True))","A",0
2754,1,58,0,4.387205," ","integrate(x**n*(a**2+x**(1+n))**(1/2),x)","\begin{cases} \frac{2 a^{2} \sqrt{a^{2} + x x^{n}}}{3 n + 3} + \frac{2 x x^{n} \sqrt{a^{2} + x x^{n}}}{3 n + 3} & \text{for}\: n \neq -1 \\\sqrt{a^{2} + 1} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*sqrt(a**2 + x*x**n)/(3*n + 3) + 2*x*x**n*sqrt(a**2 + x*x**n)/(3*n + 3), Ne(n, -1)), (sqrt(a**2 + 1)*log(x), True))","A",0
2755,1,1290,0,25.848436," ","integrate((c*x)**m*(a+b*x**n)**2,x)","\begin{cases} \frac{\left(a + b\right)^{2} \log{\left(x \right)}}{c} & \text{for}\: m = -1 \wedge n = 0 \\\frac{a^{2} \log{\left(x \right)} + \frac{2 a b x^{n}}{n} + \frac{b^{2} x^{2 n}}{2 n}}{c} & \text{for}\: m = -1 \\\frac{a^{2} \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}\: c = 0^{\frac{1}{n}} \\- \frac{c^{- 2 n} x^{- 2 n}}{2 n} & \text{otherwise} \end{cases}\right)}{c} + \frac{2 a 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}\: c = 0^{\frac{1}{n}} \\- \frac{c^{- 2 n} x^{- n}}{n} & \text{otherwise} \end{cases}\right)}{c} + \frac{b^{2} \left(\begin{cases} c^{- 2 n} \log{\left(x \right)} & \text{for}\: \left|{x}\right| < 1 \\- c^{- 2 n} \log{\left(\frac{1}{x} \right)} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- c^{- 2 n} {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + c^{- 2 n} {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} & \text{otherwise} \end{cases}\right)}{c} & \text{for}\: m = - 2 n - 1 \\\frac{a^{2} \left(\begin{cases} - \frac{x^{- n} \left(0^{\frac{1}{n}}\right)^{- n}}{n} & \text{for}\: c = 0^{\frac{1}{n}} \\\log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{c^{- n} x^{- n}}{n} & \text{otherwise} \end{cases}\right)}{c} + \frac{2 a b \left(\begin{cases} c^{- n} \log{\left(x \right)} & \text{for}\: \left|{x}\right| < 1 \\- c^{- n} \log{\left(\frac{1}{x} \right)} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- c^{- n} {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + c^{- n} {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} & \text{otherwise} \end{cases}\right)}{c} + \frac{b^{2} \left(\begin{cases} - \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}\: c = 0^{\frac{1}{n}} \\\log{\left(x \right)} & \text{for}\: n = 0 \\\frac{c^{- n} x^{n}}{n} & \text{otherwise} \end{cases}\right)}{c} & \text{for}\: m = - n - 1 \\\frac{a^{2} c^{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^{2} c^{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^{2} c^{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^{2} c^{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^{2} c^{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^{2} c^{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 b c^{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{4 a b c^{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{4 a b c^{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{4 a b c^{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 a b c^{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{b^{2} c^{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{b^{2} c^{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 b^{2} c^{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{b^{2} c^{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{b^{2} c^{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)**2*log(x)/c, Eq(m, -1) & Eq(n, 0)), ((a**2*log(x) + 2*a*b*x**n/n + b**2*x**(2*n)/(2*n))/c, Eq(m, -1)), (a**2*Piecewise((log(x), Eq(n, 0)), (-x**(-2*n)*(0**(1/n))**(-2*n)/(2*n), Eq(c, 0**(1/n))), (-c**(-2*n)*x**(-2*n)/(2*n), True))/c + 2*a*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(c, 0**(1/n))), (-c**(-2*n)*x**(-n)/n, True))/c + b**2*Piecewise((c**(-2*n)*log(x), Abs(x) < 1), (-c**(-2*n)*log(1/x), 1/Abs(x) < 1), (-c**(-2*n)*meijerg(((), (1, 1)), ((0, 0), ()), x) + c**(-2*n)*meijerg(((1, 1), ()), ((), (0, 0)), x), True))/c, Eq(m, -2*n - 1)), (a**2*Piecewise((-x**(-n)*(0**(1/n))**(-n)/n, Eq(c, 0**(1/n))), (log(x), Eq(n, 0)), (-c**(-n)*x**(-n)/n, True))/c + 2*a*b*Piecewise((c**(-n)*log(x), Abs(x) < 1), (-c**(-n)*log(1/x), 1/Abs(x) < 1), (-c**(-n)*meijerg(((), (1, 1)), ((0, 0), ()), x) + c**(-n)*meijerg(((1, 1), ()), ((), (0, 0)), x), True))/c + b**2*Piecewise((-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(c, 0**(1/n))), (log(x), Eq(n, 0)), (c**(-n)*x**n/n, True))/c, Eq(m, -n - 1)), (a**2*c**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**2*c**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**2*c**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**2*c**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**2*c**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**2*c**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*b*c**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) + 4*a*b*c**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) + 4*a*b*c**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) + 4*a*b*c**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*a*b*c**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) + b**2*c**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) + b**2*c**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*b**2*c**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) + b**2*c**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) + b**2*c**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
2756,1,352,0,1.387851," ","integrate((c*x)**m*(b*x**3+a)**2,x)","\begin{cases} \frac{- \frac{a^{2}}{6 x^{6}} - \frac{2 a b}{3 x^{3}} + b^{2} \log{\left(x \right)}}{c^{7}} & \text{for}\: m = -7 \\\frac{- \frac{a^{2}}{3 x^{3}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{3}}{3}}{c^{4}} & \text{for}\: m = -4 \\\frac{a^{2} \log{\left(x \right)} + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{6}}{6}}{c} & \text{for}\: m = -1 \\\frac{a^{2} c^{m} m^{2} x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{11 a^{2} c^{m} m x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{28 a^{2} c^{m} x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{2 a b c^{m} m^{2} x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{16 a b c^{m} m x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{14 a b c^{m} x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{b^{2} c^{m} m^{2} x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{5 b^{2} c^{m} m x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{4 b^{2} c^{m} x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**2/(6*x**6) - 2*a*b/(3*x**3) + b**2*log(x))/c**7, Eq(m, -7)), ((-a**2/(3*x**3) + 2*a*b*log(x) + b**2*x**3/3)/c**4, Eq(m, -4)), ((a**2*log(x) + 2*a*b*x**3/3 + b**2*x**6/6)/c, Eq(m, -1)), (a**2*c**m*m**2*x*x**m/(m**3 + 12*m**2 + 39*m + 28) + 11*a**2*c**m*m*x*x**m/(m**3 + 12*m**2 + 39*m + 28) + 28*a**2*c**m*x*x**m/(m**3 + 12*m**2 + 39*m + 28) + 2*a*b*c**m*m**2*x**4*x**m/(m**3 + 12*m**2 + 39*m + 28) + 16*a*b*c**m*m*x**4*x**m/(m**3 + 12*m**2 + 39*m + 28) + 14*a*b*c**m*x**4*x**m/(m**3 + 12*m**2 + 39*m + 28) + b**2*c**m*m**2*x**7*x**m/(m**3 + 12*m**2 + 39*m + 28) + 5*b**2*c**m*m*x**7*x**m/(m**3 + 12*m**2 + 39*m + 28) + 4*b**2*c**m*x**7*x**m/(m**3 + 12*m**2 + 39*m + 28), True))","A",0
2757,1,345,0,0.895879," ","integrate((c*x)**m*(b*x**2+a)**2,x)","\begin{cases} \frac{- \frac{a^{2}}{4 x^{4}} - \frac{a b}{x^{2}} + b^{2} \log{\left(x \right)}}{c^{5}} & \text{for}\: m = -5 \\\frac{- \frac{a^{2}}{2 x^{2}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{2}}{2}}{c^{3}} & \text{for}\: m = -3 \\\frac{a^{2} \log{\left(x \right)} + a b x^{2} + \frac{b^{2} x^{4}}{4}}{c} & \text{for}\: m = -1 \\\frac{a^{2} c^{m} m^{2} x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{8 a^{2} c^{m} m x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{15 a^{2} c^{m} x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{2 a b c^{m} m^{2} x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{12 a b c^{m} m x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{10 a b c^{m} x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{b^{2} c^{m} m^{2} x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{4 b^{2} c^{m} m x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{3 b^{2} c^{m} x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**2/(4*x**4) - a*b/x**2 + b**2*log(x))/c**5, Eq(m, -5)), ((-a**2/(2*x**2) + 2*a*b*log(x) + b**2*x**2/2)/c**3, Eq(m, -3)), ((a**2*log(x) + a*b*x**2 + b**2*x**4/4)/c, Eq(m, -1)), (a**2*c**m*m**2*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 8*a**2*c**m*m*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 15*a**2*c**m*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 2*a*b*c**m*m**2*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 12*a*b*c**m*m*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 10*a*b*c**m*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + b**2*c**m*m**2*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15) + 4*b**2*c**m*m*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15) + 3*b**2*c**m*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15), True))","A",0
2758,1,338,0,0.549657," ","integrate((c*x)**m*(b*x+a)**2,x)","\begin{cases} \frac{- \frac{a^{2}}{2 x^{2}} - \frac{2 a b}{x} + b^{2} \log{\left(x \right)}}{c^{3}} & \text{for}\: m = -3 \\\frac{- \frac{a^{2}}{x} + 2 a b \log{\left(x \right)} + b^{2} x}{c^{2}} & \text{for}\: m = -2 \\\frac{a^{2} \log{\left(x \right)} + 2 a b x + \frac{b^{2} x^{2}}{2}}{c} & \text{for}\: m = -1 \\\frac{a^{2} c^{m} m^{2} x x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{5 a^{2} c^{m} m x x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{6 a^{2} c^{m} x x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{2 a b c^{m} m^{2} x^{2} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{8 a b c^{m} m x^{2} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{6 a b c^{m} x^{2} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{b^{2} c^{m} m^{2} x^{3} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{3 b^{2} c^{m} m x^{3} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{2 b^{2} c^{m} x^{3} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**2/(2*x**2) - 2*a*b/x + b**2*log(x))/c**3, Eq(m, -3)), ((-a**2/x + 2*a*b*log(x) + b**2*x)/c**2, Eq(m, -2)), ((a**2*log(x) + 2*a*b*x + b**2*x**2/2)/c, Eq(m, -1)), (a**2*c**m*m**2*x*x**m/(m**3 + 6*m**2 + 11*m + 6) + 5*a**2*c**m*m*x*x**m/(m**3 + 6*m**2 + 11*m + 6) + 6*a**2*c**m*x*x**m/(m**3 + 6*m**2 + 11*m + 6) + 2*a*b*c**m*m**2*x**2*x**m/(m**3 + 6*m**2 + 11*m + 6) + 8*a*b*c**m*m*x**2*x**m/(m**3 + 6*m**2 + 11*m + 6) + 6*a*b*c**m*x**2*x**m/(m**3 + 6*m**2 + 11*m + 6) + b**2*c**m*m**2*x**3*x**m/(m**3 + 6*m**2 + 11*m + 6) + 3*b**2*c**m*m*x**3*x**m/(m**3 + 6*m**2 + 11*m + 6) + 2*b**2*c**m*x**3*x**m/(m**3 + 6*m**2 + 11*m + 6), True))","A",0
2759,1,202,0,0.574540," ","integrate((a+b/x)**2*(c*x)**m,x)","\begin{cases} \frac{a^{2} \log{\left(x \right)} - \frac{2 a b}{x} - \frac{b^{2}}{2 x^{2}}}{c} & \text{for}\: m = -1 \\a^{2} x + 2 a b \log{\left(x \right)} - \frac{b^{2}}{x} & \text{for}\: m = 0 \\c \left(\frac{a^{2} x^{2}}{2} + 2 a b x + b^{2} \log{\left(x \right)}\right) & \text{for}\: m = 1 \\\frac{a^{2} c^{m} m^{2} x^{2} x^{m}}{m^{3} x - m x} - \frac{a^{2} c^{m} m x^{2} x^{m}}{m^{3} x - m x} + \frac{2 a b c^{m} m^{2} x x^{m}}{m^{3} x - m x} - \frac{2 a b c^{m} x x^{m}}{m^{3} x - m x} + \frac{b^{2} c^{m} m^{2} x^{m}}{m^{3} x - m x} + \frac{b^{2} c^{m} m x^{m}}{m^{3} x - m x} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a**2*log(x) - 2*a*b/x - b**2/(2*x**2))/c, Eq(m, -1)), (a**2*x + 2*a*b*log(x) - b**2/x, Eq(m, 0)), (c*(a**2*x**2/2 + 2*a*b*x + b**2*log(x)), Eq(m, 1)), (a**2*c**m*m**2*x**2*x**m/(m**3*x - m*x) - a**2*c**m*m*x**2*x**m/(m**3*x - m*x) + 2*a*b*c**m*m**2*x*x**m/(m**3*x - m*x) - 2*a*b*c**m*x*x**m/(m**3*x - m*x) + b**2*c**m*m**2*x**m/(m**3*x - m*x) + b**2*c**m*m*x**m/(m**3*x - m*x), True))","A",0
2760,1,401,0,1.109205," ","integrate((a+b/x**2)**2*(c*x)**m,x)","\begin{cases} \frac{a^{2} \log{\left(x \right)} - \frac{a b}{x^{2}} - \frac{b^{2}}{4 x^{4}}}{c} & \text{for}\: m = -1 \\c \left(\frac{a^{2} x^{2}}{2} + 2 a b \log{\left(x \right)} - \frac{b^{2}}{2 x^{2}}\right) & \text{for}\: m = 1 \\c^{3} \left(\frac{a^{2} x^{4}}{4} + a b x^{2} + b^{2} \log{\left(x \right)}\right) & \text{for}\: m = 3 \\\frac{a^{2} c^{m} m^{2} x^{4} x^{m}}{m^{3} x^{3} - 3 m^{2} x^{3} - m x^{3} + 3 x^{3}} - \frac{4 a^{2} c^{m} m x^{4} x^{m}}{m^{3} x^{3} - 3 m^{2} x^{3} - m x^{3} + 3 x^{3}} + \frac{3 a^{2} c^{m} x^{4} x^{m}}{m^{3} x^{3} - 3 m^{2} x^{3} - m x^{3} + 3 x^{3}} + \frac{2 a b c^{m} m^{2} x^{2} x^{m}}{m^{3} x^{3} - 3 m^{2} x^{3} - m x^{3} + 3 x^{3}} - \frac{4 a b c^{m} m x^{2} x^{m}}{m^{3} x^{3} - 3 m^{2} x^{3} - m x^{3} + 3 x^{3}} - \frac{6 a b c^{m} x^{2} x^{m}}{m^{3} x^{3} - 3 m^{2} x^{3} - m x^{3} + 3 x^{3}} + \frac{b^{2} c^{m} m^{2} x^{m}}{m^{3} x^{3} - 3 m^{2} x^{3} - m x^{3} + 3 x^{3}} - \frac{b^{2} c^{m} x^{m}}{m^{3} x^{3} - 3 m^{2} x^{3} - m x^{3} + 3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a**2*log(x) - a*b/x**2 - b**2/(4*x**4))/c, Eq(m, -1)), (c*(a**2*x**2/2 + 2*a*b*log(x) - b**2/(2*x**2)), Eq(m, 1)), (c**3*(a**2*x**4/4 + a*b*x**2 + b**2*log(x)), Eq(m, 3)), (a**2*c**m*m**2*x**4*x**m/(m**3*x**3 - 3*m**2*x**3 - m*x**3 + 3*x**3) - 4*a**2*c**m*m*x**4*x**m/(m**3*x**3 - 3*m**2*x**3 - m*x**3 + 3*x**3) + 3*a**2*c**m*x**4*x**m/(m**3*x**3 - 3*m**2*x**3 - m*x**3 + 3*x**3) + 2*a*b*c**m*m**2*x**2*x**m/(m**3*x**3 - 3*m**2*x**3 - m*x**3 + 3*x**3) - 4*a*b*c**m*m*x**2*x**m/(m**3*x**3 - 3*m**2*x**3 - m*x**3 + 3*x**3) - 6*a*b*c**m*x**2*x**m/(m**3*x**3 - 3*m**2*x**3 - m*x**3 + 3*x**3) + b**2*c**m*m**2*x**m/(m**3*x**3 - 3*m**2*x**3 - m*x**3 + 3*x**3) - b**2*c**m*x**m/(m**3*x**3 - 3*m**2*x**3 - m*x**3 + 3*x**3), True))","A",0
2761,1,464,0,1.606497," ","integrate((a+b/x**3)**2*(c*x)**m,x)","\begin{cases} \frac{a^{2} \log{\left(x \right)} - \frac{2 a b}{3 x^{3}} - \frac{b^{2}}{6 x^{6}}}{c} & \text{for}\: m = -1 \\c^{2} \left(\frac{a^{2} x^{3}}{3} + 2 a b \log{\left(x \right)} - \frac{b^{2}}{3 x^{3}}\right) & \text{for}\: m = 2 \\c^{5} \left(\frac{a^{2} x^{6}}{6} + \frac{2 a b x^{3}}{3} + b^{2} \log{\left(x \right)}\right) & \text{for}\: m = 5 \\\frac{a^{2} c^{m} m^{2} x^{6} x^{m}}{m^{3} x^{5} - 6 m^{2} x^{5} + 3 m x^{5} + 10 x^{5}} - \frac{7 a^{2} c^{m} m x^{6} x^{m}}{m^{3} x^{5} - 6 m^{2} x^{5} + 3 m x^{5} + 10 x^{5}} + \frac{10 a^{2} c^{m} x^{6} x^{m}}{m^{3} x^{5} - 6 m^{2} x^{5} + 3 m x^{5} + 10 x^{5}} + \frac{2 a b c^{m} m^{2} x^{3} x^{m}}{m^{3} x^{5} - 6 m^{2} x^{5} + 3 m x^{5} + 10 x^{5}} - \frac{8 a b c^{m} m x^{3} x^{m}}{m^{3} x^{5} - 6 m^{2} x^{5} + 3 m x^{5} + 10 x^{5}} - \frac{10 a b c^{m} x^{3} x^{m}}{m^{3} x^{5} - 6 m^{2} x^{5} + 3 m x^{5} + 10 x^{5}} + \frac{b^{2} c^{m} m^{2} x^{m}}{m^{3} x^{5} - 6 m^{2} x^{5} + 3 m x^{5} + 10 x^{5}} - \frac{b^{2} c^{m} m x^{m}}{m^{3} x^{5} - 6 m^{2} x^{5} + 3 m x^{5} + 10 x^{5}} - \frac{2 b^{2} c^{m} x^{m}}{m^{3} x^{5} - 6 m^{2} x^{5} + 3 m x^{5} + 10 x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a**2*log(x) - 2*a*b/(3*x**3) - b**2/(6*x**6))/c, Eq(m, -1)), (c**2*(a**2*x**3/3 + 2*a*b*log(x) - b**2/(3*x**3)), Eq(m, 2)), (c**5*(a**2*x**6/6 + 2*a*b*x**3/3 + b**2*log(x)), Eq(m, 5)), (a**2*c**m*m**2*x**6*x**m/(m**3*x**5 - 6*m**2*x**5 + 3*m*x**5 + 10*x**5) - 7*a**2*c**m*m*x**6*x**m/(m**3*x**5 - 6*m**2*x**5 + 3*m*x**5 + 10*x**5) + 10*a**2*c**m*x**6*x**m/(m**3*x**5 - 6*m**2*x**5 + 3*m*x**5 + 10*x**5) + 2*a*b*c**m*m**2*x**3*x**m/(m**3*x**5 - 6*m**2*x**5 + 3*m*x**5 + 10*x**5) - 8*a*b*c**m*m*x**3*x**m/(m**3*x**5 - 6*m**2*x**5 + 3*m*x**5 + 10*x**5) - 10*a*b*c**m*x**3*x**m/(m**3*x**5 - 6*m**2*x**5 + 3*m*x**5 + 10*x**5) + b**2*c**m*m**2*x**m/(m**3*x**5 - 6*m**2*x**5 + 3*m*x**5 + 10*x**5) - b**2*c**m*m*x**m/(m**3*x**5 - 6*m**2*x**5 + 3*m*x**5 + 10*x**5) - 2*b**2*c**m*x**m/(m**3*x**5 - 6*m**2*x**5 + 3*m*x**5 + 10*x**5), True))","A",0
2762,1,54,0,3.835519," ","integrate((c*x)**(-1-1/2*n)/(a+b*x**n),x)","- \frac{2 c^{- \frac{n}{2}} x^{- \frac{n}{2}}}{a c n} - \frac{2 \sqrt{b} c^{- \frac{n}{2}} \operatorname{atan}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{a^{\frac{3}{2}} c n}"," ",0,"-2*c**(-n/2)*x**(-n/2)/(a*c*n) - 2*sqrt(b)*c**(-n/2)*atan(sqrt(b)*x**(n/2)/sqrt(a))/(a**(3/2)*c*n)","A",0
2763,1,226,0,4.287141," ","integrate((c*x)**(-1-2/3*n)/(a+b*x**n),x)","\frac{c^{- \frac{2 n}{3}} x^{- \frac{2 n}{3}} \Gamma\left(- \frac{2}{3}\right)}{a c n \Gamma\left(\frac{1}{3}\right)} - \frac{2 b^{\frac{2}{3}} c^{- \frac{2 n}{3}} e^{- \frac{i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{2}{3}\right)}{3 a^{\frac{5}{3}} c n \Gamma\left(\frac{1}{3}\right)} + \frac{2 b^{\frac{2}{3}} c^{- \frac{2 n}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{2}{3}\right)}{3 a^{\frac{5}{3}} c n \Gamma\left(\frac{1}{3}\right)} - \frac{2 b^{\frac{2}{3}} c^{- \frac{2 n}{3}} e^{\frac{i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{2}{3}\right)}{3 a^{\frac{5}{3}} c n \Gamma\left(\frac{1}{3}\right)}"," ",0,"c**(-2*n/3)*x**(-2*n/3)*gamma(-2/3)/(a*c*n*gamma(1/3)) - 2*b**(2/3)*c**(-2*n/3)*exp(-I*pi/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(-2/3)/(3*a**(5/3)*c*n*gamma(1/3)) + 2*b**(2/3)*c**(-2*n/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(I*pi)/a**(1/3))*gamma(-2/3)/(3*a**(5/3)*c*n*gamma(1/3)) - 2*b**(2/3)*c**(-2*n/3)*exp(I*pi/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(-2/3)/(3*a**(5/3)*c*n*gamma(1/3))","C",0
2764,1,309,0,4.551342," ","integrate((c*x)**(-1-3/4*n)/(a+b*x**n),x)","\frac{c^{- \frac{3 n}{4}} x^{- \frac{3 n}{4}} \Gamma\left(- \frac{3}{4}\right)}{a c n \Gamma\left(\frac{1}{4}\right)} - \frac{3 b^{\frac{3}{4}} c^{- \frac{3 n}{4}} e^{- \frac{i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{3}{4}\right)}{4 a^{\frac{7}{4}} c n \Gamma\left(\frac{1}{4}\right)} + \frac{3 i b^{\frac{3}{4}} c^{- \frac{3 n}{4}} e^{- \frac{i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{3 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{3}{4}\right)}{4 a^{\frac{7}{4}} c n \Gamma\left(\frac{1}{4}\right)} + \frac{3 b^{\frac{3}{4}} c^{- \frac{3 n}{4}} e^{- \frac{i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{5 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{3}{4}\right)}{4 a^{\frac{7}{4}} c n \Gamma\left(\frac{1}{4}\right)} - \frac{3 i b^{\frac{3}{4}} c^{- \frac{3 n}{4}} e^{- \frac{i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{7 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{3}{4}\right)}{4 a^{\frac{7}{4}} c n \Gamma\left(\frac{1}{4}\right)}"," ",0,"c**(-3*n/4)*x**(-3*n/4)*gamma(-3/4)/(a*c*n*gamma(1/4)) - 3*b**(3/4)*c**(-3*n/4)*exp(-I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(I*pi/4)/a**(1/4))*gamma(-3/4)/(4*a**(7/4)*c*n*gamma(1/4)) + 3*I*b**(3/4)*c**(-3*n/4)*exp(-I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(3*I*pi/4)/a**(1/4))*gamma(-3/4)/(4*a**(7/4)*c*n*gamma(1/4)) + 3*b**(3/4)*c**(-3*n/4)*exp(-I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(5*I*pi/4)/a**(1/4))*gamma(-3/4)/(4*a**(7/4)*c*n*gamma(1/4)) - 3*I*b**(3/4)*c**(-3*n/4)*exp(-I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(7*I*pi/4)/a**(1/4))*gamma(-3/4)/(4*a**(7/4)*c*n*gamma(1/4))","C",0
2765,1,34,0,4.106016," ","integrate((c*x)**(-1-n)/(a+b*x**n),x)","- \frac{c^{- n} x^{- n}}{a c n} + \frac{b c^{- n} \log{\left(\frac{a x^{- n}}{b} + 1 \right)}}{a^{2} c n}"," ",0,"-c**(-n)*x**(-n)/(a*c*n) + b*c**(-n)*log(a*x**(-n)/b + 1)/(a**2*c*n)","A",0
2766,1,54,0,3.779393," ","integrate((c*x)**(-1-1/2*n)/(a+b*x**n),x)","- \frac{2 c^{- \frac{n}{2}} x^{- \frac{n}{2}}}{a c n} - \frac{2 \sqrt{b} c^{- \frac{n}{2}} \operatorname{atan}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{a^{\frac{3}{2}} c n}"," ",0,"-2*c**(-n/2)*x**(-n/2)/(a*c*n) - 2*sqrt(b)*c**(-n/2)*atan(sqrt(b)*x**(n/2)/sqrt(a))/(a**(3/2)*c*n)","A",0
2767,1,216,0,4.227572," ","integrate((c*x)**(-1-1/3*n)/(a+b*x**n),x)","\frac{c^{- \frac{n}{3}} x^{- \frac{n}{3}} \Gamma\left(- \frac{1}{3}\right)}{a c n \Gamma\left(\frac{2}{3}\right)} - \frac{\sqrt[3]{b} c^{- \frac{n}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a^{\frac{4}{3}} c n \Gamma\left(\frac{2}{3}\right)} - \frac{\sqrt[3]{b} c^{- \frac{n}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a^{\frac{4}{3}} c n \Gamma\left(\frac{2}{3}\right)} - \frac{\sqrt[3]{b} c^{- \frac{n}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a^{\frac{4}{3}} c n \Gamma\left(\frac{2}{3}\right)}"," ",0,"c**(-n/3)*x**(-n/3)*gamma(-1/3)/(a*c*n*gamma(2/3)) - b**(1/3)*c**(-n/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(-1/3)/(3*a**(4/3)*c*n*gamma(2/3)) - b**(1/3)*c**(-n/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(I*pi)/a**(1/3))*gamma(-1/3)/(3*a**(4/3)*c*n*gamma(2/3)) - b**(1/3)*c**(-n/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(-1/3)/(3*a**(4/3)*c*n*gamma(2/3))","C",0
2768,1,299,0,4.655709," ","integrate((c*x)**(-1-1/4*n)/(a+b*x**n),x)","\frac{c^{- \frac{n}{4}} x^{- \frac{n}{4}} \Gamma\left(- \frac{1}{4}\right)}{a c n \Gamma\left(\frac{3}{4}\right)} - \frac{\sqrt[4]{b} c^{- \frac{n}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{1}{4}\right)}{4 a^{\frac{5}{4}} c n \Gamma\left(\frac{3}{4}\right)} - \frac{i \sqrt[4]{b} c^{- \frac{n}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{3 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{1}{4}\right)}{4 a^{\frac{5}{4}} c n \Gamma\left(\frac{3}{4}\right)} + \frac{\sqrt[4]{b} c^{- \frac{n}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{5 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{1}{4}\right)}{4 a^{\frac{5}{4}} c n \Gamma\left(\frac{3}{4}\right)} + \frac{i \sqrt[4]{b} c^{- \frac{n}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{7 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{1}{4}\right)}{4 a^{\frac{5}{4}} c n \Gamma\left(\frac{3}{4}\right)}"," ",0,"c**(-n/4)*x**(-n/4)*gamma(-1/4)/(a*c*n*gamma(3/4)) - b**(1/4)*c**(-n/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(I*pi/4)/a**(1/4))*gamma(-1/4)/(4*a**(5/4)*c*n*gamma(3/4)) - I*b**(1/4)*c**(-n/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(3*I*pi/4)/a**(1/4))*gamma(-1/4)/(4*a**(5/4)*c*n*gamma(3/4)) + b**(1/4)*c**(-n/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(5*I*pi/4)/a**(1/4))*gamma(-1/4)/(4*a**(5/4)*c*n*gamma(3/4)) + I*b**(1/4)*c**(-n/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(7*I*pi/4)/a**(1/4))*gamma(-1/4)/(4*a**(5/4)*c*n*gamma(3/4))","C",0
2769,1,82,0,4.650401," ","integrate((c*x)**(-1-3/2*n)/(a+b*x**n),x)","- \frac{2 c^{- \frac{3 n}{2}} x^{- \frac{3 n}{2}}}{3 a c n} + \frac{2 b c^{- \frac{3 n}{2}} x^{- \frac{n}{2}}}{a^{2} c n} + \frac{2 b^{\frac{3}{2}} c^{- \frac{3 n}{2}} \operatorname{atan}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{a^{\frac{5}{2}} c n}"," ",0,"-2*c**(-3*n/2)*x**(-3*n/2)/(3*a*c*n) + 2*b*c**(-3*n/2)*x**(-n/2)/(a**2*c*n) + 2*b**(3/2)*c**(-3*n/2)*atan(sqrt(b)*x**(n/2)/sqrt(a))/(a**(5/2)*c*n)","A",0
2770,1,272,0,5.169667," ","integrate((c*x)**(-1-4/3*n)/(a+b*x**n),x)","\frac{c^{- \frac{4 n}{3}} x^{- \frac{4 n}{3}} \Gamma\left(- \frac{4}{3}\right)}{a c n \Gamma\left(- \frac{1}{3}\right)} - \frac{4 b c^{- \frac{4 n}{3}} x^{- \frac{n}{3}} \Gamma\left(- \frac{4}{3}\right)}{a^{2} c n \Gamma\left(- \frac{1}{3}\right)} + \frac{4 b^{\frac{4}{3}} c^{- \frac{4 n}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{4}{3}\right)}{3 a^{\frac{7}{3}} c n \Gamma\left(- \frac{1}{3}\right)} + \frac{4 b^{\frac{4}{3}} c^{- \frac{4 n}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{4}{3}\right)}{3 a^{\frac{7}{3}} c n \Gamma\left(- \frac{1}{3}\right)} + \frac{4 b^{\frac{4}{3}} c^{- \frac{4 n}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} x^{\frac{n}{3}} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{4}{3}\right)}{3 a^{\frac{7}{3}} c n \Gamma\left(- \frac{1}{3}\right)}"," ",0,"c**(-4*n/3)*x**(-4*n/3)*gamma(-4/3)/(a*c*n*gamma(-1/3)) - 4*b*c**(-4*n/3)*x**(-n/3)*gamma(-4/3)/(a**2*c*n*gamma(-1/3)) + 4*b**(4/3)*c**(-4*n/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(-4/3)/(3*a**(7/3)*c*n*gamma(-1/3)) + 4*b**(4/3)*c**(-4*n/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(I*pi)/a**(1/3))*gamma(-4/3)/(3*a**(7/3)*c*n*gamma(-1/3)) + 4*b**(4/3)*c**(-4*n/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*x**(n/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(-4/3)/(3*a**(7/3)*c*n*gamma(-1/3))","C",0
2771,1,360,0,6.097238," ","integrate((c*x)**(-1-5/4*n)/(a+b*x**n),x)","\frac{c^{- \frac{5 n}{4}} x^{- \frac{5 n}{4}} \Gamma\left(- \frac{5}{4}\right)}{a c n \Gamma\left(- \frac{1}{4}\right)} - \frac{5 b c^{- \frac{5 n}{4}} x^{- \frac{n}{4}} \Gamma\left(- \frac{5}{4}\right)}{a^{2} c n \Gamma\left(- \frac{1}{4}\right)} + \frac{5 b^{\frac{5}{4}} c^{- \frac{5 n}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{5}{4}\right)}{4 a^{\frac{9}{4}} c n \Gamma\left(- \frac{1}{4}\right)} + \frac{5 i b^{\frac{5}{4}} c^{- \frac{5 n}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{3 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{5}{4}\right)}{4 a^{\frac{9}{4}} c n \Gamma\left(- \frac{1}{4}\right)} - \frac{5 b^{\frac{5}{4}} c^{- \frac{5 n}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{5 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{5}{4}\right)}{4 a^{\frac{9}{4}} c n \Gamma\left(- \frac{1}{4}\right)} - \frac{5 i b^{\frac{5}{4}} c^{- \frac{5 n}{4}} e^{- \frac{3 i \pi}{4}} \log{\left(1 - \frac{\sqrt[4]{b} x^{\frac{n}{4}} e^{\frac{7 i \pi}{4}}}{\sqrt[4]{a}} \right)} \Gamma\left(- \frac{5}{4}\right)}{4 a^{\frac{9}{4}} c n \Gamma\left(- \frac{1}{4}\right)}"," ",0,"c**(-5*n/4)*x**(-5*n/4)*gamma(-5/4)/(a*c*n*gamma(-1/4)) - 5*b*c**(-5*n/4)*x**(-n/4)*gamma(-5/4)/(a**2*c*n*gamma(-1/4)) + 5*b**(5/4)*c**(-5*n/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(I*pi/4)/a**(1/4))*gamma(-5/4)/(4*a**(9/4)*c*n*gamma(-1/4)) + 5*I*b**(5/4)*c**(-5*n/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(3*I*pi/4)/a**(1/4))*gamma(-5/4)/(4*a**(9/4)*c*n*gamma(-1/4)) - 5*b**(5/4)*c**(-5*n/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(5*I*pi/4)/a**(1/4))*gamma(-5/4)/(4*a**(9/4)*c*n*gamma(-1/4)) - 5*I*b**(5/4)*c**(-5*n/4)*exp(-3*I*pi/4)*log(1 - b**(1/4)*x**(n/4)*exp_polar(7*I*pi/4)/a**(1/4))*gamma(-5/4)/(4*a**(9/4)*c*n*gamma(-1/4))","C",0
2772,1,97,0,8.244397," ","integrate((c*x)**(4+n)/(a+b*x**n),x)","\frac{c^{4} c^{n} x^{5} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{5}{n}\right) \Gamma\left(1 + \frac{5}{n}\right)}{a n \Gamma\left(2 + \frac{5}{n}\right)} + \frac{5 c^{4} c^{n} x^{5} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{5}{n}\right) \Gamma\left(1 + \frac{5}{n}\right)}{a n^{2} \Gamma\left(2 + \frac{5}{n}\right)}"," ",0,"c**4*c**n*x**5*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 5/n)*gamma(1 + 5/n)/(a*n*gamma(2 + 5/n)) + 5*c**4*c**n*x**5*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 5/n)*gamma(1 + 5/n)/(a*n**2*gamma(2 + 5/n))","C",0
2773,1,97,0,5.523766," ","integrate((c*x)**(3+n)/(a+b*x**n),x)","\frac{c^{3} c^{n} x^{4} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{4}{n}\right) \Gamma\left(1 + \frac{4}{n}\right)}{a n \Gamma\left(2 + \frac{4}{n}\right)} + \frac{4 c^{3} c^{n} x^{4} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{4}{n}\right) \Gamma\left(1 + \frac{4}{n}\right)}{a n^{2} \Gamma\left(2 + \frac{4}{n}\right)}"," ",0,"c**3*c**n*x**4*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 4/n)*gamma(1 + 4/n)/(a*n*gamma(2 + 4/n)) + 4*c**3*c**n*x**4*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 4/n)*gamma(1 + 4/n)/(a*n**2*gamma(2 + 4/n))","C",0
2774,1,97,0,3.632130," ","integrate((c*x)**(2+n)/(a+b*x**n),x)","\frac{c^{2} c^{n} x^{3} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{3}{n}\right) \Gamma\left(1 + \frac{3}{n}\right)}{a n \Gamma\left(2 + \frac{3}{n}\right)} + \frac{3 c^{2} c^{n} x^{3} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{3}{n}\right) \Gamma\left(1 + \frac{3}{n}\right)}{a n^{2} \Gamma\left(2 + \frac{3}{n}\right)}"," ",0,"c**2*c**n*x**3*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 3/n)*gamma(1 + 3/n)/(a*n*gamma(2 + 3/n)) + 3*c**2*c**n*x**3*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 3/n)*gamma(1 + 3/n)/(a*n**2*gamma(2 + 3/n))","C",0
2775,1,94,0,2.646116," ","integrate((c*x)**(1+n)/(a+b*x**n),x)","\frac{c c^{n} x^{2} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{2}{n}\right) \Gamma\left(1 + \frac{2}{n}\right)}{a n \Gamma\left(2 + \frac{2}{n}\right)} + \frac{2 c c^{n} x^{2} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, 1 + \frac{2}{n}\right) \Gamma\left(1 + \frac{2}{n}\right)}{a n^{2} \Gamma\left(2 + \frac{2}{n}\right)}"," ",0,"c*c**n*x**2*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 2/n)*gamma(1 + 2/n)/(a*n*gamma(2 + 2/n)) + 2*c*c**n*x**2*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1 + 2/n)*gamma(1 + 2/n)/(a*n**2*gamma(2 + 2/n))","C",0
2776,1,41,0,1.219016," ","integrate((c*x)**n/(a+b*x**n),x)","- \frac{c^{n} x \Phi\left(\frac{a x^{- n} e^{i \pi}}{b}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{b n^{2} \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"-c**n*x*lerchphi(a*x**(-n)*exp_polar(I*pi)/b, 1, exp_polar(I*pi)/n)*gamma(1/n)/(b*n**2*gamma(1 + 1/n))","C",0
2777,1,17,0,4.800842," ","integrate((c*x)**(-1+n)/(a+b*x**n),x)","\frac{c^{n} \log{\left(1 + \frac{b x^{n}}{a} \right)}}{b c n}"," ",0,"c**n*log(1 + b*x**n/a)/(b*c*n)","A",0
2778,1,41,0,11.521397," ","integrate((c*x)**(-2+n)/(a+b*x**n),x)","\frac{c^{n} \Phi\left(\frac{a x^{- n} e^{i \pi}}{b}, 1, \frac{1}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{b c^{2} n^{2} x \Gamma\left(1 - \frac{1}{n}\right)}"," ",0,"c**n*lerchphi(a*x**(-n)*exp_polar(I*pi)/b, 1, 1/n)*gamma(-1/n)/(b*c**2*n**2*x*gamma(1 - 1/n))","C",0
2779,1,44,0,27.441970," ","integrate((c*x)**(-3+n)/(a+b*x**n),x)","\frac{2 c^{n} \Phi\left(\frac{a x^{- n} e^{i \pi}}{b}, 1, \frac{2}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{b c^{3} n^{2} x^{2} \Gamma\left(1 - \frac{2}{n}\right)}"," ",0,"2*c**n*lerchphi(a*x**(-n)*exp_polar(I*pi)/b, 1, 2/n)*gamma(-2/n)/(b*c**3*n**2*x**2*gamma(1 - 2/n))","C",0
2780,1,330,0,43.302543," ","integrate((c*x)**(-1+n)/(a+b*x**n)**2,x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge n = 0 \\- \frac{c^{n} x^{- n}}{b^{2} c n} & \text{for}\: a = 0 \\\frac{\tilde{\infty} c^{n} x^{n}}{c n} & \text{for}\: b = - a x^{- n} \\0^{n - 1} \left(\frac{n x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{n x \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{b n x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{b x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)}\right) & \text{for}\: c = 0 \\\frac{\log{\left(x \right)}}{c \left(a + b\right)^{2}} & \text{for}\: n = 0 \\\frac{c^{n} x^{n}}{a^{2} c n + a b c n x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(n, 0)), (-c**n*x**(-n)/(b**2*c*n), Eq(a, 0)), (zoo*c**n*x**n/(c*n), Eq(b, -a*x**(-n))), (0**(n - 1)*(n*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) + n*x*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) - x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) + b*n*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) - b*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n)))), Eq(c, 0)), (log(x)/(c*(a + b)**2), Eq(n, 0)), (c**n*x**n/(a**2*c*n + a*b*c*n*x**n), True))","A",0
2781,1,190,0,15.873753," ","integrate((c*x)**(-1+7/2*n)/(a+b*x**n)**(1/2),x)","\frac{5 a^{\frac{5}{2}} c^{\frac{7 n}{2}} x^{\frac{n}{2}}}{8 b^{3} c n \sqrt{1 + \frac{b x^{n}}{a}}} + \frac{5 a^{\frac{3}{2}} c^{\frac{7 n}{2}} x^{\frac{3 n}{2}}}{24 b^{2} c n \sqrt{1 + \frac{b x^{n}}{a}}} - \frac{\sqrt{a} c^{\frac{7 n}{2}} x^{\frac{5 n}{2}}}{12 b c n \sqrt{1 + \frac{b x^{n}}{a}}} - \frac{5 a^{3} c^{\frac{7 n}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{8 b^{\frac{7}{2}} c n} + \frac{c^{\frac{7 n}{2}} x^{\frac{7 n}{2}}}{3 \sqrt{a} c n \sqrt{1 + \frac{b x^{n}}{a}}}"," ",0,"5*a**(5/2)*c**(7*n/2)*x**(n/2)/(8*b**3*c*n*sqrt(1 + b*x**n/a)) + 5*a**(3/2)*c**(7*n/2)*x**(3*n/2)/(24*b**2*c*n*sqrt(1 + b*x**n/a)) - sqrt(a)*c**(7*n/2)*x**(5*n/2)/(12*b*c*n*sqrt(1 + b*x**n/a)) - 5*a**3*c**(7*n/2)*asinh(sqrt(b)*x**(n/2)/sqrt(a))/(8*b**(7/2)*c*n) + c**(7*n/2)*x**(7*n/2)/(3*sqrt(a)*c*n*sqrt(1 + b*x**n/a))","A",0
2782,1,150,0,11.851630," ","integrate((c*x)**(-1+5/2*n)/(a+b*x**n)**(1/2),x)","- \frac{3 a^{\frac{3}{2}} c^{\frac{5 n}{2}} x^{\frac{n}{2}}}{4 b^{2} c n \sqrt{1 + \frac{b x^{n}}{a}}} - \frac{\sqrt{a} c^{\frac{5 n}{2}} x^{\frac{3 n}{2}}}{4 b c n \sqrt{1 + \frac{b x^{n}}{a}}} + \frac{3 a^{2} c^{\frac{5 n}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{4 b^{\frac{5}{2}} c n} + \frac{c^{\frac{5 n}{2}} x^{\frac{5 n}{2}}}{2 \sqrt{a} c n \sqrt{1 + \frac{b x^{n}}{a}}}"," ",0,"-3*a**(3/2)*c**(5*n/2)*x**(n/2)/(4*b**2*c*n*sqrt(1 + b*x**n/a)) - sqrt(a)*c**(5*n/2)*x**(3*n/2)/(4*b*c*n*sqrt(1 + b*x**n/a)) + 3*a**2*c**(5*n/2)*asinh(sqrt(b)*x**(n/2)/sqrt(a))/(4*b**(5/2)*c*n) + c**(5*n/2)*x**(5*n/2)/(2*sqrt(a)*c*n*sqrt(1 + b*x**n/a))","A",0
2783,1,66,0,8.785290," ","integrate((c*x)**(-1+3/2*n)/(a+b*x**n)**(1/2),x)","\frac{\sqrt{a} c^{\frac{3 n}{2}} x^{\frac{n}{2}} \sqrt{1 + \frac{b x^{n}}{a}}}{b c n} - \frac{a c^{\frac{3 n}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{b^{\frac{3}{2}} c n}"," ",0,"sqrt(a)*c**(3*n/2)*x**(n/2)*sqrt(1 + b*x**n/a)/(b*c*n) - a*c**(3*n/2)*asinh(sqrt(b)*x**(n/2)/sqrt(a))/(b**(3/2)*c*n)","A",0
2784,1,31,0,7.111962," ","integrate((c*x)**(-1+1/2*n)/(a+b*x**n)**(1/2),x)","\frac{2 c^{\frac{n}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x^{\frac{n}{2}}}{\sqrt{a}} \right)}}{\sqrt{b} c n}"," ",0,"2*c**(n/2)*asinh(sqrt(b)*x**(n/2)/sqrt(a))/(sqrt(b)*c*n)","A",0
2785,1,29,0,5.454862," ","integrate((c*x)**(-1-1/2*n)/(a+b*x**n)**(1/2),x)","- \frac{2 \sqrt{b} c^{- \frac{n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{a c n}"," ",0,"-2*sqrt(b)*c**(-n/2)*sqrt(a*x**(-n)/b + 1)/(a*c*n)","A",0
2786,1,68,0,5.051595," ","integrate((c*x)**(-1-3/2*n)/(a+b*x**n)**(1/2),x)","- \frac{2 \sqrt{b} c^{- \frac{3 n}{2}} x^{- n} \sqrt{\frac{a x^{- n}}{b} + 1}}{3 a c n} + \frac{4 b^{\frac{3}{2}} c^{- \frac{3 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{3 a^{2} c n}"," ",0,"-2*sqrt(b)*c**(-3*n/2)*x**(-n)*sqrt(a*x**(-n)/b + 1)/(3*a*c*n) + 4*b**(3/2)*c**(-3*n/2)*sqrt(a*x**(-n)/b + 1)/(3*a**2*c*n)","A",0
2787,1,396,0,5.377011," ","integrate((c*x)**(-1-5/2*n)/(a+b*x**n)**(1/2),x)","- \frac{6 a^{4} b^{\frac{9}{2}} c^{- \frac{5 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(15 a^{5} b^{4} n x^{2 n} + 30 a^{4} b^{5} n x^{3 n} + 15 a^{3} b^{6} n x^{4 n}\right)} - \frac{4 a^{3} b^{\frac{11}{2}} c^{- \frac{5 n}{2}} x^{n} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(15 a^{5} b^{4} n x^{2 n} + 30 a^{4} b^{5} n x^{3 n} + 15 a^{3} b^{6} n x^{4 n}\right)} - \frac{6 a^{2} b^{\frac{13}{2}} c^{- \frac{5 n}{2}} x^{2 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(15 a^{5} b^{4} n x^{2 n} + 30 a^{4} b^{5} n x^{3 n} + 15 a^{3} b^{6} n x^{4 n}\right)} - \frac{24 a b^{\frac{15}{2}} c^{- \frac{5 n}{2}} x^{3 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(15 a^{5} b^{4} n x^{2 n} + 30 a^{4} b^{5} n x^{3 n} + 15 a^{3} b^{6} n x^{4 n}\right)} - \frac{16 b^{\frac{17}{2}} c^{- \frac{5 n}{2}} x^{4 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(15 a^{5} b^{4} n x^{2 n} + 30 a^{4} b^{5} n x^{3 n} + 15 a^{3} b^{6} n x^{4 n}\right)}"," ",0,"-6*a**4*b**(9/2)*c**(-5*n/2)*sqrt(a*x**(-n)/b + 1)/(c*(15*a**5*b**4*n*x**(2*n) + 30*a**4*b**5*n*x**(3*n) + 15*a**3*b**6*n*x**(4*n))) - 4*a**3*b**(11/2)*c**(-5*n/2)*x**n*sqrt(a*x**(-n)/b + 1)/(c*(15*a**5*b**4*n*x**(2*n) + 30*a**4*b**5*n*x**(3*n) + 15*a**3*b**6*n*x**(4*n))) - 6*a**2*b**(13/2)*c**(-5*n/2)*x**(2*n)*sqrt(a*x**(-n)/b + 1)/(c*(15*a**5*b**4*n*x**(2*n) + 30*a**4*b**5*n*x**(3*n) + 15*a**3*b**6*n*x**(4*n))) - 24*a*b**(15/2)*c**(-5*n/2)*x**(3*n)*sqrt(a*x**(-n)/b + 1)/(c*(15*a**5*b**4*n*x**(2*n) + 30*a**4*b**5*n*x**(3*n) + 15*a**3*b**6*n*x**(4*n))) - 16*b**(17/2)*c**(-5*n/2)*x**(4*n)*sqrt(a*x**(-n)/b + 1)/(c*(15*a**5*b**4*n*x**(2*n) + 30*a**4*b**5*n*x**(3*n) + 15*a**3*b**6*n*x**(4*n)))","B",0
2788,1,665,0,5.908327," ","integrate((c*x)**(-1-7/2*n)/(a+b*x**n)**(1/2),x)","- \frac{10 a^{6} b^{\frac{19}{2}} c^{- \frac{7 n}{2}} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}\right)} - \frac{18 a^{5} b^{\frac{21}{2}} c^{- \frac{7 n}{2}} x^{n} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}\right)} - \frac{10 a^{4} b^{\frac{23}{2}} c^{- \frac{7 n}{2}} x^{2 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}\right)} + \frac{10 a^{3} b^{\frac{25}{2}} c^{- \frac{7 n}{2}} x^{3 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}\right)} + \frac{60 a^{2} b^{\frac{27}{2}} c^{- \frac{7 n}{2}} x^{4 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}\right)} + \frac{80 a b^{\frac{29}{2}} c^{- \frac{7 n}{2}} x^{5 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}\right)} + \frac{32 b^{\frac{31}{2}} c^{- \frac{7 n}{2}} x^{6 n} \sqrt{\frac{a x^{- n}}{b} + 1}}{c \left(35 a^{7} b^{9} n x^{3 n} + 105 a^{6} b^{10} n x^{4 n} + 105 a^{5} b^{11} n x^{5 n} + 35 a^{4} b^{12} n x^{6 n}\right)}"," ",0,"-10*a**6*b**(19/2)*c**(-7*n/2)*sqrt(a*x**(-n)/b + 1)/(c*(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n))) - 18*a**5*b**(21/2)*c**(-7*n/2)*x**n*sqrt(a*x**(-n)/b + 1)/(c*(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n))) - 10*a**4*b**(23/2)*c**(-7*n/2)*x**(2*n)*sqrt(a*x**(-n)/b + 1)/(c*(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n))) + 10*a**3*b**(25/2)*c**(-7*n/2)*x**(3*n)*sqrt(a*x**(-n)/b + 1)/(c*(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n))) + 60*a**2*b**(27/2)*c**(-7*n/2)*x**(4*n)*sqrt(a*x**(-n)/b + 1)/(c*(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n))) + 80*a*b**(29/2)*c**(-7*n/2)*x**(5*n)*sqrt(a*x**(-n)/b + 1)/(c*(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n))) + 32*b**(31/2)*c**(-7*n/2)*x**(6*n)*sqrt(a*x**(-n)/b + 1)/(c*(35*a**7*b**9*n*x**(3*n) + 105*a**6*b**10*n*x**(4*n) + 105*a**5*b**11*n*x**(5*n) + 35*a**4*b**12*n*x**(6*n)))","B",0
2789,1,58,0,9.774185," ","integrate((c*x)**m*(a+b*x**n)**p,x)","\frac{a^{p} c^{m} x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{n} + \frac{1}{n} \\ \frac{m}{n} + 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}"," ",0,"a**p*c**m*x*x**m*gamma(m/n + 1/n)*hyper((-p, m/n + 1/n), (m/n + 1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(m/n + 1 + 1/n))","C",0
2790,1,51,0,7.632180," ","integrate((c*x)**(3*n)*(a+b*x**n)**p,x)","\frac{a^{p} c^{3 n} x x^{3 n} \Gamma\left(3 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 3 + \frac{1}{n} \\ 4 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(4 + \frac{1}{n}\right)}"," ",0,"a**p*c**(3*n)*x*x**(3*n)*gamma(3 + 1/n)*hyper((-p, 3 + 1/n), (4 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(4 + 1/n))","C",0
2791,1,51,0,8.080244," ","integrate((c*x)**(2*n)*(a+b*x**n)**p,x)","\frac{a^{p} c^{2 n} x x^{2 n} \Gamma\left(2 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 2 + \frac{1}{n} \\ 3 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(3 + \frac{1}{n}\right)}"," ",0,"a**p*c**(2*n)*x*x**(2*n)*gamma(2 + 1/n)*hyper((-p, 2 + 1/n), (3 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(3 + 1/n))","C",0
2792,1,48,0,7.318936," ","integrate((c*x)**n*(a+b*x**n)**p,x)","\frac{a^{p} c^{n} x x^{n} \Gamma\left(1 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 + \frac{1}{n} \\ 2 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(2 + \frac{1}{n}\right)}"," ",0,"a**p*c**n*x*x**n*gamma(1 + 1/n)*hyper((-p, 1 + 1/n), (2 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(2 + 1/n))","C",0
2793,1,37,0,1.640193," ","integrate((a+b*x**n)**p,x)","\frac{a^{p} x \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{n}, - p \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a**p*x*gamma(1/n)*hyper((1/n, -p), (1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1 + 1/n))","C",0
2794,1,44,0,7.575060," ","integrate((a+b*x**n)**p/((c*x)**n),x)","\frac{a^{p} c^{- n} x x^{- n} \Gamma\left(-1 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, -1 + \frac{1}{n} \\ \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(\frac{1}{n}\right)}"," ",0,"a**p*c**(-n)*x*x**(-n)*gamma(-1 + 1/n)*hyper((-p, -1 + 1/n), (1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(1/n))","C",0
2795,1,51,0,7.667737," ","integrate((a+b*x**n)**p/((c*x)**(2*n)),x)","\frac{a^{p} c^{- 2 n} x x^{- 2 n} \Gamma\left(-2 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, -2 + \frac{1}{n} \\ -1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(-1 + \frac{1}{n}\right)}"," ",0,"a**p*c**(-2*n)*x*x**(-2*n)*gamma(-2 + 1/n)*hyper((-p, -2 + 1/n), (-1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(-1 + 1/n))","C",0
2796,1,51,0,7.626430," ","integrate((a+b*x**n)**p/((c*x)**(3*n)),x)","\frac{a^{p} c^{- 3 n} x x^{- 3 n} \Gamma\left(-3 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, -3 + \frac{1}{n} \\ -2 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{n \Gamma\left(-2 + \frac{1}{n}\right)}"," ",0,"a**p*c**(-3*n)*x*x**(-3*n)*gamma(-3 + 1/n)*hyper((-p, -3 + 1/n), (-2 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(n*gamma(-2 + 1/n))","C",0
2797,1,44,0,119.276386," ","integrate((c*x)**(-n*p-1)*(a+b*x**n)**p,x)","\frac{a^{p} c^{- n p} x^{- n p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{c n \Gamma\left(1 - p\right)}"," ",0,"a**p*c**(-n*p)*x**(-n*p)*gamma(-p)*hyper((-p, -p), (1 - p,), b*x**n*exp_polar(I*pi)/a)/(c*n*gamma(1 - p))","C",0
2798,-1,0,0,0.000000," ","integrate((c*x)**(-n*p-n-1)*(a+b*x**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2799,-1,0,0,0.000000," ","integrate((c*x)**(-n*p-2*n-1)*(a+b*x**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2800,-1,0,0,0.000000," ","integrate((c*x)**(-n*p-3*n-1)*(a+b*x**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2801,-1,0,0,0.000000," ","integrate((c*x)**(-n*p-4*n-1)*(a+b*x**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2802,0,0,0,0.000000," ","integrate((c*(b*x+a)**2)**(5/2),x)","\int \left(c \left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((c*(a + b*x)**2)**(5/2), x)","F",0
2803,0,0,0,0.000000," ","integrate((c*(b*x+a)**2)**(3/2),x)","\int \left(c \left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c*(a + b*x)**2)**(3/2), x)","F",0
2804,0,0,0,0.000000," ","integrate((c*(b*x+a)**2)**(1/2),x)","\int \sqrt{c \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(sqrt(c*(a + b*x)**2), x)","F",0
2805,0,0,0,0.000000," ","integrate(1/(c*(b*x+a)**2)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a + b x\right)^{2}}}\, dx"," ",0,"Integral(1/sqrt(c*(a + b*x)**2), x)","F",0
2806,0,0,0,0.000000," ","integrate(1/(c*(b*x+a)**2)**(3/2),x)","\int \frac{1}{\left(c \left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*(a + b*x)**2)**(-3/2), x)","F",0
2807,0,0,0,0.000000," ","integrate(1/(c*(b*x+a)**2)**(5/2),x)","\int \frac{1}{\left(c \left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c*(a + b*x)**2)**(-5/2), x)","F",0
2808,1,8,0,0.069834," ","integrate(((3+5*x)**2)**(1/2),x)","\frac{5 x^{2}}{2} + 3 x"," ",0,"5*x**2/2 + 3*x","A",0
2809,1,7,0,0.072203," ","integrate(((6+10*x)**2)**(1/2),x)","5 x^{2} + 6 x"," ",0,"5*x**2 + 6*x","A",0
2810,1,7,0,0.074945," ","integrate(1/((3+5*x)**2)**(1/2),x)","\frac{\log{\left(5 x + 3 \right)}}{5}"," ",0,"log(5*x + 3)/5","A",0
2811,1,7,0,0.075408," ","integrate(1/((6+10*x)**2)**(1/2),x)","\frac{\log{\left(10 x + 6 \right)}}{10}"," ",0,"log(10*x + 6)/10","A",0
2812,0,0,0,0.000000," ","integrate(1/(-(2+3*x)**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(3 x + 2\right)^{2}}}\, dx"," ",0,"Integral(1/sqrt(-(3*x + 2)**2), x)","F",0
2813,0,0,0,0.000000," ","integrate((c*(b*x+a)**3)**(5/2),x)","\int \left(c \left(a + b x\right)^{3}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((c*(a + b*x)**3)**(5/2), x)","F",0
2814,0,0,0,0.000000," ","integrate((c*(b*x+a)**3)**(3/2),x)","\int \left(c \left(a + b x\right)^{3}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c*(a + b*x)**3)**(3/2), x)","F",0
2815,0,0,0,0.000000," ","integrate((c*(b*x+a)**3)**(1/2),x)","\int \sqrt{c \left(a + b x\right)^{3}}\, dx"," ",0,"Integral(sqrt(c*(a + b*x)**3), x)","F",0
2816,0,0,0,0.000000," ","integrate(1/(c*(b*x+a)**3)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a + b x\right)^{3}}}\, dx"," ",0,"Integral(1/sqrt(c*(a + b*x)**3), x)","F",0
2817,0,0,0,0.000000," ","integrate(1/(c*(b*x+a)**3)**(3/2),x)","\int \frac{1}{\left(c \left(a + b x\right)^{3}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*(a + b*x)**3)**(-3/2), x)","F",0
2818,0,0,0,0.000000," ","integrate(1/(c*(b*x+a)**3)**(5/2),x)","\int \frac{1}{\left(c \left(a + b x\right)^{3}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c*(a + b*x)**3)**(-5/2), x)","F",0
2819,1,51,0,3.592717," ","integrate((c/(b*x+a))**(5/2),x)","\begin{cases} - \frac{2 a c^{\frac{5}{2}} \left(\frac{1}{a + b x}\right)^{\frac{5}{2}}}{3 b} - \frac{2 c^{\frac{5}{2}} x \left(\frac{1}{a + b x}\right)^{\frac{5}{2}}}{3} & \text{for}\: b \neq 0 \\x \left(\frac{c}{a}\right)^{\frac{5}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*c**(5/2)*(1/(a + b*x))**(5/2)/(3*b) - 2*c**(5/2)*x*(1/(a + b*x))**(5/2)/3, Ne(b, 0)), (x*(c/a)**(5/2), True))","A",0
2820,1,48,0,1.234438," ","integrate((c/(b*x+a))**(3/2),x)","\begin{cases} - \frac{2 a c^{\frac{3}{2}} \left(\frac{1}{a + b x}\right)^{\frac{3}{2}}}{b} - 2 c^{\frac{3}{2}} x \left(\frac{1}{a + b x}\right)^{\frac{3}{2}} & \text{for}\: b \neq 0 \\x \left(\frac{c}{a}\right)^{\frac{3}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*c**(3/2)*(1/(a + b*x))**(3/2)/b - 2*c**(3/2)*x*(1/(a + b*x))**(3/2), Ne(b, 0)), (x*(c/a)**(3/2), True))","A",0
2821,1,46,0,0.340555," ","integrate((c/(b*x+a))**(1/2),x)","\begin{cases} \frac{2 a \sqrt{c} \sqrt{\frac{1}{a + b x}}}{b} + 2 \sqrt{c} x \sqrt{\frac{1}{a + b x}} & \text{for}\: b \neq 0 \\x \sqrt{\frac{c}{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*sqrt(c)*sqrt(1/(a + b*x))/b + 2*sqrt(c)*x*sqrt(1/(a + b*x)), Ne(b, 0)), (x*sqrt(c/a), True))","A",0
2822,1,49,0,1.623847," ","integrate(1/(c/(b*x+a))**(1/2),x)","\begin{cases} \frac{2 a}{3 b \sqrt{c} \sqrt{\frac{1}{a + b x}}} + \frac{2 x}{3 \sqrt{c} \sqrt{\frac{1}{a + b x}}} & \text{for}\: b \neq 0 \\\frac{x}{\sqrt{\frac{c}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a/(3*b*sqrt(c)*sqrt(1/(a + b*x))) + 2*x/(3*sqrt(c)*sqrt(1/(a + b*x))), Ne(b, 0)), (x/sqrt(c/a), True))","A",0
2823,1,49,0,1.688379," ","integrate(1/(c/(b*x+a))**(3/2),x)","\begin{cases} \frac{2 a}{5 b c^{\frac{3}{2}} \left(\frac{1}{a + b x}\right)^{\frac{3}{2}}} + \frac{2 x}{5 c^{\frac{3}{2}} \left(\frac{1}{a + b x}\right)^{\frac{3}{2}}} & \text{for}\: b \neq 0 \\\frac{x}{\left(\frac{c}{a}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a/(5*b*c**(3/2)*(1/(a + b*x))**(3/2)) + 2*x/(5*c**(3/2)*(1/(a + b*x))**(3/2)), Ne(b, 0)), (x/(c/a)**(3/2), True))","A",0
2824,1,49,0,2.571703," ","integrate(1/(c/(b*x+a))**(5/2),x)","\begin{cases} \frac{2 a}{7 b c^{\frac{5}{2}} \left(\frac{1}{a + b x}\right)^{\frac{5}{2}}} + \frac{2 x}{7 c^{\frac{5}{2}} \left(\frac{1}{a + b x}\right)^{\frac{5}{2}}} & \text{for}\: b \neq 0 \\\frac{x}{\left(\frac{c}{a}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a/(7*b*c**(5/2)*(1/(a + b*x))**(5/2)) + 2*x/(7*c**(5/2)*(1/(a + b*x))**(5/2)), Ne(b, 0)), (x/(c/a)**(5/2), True))","A",0
2825,0,0,0,0.000000," ","integrate((c/(b*x+a)**2)**(5/2),x)","\int \left(\frac{c}{\left(a + b x\right)^{2}}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((c/(a + b*x)**2)**(5/2), x)","F",0
2826,0,0,0,0.000000," ","integrate((c/(b*x+a)**2)**(3/2),x)","\int \left(\frac{c}{\left(a + b x\right)^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c/(a + b*x)**2)**(3/2), x)","F",0
2827,0,0,0,0.000000," ","integrate((c/(b*x+a)**2)**(1/2),x)","\int \sqrt{\frac{c}{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral(sqrt(c/(a + b*x)**2), x)","F",0
2828,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)**2)**(1/2),x)","\int \frac{1}{\sqrt{\frac{c}{\left(a + b x\right)^{2}}}}\, dx"," ",0,"Integral(1/sqrt(c/(a + b*x)**2), x)","F",0
2829,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)**2)**(3/2),x)","\int \frac{1}{\left(\frac{c}{\left(a + b x\right)^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c/(a + b*x)**2)**(-3/2), x)","F",0
2830,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)**2)**(5/2),x)","\int \frac{1}{\left(\frac{c}{\left(a + b x\right)^{2}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c/(a + b*x)**2)**(-5/2), x)","F",0
2831,1,1294,0,113.936393," ","integrate((c/(b*x+a)**3)**(5/2),x)","\begin{cases} - \frac{638 a^{6} c^{\frac{5}{2}} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{5}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} - \frac{3828 a^{5} b c^{\frac{5}{2}} x \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{5}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} - \frac{9570 a^{4} b^{2} c^{\frac{5}{2}} x^{2} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{5}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} - \frac{12760 a^{3} b^{3} c^{\frac{5}{2}} x^{3} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{5}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} - \frac{1170 a^{3} c^{\frac{5}{2}} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{3}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} - \frac{9570 a^{2} b^{4} c^{\frac{5}{2}} x^{4} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{5}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} - \frac{3510 a^{2} b c^{\frac{5}{2}} x \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{3}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} - \frac{3828 a b^{5} c^{\frac{5}{2}} x^{5} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{5}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} - \frac{3510 a b^{2} c^{\frac{5}{2}} x^{2} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{3}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} - \frac{638 b^{6} c^{\frac{5}{2}} x^{6} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{5}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} - \frac{1170 b^{3} c^{\frac{5}{2}} x^{3} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{3}{2}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} + \frac{1794 c^{\frac{5}{2}} \sqrt{\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}}}{91 a^{5} b + 455 a^{4} b^{2} x + 910 a^{3} b^{3} x^{2} + 910 a^{2} b^{4} x^{3} + 455 a b^{5} x^{4} + 91 b^{6} x^{5}} & \text{for}\: b \neq 0 \\x \left(\frac{c}{a^{3}}\right)^{\frac{5}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-638*a**6*c**(5/2)*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(5/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) - 3828*a**5*b*c**(5/2)*x*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(5/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) - 9570*a**4*b**2*c**(5/2)*x**2*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(5/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) - 12760*a**3*b**3*c**(5/2)*x**3*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(5/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) - 1170*a**3*c**(5/2)*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(3/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) - 9570*a**2*b**4*c**(5/2)*x**4*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(5/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) - 3510*a**2*b*c**(5/2)*x*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(3/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) - 3828*a*b**5*c**(5/2)*x**5*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(5/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) - 3510*a*b**2*c**(5/2)*x**2*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(3/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) - 638*b**6*c**(5/2)*x**6*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(5/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) - 1170*b**3*c**(5/2)*x**3*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(3/2)/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5) + 1794*c**(5/2)*sqrt(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))/(91*a**5*b + 455*a**4*b**2*x + 910*a**3*b**3*x**2 + 910*a**2*b**4*x**3 + 455*a*b**5*x**4 + 91*b**6*x**5), Ne(b, 0)), (x*(c/a**3)**(5/2), True))","A",0
2832,1,357,0,8.922498," ","integrate((c/(b*x+a)**3)**(3/2),x)","\begin{cases} - \frac{67 a^{3} c^{\frac{3}{2}} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{3}{2}}}{14 a^{2} b + 28 a b^{2} x + 14 b^{3} x^{2}} - \frac{201 a^{2} b c^{\frac{3}{2}} x \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{3}{2}}}{14 a^{2} b + 28 a b^{2} x + 14 b^{3} x^{2}} - \frac{201 a b^{2} c^{\frac{3}{2}} x^{2} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{3}{2}}}{14 a^{2} b + 28 a b^{2} x + 14 b^{3} x^{2}} - \frac{67 b^{3} c^{\frac{3}{2}} x^{3} \left(\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}\right)^{\frac{3}{2}}}{14 a^{2} b + 28 a b^{2} x + 14 b^{3} x^{2}} + \frac{63 c^{\frac{3}{2}} \sqrt{\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}}}{14 a^{2} b + 28 a b^{2} x + 14 b^{3} x^{2}} & \text{for}\: b \neq 0 \\x \left(\frac{c}{a^{3}}\right)^{\frac{3}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-67*a**3*c**(3/2)*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(3/2)/(14*a**2*b + 28*a*b**2*x + 14*b**3*x**2) - 201*a**2*b*c**(3/2)*x*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(3/2)/(14*a**2*b + 28*a*b**2*x + 14*b**3*x**2) - 201*a*b**2*c**(3/2)*x**2*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(3/2)/(14*a**2*b + 28*a*b**2*x + 14*b**3*x**2) - 67*b**3*c**(3/2)*x**3*(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))**(3/2)/(14*a**2*b + 28*a*b**2*x + 14*b**3*x**2) + 63*c**(3/2)*sqrt(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))/(14*a**2*b + 28*a*b**2*x + 14*b**3*x**2), Ne(b, 0)), (x*(c/a**3)**(3/2), True))","A",0
2833,1,97,0,0.870098," ","integrate((c/(b*x+a)**3)**(1/2),x)","\begin{cases} - \frac{2 a \sqrt{c} \sqrt{\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}}}{b} - 2 \sqrt{c} x \sqrt{\frac{1}{a^{3} + 3 a^{2} b x + 3 a b^{2} x^{2} + b^{3} x^{3}}} & \text{for}\: b \neq 0 \\x \sqrt{\frac{c}{a^{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*sqrt(c)*sqrt(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3))/b - 2*sqrt(c)*x*sqrt(1/(a**3 + 3*a**2*b*x + 3*a*b**2*x**2 + b**3*x**3)), Ne(b, 0)), (x*sqrt(c/a**3), True))","A",0
2834,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)**3)**(1/2),x)","\int \frac{1}{\sqrt{\frac{c}{\left(a + b x\right)^{3}}}}\, dx"," ",0,"Integral(1/sqrt(c/(a + b*x)**3), x)","F",0
2835,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)**3)**(3/2),x)","\int \frac{1}{\left(\frac{c}{\left(a + b x\right)^{3}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c/(a + b*x)**3)**(-3/2), x)","F",0
2836,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)**3)**(5/2),x)","\int \frac{1}{\left(\frac{c}{\left(a + b x\right)^{3}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c/(a + b*x)**3)**(-5/2), x)","F",0
2837,0,0,0,0.000000," ","integrate((c*(b*x+a)**(3/2))**(2/3),x)","\int \left(c \left(a + b x\right)^{\frac{3}{2}}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((c*(a + b*x)**(3/2))**(2/3), x)","F",0
2838,1,65,0,4.604336," ","integrate((c*(b*x+a)**(2/3))**(3/2),x)","\begin{cases} \frac{2 a^{2} c^{\frac{3}{2}} x}{2 a + 2 b x} + \frac{3 a b c^{\frac{3}{2}} x^{2}}{2 a + 2 b x} + \frac{b^{2} c^{\frac{3}{2}} x^{3}}{2 a + 2 b x} & \text{for}\: a \neq 0 \vee b \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*c**(3/2)*x/(2*a + 2*b*x) + 3*a*b*c**(3/2)*x**2/(2*a + 2*b*x) + b**2*c**(3/2)*x**3/(2*a + 2*b*x), Ne(a, 0) | Ne(b, 0)), (0, True))","A",0
2839,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)**(3/2))**(2/3),x)","\int \frac{1}{\left(\frac{c}{\left(a + b x\right)^{\frac{3}{2}}}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((c/(a + b*x)**(3/2))**(-2/3), x)","F",0
2840,1,76,0,3.151691," ","integrate(1/(c/(b*x+a)**(2/3))**(3/2),x)","\begin{cases} \frac{2 a x}{\frac{2 a c^{\frac{3}{2}}}{a + b x} + \frac{2 b c^{\frac{3}{2}} x}{a + b x}} + \frac{b x^{2}}{\frac{2 a c^{\frac{3}{2}}}{a + b x} + \frac{2 b c^{\frac{3}{2}} x}{a + b x}} & \text{for}\: a \neq 0 \vee b \neq 0 \\\frac{x}{\left(\tilde{\infty} c\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*x/(2*a*c**(3/2)/(a + b*x) + 2*b*c**(3/2)*x/(a + b*x)) + b*x**2/(2*a*c**(3/2)/(a + b*x) + 2*b*c**(3/2)*x/(a + b*x)), Ne(a, 0) | Ne(b, 0)), (x/(zoo*c)**(3/2), True))","A",0
2841,1,99,0,0.112370," ","integrate((d*x+c)**3*(a+b*(d*x+c)**2),x)","b c d^{4} x^{5} + \frac{b d^{5} x^{6}}{6} + x^{4} \left(\frac{a d^{3}}{4} + \frac{5 b c^{2} d^{3}}{2}\right) + x^{3} \left(a c d^{2} + \frac{10 b c^{3} d^{2}}{3}\right) + x^{2} \left(\frac{3 a c^{2} d}{2} + \frac{5 b c^{4} d}{2}\right) + x \left(a c^{3} + b c^{5}\right)"," ",0,"b*c*d**4*x**5 + b*d**5*x**6/6 + x**4*(a*d**3/4 + 5*b*c**2*d**3/2) + x**3*(a*c*d**2 + 10*b*c**3*d**2/3) + x**2*(3*a*c**2*d/2 + 5*b*c**4*d/2) + x*(a*c**3 + b*c**5)","B",0
2842,1,209,0,0.155216," ","integrate((d*x+c)**3*(a+b*(d*x+c)**2)**2,x)","b^{2} c d^{6} x^{7} + \frac{b^{2} d^{7} x^{8}}{8} + x^{6} \left(\frac{a b d^{5}}{3} + \frac{7 b^{2} c^{2} d^{5}}{2}\right) + x^{5} \left(2 a b c d^{4} + 7 b^{2} c^{3} d^{4}\right) + x^{4} \left(\frac{a^{2} d^{3}}{4} + 5 a b c^{2} d^{3} + \frac{35 b^{2} c^{4} d^{3}}{4}\right) + x^{3} \left(a^{2} c d^{2} + \frac{20 a b c^{3} d^{2}}{3} + 7 b^{2} c^{5} d^{2}\right) + x^{2} \left(\frac{3 a^{2} c^{2} d}{2} + 5 a b c^{4} d + \frac{7 b^{2} c^{6} d}{2}\right) + x \left(a^{2} c^{3} + 2 a b c^{5} + b^{2} c^{7}\right)"," ",0,"b**2*c*d**6*x**7 + b**2*d**7*x**8/8 + x**6*(a*b*d**5/3 + 7*b**2*c**2*d**5/2) + x**5*(2*a*b*c*d**4 + 7*b**2*c**3*d**4) + x**4*(a**2*d**3/4 + 5*a*b*c**2*d**3 + 35*b**2*c**4*d**3/4) + x**3*(a**2*c*d**2 + 20*a*b*c**3*d**2/3 + 7*b**2*c**5*d**2) + x**2*(3*a**2*c**2*d/2 + 5*a*b*c**4*d + 7*b**2*c**6*d/2) + x*(a**2*c**3 + 2*a*b*c**5 + b**2*c**7)","B",0
2843,1,357,0,0.189734," ","integrate((d*x+c)**3*(a+b*(d*x+c)**2)**3,x)","b^{3} c d^{8} x^{9} + \frac{b^{3} d^{9} x^{10}}{10} + x^{8} \left(\frac{3 a b^{2} d^{7}}{8} + \frac{9 b^{3} c^{2} d^{7}}{2}\right) + x^{7} \left(3 a b^{2} c d^{6} + 12 b^{3} c^{3} d^{6}\right) + x^{6} \left(\frac{a^{2} b d^{5}}{2} + \frac{21 a b^{2} c^{2} d^{5}}{2} + 21 b^{3} c^{4} d^{5}\right) + x^{5} \left(3 a^{2} b c d^{4} + 21 a b^{2} c^{3} d^{4} + \frac{126 b^{3} c^{5} d^{4}}{5}\right) + x^{4} \left(\frac{a^{3} d^{3}}{4} + \frac{15 a^{2} b c^{2} d^{3}}{2} + \frac{105 a b^{2} c^{4} d^{3}}{4} + 21 b^{3} c^{6} d^{3}\right) + x^{3} \left(a^{3} c d^{2} + 10 a^{2} b c^{3} d^{2} + 21 a b^{2} c^{5} d^{2} + 12 b^{3} c^{7} d^{2}\right) + x^{2} \left(\frac{3 a^{3} c^{2} d}{2} + \frac{15 a^{2} b c^{4} d}{2} + \frac{21 a b^{2} c^{6} d}{2} + \frac{9 b^{3} c^{8} d}{2}\right) + x \left(a^{3} c^{3} + 3 a^{2} b c^{5} + 3 a b^{2} c^{7} + b^{3} c^{9}\right)"," ",0,"b**3*c*d**8*x**9 + b**3*d**9*x**10/10 + x**8*(3*a*b**2*d**7/8 + 9*b**3*c**2*d**7/2) + x**7*(3*a*b**2*c*d**6 + 12*b**3*c**3*d**6) + x**6*(a**2*b*d**5/2 + 21*a*b**2*c**2*d**5/2 + 21*b**3*c**4*d**5) + x**5*(3*a**2*b*c*d**4 + 21*a*b**2*c**3*d**4 + 126*b**3*c**5*d**4/5) + x**4*(a**3*d**3/4 + 15*a**2*b*c**2*d**3/2 + 105*a*b**2*c**4*d**3/4 + 21*b**3*c**6*d**3) + x**3*(a**3*c*d**2 + 10*a**2*b*c**3*d**2 + 21*a*b**2*c**5*d**2 + 12*b**3*c**7*d**2) + x**2*(3*a**3*c**2*d/2 + 15*a**2*b*c**4*d/2 + 21*a*b**2*c**6*d/2 + 9*b**3*c**8*d/2) + x*(a**3*c**3 + 3*a**2*b*c**5 + 3*a*b**2*c**7 + b**3*c**9)","B",0
2844,1,10,0,0.108583," ","integrate((2+x)/(1+(2+x)**2),x)","\frac{\log{\left(x^{2} + 4 x + 5 \right)}}{2}"," ",0,"log(x**2 + 4*x + 5)/2","A",0
2845,1,12,0,0.120044," ","integrate((2+x)/(1+(2+x)**2)**2,x)","- \frac{1}{2 x^{2} + 8 x + 10}"," ",0,"-1/(2*x**2 + 8*x + 10)","A",0
2846,1,22,0,0.143372," ","integrate((2+x)/(1+(2+x)**2)**3,x)","- \frac{1}{4 x^{4} + 32 x^{3} + 104 x^{2} + 160 x + 100}"," ",0,"-1/(4*x**4 + 32*x**3 + 104*x**2 + 160*x + 100)","A",0
2847,-1,0,0,0.000000," ","integrate((d*x+c)**5*(a+b*(d*x+c)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2848,-1,0,0,0.000000," ","integrate((d*x+c)**4*(a+b*(d*x+c)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2849,-1,0,0,0.000000," ","integrate((d*x+c)**3*(a+b*(d*x+c)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2850,-1,0,0,0.000000," ","integrate((d*x+c)**2*(a+b*(d*x+c)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2851,-1,0,0,0.000000," ","integrate((d*x+c)*(a+b*(d*x+c)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2852,-1,0,0,0.000000," ","integrate((a+b*(d*x+c)**2)**p/(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2853,1,107,0,0.088646," ","integrate((d*x+c)**3*(a+b*(d*x+c)**3),x)","3 b c^{2} d^{4} x^{5} + b c d^{5} x^{6} + \frac{b d^{6} x^{7}}{7} + x^{4} \left(\frac{a d^{3}}{4} + 5 b c^{3} d^{3}\right) + x^{3} \left(a c d^{2} + 5 b c^{4} d^{2}\right) + x^{2} \left(\frac{3 a c^{2} d}{2} + 3 b c^{5} d\right) + x \left(a c^{3} + b c^{6}\right)"," ",0,"3*b*c**2*d**4*x**5 + b*c*d**5*x**6 + b*d**6*x**7/7 + x**4*(a*d**3/4 + 5*b*c**3*d**3) + x**3*(a*c*d**2 + 5*b*c**4*d**2) + x**2*(3*a*c**2*d/2 + 3*b*c**5*d) + x*(a*c**3 + b*c**6)","B",0
2854,1,252,0,0.127213," ","integrate((d*x+c)**3*(a+b*(d*x+c)**3)**2,x)","\frac{9 b^{2} c^{2} d^{7} x^{8}}{2} + b^{2} c d^{8} x^{9} + \frac{b^{2} d^{9} x^{10}}{10} + x^{7} \left(\frac{2 a b d^{6}}{7} + 12 b^{2} c^{3} d^{6}\right) + x^{6} \left(2 a b c d^{5} + 21 b^{2} c^{4} d^{5}\right) + x^{5} \left(6 a b c^{2} d^{4} + \frac{126 b^{2} c^{5} d^{4}}{5}\right) + x^{4} \left(\frac{a^{2} d^{3}}{4} + 10 a b c^{3} d^{3} + 21 b^{2} c^{6} d^{3}\right) + x^{3} \left(a^{2} c d^{2} + 10 a b c^{4} d^{2} + 12 b^{2} c^{7} d^{2}\right) + x^{2} \left(\frac{3 a^{2} c^{2} d}{2} + 6 a b c^{5} d + \frac{9 b^{2} c^{8} d}{2}\right) + x \left(a^{2} c^{3} + 2 a b c^{6} + b^{2} c^{9}\right)"," ",0,"9*b**2*c**2*d**7*x**8/2 + b**2*c*d**8*x**9 + b**2*d**9*x**10/10 + x**7*(2*a*b*d**6/7 + 12*b**2*c**3*d**6) + x**6*(2*a*b*c*d**5 + 21*b**2*c**4*d**5) + x**5*(6*a*b*c**2*d**4 + 126*b**2*c**5*d**4/5) + x**4*(a**2*d**3/4 + 10*a*b*c**3*d**3 + 21*b**2*c**6*d**3) + x**3*(a**2*c*d**2 + 10*a*b*c**4*d**2 + 12*b**2*c**7*d**2) + x**2*(3*a**2*c**2*d/2 + 6*a*b*c**5*d + 9*b**2*c**8*d/2) + x*(a**2*c**3 + 2*a*b*c**6 + b**2*c**9)","B",0
2855,1,437,0,0.169610," ","integrate((d*x+c)**3*(a+b*(d*x+c)**3)**3,x)","6 b^{3} c^{2} d^{10} x^{11} + b^{3} c d^{11} x^{12} + \frac{b^{3} d^{12} x^{13}}{13} + x^{10} \left(\frac{3 a b^{2} d^{9}}{10} + 22 b^{3} c^{3} d^{9}\right) + x^{9} \left(3 a b^{2} c d^{8} + 55 b^{3} c^{4} d^{8}\right) + x^{8} \left(\frac{27 a b^{2} c^{2} d^{7}}{2} + 99 b^{3} c^{5} d^{7}\right) + x^{7} \left(\frac{3 a^{2} b d^{6}}{7} + 36 a b^{2} c^{3} d^{6} + 132 b^{3} c^{6} d^{6}\right) + x^{6} \left(3 a^{2} b c d^{5} + 63 a b^{2} c^{4} d^{5} + 132 b^{3} c^{7} d^{5}\right) + x^{5} \left(9 a^{2} b c^{2} d^{4} + \frac{378 a b^{2} c^{5} d^{4}}{5} + 99 b^{3} c^{8} d^{4}\right) + x^{4} \left(\frac{a^{3} d^{3}}{4} + 15 a^{2} b c^{3} d^{3} + 63 a b^{2} c^{6} d^{3} + 55 b^{3} c^{9} d^{3}\right) + x^{3} \left(a^{3} c d^{2} + 15 a^{2} b c^{4} d^{2} + 36 a b^{2} c^{7} d^{2} + 22 b^{3} c^{10} d^{2}\right) + x^{2} \left(\frac{3 a^{3} c^{2} d}{2} + 9 a^{2} b c^{5} d + \frac{27 a b^{2} c^{8} d}{2} + 6 b^{3} c^{11} d\right) + x \left(a^{3} c^{3} + 3 a^{2} b c^{6} + 3 a b^{2} c^{9} + b^{3} c^{12}\right)"," ",0,"6*b**3*c**2*d**10*x**11 + b**3*c*d**11*x**12 + b**3*d**12*x**13/13 + x**10*(3*a*b**2*d**9/10 + 22*b**3*c**3*d**9) + x**9*(3*a*b**2*c*d**8 + 55*b**3*c**4*d**8) + x**8*(27*a*b**2*c**2*d**7/2 + 99*b**3*c**5*d**7) + x**7*(3*a**2*b*d**6/7 + 36*a*b**2*c**3*d**6 + 132*b**3*c**6*d**6) + x**6*(3*a**2*b*c*d**5 + 63*a*b**2*c**4*d**5 + 132*b**3*c**7*d**5) + x**5*(9*a**2*b*c**2*d**4 + 378*a*b**2*c**5*d**4/5 + 99*b**3*c**8*d**4) + x**4*(a**3*d**3/4 + 15*a**2*b*c**3*d**3 + 63*a*b**2*c**6*d**3 + 55*b**3*c**9*d**3) + x**3*(a**3*c*d**2 + 15*a**2*b*c**4*d**2 + 36*a*b**2*c**7*d**2 + 22*b**3*c**10*d**2) + x**2*(3*a**3*c**2*d/2 + 9*a**2*b*c**5*d + 27*a*b**2*c**8*d/2 + 6*b**3*c**11*d) + x*(a**3*c**3 + 3*a**2*b*c**6 + 3*a*b**2*c**9 + b**3*c**12)","B",0
2856,1,144,0,0.105117," ","integrate((d*e*x+c*e)**3*(a+b*(d*x+c)**3),x)","3 b c^{2} d^{4} e^{3} x^{5} + b c d^{5} e^{3} x^{6} + \frac{b d^{6} e^{3} x^{7}}{7} + x^{4} \left(\frac{a d^{3} e^{3}}{4} + 5 b c^{3} d^{3} e^{3}\right) + x^{3} \left(a c d^{2} e^{3} + 5 b c^{4} d^{2} e^{3}\right) + x^{2} \left(\frac{3 a c^{2} d e^{3}}{2} + 3 b c^{5} d e^{3}\right) + x \left(a c^{3} e^{3} + b c^{6} e^{3}\right)"," ",0,"3*b*c**2*d**4*e**3*x**5 + b*c*d**5*e**3*x**6 + b*d**6*e**3*x**7/7 + x**4*(a*d**3*e**3/4 + 5*b*c**3*d**3*e**3) + x**3*(a*c*d**2*e**3 + 5*b*c**4*d**2*e**3) + x**2*(3*a*c**2*d*e**3/2 + 3*b*c**5*d*e**3) + x*(a*c**3*e**3 + b*c**6*e**3)","B",0
2857,1,323,0,0.142896," ","integrate((d*e*x+c*e)**3*(a+b*(d*x+c)**3)**2,x)","\frac{9 b^{2} c^{2} d^{7} e^{3} x^{8}}{2} + b^{2} c d^{8} e^{3} x^{9} + \frac{b^{2} d^{9} e^{3} x^{10}}{10} + x^{7} \left(\frac{2 a b d^{6} e^{3}}{7} + 12 b^{2} c^{3} d^{6} e^{3}\right) + x^{6} \left(2 a b c d^{5} e^{3} + 21 b^{2} c^{4} d^{5} e^{3}\right) + x^{5} \left(6 a b c^{2} d^{4} e^{3} + \frac{126 b^{2} c^{5} d^{4} e^{3}}{5}\right) + x^{4} \left(\frac{a^{2} d^{3} e^{3}}{4} + 10 a b c^{3} d^{3} e^{3} + 21 b^{2} c^{6} d^{3} e^{3}\right) + x^{3} \left(a^{2} c d^{2} e^{3} + 10 a b c^{4} d^{2} e^{3} + 12 b^{2} c^{7} d^{2} e^{3}\right) + x^{2} \left(\frac{3 a^{2} c^{2} d e^{3}}{2} + 6 a b c^{5} d e^{3} + \frac{9 b^{2} c^{8} d e^{3}}{2}\right) + x \left(a^{2} c^{3} e^{3} + 2 a b c^{6} e^{3} + b^{2} c^{9} e^{3}\right)"," ",0,"9*b**2*c**2*d**7*e**3*x**8/2 + b**2*c*d**8*e**3*x**9 + b**2*d**9*e**3*x**10/10 + x**7*(2*a*b*d**6*e**3/7 + 12*b**2*c**3*d**6*e**3) + x**6*(2*a*b*c*d**5*e**3 + 21*b**2*c**4*d**5*e**3) + x**5*(6*a*b*c**2*d**4*e**3 + 126*b**2*c**5*d**4*e**3/5) + x**4*(a**2*d**3*e**3/4 + 10*a*b*c**3*d**3*e**3 + 21*b**2*c**6*d**3*e**3) + x**3*(a**2*c*d**2*e**3 + 10*a*b*c**4*d**2*e**3 + 12*b**2*c**7*d**2*e**3) + x**2*(3*a**2*c**2*d*e**3/2 + 6*a*b*c**5*d*e**3 + 9*b**2*c**8*d*e**3/2) + x*(a**2*c**3*e**3 + 2*a*b*c**6*e**3 + b**2*c**9*e**3)","B",0
2858,1,552,0,0.186952," ","integrate((d*e*x+c*e)**3*(a+b*(d*x+c)**3)**3,x)","6 b^{3} c^{2} d^{10} e^{3} x^{11} + b^{3} c d^{11} e^{3} x^{12} + \frac{b^{3} d^{12} e^{3} x^{13}}{13} + x^{10} \left(\frac{3 a b^{2} d^{9} e^{3}}{10} + 22 b^{3} c^{3} d^{9} e^{3}\right) + x^{9} \left(3 a b^{2} c d^{8} e^{3} + 55 b^{3} c^{4} d^{8} e^{3}\right) + x^{8} \left(\frac{27 a b^{2} c^{2} d^{7} e^{3}}{2} + 99 b^{3} c^{5} d^{7} e^{3}\right) + x^{7} \left(\frac{3 a^{2} b d^{6} e^{3}}{7} + 36 a b^{2} c^{3} d^{6} e^{3} + 132 b^{3} c^{6} d^{6} e^{3}\right) + x^{6} \left(3 a^{2} b c d^{5} e^{3} + 63 a b^{2} c^{4} d^{5} e^{3} + 132 b^{3} c^{7} d^{5} e^{3}\right) + x^{5} \left(9 a^{2} b c^{2} d^{4} e^{3} + \frac{378 a b^{2} c^{5} d^{4} e^{3}}{5} + 99 b^{3} c^{8} d^{4} e^{3}\right) + x^{4} \left(\frac{a^{3} d^{3} e^{3}}{4} + 15 a^{2} b c^{3} d^{3} e^{3} + 63 a b^{2} c^{6} d^{3} e^{3} + 55 b^{3} c^{9} d^{3} e^{3}\right) + x^{3} \left(a^{3} c d^{2} e^{3} + 15 a^{2} b c^{4} d^{2} e^{3} + 36 a b^{2} c^{7} d^{2} e^{3} + 22 b^{3} c^{10} d^{2} e^{3}\right) + x^{2} \left(\frac{3 a^{3} c^{2} d e^{3}}{2} + 9 a^{2} b c^{5} d e^{3} + \frac{27 a b^{2} c^{8} d e^{3}}{2} + 6 b^{3} c^{11} d e^{3}\right) + x \left(a^{3} c^{3} e^{3} + 3 a^{2} b c^{6} e^{3} + 3 a b^{2} c^{9} e^{3} + b^{3} c^{12} e^{3}\right)"," ",0,"6*b**3*c**2*d**10*e**3*x**11 + b**3*c*d**11*e**3*x**12 + b**3*d**12*e**3*x**13/13 + x**10*(3*a*b**2*d**9*e**3/10 + 22*b**3*c**3*d**9*e**3) + x**9*(3*a*b**2*c*d**8*e**3 + 55*b**3*c**4*d**8*e**3) + x**8*(27*a*b**2*c**2*d**7*e**3/2 + 99*b**3*c**5*d**7*e**3) + x**7*(3*a**2*b*d**6*e**3/7 + 36*a*b**2*c**3*d**6*e**3 + 132*b**3*c**6*d**6*e**3) + x**6*(3*a**2*b*c*d**5*e**3 + 63*a*b**2*c**4*d**5*e**3 + 132*b**3*c**7*d**5*e**3) + x**5*(9*a**2*b*c**2*d**4*e**3 + 378*a*b**2*c**5*d**4*e**3/5 + 99*b**3*c**8*d**4*e**3) + x**4*(a**3*d**3*e**3/4 + 15*a**2*b*c**3*d**3*e**3 + 63*a*b**2*c**6*d**3*e**3 + 55*b**3*c**9*d**3*e**3) + x**3*(a**3*c*d**2*e**3 + 15*a**2*b*c**4*d**2*e**3 + 36*a*b**2*c**7*d**2*e**3 + 22*b**3*c**10*d**2*e**3) + x**2*(3*a**3*c**2*d*e**3/2 + 9*a**2*b*c**5*d*e**3 + 27*a*b**2*c**8*d*e**3/2 + 6*b**3*c**11*d*e**3) + x*(a**3*c**3*e**3 + 3*a**2*b*c**6*e**3 + 3*a*b**2*c**9*e**3 + b**3*c**12*e**3)","B",0
2859,1,46,0,0.367671," ","integrate((d*x+c)**4/(a+b*(d*x+c)**3),x)","\frac{\operatorname{RootSum} {\left(27 t^{3} b^{5} - a^{2}, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} b^{3} + a c}{a d} \right)} \right)\right)}}{d} + \frac{c x}{b} + \frac{d x^{2}}{2 b}"," ",0,"RootSum(27*_t**3*b**5 - a**2, Lambda(_t, _t*log(x + (9*_t**2*b**3 + a*c)/(a*d))))/d + c*x/b + d*x**2/(2*b)","A",0
2860,1,27,0,0.312453," ","integrate((d*x+c)**3/(a+b*(d*x+c)**3),x)","\frac{\operatorname{RootSum} {\left(27 t^{3} b^{4} + a, \left( t \mapsto t \log{\left(x + \frac{- 3 t b + c}{d} \right)} \right)\right)}}{d} + \frac{x}{b}"," ",0,"RootSum(27*_t**3*b**4 + a, Lambda(_t, _t*log(x + (-3*_t*b + c)/d)))/d + x/b","A",0
2861,1,42,0,0.271686," ","integrate((d*x+c)**2/(a+b*(d*x+c)**3),x)","\frac{\log{\left(a + b c^{3} + 3 b c^{2} d x + 3 b c d^{2} x^{2} + b d^{3} x^{3} \right)}}{3 b d}"," ",0,"log(a + b*c**3 + 3*b*c**2*d*x + 3*b*c*d**2*x**2 + b*d**3*x**3)/(3*b*d)","B",0
2862,1,29,0,0.257861," ","integrate((d*x+c)/(a+b*(d*x+c)**3),x)","\frac{\operatorname{RootSum} {\left(27 t^{3} a b^{2} + 1, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} a b + c}{d} \right)} \right)\right)}}{d}"," ",0,"RootSum(27*_t**3*a*b**2 + 1, Lambda(_t, _t*log(x + (9*_t**2*a*b + c)/d)))/d","A",0
2863,1,26,0,0.261727," ","integrate(1/(a+b*(d*x+c)**3),x)","\frac{\operatorname{RootSum} {\left(27 t^{3} a^{2} b - 1, \left( t \mapsto t \log{\left(x + \frac{3 t a + c}{d} \right)} \right)\right)}}{d}"," ",0,"RootSum(27*_t**3*a**2*b - 1, Lambda(_t, _t*log(x + (3*_t*a + c)/d)))/d","A",0
2864,1,49,0,0.471937," ","integrate(1/(d*x+c)/(a+b*(d*x+c)**3),x)","\frac{\log{\left(\frac{c}{d} + x \right)}}{a d} - \frac{\log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{3 a d}"," ",0,"log(c/d + x)/(a*d) - log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(3*a*d)","A",0
2865,1,44,0,0.660011," ","integrate(1/(d*x+c)**2/(a+b*(d*x+c)**3),x)","- \frac{1}{a c d + a d^{2} x} + \frac{\operatorname{RootSum} {\left(27 t^{3} a^{4} - b, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} a^{3} + b c}{b d} \right)} \right)\right)}}{d}"," ",0,"-1/(a*c*d + a*d**2*x) + RootSum(27*_t**3*a**4 - b, Lambda(_t, _t*log(x + (9*_t**2*a**3 + b*c)/(b*d))))/d","A",0
2866,1,61,0,0.869899," ","integrate(1/(d*x+c)**3/(a+b*(d*x+c)**3),x)","- \frac{1}{2 a c^{2} d + 4 a c d^{2} x + 2 a d^{3} x^{2}} + \frac{\operatorname{RootSum} {\left(27 t^{3} a^{5} + b^{2}, \left( t \mapsto t \log{\left(x + \frac{- 3 t a^{2} + b c}{b d} \right)} \right)\right)}}{d}"," ",0,"-1/(2*a*c**2*d + 4*a*c*d**2*x + 2*a*d**3*x**2) + RootSum(27*_t**3*a**5 + b**2, Lambda(_t, _t*log(x + (-3*_t*a**2 + b*c)/(b*d))))/d","A",0
2867,1,100,0,1.279774," ","integrate(1/(d*x+c)**4/(a+b*(d*x+c)**3),x)","- \frac{1}{3 a c^{3} d + 9 a c^{2} d^{2} x + 9 a c d^{3} x^{2} + 3 a d^{4} x^{3}} - \frac{b \log{\left(\frac{c}{d} + x \right)}}{a^{2} d} + \frac{b \log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{3 a^{2} d}"," ",0,"-1/(3*a*c**3*d + 9*a*c**2*d**2*x + 9*a*c*d**3*x**2 + 3*a*d**4*x**3) - b*log(c/d + x)/(a**2*d) + b*log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(3*a**2*d)","B",0
2868,1,109,0,1.110150," ","integrate((d*x+c)**4/(a+b*(d*x+c)**3)**2,x)","\frac{- c^{2} - 2 c d x - d^{2} x^{2}}{3 a b d + 3 b^{2} c^{3} d + 9 b^{2} c^{2} d^{2} x + 9 b^{2} c d^{3} x^{2} + 3 b^{2} d^{4} x^{3}} + \frac{\operatorname{RootSum} {\left(729 t^{3} a b^{5} + 8, \left( t \mapsto t \log{\left(x + \frac{81 t^{2} a b^{3} + 4 c}{4 d} \right)} \right)\right)}}{d}"," ",0,"(-c**2 - 2*c*d*x - d**2*x**2)/(3*a*b*d + 3*b**2*c**3*d + 9*b**2*c**2*d**2*x + 9*b**2*c*d**3*x**2 + 3*b**2*d**4*x**3) + RootSum(729*_t**3*a*b**5 + 8, Lambda(_t, _t*log(x + (81*_t**2*a*b**3 + 4*c)/(4*d))))/d","A",0
2869,1,92,0,1.030891," ","integrate((d*x+c)**3/(a+b*(d*x+c)**3)**2,x)","\frac{- c - d x}{3 a b d + 3 b^{2} c^{3} d + 9 b^{2} c^{2} d^{2} x + 9 b^{2} c d^{3} x^{2} + 3 b^{2} d^{4} x^{3}} + \frac{\operatorname{RootSum} {\left(729 t^{3} a^{2} b^{4} - 1, \left( t \mapsto t \log{\left(x + \frac{9 t a b + c}{d} \right)} \right)\right)}}{d}"," ",0,"(-c - d*x)/(3*a*b*d + 3*b**2*c**3*d + 9*b**2*c**2*d**2*x + 9*b**2*c*d**3*x**2 + 3*b**2*d**4*x**3) + RootSum(729*_t**3*a**2*b**4 - 1, Lambda(_t, _t*log(x + (9*_t*a*b + c)/d)))/d","A",0
2870,1,58,0,0.960706," ","integrate((d*x+c)**2/(a+b*(d*x+c)**3)**2,x)","- \frac{1}{3 a b d + 3 b^{2} c^{3} d + 9 b^{2} c^{2} d^{2} x + 9 b^{2} c d^{3} x^{2} + 3 b^{2} d^{4} x^{3}}"," ",0,"-1/(3*a*b*d + 3*b**2*c**3*d + 9*b**2*c**2*d**2*x + 9*b**2*c*d**3*x**2 + 3*b**2*d**4*x**3)","B",0
2871,1,105,0,1.000586," ","integrate((d*x+c)/(a+b*(d*x+c)**3)**2,x)","\frac{c^{2} + 2 c d x + d^{2} x^{2}}{3 a^{2} d + 3 a b c^{3} d + 9 a b c^{2} d^{2} x + 9 a b c d^{3} x^{2} + 3 a b d^{4} x^{3}} + \frac{\operatorname{RootSum} {\left(729 t^{3} a^{4} b^{2} + 1, \left( t \mapsto t \log{\left(x + \frac{81 t^{2} a^{3} b + c}{d} \right)} \right)\right)}}{d}"," ",0,"(c**2 + 2*c*d*x + d**2*x**2)/(3*a**2*d + 3*a*b*c**3*d + 9*a*b*c**2*d**2*x + 9*a*b*c*d**3*x**2 + 3*a*b*d**4*x**3) + RootSum(729*_t**3*a**4*b**2 + 1, Lambda(_t, _t*log(x + (81*_t**2*a**3*b + c)/d)))/d","A",0
2872,1,92,0,0.944549," ","integrate(1/(a+b*(d*x+c)**3)**2,x)","\frac{c + d x}{3 a^{2} d + 3 a b c^{3} d + 9 a b c^{2} d^{2} x + 9 a b c d^{3} x^{2} + 3 a b d^{4} x^{3}} + \frac{\operatorname{RootSum} {\left(729 t^{3} a^{5} b - 8, \left( t \mapsto t \log{\left(x + \frac{9 t a^{2} + 2 c}{2 d} \right)} \right)\right)}}{d}"," ",0,"(c + d*x)/(3*a**2*d + 3*a*b*c**3*d + 9*a*b*c**2*d**2*x + 9*a*b*c*d**3*x**2 + 3*a*b*d**4*x**3) + RootSum(729*_t**3*a**5*b - 8, Lambda(_t, _t*log(x + (9*_t*a**2 + 2*c)/(2*d))))/d","A",0
2873,1,110,0,1.482985," ","integrate(1/(d*x+c)/(a+b*(d*x+c)**3)**2,x)","\frac{1}{3 a^{2} d + 3 a b c^{3} d + 9 a b c^{2} d^{2} x + 9 a b c d^{3} x^{2} + 3 a b d^{4} x^{3}} + \frac{\log{\left(\frac{c}{d} + x \right)}}{a^{2} d} - \frac{\log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{3 a^{2} d}"," ",0,"1/(3*a**2*d + 3*a*b*c**3*d + 9*a*b*c**2*d**2*x + 9*a*b*c*d**3*x**2 + 3*a*b*d**4*x**3) + log(c/d + x)/(a**2*d) - log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(3*a**2*d)","B",0
2874,1,170,0,1.953810," ","integrate(1/(d*x+c)**2/(a+b*(d*x+c)**3)**2,x)","\frac{- 3 a - 4 b c^{3} - 12 b c^{2} d x - 12 b c d^{2} x^{2} - 4 b d^{3} x^{3}}{3 a^{3} c d + 3 a^{2} b c^{4} d + 18 a^{2} b c^{2} d^{3} x^{2} + 12 a^{2} b c d^{4} x^{3} + 3 a^{2} b d^{5} x^{4} + x \left(3 a^{3} d^{2} + 12 a^{2} b c^{3} d^{2}\right)} + \frac{\operatorname{RootSum} {\left(729 t^{3} a^{7} - 64 b, \left( t \mapsto t \log{\left(x + \frac{81 t^{2} a^{5} + 16 b c}{16 b d} \right)} \right)\right)}}{d}"," ",0,"(-3*a - 4*b*c**3 - 12*b*c**2*d*x - 12*b*c*d**2*x**2 - 4*b*d**3*x**3)/(3*a**3*c*d + 3*a**2*b*c**4*d + 18*a**2*b*c**2*d**3*x**2 + 12*a**2*b*c*d**4*x**3 + 3*a**2*b*d**5*x**4 + x*(3*a**3*d**2 + 12*a**2*b*c**3*d**2)) + RootSum(729*_t**3*a**7 - 64*b, Lambda(_t, _t*log(x + (81*_t**2*a**5 + 16*b*c)/(16*b*d))))/d","A",0
2875,1,199,0,2.500484," ","integrate(1/(d*x+c)**3/(a+b*(d*x+c)**3)**2,x)","\frac{- 3 a - 5 b c^{3} - 15 b c^{2} d x - 15 b c d^{2} x^{2} - 5 b d^{3} x^{3}}{6 a^{3} c^{2} d + 6 a^{2} b c^{5} d + 60 a^{2} b c^{2} d^{4} x^{3} + 30 a^{2} b c d^{5} x^{4} + 6 a^{2} b d^{6} x^{5} + x^{2} \left(6 a^{3} d^{3} + 60 a^{2} b c^{3} d^{3}\right) + x \left(12 a^{3} c d^{2} + 30 a^{2} b c^{4} d^{2}\right)} + \frac{\operatorname{RootSum} {\left(729 t^{3} a^{8} + 125 b^{2}, \left( t \mapsto t \log{\left(x + \frac{- 9 t a^{3} + 5 b c}{5 b d} \right)} \right)\right)}}{d}"," ",0,"(-3*a - 5*b*c**3 - 15*b*c**2*d*x - 15*b*c*d**2*x**2 - 5*b*d**3*x**3)/(6*a**3*c**2*d + 6*a**2*b*c**5*d + 60*a**2*b*c**2*d**4*x**3 + 30*a**2*b*c*d**5*x**4 + 6*a**2*b*d**6*x**5 + x**2*(6*a**3*d**3 + 60*a**2*b*c**3*d**3) + x*(12*a**3*c*d**2 + 30*a**2*b*c**4*d**2)) + RootSum(729*_t**3*a**8 + 125*b**2, Lambda(_t, _t*log(x + (-9*_t*a**3 + 5*b*c)/(5*b*d))))/d","A",0
2876,1,250,0,3.578029," ","integrate(1/(d*x+c)**4/(a+b*(d*x+c)**3)**2,x)","\frac{- a - 2 b c^{3} - 6 b c^{2} d x - 6 b c d^{2} x^{2} - 2 b d^{3} x^{3}}{3 a^{3} c^{3} d + 3 a^{2} b c^{6} d + 45 a^{2} b c^{2} d^{5} x^{4} + 18 a^{2} b c d^{6} x^{5} + 3 a^{2} b d^{7} x^{6} + x^{3} \left(3 a^{3} d^{4} + 60 a^{2} b c^{3} d^{4}\right) + x^{2} \left(9 a^{3} c d^{3} + 45 a^{2} b c^{4} d^{3}\right) + x \left(9 a^{3} c^{2} d^{2} + 18 a^{2} b c^{5} d^{2}\right)} - \frac{2 b \log{\left(\frac{c}{d} + x \right)}}{a^{3} d} + \frac{2 b \log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{3 a^{3} d}"," ",0,"(-a - 2*b*c**3 - 6*b*c**2*d*x - 6*b*c*d**2*x**2 - 2*b*d**3*x**3)/(3*a**3*c**3*d + 3*a**2*b*c**6*d + 45*a**2*b*c**2*d**5*x**4 + 18*a**2*b*c*d**6*x**5 + 3*a**2*b*d**7*x**6 + x**3*(3*a**3*d**4 + 60*a**2*b*c**3*d**4) + x**2*(9*a**3*c*d**3 + 45*a**2*b*c**4*d**3) + x*(9*a**3*c**2*d**2 + 18*a**2*b*c**5*d**2)) - 2*b*log(c/d + x)/(a**3*d) + 2*b*log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(3*a**3*d)","B",0
2877,1,287,0,3.442327," ","integrate((d*x+c)**4/(a+b*(d*x+c)**3)**3,x)","\frac{- a c^{2} + 2 b c^{5} + 20 b c^{2} d^{3} x^{3} + 10 b c d^{4} x^{4} + 2 b d^{5} x^{5} + x^{2} \left(- a d^{2} + 20 b c^{3} d^{2}\right) + x \left(- 2 a c d + 10 b c^{4} d\right)}{18 a^{3} b d + 36 a^{2} b^{2} c^{3} d + 18 a b^{3} c^{6} d + 270 a b^{3} c^{2} d^{5} x^{4} + 108 a b^{3} c d^{6} x^{5} + 18 a b^{3} d^{7} x^{6} + x^{3} \left(36 a^{2} b^{2} d^{4} + 360 a b^{3} c^{3} d^{4}\right) + x^{2} \left(108 a^{2} b^{2} c d^{3} + 270 a b^{3} c^{4} d^{3}\right) + x \left(108 a^{2} b^{2} c^{2} d^{2} + 108 a b^{3} c^{5} d^{2}\right)} + \frac{\operatorname{RootSum} {\left(19683 t^{3} a^{4} b^{5} + 1, \left( t \mapsto t \log{\left(x + \frac{729 t^{2} a^{3} b^{3} + c}{d} \right)} \right)\right)}}{d}"," ",0,"(-a*c**2 + 2*b*c**5 + 20*b*c**2*d**3*x**3 + 10*b*c*d**4*x**4 + 2*b*d**5*x**5 + x**2*(-a*d**2 + 20*b*c**3*d**2) + x*(-2*a*c*d + 10*b*c**4*d))/(18*a**3*b*d + 36*a**2*b**2*c**3*d + 18*a*b**3*c**6*d + 270*a*b**3*c**2*d**5*x**4 + 108*a*b**3*c*d**6*x**5 + 18*a*b**3*d**7*x**6 + x**3*(36*a**2*b**2*d**4 + 360*a*b**3*c**3*d**4) + x**2*(108*a**2*b**2*c*d**3 + 270*a*b**3*c**4*d**3) + x*(108*a**2*b**2*c**2*d**2 + 108*a*b**3*c**5*d**2)) + RootSum(19683*_t**3*a**4*b**5 + 1, Lambda(_t, _t*log(x + (729*_t**2*a**3*b**3 + c)/d)))/d","A",0
2878,1,260,0,3.313937," ","integrate((d*x+c)**3/(a+b*(d*x+c)**3)**3,x)","\frac{- 2 a c + b c^{4} + 6 b c^{2} d^{2} x^{2} + 4 b c d^{3} x^{3} + b d^{4} x^{4} + x \left(- 2 a d + 4 b c^{3} d\right)}{18 a^{3} b d + 36 a^{2} b^{2} c^{3} d + 18 a b^{3} c^{6} d + 270 a b^{3} c^{2} d^{5} x^{4} + 108 a b^{3} c d^{6} x^{5} + 18 a b^{3} d^{7} x^{6} + x^{3} \left(36 a^{2} b^{2} d^{4} + 360 a b^{3} c^{3} d^{4}\right) + x^{2} \left(108 a^{2} b^{2} c d^{3} + 270 a b^{3} c^{4} d^{3}\right) + x \left(108 a^{2} b^{2} c^{2} d^{2} + 108 a b^{3} c^{5} d^{2}\right)} + \frac{\operatorname{RootSum} {\left(19683 t^{3} a^{5} b^{4} - 1, \left( t \mapsto t \log{\left(x + \frac{27 t a^{2} b + c}{d} \right)} \right)\right)}}{d}"," ",0,"(-2*a*c + b*c**4 + 6*b*c**2*d**2*x**2 + 4*b*c*d**3*x**3 + b*d**4*x**4 + x*(-2*a*d + 4*b*c**3*d))/(18*a**3*b*d + 36*a**2*b**2*c**3*d + 18*a*b**3*c**6*d + 270*a*b**3*c**2*d**5*x**4 + 108*a*b**3*c*d**6*x**5 + 18*a*b**3*d**7*x**6 + x**3*(36*a**2*b**2*d**4 + 360*a*b**3*c**3*d**4) + x**2*(108*a**2*b**2*c*d**3 + 270*a*b**3*c**4*d**3) + x*(108*a**2*b**2*c**2*d**2 + 108*a*b**3*c**5*d**2)) + RootSum(19683*_t**3*a**5*b**4 - 1, Lambda(_t, _t*log(x + (27*_t*a**2*b + c)/d)))/d","A",0
2879,1,153,0,3.054666," ","integrate((d*x+c)**2/(a+b*(d*x+c)**3)**3,x)","- \frac{1}{6 a^{2} b d + 12 a b^{2} c^{3} d + 6 b^{3} c^{6} d + 90 b^{3} c^{2} d^{5} x^{4} + 36 b^{3} c d^{6} x^{5} + 6 b^{3} d^{7} x^{6} + x^{3} \left(12 a b^{2} d^{4} + 120 b^{3} c^{3} d^{4}\right) + x^{2} \left(36 a b^{2} c d^{3} + 90 b^{3} c^{4} d^{3}\right) + x \left(36 a b^{2} c^{2} d^{2} + 36 b^{3} c^{5} d^{2}\right)}"," ",0,"-1/(6*a**2*b*d + 12*a*b**2*c**3*d + 6*b**3*c**6*d + 90*b**3*c**2*d**5*x**4 + 36*b**3*c*d**6*x**5 + 6*b**3*d**7*x**6 + x**3*(12*a*b**2*d**4 + 120*b**3*c**3*d**4) + x**2*(36*a*b**2*c*d**3 + 90*b**3*c**4*d**3) + x*(36*a*b**2*c**2*d**2 + 36*b**3*c**5*d**2))","B",0
2880,1,296,0,3.276719," ","integrate((d*x+c)/(a+b*(d*x+c)**3)**3,x)","\frac{7 a c^{2} + 4 b c^{5} + 40 b c^{2} d^{3} x^{3} + 20 b c d^{4} x^{4} + 4 b d^{5} x^{5} + x^{2} \left(7 a d^{2} + 40 b c^{3} d^{2}\right) + x \left(14 a c d + 20 b c^{4} d\right)}{18 a^{4} d + 36 a^{3} b c^{3} d + 18 a^{2} b^{2} c^{6} d + 270 a^{2} b^{2} c^{2} d^{5} x^{4} + 108 a^{2} b^{2} c d^{6} x^{5} + 18 a^{2} b^{2} d^{7} x^{6} + x^{3} \left(36 a^{3} b d^{4} + 360 a^{2} b^{2} c^{3} d^{4}\right) + x^{2} \left(108 a^{3} b c d^{3} + 270 a^{2} b^{2} c^{4} d^{3}\right) + x \left(108 a^{3} b c^{2} d^{2} + 108 a^{2} b^{2} c^{5} d^{2}\right)} + \frac{\operatorname{RootSum} {\left(19683 t^{3} a^{7} b^{2} + 8, \left( t \mapsto t \log{\left(x + \frac{729 t^{2} a^{5} b + 4 c}{4 d} \right)} \right)\right)}}{d}"," ",0,"(7*a*c**2 + 4*b*c**5 + 40*b*c**2*d**3*x**3 + 20*b*c*d**4*x**4 + 4*b*d**5*x**5 + x**2*(7*a*d**2 + 40*b*c**3*d**2) + x*(14*a*c*d + 20*b*c**4*d))/(18*a**4*d + 36*a**3*b*c**3*d + 18*a**2*b**2*c**6*d + 270*a**2*b**2*c**2*d**5*x**4 + 108*a**2*b**2*c*d**6*x**5 + 18*a**2*b**2*d**7*x**6 + x**3*(36*a**3*b*d**4 + 360*a**2*b**2*c**3*d**4) + x**2*(108*a**3*b*c*d**3 + 270*a**2*b**2*c**4*d**3) + x*(108*a**3*b*c**2*d**2 + 108*a**2*b**2*c**5*d**2)) + RootSum(19683*_t**3*a**7*b**2 + 8, Lambda(_t, _t*log(x + (729*_t**2*a**5*b + 4*c)/(4*d))))/d","A",0
2881,1,267,0,3.271710," ","integrate(1/(a+b*(d*x+c)**3)**3,x)","\frac{8 a c + 5 b c^{4} + 30 b c^{2} d^{2} x^{2} + 20 b c d^{3} x^{3} + 5 b d^{4} x^{4} + x \left(8 a d + 20 b c^{3} d\right)}{18 a^{4} d + 36 a^{3} b c^{3} d + 18 a^{2} b^{2} c^{6} d + 270 a^{2} b^{2} c^{2} d^{5} x^{4} + 108 a^{2} b^{2} c d^{6} x^{5} + 18 a^{2} b^{2} d^{7} x^{6} + x^{3} \left(36 a^{3} b d^{4} + 360 a^{2} b^{2} c^{3} d^{4}\right) + x^{2} \left(108 a^{3} b c d^{3} + 270 a^{2} b^{2} c^{4} d^{3}\right) + x \left(108 a^{3} b c^{2} d^{2} + 108 a^{2} b^{2} c^{5} d^{2}\right)} + \frac{\operatorname{RootSum} {\left(19683 t^{3} a^{8} b - 125, \left( t \mapsto t \log{\left(x + \frac{27 t a^{3} + 5 c}{5 d} \right)} \right)\right)}}{d}"," ",0,"(8*a*c + 5*b*c**4 + 30*b*c**2*d**2*x**2 + 20*b*c*d**3*x**3 + 5*b*d**4*x**4 + x*(8*a*d + 20*b*c**3*d))/(18*a**4*d + 36*a**3*b*c**3*d + 18*a**2*b**2*c**6*d + 270*a**2*b**2*c**2*d**5*x**4 + 108*a**2*b**2*c*d**6*x**5 + 18*a**2*b**2*d**7*x**6 + x**3*(36*a**3*b*d**4 + 360*a**2*b**2*c**3*d**4) + x**2*(108*a**3*b*c*d**3 + 270*a**2*b**2*c**4*d**3) + x*(108*a**3*b*c**2*d**2 + 108*a**2*b**2*c**5*d**2)) + RootSum(19683*_t**3*a**8*b - 125, Lambda(_t, _t*log(x + (27*_t*a**3 + 5*c)/(5*d))))/d","A",0
2882,1,269,0,4.762121," ","integrate(1/(d*x+c)/(a+b*(d*x+c)**3)**3,x)","\frac{3 a + 2 b c^{3} + 6 b c^{2} d x + 6 b c d^{2} x^{2} + 2 b d^{3} x^{3}}{6 a^{4} d + 12 a^{3} b c^{3} d + 6 a^{2} b^{2} c^{6} d + 90 a^{2} b^{2} c^{2} d^{5} x^{4} + 36 a^{2} b^{2} c d^{6} x^{5} + 6 a^{2} b^{2} d^{7} x^{6} + x^{3} \left(12 a^{3} b d^{4} + 120 a^{2} b^{2} c^{3} d^{4}\right) + x^{2} \left(36 a^{3} b c d^{3} + 90 a^{2} b^{2} c^{4} d^{3}\right) + x \left(36 a^{3} b c^{2} d^{2} + 36 a^{2} b^{2} c^{5} d^{2}\right)} + \frac{\log{\left(\frac{c}{d} + x \right)}}{a^{3} d} - \frac{\log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{3 a^{3} d}"," ",0,"(3*a + 2*b*c**3 + 6*b*c**2*d*x + 6*b*c*d**2*x**2 + 2*b*d**3*x**3)/(6*a**4*d + 12*a**3*b*c**3*d + 6*a**2*b**2*c**6*d + 90*a**2*b**2*c**2*d**5*x**4 + 36*a**2*b**2*c*d**6*x**5 + 6*a**2*b**2*d**7*x**6 + x**3*(12*a**3*b*d**4 + 120*a**2*b**2*c**3*d**4) + x**2*(36*a**3*b*c*d**3 + 90*a**2*b**2*c**4*d**3) + x*(36*a**3*b*c**2*d**2 + 36*a**2*b**2*c**5*d**2)) + log(c/d + x)/(a**3*d) - log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(3*a**3*d)","B",0
2883,1,391,0,5.968932," ","integrate(1/(d*x+c)**2/(a+b*(d*x+c)**3)**3,x)","\frac{- 18 a^{2} - 49 a b c^{3} - 28 b^{2} c^{6} - 420 b^{2} c^{2} d^{4} x^{4} - 168 b^{2} c d^{5} x^{5} - 28 b^{2} d^{6} x^{6} + x^{3} \left(- 49 a b d^{3} - 560 b^{2} c^{3} d^{3}\right) + x^{2} \left(- 147 a b c d^{2} - 420 b^{2} c^{4} d^{2}\right) + x \left(- 147 a b c^{2} d - 168 b^{2} c^{5} d\right)}{18 a^{5} c d + 36 a^{4} b c^{4} d + 18 a^{3} b^{2} c^{7} d + 378 a^{3} b^{2} c^{2} d^{6} x^{5} + 126 a^{3} b^{2} c d^{7} x^{6} + 18 a^{3} b^{2} d^{8} x^{7} + x^{4} \left(36 a^{4} b d^{5} + 630 a^{3} b^{2} c^{3} d^{5}\right) + x^{3} \left(144 a^{4} b c d^{4} + 630 a^{3} b^{2} c^{4} d^{4}\right) + x^{2} \left(216 a^{4} b c^{2} d^{3} + 378 a^{3} b^{2} c^{5} d^{3}\right) + x \left(18 a^{5} d^{2} + 144 a^{4} b c^{3} d^{2} + 126 a^{3} b^{2} c^{6} d^{2}\right)} + \frac{\operatorname{RootSum} {\left(19683 t^{3} a^{10} - 2744 b, \left( t \mapsto t \log{\left(x + \frac{729 t^{2} a^{7} + 196 b c}{196 b d} \right)} \right)\right)}}{d}"," ",0,"(-18*a**2 - 49*a*b*c**3 - 28*b**2*c**6 - 420*b**2*c**2*d**4*x**4 - 168*b**2*c*d**5*x**5 - 28*b**2*d**6*x**6 + x**3*(-49*a*b*d**3 - 560*b**2*c**3*d**3) + x**2*(-147*a*b*c*d**2 - 420*b**2*c**4*d**2) + x*(-147*a*b*c**2*d - 168*b**2*c**5*d))/(18*a**5*c*d + 36*a**4*b*c**4*d + 18*a**3*b**2*c**7*d + 378*a**3*b**2*c**2*d**6*x**5 + 126*a**3*b**2*c*d**7*x**6 + 18*a**3*b**2*d**8*x**7 + x**4*(36*a**4*b*d**5 + 630*a**3*b**2*c**3*d**5) + x**3*(144*a**4*b*c*d**4 + 630*a**3*b**2*c**4*d**4) + x**2*(216*a**4*b*c**2*d**3 + 378*a**3*b**2*c**5*d**3) + x*(18*a**5*d**2 + 144*a**4*b*c**3*d**2 + 126*a**3*b**2*c**6*d**2)) + RootSum(19683*_t**3*a**10 - 2744*b, Lambda(_t, _t*log(x + (729*_t**2*a**7 + 196*b*c)/(196*b*d))))/d","B",0
2884,1,435,0,6.632310," ","integrate(1/(d*x+c)**3/(a+b*(d*x+c)**3)**3,x)","\frac{- 9 a^{2} - 32 a b c^{3} - 20 b^{2} c^{6} - 300 b^{2} c^{2} d^{4} x^{4} - 120 b^{2} c d^{5} x^{5} - 20 b^{2} d^{6} x^{6} + x^{3} \left(- 32 a b d^{3} - 400 b^{2} c^{3} d^{3}\right) + x^{2} \left(- 96 a b c d^{2} - 300 b^{2} c^{4} d^{2}\right) + x \left(- 96 a b c^{2} d - 120 b^{2} c^{5} d\right)}{18 a^{5} c^{2} d + 36 a^{4} b c^{5} d + 18 a^{3} b^{2} c^{8} d + 504 a^{3} b^{2} c^{2} d^{7} x^{6} + 144 a^{3} b^{2} c d^{8} x^{7} + 18 a^{3} b^{2} d^{9} x^{8} + x^{5} \left(36 a^{4} b d^{6} + 1008 a^{3} b^{2} c^{3} d^{6}\right) + x^{4} \left(180 a^{4} b c d^{5} + 1260 a^{3} b^{2} c^{4} d^{5}\right) + x^{3} \left(360 a^{4} b c^{2} d^{4} + 1008 a^{3} b^{2} c^{5} d^{4}\right) + x^{2} \left(18 a^{5} d^{3} + 360 a^{4} b c^{3} d^{3} + 504 a^{3} b^{2} c^{6} d^{3}\right) + x \left(36 a^{5} c d^{2} + 180 a^{4} b c^{4} d^{2} + 144 a^{3} b^{2} c^{7} d^{2}\right)} + \frac{\operatorname{RootSum} {\left(19683 t^{3} a^{11} + 8000 b^{2}, \left( t \mapsto t \log{\left(x + \frac{- 27 t a^{4} + 20 b c}{20 b d} \right)} \right)\right)}}{d}"," ",0,"(-9*a**2 - 32*a*b*c**3 - 20*b**2*c**6 - 300*b**2*c**2*d**4*x**4 - 120*b**2*c*d**5*x**5 - 20*b**2*d**6*x**6 + x**3*(-32*a*b*d**3 - 400*b**2*c**3*d**3) + x**2*(-96*a*b*c*d**2 - 300*b**2*c**4*d**2) + x*(-96*a*b*c**2*d - 120*b**2*c**5*d))/(18*a**5*c**2*d + 36*a**4*b*c**5*d + 18*a**3*b**2*c**8*d + 504*a**3*b**2*c**2*d**7*x**6 + 144*a**3*b**2*c*d**8*x**7 + 18*a**3*b**2*d**9*x**8 + x**5*(36*a**4*b*d**6 + 1008*a**3*b**2*c**3*d**6) + x**4*(180*a**4*b*c*d**5 + 1260*a**3*b**2*c**4*d**5) + x**3*(360*a**4*b*c**2*d**4 + 1008*a**3*b**2*c**5*d**4) + x**2*(18*a**5*d**3 + 360*a**4*b*c**3*d**3 + 504*a**3*b**2*c**6*d**3) + x*(36*a**5*c*d**2 + 180*a**4*b*c**4*d**2 + 144*a**3*b**2*c**7*d**2)) + RootSum(19683*_t**3*a**11 + 8000*b**2, Lambda(_t, _t*log(x + (-27*_t*a**4 + 20*b*c)/(20*b*d))))/d","B",0
2885,1,500,0,7.804656," ","integrate(1/(d*x+c)**4/(a+b*(d*x+c)**3)**3,x)","\frac{- 2 a^{2} - 9 a b c^{3} - 6 b^{2} c^{6} - 90 b^{2} c^{2} d^{4} x^{4} - 36 b^{2} c d^{5} x^{5} - 6 b^{2} d^{6} x^{6} + x^{3} \left(- 9 a b d^{3} - 120 b^{2} c^{3} d^{3}\right) + x^{2} \left(- 27 a b c d^{2} - 90 b^{2} c^{4} d^{2}\right) + x \left(- 27 a b c^{2} d - 36 b^{2} c^{5} d\right)}{6 a^{5} c^{3} d + 12 a^{4} b c^{6} d + 6 a^{3} b^{2} c^{9} d + 216 a^{3} b^{2} c^{2} d^{8} x^{7} + 54 a^{3} b^{2} c d^{9} x^{8} + 6 a^{3} b^{2} d^{10} x^{9} + x^{6} \left(12 a^{4} b d^{7} + 504 a^{3} b^{2} c^{3} d^{7}\right) + x^{5} \left(72 a^{4} b c d^{6} + 756 a^{3} b^{2} c^{4} d^{6}\right) + x^{4} \left(180 a^{4} b c^{2} d^{5} + 756 a^{3} b^{2} c^{5} d^{5}\right) + x^{3} \left(6 a^{5} d^{4} + 240 a^{4} b c^{3} d^{4} + 504 a^{3} b^{2} c^{6} d^{4}\right) + x^{2} \left(18 a^{5} c d^{3} + 180 a^{4} b c^{4} d^{3} + 216 a^{3} b^{2} c^{7} d^{3}\right) + x \left(18 a^{5} c^{2} d^{2} + 72 a^{4} b c^{5} d^{2} + 54 a^{3} b^{2} c^{8} d^{2}\right)} - \frac{3 b \log{\left(\frac{c}{d} + x \right)}}{a^{4} d} + \frac{b \log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{a^{4} d}"," ",0,"(-2*a**2 - 9*a*b*c**3 - 6*b**2*c**6 - 90*b**2*c**2*d**4*x**4 - 36*b**2*c*d**5*x**5 - 6*b**2*d**6*x**6 + x**3*(-9*a*b*d**3 - 120*b**2*c**3*d**3) + x**2*(-27*a*b*c*d**2 - 90*b**2*c**4*d**2) + x*(-27*a*b*c**2*d - 36*b**2*c**5*d))/(6*a**5*c**3*d + 12*a**4*b*c**6*d + 6*a**3*b**2*c**9*d + 216*a**3*b**2*c**2*d**8*x**7 + 54*a**3*b**2*c*d**9*x**8 + 6*a**3*b**2*d**10*x**9 + x**6*(12*a**4*b*d**7 + 504*a**3*b**2*c**3*d**7) + x**5*(72*a**4*b*c*d**6 + 756*a**3*b**2*c**4*d**6) + x**4*(180*a**4*b*c**2*d**5 + 756*a**3*b**2*c**5*d**5) + x**3*(6*a**5*d**4 + 240*a**4*b*c**3*d**4 + 504*a**3*b**2*c**6*d**4) + x**2*(18*a**5*c*d**3 + 180*a**4*b*c**4*d**3 + 216*a**3*b**2*c**7*d**3) + x*(18*a**5*c**2*d**2 + 72*a**4*b*c**5*d**2 + 54*a**3*b**2*c**8*d**2)) - 3*b*log(c/d + x)/(a**4*d) + b*log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(a**4*d)","B",0
2886,1,66,0,0.543181," ","integrate((d*e*x+c*e)**4/(a+b*(d*x+c)**3),x)","\frac{e^{4} \operatorname{RootSum} {\left(27 t^{3} b^{5} - a^{2}, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} b^{3} e^{8} + a c e^{8}}{a d e^{8}} \right)} \right)\right)}}{d} + \frac{c e^{4} x}{b} + \frac{d e^{4} x^{2}}{2 b}"," ",0,"e**4*RootSum(27*_t**3*b**5 - a**2, Lambda(_t, _t*log(x + (9*_t**2*b**3*e**8 + a*c*e**8)/(a*d*e**8))))/d + c*e**4*x/b + d*e**4*x**2/(2*b)","A",0
2887,1,44,0,0.495625," ","integrate((d*e*x+c*e)**3/(a+b*(d*x+c)**3),x)","\frac{e^{3} \operatorname{RootSum} {\left(27 t^{3} b^{4} + a, \left( t \mapsto t \log{\left(x + \frac{- 3 t b e^{3} + c e^{3}}{d e^{3}} \right)} \right)\right)}}{d} + \frac{e^{3} x}{b}"," ",0,"e**3*RootSum(27*_t**3*b**4 + a, Lambda(_t, _t*log(x + (-3*_t*b*e**3 + c*e**3)/(d*e**3))))/d + e**3*x/b","A",0
2888,1,46,0,0.410067," ","integrate((d*e*x+c*e)**2/(a+b*(d*x+c)**3),x)","\frac{e^{2} \log{\left(a + b c^{3} + 3 b c^{2} d x + 3 b c d^{2} x^{2} + b d^{3} x^{3} \right)}}{3 b d}"," ",0,"e**2*log(a + b*c**3 + 3*b*c**2*d*x + 3*b*c*d**2*x**2 + b*d**3*x**3)/(3*b*d)","B",0
2889,1,41,0,0.407856," ","integrate((d*e*x+c*e)/(a+b*(d*x+c)**3),x)","\frac{e \operatorname{RootSum} {\left(27 t^{3} a b^{2} + 1, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} a b e^{2} + c e^{2}}{d e^{2}} \right)} \right)\right)}}{d}"," ",0,"e*RootSum(27*_t**3*a*b**2 + 1, Lambda(_t, _t*log(x + (9*_t**2*a*b*e**2 + c*e**2)/(d*e**2))))/d","A",0
2890,1,53,0,0.750918," ","integrate(1/(d*e*x+c*e)/(a+b*(d*x+c)**3),x)","\frac{\log{\left(\frac{c}{d} + x \right)}}{a d e} - \frac{\log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{3 a d e}"," ",0,"log(c/d + x)/(a*d*e) - log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(3*a*d*e)","A",0
2891,1,54,0,0.992372," ","integrate(1/(d*e*x+c*e)**2/(a+b*(d*x+c)**3),x)","- \frac{1}{a c d e^{2} + a d^{2} e^{2} x} + \frac{\operatorname{RootSum} {\left(27 t^{3} a^{4} - b, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} a^{3} + b c}{b d} \right)} \right)\right)}}{d e^{2}}"," ",0,"-1/(a*c*d*e**2 + a*d**2*e**2*x) + RootSum(27*_t**3*a**4 - b, Lambda(_t, _t*log(x + (9*_t**2*a**3 + b*c)/(b*d))))/(d*e**2)","A",0
2892,1,75,0,1.354541," ","integrate(1/(d*e*x+c*e)**3/(a+b*(d*x+c)**3),x)","- \frac{1}{2 a c^{2} d e^{3} + 4 a c d^{2} e^{3} x + 2 a d^{3} e^{3} x^{2}} + \frac{\operatorname{RootSum} {\left(27 t^{3} a^{5} + b^{2}, \left( t \mapsto t \log{\left(x + \frac{- 3 t a^{2} + b c}{b d} \right)} \right)\right)}}{d e^{3}}"," ",0,"-1/(2*a*c**2*d*e**3 + 4*a*c*d**2*e**3*x + 2*a*d**3*e**3*x**2) + RootSum(27*_t**3*a**5 + b**2, Lambda(_t, _t*log(x + (-3*_t*a**2 + b*c)/(b*d))))/(d*e**3)","A",0
2893,1,121,0,2.100772," ","integrate(1/(d*e*x+c*e)**4/(a+b*(d*x+c)**3),x)","- \frac{1}{3 a c^{3} d e^{4} + 9 a c^{2} d^{2} e^{4} x + 9 a c d^{3} e^{4} x^{2} + 3 a d^{4} e^{4} x^{3}} - \frac{b \log{\left(\frac{c}{d} + x \right)}}{a^{2} d e^{4}} + \frac{b \log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{3 a^{2} d e^{4}}"," ",0,"-1/(3*a*c**3*d*e**4 + 9*a*c**2*d**2*e**4*x + 9*a*c*d**3*e**4*x**2 + 3*a*d**4*e**4*x**3) - b*log(c/d + x)/(a**2*d*e**4) + b*log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(3*a**2*d*e**4)","B",0
2894,1,133,0,1.674113," ","integrate((d*e*x+c*e)**4/(a+b*(d*x+c)**3)**2,x)","\frac{- c^{2} e^{4} - 2 c d e^{4} x - d^{2} e^{4} x^{2}}{3 a b d + 3 b^{2} c^{3} d + 9 b^{2} c^{2} d^{2} x + 9 b^{2} c d^{3} x^{2} + 3 b^{2} d^{4} x^{3}} + \frac{e^{4} \operatorname{RootSum} {\left(729 t^{3} a b^{5} + 8, \left( t \mapsto t \log{\left(x + \frac{81 t^{2} a b^{3} e^{8} + 4 c e^{8}}{4 d e^{8}} \right)} \right)\right)}}{d}"," ",0,"(-c**2*e**4 - 2*c*d*e**4*x - d**2*e**4*x**2)/(3*a*b*d + 3*b**2*c**3*d + 9*b**2*c**2*d**2*x + 9*b**2*c*d**3*x**2 + 3*b**2*d**4*x**3) + e**4*RootSum(729*_t**3*a*b**5 + 8, Lambda(_t, _t*log(x + (81*_t**2*a*b**3*e**8 + 4*c*e**8)/(4*d*e**8))))/d","A",0
2895,1,112,0,1.548398," ","integrate((d*e*x+c*e)**3/(a+b*(d*x+c)**3)**2,x)","\frac{- c e^{3} - d e^{3} x}{3 a b d + 3 b^{2} c^{3} d + 9 b^{2} c^{2} d^{2} x + 9 b^{2} c d^{3} x^{2} + 3 b^{2} d^{4} x^{3}} + \frac{e^{3} \operatorname{RootSum} {\left(729 t^{3} a^{2} b^{4} - 1, \left( t \mapsto t \log{\left(x + \frac{9 t a b e^{3} + c e^{3}}{d e^{3}} \right)} \right)\right)}}{d}"," ",0,"(-c*e**3 - d*e**3*x)/(3*a*b*d + 3*b**2*c**3*d + 9*b**2*c**2*d**2*x + 9*b**2*c*d**3*x**2 + 3*b**2*d**4*x**3) + e**3*RootSum(729*_t**3*a**2*b**4 - 1, Lambda(_t, _t*log(x + (9*_t*a*b*e**3 + c*e**3)/(d*e**3))))/d","A",0
2896,1,60,0,1.374291," ","integrate((d*e*x+c*e)**2/(a+b*(d*x+c)**3)**2,x)","- \frac{e^{2}}{3 a b d + 3 b^{2} c^{3} d + 9 b^{2} c^{2} d^{2} x + 9 b^{2} c d^{3} x^{2} + 3 b^{2} d^{4} x^{3}}"," ",0,"-e**2/(3*a*b*d + 3*b**2*c**3*d + 9*b**2*c**2*d**2*x + 9*b**2*c*d**3*x**2 + 3*b**2*d**4*x**3)","B",0
2897,1,122,0,1.373363," ","integrate((d*e*x+c*e)/(a+b*(d*x+c)**3)**2,x)","\frac{c^{2} e + 2 c d e x + d^{2} e x^{2}}{3 a^{2} d + 3 a b c^{3} d + 9 a b c^{2} d^{2} x + 9 a b c d^{3} x^{2} + 3 a b d^{4} x^{3}} + \frac{e \operatorname{RootSum} {\left(729 t^{3} a^{4} b^{2} + 1, \left( t \mapsto t \log{\left(x + \frac{81 t^{2} a^{3} b e^{2} + c e^{2}}{d e^{2}} \right)} \right)\right)}}{d}"," ",0,"(c**2*e + 2*c*d*e*x + d**2*e*x**2)/(3*a**2*d + 3*a*b*c**3*d + 9*a*b*c**2*d**2*x + 9*a*b*c*d**3*x**2 + 3*a*b*d**4*x**3) + e*RootSum(729*_t**3*a**4*b**2 + 1, Lambda(_t, _t*log(x + (81*_t**2*a**3*b*e**2 + c*e**2)/(d*e**2))))/d","A",0
2898,1,122,0,2.167646," ","integrate(1/(d*e*x+c*e)/(a+b*(d*x+c)**3)**2,x)","\frac{1}{3 a^{2} d e + 3 a b c^{3} d e + 9 a b c^{2} d^{2} e x + 9 a b c d^{3} e x^{2} + 3 a b d^{4} e x^{3}} + \frac{\log{\left(\frac{c}{d} + x \right)}}{a^{2} d e} - \frac{\log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{3 a^{2} d e}"," ",0,"1/(3*a**2*d*e + 3*a*b*c**3*d*e + 9*a*b*c**2*d**2*e*x + 9*a*b*c*d**3*e*x**2 + 3*a*b*d**4*e*x**3) + log(c/d + x)/(a**2*d*e) - log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(3*a**2*d*e)","B",0
2899,1,197,0,2.772546," ","integrate(1/(d*e*x+c*e)**2/(a+b*(d*x+c)**3)**2,x)","\frac{- 3 a - 4 b c^{3} - 12 b c^{2} d x - 12 b c d^{2} x^{2} - 4 b d^{3} x^{3}}{3 a^{3} c d e^{2} + 3 a^{2} b c^{4} d e^{2} + 18 a^{2} b c^{2} d^{3} e^{2} x^{2} + 12 a^{2} b c d^{4} e^{2} x^{3} + 3 a^{2} b d^{5} e^{2} x^{4} + x \left(3 a^{3} d^{2} e^{2} + 12 a^{2} b c^{3} d^{2} e^{2}\right)} + \frac{\operatorname{RootSum} {\left(729 t^{3} a^{7} - 64 b, \left( t \mapsto t \log{\left(x + \frac{81 t^{2} a^{5} + 16 b c}{16 b d} \right)} \right)\right)}}{d e^{2}}"," ",0,"(-3*a - 4*b*c**3 - 12*b*c**2*d*x - 12*b*c*d**2*x**2 - 4*b*d**3*x**3)/(3*a**3*c*d*e**2 + 3*a**2*b*c**4*d*e**2 + 18*a**2*b*c**2*d**3*e**2*x**2 + 12*a**2*b*c*d**4*e**2*x**3 + 3*a**2*b*d**5*e**2*x**4 + x*(3*a**3*d**2*e**2 + 12*a**2*b*c**3*d**2*e**2)) + RootSum(729*_t**3*a**7 - 64*b, Lambda(_t, _t*log(x + (81*_t**2*a**5 + 16*b*c)/(16*b*d))))/(d*e**2)","A",0
2900,1,233,0,4.105335," ","integrate(1/(d*e*x+c*e)**3/(a+b*(d*x+c)**3)**2,x)","\frac{- 3 a - 5 b c^{3} - 15 b c^{2} d x - 15 b c d^{2} x^{2} - 5 b d^{3} x^{3}}{6 a^{3} c^{2} d e^{3} + 6 a^{2} b c^{5} d e^{3} + 60 a^{2} b c^{2} d^{4} e^{3} x^{3} + 30 a^{2} b c d^{5} e^{3} x^{4} + 6 a^{2} b d^{6} e^{3} x^{5} + x^{2} \left(6 a^{3} d^{3} e^{3} + 60 a^{2} b c^{3} d^{3} e^{3}\right) + x \left(12 a^{3} c d^{2} e^{3} + 30 a^{2} b c^{4} d^{2} e^{3}\right)} + \frac{\operatorname{RootSum} {\left(729 t^{3} a^{8} + 125 b^{2}, \left( t \mapsto t \log{\left(x + \frac{- 9 t a^{3} + 5 b c}{5 b d} \right)} \right)\right)}}{d e^{3}}"," ",0,"(-3*a - 5*b*c**3 - 15*b*c**2*d*x - 15*b*c*d**2*x**2 - 5*b*d**3*x**3)/(6*a**3*c**2*d*e**3 + 6*a**2*b*c**5*d*e**3 + 60*a**2*b*c**2*d**4*e**3*x**3 + 30*a**2*b*c*d**5*e**3*x**4 + 6*a**2*b*d**6*e**3*x**5 + x**2*(6*a**3*d**3*e**3 + 60*a**2*b*c**3*d**3*e**3) + x*(12*a**3*c*d**2*e**3 + 30*a**2*b*c**4*d**2*e**3)) + RootSum(729*_t**3*a**8 + 125*b**2, Lambda(_t, _t*log(x + (-9*_t*a**3 + 5*b*c)/(5*b*d))))/(d*e**3)","A",0
2901,1,294,0,5.097943," ","integrate(1/(d*e*x+c*e)**4/(a+b*(d*x+c)**3)**2,x)","\frac{- a - 2 b c^{3} - 6 b c^{2} d x - 6 b c d^{2} x^{2} - 2 b d^{3} x^{3}}{3 a^{3} c^{3} d e^{4} + 3 a^{2} b c^{6} d e^{4} + 45 a^{2} b c^{2} d^{5} e^{4} x^{4} + 18 a^{2} b c d^{6} e^{4} x^{5} + 3 a^{2} b d^{7} e^{4} x^{6} + x^{3} \left(3 a^{3} d^{4} e^{4} + 60 a^{2} b c^{3} d^{4} e^{4}\right) + x^{2} \left(9 a^{3} c d^{3} e^{4} + 45 a^{2} b c^{4} d^{3} e^{4}\right) + x \left(9 a^{3} c^{2} d^{2} e^{4} + 18 a^{2} b c^{5} d^{2} e^{4}\right)} - \frac{2 b \log{\left(\frac{c}{d} + x \right)}}{a^{3} d e^{4}} + \frac{2 b \log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{3 a^{3} d e^{4}}"," ",0,"(-a - 2*b*c**3 - 6*b*c**2*d*x - 6*b*c*d**2*x**2 - 2*b*d**3*x**3)/(3*a**3*c**3*d*e**4 + 3*a**2*b*c**6*d*e**4 + 45*a**2*b*c**2*d**5*e**4*x**4 + 18*a**2*b*c*d**6*e**4*x**5 + 3*a**2*b*d**7*e**4*x**6 + x**3*(3*a**3*d**4*e**4 + 60*a**2*b*c**3*d**4*e**4) + x**2*(9*a**3*c*d**3*e**4 + 45*a**2*b*c**4*d**3*e**4) + x*(9*a**3*c**2*d**2*e**4 + 18*a**2*b*c**5*d**2*e**4)) - 2*b*log(c/d + x)/(a**3*d*e**4) + 2*b*log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(3*a**3*d*e**4)","B",0
2902,1,332,0,3.847871," ","integrate((d*e*x+c*e)**4/(a+b*(d*x+c)**3)**3,x)","\frac{- a c^{2} e^{4} + 2 b c^{5} e^{4} + 20 b c^{2} d^{3} e^{4} x^{3} + 10 b c d^{4} e^{4} x^{4} + 2 b d^{5} e^{4} x^{5} + x^{2} \left(- a d^{2} e^{4} + 20 b c^{3} d^{2} e^{4}\right) + x \left(- 2 a c d e^{4} + 10 b c^{4} d e^{4}\right)}{18 a^{3} b d + 36 a^{2} b^{2} c^{3} d + 18 a b^{3} c^{6} d + 270 a b^{3} c^{2} d^{5} x^{4} + 108 a b^{3} c d^{6} x^{5} + 18 a b^{3} d^{7} x^{6} + x^{3} \left(36 a^{2} b^{2} d^{4} + 360 a b^{3} c^{3} d^{4}\right) + x^{2} \left(108 a^{2} b^{2} c d^{3} + 270 a b^{3} c^{4} d^{3}\right) + x \left(108 a^{2} b^{2} c^{2} d^{2} + 108 a b^{3} c^{5} d^{2}\right)} + \frac{e^{4} \operatorname{RootSum} {\left(19683 t^{3} a^{4} b^{5} + 1, \left( t \mapsto t \log{\left(x + \frac{729 t^{2} a^{3} b^{3} e^{8} + c e^{8}}{d e^{8}} \right)} \right)\right)}}{d}"," ",0,"(-a*c**2*e**4 + 2*b*c**5*e**4 + 20*b*c**2*d**3*e**4*x**3 + 10*b*c*d**4*e**4*x**4 + 2*b*d**5*e**4*x**5 + x**2*(-a*d**2*e**4 + 20*b*c**3*d**2*e**4) + x*(-2*a*c*d*e**4 + 10*b*c**4*d*e**4))/(18*a**3*b*d + 36*a**2*b**2*c**3*d + 18*a*b**3*c**6*d + 270*a*b**3*c**2*d**5*x**4 + 108*a*b**3*c*d**6*x**5 + 18*a*b**3*d**7*x**6 + x**3*(36*a**2*b**2*d**4 + 360*a*b**3*c**3*d**4) + x**2*(108*a**2*b**2*c*d**3 + 270*a*b**3*c**4*d**3) + x*(108*a**2*b**2*c**2*d**2 + 108*a*b**3*c**5*d**2)) + e**4*RootSum(19683*_t**3*a**4*b**5 + 1, Lambda(_t, _t*log(x + (729*_t**2*a**3*b**3*e**8 + c*e**8)/(d*e**8))))/d","A",0
2903,1,298,0,3.664657," ","integrate((d*e*x+c*e)**3/(a+b*(d*x+c)**3)**3,x)","\frac{- 2 a c e^{3} + b c^{4} e^{3} + 6 b c^{2} d^{2} e^{3} x^{2} + 4 b c d^{3} e^{3} x^{3} + b d^{4} e^{3} x^{4} + x \left(- 2 a d e^{3} + 4 b c^{3} d e^{3}\right)}{18 a^{3} b d + 36 a^{2} b^{2} c^{3} d + 18 a b^{3} c^{6} d + 270 a b^{3} c^{2} d^{5} x^{4} + 108 a b^{3} c d^{6} x^{5} + 18 a b^{3} d^{7} x^{6} + x^{3} \left(36 a^{2} b^{2} d^{4} + 360 a b^{3} c^{3} d^{4}\right) + x^{2} \left(108 a^{2} b^{2} c d^{3} + 270 a b^{3} c^{4} d^{3}\right) + x \left(108 a^{2} b^{2} c^{2} d^{2} + 108 a b^{3} c^{5} d^{2}\right)} + \frac{e^{3} \operatorname{RootSum} {\left(19683 t^{3} a^{5} b^{4} - 1, \left( t \mapsto t \log{\left(x + \frac{27 t a^{2} b e^{3} + c e^{3}}{d e^{3}} \right)} \right)\right)}}{d}"," ",0,"(-2*a*c*e**3 + b*c**4*e**3 + 6*b*c**2*d**2*e**3*x**2 + 4*b*c*d**3*e**3*x**3 + b*d**4*e**3*x**4 + x*(-2*a*d*e**3 + 4*b*c**3*d*e**3))/(18*a**3*b*d + 36*a**2*b**2*c**3*d + 18*a*b**3*c**6*d + 270*a*b**3*c**2*d**5*x**4 + 108*a*b**3*c*d**6*x**5 + 18*a*b**3*d**7*x**6 + x**3*(36*a**2*b**2*d**4 + 360*a*b**3*c**3*d**4) + x**2*(108*a**2*b**2*c*d**3 + 270*a*b**3*c**4*d**3) + x*(108*a**2*b**2*c**2*d**2 + 108*a*b**3*c**5*d**2)) + e**3*RootSum(19683*_t**3*a**5*b**4 - 1, Lambda(_t, _t*log(x + (27*_t*a**2*b*e**3 + c*e**3)/(d*e**3))))/d","A",0
2904,1,155,0,3.373075," ","integrate((d*e*x+c*e)**2/(a+b*(d*x+c)**3)**3,x)","- \frac{e^{2}}{6 a^{2} b d + 12 a b^{2} c^{3} d + 6 b^{3} c^{6} d + 90 b^{3} c^{2} d^{5} x^{4} + 36 b^{3} c d^{6} x^{5} + 6 b^{3} d^{7} x^{6} + x^{3} \left(12 a b^{2} d^{4} + 120 b^{3} c^{3} d^{4}\right) + x^{2} \left(36 a b^{2} c d^{3} + 90 b^{3} c^{4} d^{3}\right) + x \left(36 a b^{2} c^{2} d^{2} + 36 b^{3} c^{5} d^{2}\right)}"," ",0,"-e**2/(6*a**2*b*d + 12*a*b**2*c**3*d + 6*b**3*c**6*d + 90*b**3*c**2*d**5*x**4 + 36*b**3*c*d**6*x**5 + 6*b**3*d**7*x**6 + x**3*(12*a*b**2*d**4 + 120*b**3*c**3*d**4) + x**2*(36*a*b**2*c*d**3 + 90*b**3*c**4*d**3) + x*(36*a*b**2*c**2*d**2 + 36*b**3*c**5*d**2))","B",0
2905,1,323,0,3.590189," ","integrate((d*e*x+c*e)/(a+b*(d*x+c)**3)**3,x)","\frac{7 a c^{2} e + 4 b c^{5} e + 40 b c^{2} d^{3} e x^{3} + 20 b c d^{4} e x^{4} + 4 b d^{5} e x^{5} + x^{2} \left(7 a d^{2} e + 40 b c^{3} d^{2} e\right) + x \left(14 a c d e + 20 b c^{4} d e\right)}{18 a^{4} d + 36 a^{3} b c^{3} d + 18 a^{2} b^{2} c^{6} d + 270 a^{2} b^{2} c^{2} d^{5} x^{4} + 108 a^{2} b^{2} c d^{6} x^{5} + 18 a^{2} b^{2} d^{7} x^{6} + x^{3} \left(36 a^{3} b d^{4} + 360 a^{2} b^{2} c^{3} d^{4}\right) + x^{2} \left(108 a^{3} b c d^{3} + 270 a^{2} b^{2} c^{4} d^{3}\right) + x \left(108 a^{3} b c^{2} d^{2} + 108 a^{2} b^{2} c^{5} d^{2}\right)} + \frac{e \operatorname{RootSum} {\left(19683 t^{3} a^{7} b^{2} + 8, \left( t \mapsto t \log{\left(x + \frac{729 t^{2} a^{5} b e^{2} + 4 c e^{2}}{4 d e^{2}} \right)} \right)\right)}}{d}"," ",0,"(7*a*c**2*e + 4*b*c**5*e + 40*b*c**2*d**3*e*x**3 + 20*b*c*d**4*e*x**4 + 4*b*d**5*e*x**5 + x**2*(7*a*d**2*e + 40*b*c**3*d**2*e) + x*(14*a*c*d*e + 20*b*c**4*d*e))/(18*a**4*d + 36*a**3*b*c**3*d + 18*a**2*b**2*c**6*d + 270*a**2*b**2*c**2*d**5*x**4 + 108*a**2*b**2*c*d**6*x**5 + 18*a**2*b**2*d**7*x**6 + x**3*(36*a**3*b*d**4 + 360*a**2*b**2*c**3*d**4) + x**2*(108*a**3*b*c*d**3 + 270*a**2*b**2*c**4*d**3) + x*(108*a**3*b*c**2*d**2 + 108*a**2*b**2*c**5*d**2)) + e*RootSum(19683*_t**3*a**7*b**2 + 8, Lambda(_t, _t*log(x + (729*_t**2*a**5*b*e**2 + 4*c*e**2)/(4*d*e**2))))/d","A",0
2906,1,292,0,5.059873," ","integrate(1/(d*e*x+c*e)/(a+b*(d*x+c)**3)**3,x)","\frac{3 a + 2 b c^{3} + 6 b c^{2} d x + 6 b c d^{2} x^{2} + 2 b d^{3} x^{3}}{6 a^{4} d e + 12 a^{3} b c^{3} d e + 6 a^{2} b^{2} c^{6} d e + 90 a^{2} b^{2} c^{2} d^{5} e x^{4} + 36 a^{2} b^{2} c d^{6} e x^{5} + 6 a^{2} b^{2} d^{7} e x^{6} + x^{3} \left(12 a^{3} b d^{4} e + 120 a^{2} b^{2} c^{3} d^{4} e\right) + x^{2} \left(36 a^{3} b c d^{3} e + 90 a^{2} b^{2} c^{4} d^{3} e\right) + x \left(36 a^{3} b c^{2} d^{2} e + 36 a^{2} b^{2} c^{5} d^{2} e\right)} + \frac{\log{\left(\frac{c}{d} + x \right)}}{a^{3} d e} - \frac{\log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{3 a^{3} d e}"," ",0,"(3*a + 2*b*c**3 + 6*b*c**2*d*x + 6*b*c*d**2*x**2 + 2*b*d**3*x**3)/(6*a**4*d*e + 12*a**3*b*c**3*d*e + 6*a**2*b**2*c**6*d*e + 90*a**2*b**2*c**2*d**5*e*x**4 + 36*a**2*b**2*c*d**6*e*x**5 + 6*a**2*b**2*d**7*e*x**6 + x**3*(12*a**3*b*d**4*e + 120*a**2*b**2*c**3*d**4*e) + x**2*(36*a**3*b*c*d**3*e + 90*a**2*b**2*c**4*d**3*e) + x*(36*a**3*b*c**2*d**2*e + 36*a**2*b**2*c**5*d**2*e)) + log(c/d + x)/(a**3*d*e) - log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(3*a**3*d*e)","B",0
2907,1,445,0,6.126323," ","integrate(1/(d*e*x+c*e)**2/(a+b*(d*x+c)**3)**3,x)","\frac{- 18 a^{2} - 49 a b c^{3} - 28 b^{2} c^{6} - 420 b^{2} c^{2} d^{4} x^{4} - 168 b^{2} c d^{5} x^{5} - 28 b^{2} d^{6} x^{6} + x^{3} \left(- 49 a b d^{3} - 560 b^{2} c^{3} d^{3}\right) + x^{2} \left(- 147 a b c d^{2} - 420 b^{2} c^{4} d^{2}\right) + x \left(- 147 a b c^{2} d - 168 b^{2} c^{5} d\right)}{18 a^{5} c d e^{2} + 36 a^{4} b c^{4} d e^{2} + 18 a^{3} b^{2} c^{7} d e^{2} + 378 a^{3} b^{2} c^{2} d^{6} e^{2} x^{5} + 126 a^{3} b^{2} c d^{7} e^{2} x^{6} + 18 a^{3} b^{2} d^{8} e^{2} x^{7} + x^{4} \left(36 a^{4} b d^{5} e^{2} + 630 a^{3} b^{2} c^{3} d^{5} e^{2}\right) + x^{3} \left(144 a^{4} b c d^{4} e^{2} + 630 a^{3} b^{2} c^{4} d^{4} e^{2}\right) + x^{2} \left(216 a^{4} b c^{2} d^{3} e^{2} + 378 a^{3} b^{2} c^{5} d^{3} e^{2}\right) + x \left(18 a^{5} d^{2} e^{2} + 144 a^{4} b c^{3} d^{2} e^{2} + 126 a^{3} b^{2} c^{6} d^{2} e^{2}\right)} + \frac{\operatorname{RootSum} {\left(19683 t^{3} a^{10} - 2744 b, \left( t \mapsto t \log{\left(x + \frac{729 t^{2} a^{7} + 196 b c}{196 b d} \right)} \right)\right)}}{d e^{2}}"," ",0,"(-18*a**2 - 49*a*b*c**3 - 28*b**2*c**6 - 420*b**2*c**2*d**4*x**4 - 168*b**2*c*d**5*x**5 - 28*b**2*d**6*x**6 + x**3*(-49*a*b*d**3 - 560*b**2*c**3*d**3) + x**2*(-147*a*b*c*d**2 - 420*b**2*c**4*d**2) + x*(-147*a*b*c**2*d - 168*b**2*c**5*d))/(18*a**5*c*d*e**2 + 36*a**4*b*c**4*d*e**2 + 18*a**3*b**2*c**7*d*e**2 + 378*a**3*b**2*c**2*d**6*e**2*x**5 + 126*a**3*b**2*c*d**7*e**2*x**6 + 18*a**3*b**2*d**8*e**2*x**7 + x**4*(36*a**4*b*d**5*e**2 + 630*a**3*b**2*c**3*d**5*e**2) + x**3*(144*a**4*b*c*d**4*e**2 + 630*a**3*b**2*c**4*d**4*e**2) + x**2*(216*a**4*b*c**2*d**3*e**2 + 378*a**3*b**2*c**5*d**3*e**2) + x*(18*a**5*d**2*e**2 + 144*a**4*b*c**3*d**2*e**2 + 126*a**3*b**2*c**6*d**2*e**2)) + RootSum(19683*_t**3*a**10 - 2744*b, Lambda(_t, _t*log(x + (729*_t**2*a**7 + 196*b*c)/(196*b*d))))/(d*e**2)","B",0
2908,1,500,0,7.361245," ","integrate(1/(d*e*x+c*e)**3/(a+b*(d*x+c)**3)**3,x)","\frac{- 9 a^{2} - 32 a b c^{3} - 20 b^{2} c^{6} - 300 b^{2} c^{2} d^{4} x^{4} - 120 b^{2} c d^{5} x^{5} - 20 b^{2} d^{6} x^{6} + x^{3} \left(- 32 a b d^{3} - 400 b^{2} c^{3} d^{3}\right) + x^{2} \left(- 96 a b c d^{2} - 300 b^{2} c^{4} d^{2}\right) + x \left(- 96 a b c^{2} d - 120 b^{2} c^{5} d\right)}{18 a^{5} c^{2} d e^{3} + 36 a^{4} b c^{5} d e^{3} + 18 a^{3} b^{2} c^{8} d e^{3} + 504 a^{3} b^{2} c^{2} d^{7} e^{3} x^{6} + 144 a^{3} b^{2} c d^{8} e^{3} x^{7} + 18 a^{3} b^{2} d^{9} e^{3} x^{8} + x^{5} \left(36 a^{4} b d^{6} e^{3} + 1008 a^{3} b^{2} c^{3} d^{6} e^{3}\right) + x^{4} \left(180 a^{4} b c d^{5} e^{3} + 1260 a^{3} b^{2} c^{4} d^{5} e^{3}\right) + x^{3} \left(360 a^{4} b c^{2} d^{4} e^{3} + 1008 a^{3} b^{2} c^{5} d^{4} e^{3}\right) + x^{2} \left(18 a^{5} d^{3} e^{3} + 360 a^{4} b c^{3} d^{3} e^{3} + 504 a^{3} b^{2} c^{6} d^{3} e^{3}\right) + x \left(36 a^{5} c d^{2} e^{3} + 180 a^{4} b c^{4} d^{2} e^{3} + 144 a^{3} b^{2} c^{7} d^{2} e^{3}\right)} + \frac{\operatorname{RootSum} {\left(19683 t^{3} a^{11} + 8000 b^{2}, \left( t \mapsto t \log{\left(x + \frac{- 27 t a^{4} + 20 b c}{20 b d} \right)} \right)\right)}}{d e^{3}}"," ",0,"(-9*a**2 - 32*a*b*c**3 - 20*b**2*c**6 - 300*b**2*c**2*d**4*x**4 - 120*b**2*c*d**5*x**5 - 20*b**2*d**6*x**6 + x**3*(-32*a*b*d**3 - 400*b**2*c**3*d**3) + x**2*(-96*a*b*c*d**2 - 300*b**2*c**4*d**2) + x*(-96*a*b*c**2*d - 120*b**2*c**5*d))/(18*a**5*c**2*d*e**3 + 36*a**4*b*c**5*d*e**3 + 18*a**3*b**2*c**8*d*e**3 + 504*a**3*b**2*c**2*d**7*e**3*x**6 + 144*a**3*b**2*c*d**8*e**3*x**7 + 18*a**3*b**2*d**9*e**3*x**8 + x**5*(36*a**4*b*d**6*e**3 + 1008*a**3*b**2*c**3*d**6*e**3) + x**4*(180*a**4*b*c*d**5*e**3 + 1260*a**3*b**2*c**4*d**5*e**3) + x**3*(360*a**4*b*c**2*d**4*e**3 + 1008*a**3*b**2*c**5*d**4*e**3) + x**2*(18*a**5*d**3*e**3 + 360*a**4*b*c**3*d**3*e**3 + 504*a**3*b**2*c**6*d**3*e**3) + x*(36*a**5*c*d**2*e**3 + 180*a**4*b*c**4*d**2*e**3 + 144*a**3*b**2*c**7*d**2*e**3)) + RootSum(19683*_t**3*a**11 + 8000*b**2, Lambda(_t, _t*log(x + (-27*_t*a**4 + 20*b*c)/(20*b*d))))/(d*e**3)","B",0
2909,1,578,0,8.761221," ","integrate(1/(d*e*x+c*e)**4/(a+b*(d*x+c)**3)**3,x)","\frac{- 2 a^{2} - 9 a b c^{3} - 6 b^{2} c^{6} - 90 b^{2} c^{2} d^{4} x^{4} - 36 b^{2} c d^{5} x^{5} - 6 b^{2} d^{6} x^{6} + x^{3} \left(- 9 a b d^{3} - 120 b^{2} c^{3} d^{3}\right) + x^{2} \left(- 27 a b c d^{2} - 90 b^{2} c^{4} d^{2}\right) + x \left(- 27 a b c^{2} d - 36 b^{2} c^{5} d\right)}{6 a^{5} c^{3} d e^{4} + 12 a^{4} b c^{6} d e^{4} + 6 a^{3} b^{2} c^{9} d e^{4} + 216 a^{3} b^{2} c^{2} d^{8} e^{4} x^{7} + 54 a^{3} b^{2} c d^{9} e^{4} x^{8} + 6 a^{3} b^{2} d^{10} e^{4} x^{9} + x^{6} \left(12 a^{4} b d^{7} e^{4} + 504 a^{3} b^{2} c^{3} d^{7} e^{4}\right) + x^{5} \left(72 a^{4} b c d^{6} e^{4} + 756 a^{3} b^{2} c^{4} d^{6} e^{4}\right) + x^{4} \left(180 a^{4} b c^{2} d^{5} e^{4} + 756 a^{3} b^{2} c^{5} d^{5} e^{4}\right) + x^{3} \left(6 a^{5} d^{4} e^{4} + 240 a^{4} b c^{3} d^{4} e^{4} + 504 a^{3} b^{2} c^{6} d^{4} e^{4}\right) + x^{2} \left(18 a^{5} c d^{3} e^{4} + 180 a^{4} b c^{4} d^{3} e^{4} + 216 a^{3} b^{2} c^{7} d^{3} e^{4}\right) + x \left(18 a^{5} c^{2} d^{2} e^{4} + 72 a^{4} b c^{5} d^{2} e^{4} + 54 a^{3} b^{2} c^{8} d^{2} e^{4}\right)} - \frac{3 b \log{\left(\frac{c}{d} + x \right)}}{a^{4} d e^{4}} + \frac{b \log{\left(\frac{3 c^{2} x}{d^{2}} + \frac{3 c x^{2}}{d} + x^{3} + \frac{a + b c^{3}}{b d^{3}} \right)}}{a^{4} d e^{4}}"," ",0,"(-2*a**2 - 9*a*b*c**3 - 6*b**2*c**6 - 90*b**2*c**2*d**4*x**4 - 36*b**2*c*d**5*x**5 - 6*b**2*d**6*x**6 + x**3*(-9*a*b*d**3 - 120*b**2*c**3*d**3) + x**2*(-27*a*b*c*d**2 - 90*b**2*c**4*d**2) + x*(-27*a*b*c**2*d - 36*b**2*c**5*d))/(6*a**5*c**3*d*e**4 + 12*a**4*b*c**6*d*e**4 + 6*a**3*b**2*c**9*d*e**4 + 216*a**3*b**2*c**2*d**8*e**4*x**7 + 54*a**3*b**2*c*d**9*e**4*x**8 + 6*a**3*b**2*d**10*e**4*x**9 + x**6*(12*a**4*b*d**7*e**4 + 504*a**3*b**2*c**3*d**7*e**4) + x**5*(72*a**4*b*c*d**6*e**4 + 756*a**3*b**2*c**4*d**6*e**4) + x**4*(180*a**4*b*c**2*d**5*e**4 + 756*a**3*b**2*c**5*d**5*e**4) + x**3*(6*a**5*d**4*e**4 + 240*a**4*b*c**3*d**4*e**4 + 504*a**3*b**2*c**6*d**4*e**4) + x**2*(18*a**5*c*d**3*e**4 + 180*a**4*b*c**4*d**3*e**4 + 216*a**3*b**2*c**7*d**3*e**4) + x*(18*a**5*c**2*d**2*e**4 + 72*a**4*b*c**5*d**2*e**4 + 54*a**3*b**2*c**8*d**2*e**4)) - 3*b*log(c/d + x)/(a**4*d*e**4) + b*log(3*c**2*x/d**2 + 3*c*x**2/d + x**3 + (a + b*c**3)/(b*d**3))/(a**4*d*e**4)","B",0
2910,-1,0,0,0.000000," ","integrate((d*x+c)**3*(a+b*(d*x+c)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2911,1,126,0,0.095249," ","integrate((d*x+c)**3*(a+b*(d*x+c)**4),x)","7 b c^{3} d^{4} x^{5} + \frac{7 b c^{2} d^{5} x^{6}}{2} + b c d^{6} x^{7} + \frac{b d^{7} x^{8}}{8} + x^{4} \left(\frac{a d^{3}}{4} + \frac{35 b c^{4} d^{3}}{4}\right) + x^{3} \left(a c d^{2} + 7 b c^{5} d^{2}\right) + x^{2} \left(\frac{3 a c^{2} d}{2} + \frac{7 b c^{6} d}{2}\right) + x \left(a c^{3} + b c^{7}\right)"," ",0,"7*b*c**3*d**4*x**5 + 7*b*c**2*d**5*x**6/2 + b*c*d**6*x**7 + b*d**7*x**8/8 + x**4*(a*d**3/4 + 35*b*c**4*d**3/4) + x**3*(a*c*d**2 + 7*b*c**5*d**2) + x**2*(3*a*c**2*d/2 + 7*b*c**6*d/2) + x*(a*c**3 + b*c**7)","B",0
2912,1,299,0,0.143788," ","integrate((d*x+c)**3*(a+b*(d*x+c)**4)**2,x)","\frac{55 b^{2} c^{3} d^{8} x^{9}}{3} + \frac{11 b^{2} c^{2} d^{9} x^{10}}{2} + b^{2} c d^{10} x^{11} + \frac{b^{2} d^{11} x^{12}}{12} + x^{8} \left(\frac{a b d^{7}}{4} + \frac{165 b^{2} c^{4} d^{7}}{4}\right) + x^{7} \left(2 a b c d^{6} + 66 b^{2} c^{5} d^{6}\right) + x^{6} \left(7 a b c^{2} d^{5} + 77 b^{2} c^{6} d^{5}\right) + x^{5} \left(14 a b c^{3} d^{4} + 66 b^{2} c^{7} d^{4}\right) + x^{4} \left(\frac{a^{2} d^{3}}{4} + \frac{35 a b c^{4} d^{3}}{2} + \frac{165 b^{2} c^{8} d^{3}}{4}\right) + x^{3} \left(a^{2} c d^{2} + 14 a b c^{5} d^{2} + \frac{55 b^{2} c^{9} d^{2}}{3}\right) + x^{2} \left(\frac{3 a^{2} c^{2} d}{2} + 7 a b c^{6} d + \frac{11 b^{2} c^{10} d}{2}\right) + x \left(a^{2} c^{3} + 2 a b c^{7} + b^{2} c^{11}\right)"," ",0,"55*b**2*c**3*d**8*x**9/3 + 11*b**2*c**2*d**9*x**10/2 + b**2*c*d**10*x**11 + b**2*d**11*x**12/12 + x**8*(a*b*d**7/4 + 165*b**2*c**4*d**7/4) + x**7*(2*a*b*c*d**6 + 66*b**2*c**5*d**6) + x**6*(7*a*b*c**2*d**5 + 77*b**2*c**6*d**5) + x**5*(14*a*b*c**3*d**4 + 66*b**2*c**7*d**4) + x**4*(a**2*d**3/4 + 35*a*b*c**4*d**3/2 + 165*b**2*c**8*d**3/4) + x**3*(a**2*c*d**2 + 14*a*b*c**5*d**2 + 55*b**2*c**9*d**2/3) + x**2*(3*a**2*c**2*d/2 + 7*a*b*c**6*d + 11*b**2*c**10*d/2) + x*(a**2*c**3 + 2*a*b*c**7 + b**2*c**11)","B",0
2913,1,541,0,0.233038," ","integrate((d*x+c)**3*(a+b*(d*x+c)**4)**3,x)","35 b^{3} c^{3} d^{12} x^{13} + \frac{15 b^{3} c^{2} d^{13} x^{14}}{2} + b^{3} c d^{14} x^{15} + \frac{b^{3} d^{15} x^{16}}{16} + x^{12} \left(\frac{a b^{2} d^{11}}{4} + \frac{455 b^{3} c^{4} d^{11}}{4}\right) + x^{11} \left(3 a b^{2} c d^{10} + 273 b^{3} c^{5} d^{10}\right) + x^{10} \left(\frac{33 a b^{2} c^{2} d^{9}}{2} + \frac{1001 b^{3} c^{6} d^{9}}{2}\right) + x^{9} \left(55 a b^{2} c^{3} d^{8} + 715 b^{3} c^{7} d^{8}\right) + x^{8} \left(\frac{3 a^{2} b d^{7}}{8} + \frac{495 a b^{2} c^{4} d^{7}}{4} + \frac{6435 b^{3} c^{8} d^{7}}{8}\right) + x^{7} \left(3 a^{2} b c d^{6} + 198 a b^{2} c^{5} d^{6} + 715 b^{3} c^{9} d^{6}\right) + x^{6} \left(\frac{21 a^{2} b c^{2} d^{5}}{2} + 231 a b^{2} c^{6} d^{5} + \frac{1001 b^{3} c^{10} d^{5}}{2}\right) + x^{5} \left(21 a^{2} b c^{3} d^{4} + 198 a b^{2} c^{7} d^{4} + 273 b^{3} c^{11} d^{4}\right) + x^{4} \left(\frac{a^{3} d^{3}}{4} + \frac{105 a^{2} b c^{4} d^{3}}{4} + \frac{495 a b^{2} c^{8} d^{3}}{4} + \frac{455 b^{3} c^{12} d^{3}}{4}\right) + x^{3} \left(a^{3} c d^{2} + 21 a^{2} b c^{5} d^{2} + 55 a b^{2} c^{9} d^{2} + 35 b^{3} c^{13} d^{2}\right) + x^{2} \left(\frac{3 a^{3} c^{2} d}{2} + \frac{21 a^{2} b c^{6} d}{2} + \frac{33 a b^{2} c^{10} d}{2} + \frac{15 b^{3} c^{14} d}{2}\right) + x \left(a^{3} c^{3} + 3 a^{2} b c^{7} + 3 a b^{2} c^{11} + b^{3} c^{15}\right)"," ",0,"35*b**3*c**3*d**12*x**13 + 15*b**3*c**2*d**13*x**14/2 + b**3*c*d**14*x**15 + b**3*d**15*x**16/16 + x**12*(a*b**2*d**11/4 + 455*b**3*c**4*d**11/4) + x**11*(3*a*b**2*c*d**10 + 273*b**3*c**5*d**10) + x**10*(33*a*b**2*c**2*d**9/2 + 1001*b**3*c**6*d**9/2) + x**9*(55*a*b**2*c**3*d**8 + 715*b**3*c**7*d**8) + x**8*(3*a**2*b*d**7/8 + 495*a*b**2*c**4*d**7/4 + 6435*b**3*c**8*d**7/8) + x**7*(3*a**2*b*c*d**6 + 198*a*b**2*c**5*d**6 + 715*b**3*c**9*d**6) + x**6*(21*a**2*b*c**2*d**5/2 + 231*a*b**2*c**6*d**5 + 1001*b**3*c**10*d**5/2) + x**5*(21*a**2*b*c**3*d**4 + 198*a*b**2*c**7*d**4 + 273*b**3*c**11*d**4) + x**4*(a**3*d**3/4 + 105*a**2*b*c**4*d**3/4 + 495*a*b**2*c**8*d**3/4 + 455*b**3*c**12*d**3/4) + x**3*(a**3*c*d**2 + 21*a**2*b*c**5*d**2 + 55*a*b**2*c**9*d**2 + 35*b**3*c**13*d**2) + x**2*(3*a**3*c**2*d/2 + 21*a**2*b*c**6*d/2 + 33*a*b**2*c**10*d/2 + 15*b**3*c**14*d/2) + x*(a**3*c**3 + 3*a**2*b*c**7 + 3*a*b**2*c**11 + b**3*c**15)","B",0
2914,1,56,0,0.437298," ","integrate((d*x+c)**3/(a+b*(d*x+c)**4),x)","\frac{\log{\left(a + b c^{4} + 4 b c^{3} d x + 6 b c^{2} d^{2} x^{2} + 4 b c d^{3} x^{3} + b d^{4} x^{4} \right)}}{4 b d}"," ",0,"log(a + b*c**4 + 4*b*c**3*d*x + 6*b*c**2*d**2*x**2 + 4*b*c*d**3*x**3 + b*d**4*x**4)/(4*b*d)","B",0
2915,1,73,0,2.024695," ","integrate((d*x+c)**3/(a+b*(d*x+c)**4)**2,x)","- \frac{1}{4 a b d + 4 b^{2} c^{4} d + 16 b^{2} c^{3} d^{2} x + 24 b^{2} c^{2} d^{3} x^{2} + 16 b^{2} c d^{4} x^{3} + 4 b^{2} d^{5} x^{4}}"," ",0,"-1/(4*a*b*d + 4*b**2*c**4*d + 16*b**2*c**3*d**2*x + 24*b**2*c**2*d**3*x**2 + 16*b**2*c*d**4*x**3 + 4*b**2*d**5*x**4)","B",0
2916,1,197,0,5.421723," ","integrate((d*x+c)**3/(a+b*(d*x+c)**4)**3,x)","- \frac{1}{8 a^{2} b d + 16 a b^{2} c^{4} d + 8 b^{3} c^{8} d + 448 b^{3} c^{3} d^{6} x^{5} + 224 b^{3} c^{2} d^{7} x^{6} + 64 b^{3} c d^{8} x^{7} + 8 b^{3} d^{9} x^{8} + x^{4} \left(16 a b^{2} d^{5} + 560 b^{3} c^{4} d^{5}\right) + x^{3} \left(64 a b^{2} c d^{4} + 448 b^{3} c^{5} d^{4}\right) + x^{2} \left(96 a b^{2} c^{2} d^{3} + 224 b^{3} c^{6} d^{3}\right) + x \left(64 a b^{2} c^{3} d^{2} + 64 b^{3} c^{7} d^{2}\right)}"," ",0,"-1/(8*a**2*b*d + 16*a*b**2*c**4*d + 8*b**3*c**8*d + 448*b**3*c**3*d**6*x**5 + 224*b**3*c**2*d**7*x**6 + 64*b**3*c*d**8*x**7 + 8*b**3*d**9*x**8 + x**4*(16*a*b**2*d**5 + 560*b**3*c**4*d**5) + x**3*(64*a*b**2*c*d**4 + 448*b**3*c**5*d**4) + x**2*(96*a*b**2*c**2*d**3 + 224*b**3*c**6*d**3) + x*(64*a*b**2*c**3*d**2 + 64*b**3*c**7*d**2))","B",0
2917,0,0,0,0.000000," ","integrate(1/(a+b*(d*x+c)**4)**(1/2),x)","\int \frac{1}{\sqrt{a + b \left(c + d x\right)^{4}}}\, dx"," ",0,"Integral(1/sqrt(a + b*(c + d*x)**4), x)","F",0
2918,0,0,0,0.000000," ","integrate(x/(a+b*(d*x+c)**4)**(1/2),x)","\int \frac{x}{\sqrt{a + b c^{4} + 4 b c^{3} d x + 6 b c^{2} d^{2} x^{2} + 4 b c d^{3} x^{3} + b d^{4} x^{4}}}\, dx"," ",0,"Integral(x/sqrt(a + b*c**4 + 4*b*c**3*d*x + 6*b*c**2*d**2*x**2 + 4*b*c*d**3*x**3 + b*d**4*x**4), x)","F",0
2919,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*(c*x)**(3/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b \left(c x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*(c*x)**(3/2)), x)","F",0
2920,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*(c*x)**(1/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b \sqrt{c x}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*sqrt(c*x)), x)","F",0
2921,0,0,0,0.000000," ","integrate((d*x)**m*(a+b/(c*x)**(1/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\sqrt{c x}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b/sqrt(c*x)), x)","F",0
2922,0,0,0,0.000000," ","integrate((d*x)**m*(a+b/(c*x)**(3/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\left(c x\right)^{\frac{3}{2}}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b/(c*x)**(3/2)), x)","F",0
2923,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*(c*x)**n)**p,x)","\int \left(d x\right)^{m} \left(a + b \left(c x\right)^{n}\right)^{p}\, dx"," ",0,"Integral((d*x)**m*(a + b*(c*x)**n)**p, x)","F",0
2924,0,0,0,0.000000," ","integrate(x**2*(a+b*(c*x)**n)**p,x)","\int x^{2} \left(a + b \left(c x\right)^{n}\right)^{p}\, dx"," ",0,"Integral(x**2*(a + b*(c*x)**n)**p, x)","F",0
2925,0,0,0,0.000000," ","integrate(x*(a+b*(c*x)**n)**p,x)","\int x \left(a + b \left(c x\right)^{n}\right)^{p}\, dx"," ",0,"Integral(x*(a + b*(c*x)**n)**p, x)","F",0
2926,0,0,0,0.000000," ","integrate((a+b*(c*x)**n)**p,x)","\int \left(a + b \left(c x\right)^{n}\right)^{p}\, dx"," ",0,"Integral((a + b*(c*x)**n)**p, x)","F",0
2927,0,0,0,0.000000," ","integrate((a+b*(c*x)**n)**p/x,x)","\int \frac{\left(a + b \left(c x\right)^{n}\right)^{p}}{x}\, dx"," ",0,"Integral((a + b*(c*x)**n)**p/x, x)","F",0
2928,0,0,0,0.000000," ","integrate((a+b*(c*x)**n)**p/x**2,x)","\int \frac{\left(a + b \left(c x\right)^{n}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((a + b*(c*x)**n)**p/x**2, x)","F",0
2929,1,41,0,0.191650," ","integrate(1/(1+(x**2)**(3/2)),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}"," ",0,"log(x + 1)/3 - log(x**2 - x + 1)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
2930,0,0,0,0.000000," ","integrate(x**5*(a+b*(c*x**2)**(1/2))**(1/2),x)","\int x^{5} \sqrt{a + b \sqrt{c x^{2}}}\, dx"," ",0,"Integral(x**5*sqrt(a + b*sqrt(c*x**2)), x)","F",0
2931,0,0,0,0.000000," ","integrate(x**3*(a+b*(c*x**2)**(1/2))**(1/2),x)","\int x^{3} \sqrt{a + b \sqrt{c x^{2}}}\, dx"," ",0,"Integral(x**3*sqrt(a + b*sqrt(c*x**2)), x)","F",0
2932,0,0,0,0.000000," ","integrate(x*(a+b*(c*x**2)**(1/2))**(1/2),x)","\int x \sqrt{a + b \sqrt{c x^{2}}}\, dx"," ",0,"Integral(x*sqrt(a + b*sqrt(c*x**2)), x)","F",0
2933,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(1/2))**(1/2)/x,x)","\int \frac{\sqrt{a + b \sqrt{c x^{2}}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**2))/x, x)","F",0
2934,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(1/2))**(1/2)/x**3,x)","\int \frac{\sqrt{a + b \sqrt{c x^{2}}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**2))/x**3, x)","F",0
2935,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(1/2))**(1/2)/x**5,x)","\int \frac{\sqrt{a + b \sqrt{c x^{2}}}}{x^{5}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**2))/x**5, x)","F",0
2936,0,0,0,0.000000," ","integrate(x**4*(a+b*(c*x**2)**(1/2))**(1/2),x)","\int x^{4} \sqrt{a + b \sqrt{c x^{2}}}\, dx"," ",0,"Integral(x**4*sqrt(a + b*sqrt(c*x**2)), x)","F",0
2937,0,0,0,0.000000," ","integrate(x**2*(a+b*(c*x**2)**(1/2))**(1/2),x)","\int x^{2} \sqrt{a + b \sqrt{c x^{2}}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*sqrt(c*x**2)), x)","F",0
2938,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(1/2))**(1/2),x)","\int \sqrt{a + b \sqrt{c x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**2)), x)","F",0
2939,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(1/2))**(1/2)/x**2,x)","\int \frac{\sqrt{a + b \sqrt{c x^{2}}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**2))/x**2, x)","F",0
2940,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(1/2))**(1/2)/x**4,x)","\int \frac{\sqrt{a + b \sqrt{c x^{2}}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**2))/x**4, x)","F",0
2941,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(1/2))**(1/2)/x**6,x)","\int \frac{\sqrt{a + b \sqrt{c x^{2}}}}{x^{6}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**2))/x**6, x)","F",0
2942,0,0,0,0.000000," ","integrate(x**8*(a+b*(c*x**2)**(3/2))**(1/2),x)","\int x^{8} \sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**8*sqrt(a + b*(c*x**2)**(3/2)), x)","F",0
2943,0,0,0,0.000000," ","integrate(x**5*(a+b*(c*x**2)**(3/2))**(1/2),x)","\int x^{5} \sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**5*sqrt(a + b*(c*x**2)**(3/2)), x)","F",0
2944,0,0,0,0.000000," ","integrate(x**2*(a+b*(c*x**2)**(3/2))**(1/2),x)","\int x^{2} \sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*(c*x**2)**(3/2)), x)","F",0
2945,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(3/2))**(1/2)/x,x)","\int \frac{\sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**2)**(3/2))/x, x)","F",0
2946,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(3/2))**(1/2)/x**4,x)","\int \frac{\sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**2)**(3/2))/x**4, x)","F",0
2947,0,0,0,0.000000," ","integrate(x**3*(a+b*(c*x**2)**(3/2))**(1/2),x)","\int x^{3} \sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*sqrt(a + b*(c*x**2)**(3/2)), x)","F",0
2948,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(3/2))**(1/2),x)","\int \sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**2)**(3/2)), x)","F",0
2949,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(3/2))**(1/2)/x**3,x)","\int \frac{\sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**2)**(3/2))/x**3, x)","F",0
2950,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(3/2))**(1/2)/x**6,x)","\int \frac{\sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}}{x^{6}}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**2)**(3/2))/x**6, x)","F",0
2951,0,0,0,0.000000," ","integrate(x**4*(a+b*(c*x**2)**(3/2))**(1/2),x)","\int x^{4} \sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4*sqrt(a + b*(c*x**2)**(3/2)), x)","F",0
2952,0,0,0,0.000000," ","integrate(x*(a+b*(c*x**2)**(3/2))**(1/2),x)","\int x \sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*sqrt(a + b*(c*x**2)**(3/2)), x)","F",0
2953,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(3/2))**(1/2)/x**2,x)","\int \frac{\sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**2)**(3/2))/x**2, x)","F",0
2954,0,0,0,0.000000," ","integrate((a+b*(c*x**2)**(3/2))**(1/2)/x**5,x)","\int \frac{\sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}}{x^{5}}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**2)**(3/2))/x**5, x)","F",0
2955,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*(c*x**2)**(3/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b \left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*(c*x**2)**(3/2)), x)","F",0
2956,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*(c*x**2)**(1/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b \sqrt{c x^{2}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*sqrt(c*x**2)), x)","F",0
2957,0,0,0,0.000000," ","integrate((d*x)**m*(a+b/(c*x**2)**(1/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\sqrt{c x^{2}}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b/sqrt(c*x**2)), x)","F",0
2958,0,0,0,0.000000," ","integrate((d*x)**m*(a+b/(c*x**2)**(3/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\left(c x^{2}\right)^{\frac{3}{2}}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b/(c*x**2)**(3/2)), x)","F",0
2959,1,2,0,0.133286," ","integrate(1/(1+(x**3)**(2/3)),x)","\operatorname{atan}{\left(x \right)}"," ",0,"atan(x)","A",0
2960,0,0,0,0.000000," ","integrate(x**5*(a+b*(c*x**3)**(1/2))**(1/2),x)","\int x^{5} \sqrt{a + b \sqrt{c x^{3}}}\, dx"," ",0,"Integral(x**5*sqrt(a + b*sqrt(c*x**3)), x)","F",0
2961,0,0,0,0.000000," ","integrate(x**2*(a+b*(c*x**3)**(1/2))**(1/2),x)","\int x^{2} \sqrt{a + b \sqrt{c x^{3}}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*sqrt(c*x**3)), x)","F",0
2962,0,0,0,0.000000," ","integrate((a+b*(c*x**3)**(1/2))**(1/2)/x,x)","\int \frac{\sqrt{a + b \sqrt{c x^{3}}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**3))/x, x)","F",0
2963,0,0,0,0.000000," ","integrate((a+b*(c*x**3)**(1/2))**(1/2)/x**4,x)","\int \frac{\sqrt{a + b \sqrt{c x^{3}}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**3))/x**4, x)","F",0
2964,0,0,0,0.000000," ","integrate(x*(a+b*(c*x**3)**(1/2))**(1/2),x)","\int x \sqrt{a + b \sqrt{c x^{3}}}\, dx"," ",0,"Integral(x*sqrt(a + b*sqrt(c*x**3)), x)","F",0
2965,0,0,0,0.000000," ","integrate((a+b*(c*x**3)**(1/2))**(1/2)/x**2,x)","\int \frac{\sqrt{a + b \sqrt{c x^{3}}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**3))/x**2, x)","F",0
2966,0,0,0,0.000000," ","integrate((a+b*(c*x**3)**(1/2))**(1/2)/x**5,x)","\int \frac{\sqrt{a + b \sqrt{c x^{3}}}}{x^{5}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**3))/x**5, x)","F",0
2967,0,0,0,0.000000," ","integrate(x**3*(a+b*(c*x**3)**(1/2))**(1/2),x)","\int x^{3} \sqrt{a + b \sqrt{c x^{3}}}\, dx"," ",0,"Integral(x**3*sqrt(a + b*sqrt(c*x**3)), x)","F",0
2968,0,0,0,0.000000," ","integrate((a+b*(c*x**3)**(1/2))**(1/2),x)","\int \sqrt{a + b \sqrt{c x^{3}}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**3)), x)","F",0
2969,0,0,0,0.000000," ","integrate((a+b*(c*x**3)**(1/2))**(1/2)/x**3,x)","\int \frac{\sqrt{a + b \sqrt{c x^{3}}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c*x**3))/x**3, x)","F",0
2970,0,0,0,0.000000," ","integrate(x**17*(a+b*(c*x**3)**(3/2))**(1/2),x)","\int x^{17} \sqrt{a + b \left(c x^{3}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**17*sqrt(a + b*(c*x**3)**(3/2)), x)","F",0
2971,0,0,0,0.000000," ","integrate(x**8*(a+b*(c*x**3)**(3/2))**(1/2),x)","\int x^{8} \sqrt{a + b \left(c x^{3}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**8*sqrt(a + b*(c*x**3)**(3/2)), x)","F",0
2972,0,0,0,0.000000," ","integrate((a+b*(c*x**3)**(3/2))**(1/2)/x,x)","\int \frac{\sqrt{a + b \left(c x^{3}\right)^{\frac{3}{2}}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**3)**(3/2))/x, x)","F",0
2973,0,0,0,0.000000," ","integrate((a+b*(c*x**3)**(3/2))**(1/2)/x**10,x)","\int \frac{\sqrt{a + b \left(c x^{3}\right)^{\frac{3}{2}}}}{x^{10}}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**3)**(3/2))/x**10, x)","F",0
2974,0,0,0,0.000000," ","integrate(x**2*(a+b*(c*x**3)**(3/2))**(1/2),x)","\int x^{2} \sqrt{a + b \left(c x^{3}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*(c*x**3)**(3/2)), x)","F",0
2975,0,0,0,0.000000," ","integrate(x**9*(a+b*(c*x**3)**(3/2))**(1/2),x)","\int x^{9} \sqrt{a + b \left(c x^{3}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**9*sqrt(a + b*(c*x**3)**(3/2)), x)","F",0
2976,0,0,0,0.000000," ","integrate((a+b*(c*x**3)**(3/2))**(1/2),x)","\int \sqrt{a + b \left(c x^{3}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**3)**(3/2)), x)","F",0
2977,0,0,0,0.000000," ","integrate((a+b*(c*x**3)**(3/2))**(1/2)/x**9,x)","\int \frac{\sqrt{a + b \left(c x^{3}\right)^{\frac{3}{2}}}}{x^{9}}\, dx"," ",0,"Integral(sqrt(a + b*(c*x**3)**(3/2))/x**9, x)","F",0
2978,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*(c*x**3)**(3/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b \left(c x^{3}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*(c*x**3)**(3/2)), x)","F",0
2979,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*(c*x**3)**(1/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b \sqrt{c x^{3}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*sqrt(c*x**3)), x)","F",0
2980,0,0,0,0.000000," ","integrate((d*x)**m*(a+b/(c*x**3)**(1/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\sqrt{c x^{3}}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b/sqrt(c*x**3)), x)","F",0
2981,0,0,0,0.000000," ","integrate((d*x)**m*(a+b/(c*x**3)**(3/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\left(c x^{3}\right)^{\frac{3}{2}}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b/(c*x**3)**(3/2)), x)","F",0
2982,0,0,0,0.000000," ","integrate(x*(a+b*(c/x)**(1/2))**(1/2),x)","\int x \sqrt{a + b \sqrt{\frac{c}{x}}}\, dx"," ",0,"Integral(x*sqrt(a + b*sqrt(c/x)), x)","F",0
2983,0,0,0,0.000000," ","integrate((a+b*(c/x)**(1/2))**(1/2),x)","\int \sqrt{a + b \sqrt{\frac{c}{x}}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c/x)), x)","F",0
2984,0,0,0,0.000000," ","integrate((a+b*(c/x)**(1/2))**(1/2)/x,x)","\int \frac{\sqrt{a + b \sqrt{\frac{c}{x}}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c/x))/x, x)","F",0
2985,0,0,0,0.000000," ","integrate((a+b*(c/x)**(1/2))**(1/2)/x**2,x)","\int \frac{\sqrt{a + b \sqrt{\frac{c}{x}}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c/x))/x**2, x)","F",0
2986,0,0,0,0.000000," ","integrate((a+b*(c/x)**(1/2))**(1/2)/x**3,x)","\int \frac{\sqrt{a + b \sqrt{\frac{c}{x}}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c/x))/x**3, x)","F",0
2987,0,0,0,0.000000," ","integrate((a+b*(c/x)**(1/2))**(1/2)/x**4,x)","\int \frac{\sqrt{a + b \sqrt{\frac{c}{x}}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c/x))/x**4, x)","F",0
2988,0,0,0,0.000000," ","integrate(x/(a+b*(c/x)**(1/2))**(1/2),x)","\int \frac{x}{\sqrt{a + b \sqrt{\frac{c}{x}}}}\, dx"," ",0,"Integral(x/sqrt(a + b*sqrt(c/x)), x)","F",0
2989,0,0,0,0.000000," ","integrate(1/(a+b*(c/x)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{a + b \sqrt{\frac{c}{x}}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sqrt(c/x)), x)","F",0
2990,0,0,0,0.000000," ","integrate(1/x/(a+b*(c/x)**(1/2))**(1/2),x)","\int \frac{1}{x \sqrt{a + b \sqrt{\frac{c}{x}}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*sqrt(c/x))), x)","F",0
2991,0,0,0,0.000000," ","integrate(1/x**2/(a+b*(c/x)**(1/2))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a + b \sqrt{\frac{c}{x}}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a + b*sqrt(c/x))), x)","F",0
2992,0,0,0,0.000000," ","integrate(1/x**3/(a+b*(c/x)**(1/2))**(1/2),x)","\int \frac{1}{x^{3} \sqrt{a + b \sqrt{\frac{c}{x}}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(a + b*sqrt(c/x))), x)","F",0
2993,0,0,0,0.000000," ","integrate(1/x**4/(a+b*(c/x)**(1/2))**(1/2),x)","\int \frac{1}{x^{4} \sqrt{a + b \sqrt{\frac{c}{x}}}}\, dx"," ",0,"Integral(1/(x**4*sqrt(a + b*sqrt(c/x))), x)","F",0
2994,0,0,0,0.000000," ","integrate(1/(1+(1/x)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{\sqrt{\frac{1}{x}} + 1}}\, dx"," ",0,"Integral(1/sqrt(sqrt(1/x) + 1), x)","F",0
2995,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*(c/x)**(3/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b \left(\frac{c}{x}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*(c/x)**(3/2)), x)","F",0
2996,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*(c/x)**(1/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b \sqrt{\frac{c}{x}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*sqrt(c/x)), x)","F",0
2997,0,0,0,0.000000," ","integrate((d*x)**m*(a+b/(c/x)**(1/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\sqrt{\frac{c}{x}}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b/sqrt(c/x)), x)","F",0
2998,0,0,0,0.000000," ","integrate((d*x)**m*(a+b/(c/x)**(3/2))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\left(\frac{c}{x}\right)^{\frac{3}{2}}}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b/(c/x)**(3/2)), x)","F",0
2999,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*(c/x)**(3/2))**(1/2),x)","\int \frac{\left(d x\right)^{m}}{\sqrt{a + b \left(\frac{c}{x}\right)^{\frac{3}{2}}}}\, dx"," ",0,"Integral((d*x)**m/sqrt(a + b*(c/x)**(3/2)), x)","F",0
3000,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*(c/x)**(1/2))**(1/2),x)","\int \frac{\left(d x\right)^{m}}{\sqrt{a + b \sqrt{\frac{c}{x}}}}\, dx"," ",0,"Integral((d*x)**m/sqrt(a + b*sqrt(c/x)), x)","F",0
3001,0,0,0,0.000000," ","integrate((d*x)**m/(a+b/(c/x)**(1/2))**(1/2),x)","\int \frac{\left(d x\right)^{m}}{\sqrt{a + \frac{b}{\sqrt{\frac{c}{x}}}}}\, dx"," ",0,"Integral((d*x)**m/sqrt(a + b/sqrt(c/x)), x)","F",0
3002,0,0,0,0.000000," ","integrate((d*x)**m/(a+b/(c/x)**(3/2))**(1/2),x)","\int \frac{\left(d x\right)^{m}}{\sqrt{a + \frac{b}{\left(\frac{c}{x}\right)^{\frac{3}{2}}}}}\, dx"," ",0,"Integral((d*x)**m/sqrt(a + b/(c/x)**(3/2)), x)","F",0
3003,1,19,0,0.238273," ","integrate(a+b*(c*x**n)**(1/n),x)","a x + \frac{b c^{\frac{1}{n}} x \left(x^{n}\right)^{\frac{1}{n}}}{2}"," ",0,"a*x + b*c**(1/n)*x*(x**n)**(1/n)/2","A",0
3004,1,39,0,0.431430," ","integrate((a+b*(c*x**n)**(1/n))**2,x)","a^{2} x + a b c^{\frac{1}{n}} x \left(x^{n}\right)^{\frac{1}{n}} + \frac{b^{2} c^{\frac{2}{n}} x \left(x^{n}\right)^{\frac{2}{n}}}{3}"," ",0,"a**2*x + a*b*c**(1/n)*x*(x**n)**(1/n) + b**2*c**(2/n)*x*(x**n)**(2/n)/3","A",0
3005,1,63,0,0.780957," ","integrate((a+b*(c*x**n)**(1/n))**3,x)","a^{3} x + \frac{3 a^{2} b c^{\frac{1}{n}} x \left(x^{n}\right)^{\frac{1}{n}}}{2} + a b^{2} c^{\frac{2}{n}} x \left(x^{n}\right)^{\frac{2}{n}} + \frac{b^{3} c^{\frac{3}{n}} x \left(x^{n}\right)^{\frac{3}{n}}}{4}"," ",0,"a**3*x + 3*a**2*b*c**(1/n)*x*(x**n)**(1/n)/2 + a*b**2*c**(2/n)*x*(x**n)**(2/n) + b**3*c**(3/n)*x*(x**n)**(3/n)/4","B",0
3006,0,0,0,0.000000," ","integrate(x**3/(a+b*(c*x**n)**(1/n)),x)","\int \frac{x^{3}}{a + b \left(c x^{n}\right)^{\frac{1}{n}}}\, dx"," ",0,"Integral(x**3/(a + b*(c*x**n)**(1/n)), x)","F",0
3007,0,0,0,0.000000," ","integrate(x**2/(a+b*(c*x**n)**(1/n)),x)","\int \frac{x^{2}}{a + b \left(c x^{n}\right)^{\frac{1}{n}}}\, dx"," ",0,"Integral(x**2/(a + b*(c*x**n)**(1/n)), x)","F",0
3008,0,0,0,0.000000," ","integrate(x/(a+b*(c*x**n)**(1/n)),x)","\int \frac{x}{a + b \left(c x^{n}\right)^{\frac{1}{n}}}\, dx"," ",0,"Integral(x/(a + b*(c*x**n)**(1/n)), x)","F",0
3009,0,0,0,0.000000," ","integrate(1/(a+b*(c*x**n)**(1/n)),x)","\int \frac{1}{a + b \left(c x^{n}\right)^{\frac{1}{n}}}\, dx"," ",0,"Integral(1/(a + b*(c*x**n)**(1/n)), x)","F",0
3010,1,56,0,1.553128," ","integrate(1/x/(a+b*(c*x**n)**(1/n)),x)","\begin{cases} \tilde{\infty} c^{- \frac{1}{n}} \left(x^{n}\right)^{- \frac{1}{n}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{c^{- \frac{1}{n}} \left(x^{n}\right)^{- \frac{1}{n}}}{b} & \text{for}\: a = 0 \\\frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + c^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*c**(-1/n)*(x**n)**(-1/n), Eq(a, 0) & Eq(b, 0)), (-c**(-1/n)*(x**n)**(-1/n)/b, Eq(a, 0)), (log(x)/a, Eq(b, 0)), (log(x)/a - log(a/b + c**(1/n)*(x**n)**(1/n))/a, True))","A",0
3011,0,0,0,0.000000," ","integrate(1/x**2/(a+b*(c*x**n)**(1/n)),x)","\int \frac{1}{x^{2} \left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)}\, dx"," ",0,"Integral(1/(x**2*(a + b*(c*x**n)**(1/n))), x)","F",0
3012,0,0,0,0.000000," ","integrate(1/x**3/(a+b*(c*x**n)**(1/n)),x)","\int \frac{1}{x^{3} \left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)}\, dx"," ",0,"Integral(1/(x**3*(a + b*(c*x**n)**(1/n))), x)","F",0
3013,0,0,0,0.000000," ","integrate(x**3/(a+b*(c*x**n)**(1/n))**2,x)","\int \frac{x^{3}}{\left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{2}}\, dx"," ",0,"Integral(x**3/(a + b*(c*x**n)**(1/n))**2, x)","F",0
3014,0,0,0,0.000000," ","integrate(x**2/(a+b*(c*x**n)**(1/n))**2,x)","\int \frac{x^{2}}{\left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{2}}\, dx"," ",0,"Integral(x**2/(a + b*(c*x**n)**(1/n))**2, x)","F",0
3015,0,0,0,0.000000," ","integrate(x/(a+b*(c*x**n)**(1/n))**2,x)","\int \frac{x}{\left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{2}}\, dx"," ",0,"Integral(x/(a + b*(c*x**n)**(1/n))**2, x)","F",0
3016,1,80,0,169.224885," ","integrate(1/(a+b*(c*x**n)**(1/n))**2,x)","\begin{cases} \tilde{\infty} c^{- \frac{2}{n}} x \left(x^{n}\right)^{- \frac{2}{n}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{c^{- \frac{2}{n}} x \left(x^{n}\right)^{- \frac{2}{n}}}{b^{2}} & \text{for}\: a = 0 \\\tilde{\infty} c^{\frac{2}{n}} x \left(x^{n}\right)^{\frac{2}{n}} & \text{for}\: b = - a c^{- \frac{1}{n}} \left(x^{n}\right)^{- \frac{1}{n}} \\\frac{x}{a^{2} + a b c^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*c**(-2/n)*x*(x**n)**(-2/n), Eq(a, 0) & Eq(b, 0)), (-c**(-2/n)*x*(x**n)**(-2/n)/b**2, Eq(a, 0)), (zoo*c**(2/n)*x*(x**n)**(2/n), Eq(b, -a*c**(-1/n)*(x**n)**(-1/n))), (x/(a**2 + a*b*c**(1/n)*(x**n)**(1/n)), True))","A",0
3017,-1,0,0,0.000000," ","integrate(1/x/(a+b*(c*x**n)**(1/n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3018,0,0,0,0.000000," ","integrate(1/x**2/(a+b*(c*x**n)**(1/n))**2,x)","\int \frac{1}{x^{2} \left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{2}}\, dx"," ",0,"Integral(1/(x**2*(a + b*(c*x**n)**(1/n))**2), x)","F",0
3019,0,0,0,0.000000," ","integrate(1/x**3/(a+b*(c*x**n)**(1/n))**2,x)","\int \frac{1}{x^{3} \left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{2}}\, dx"," ",0,"Integral(1/(x**3*(a + b*(c*x**n)**(1/n))**2), x)","F",0
3020,-1,0,0,0.000000," ","integrate(1/(a+b*(c*x**n)**(1/n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3021,1,19,0,0.111461," ","integrate(x/(1+(x**n)**(1/n))**2,x)","\log{\left(\left(x^{n}\right)^{\frac{1}{n}} + 1 \right)} + \frac{1}{\left(x^{n}\right)^{\frac{1}{n}} + 1}"," ",0,"log((x**n)**(1/n) + 1) + 1/((x**n)**(1/n) + 1)","A",0
3022,0,0,0,0.000000," ","integrate(x**3*(a+b*(c*x**n)**(1/n))**p,x)","\int x^{3} \left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{p}\, dx"," ",0,"Integral(x**3*(a + b*(c*x**n)**(1/n))**p, x)","F",0
3023,0,0,0,0.000000," ","integrate(x**2*(a+b*(c*x**n)**(1/n))**p,x)","\int x^{2} \left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{p}\, dx"," ",0,"Integral(x**2*(a + b*(c*x**n)**(1/n))**p, x)","F",0
3024,0,0,0,0.000000," ","integrate(x*(a+b*(c*x**n)**(1/n))**p,x)","\int x \left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{p}\, dx"," ",0,"Integral(x*(a + b*(c*x**n)**(1/n))**p, x)","F",0
3025,0,0,0,0.000000," ","integrate((a+b*(c*x**n)**(1/n))**p,x)","\int \left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{p}\, dx"," ",0,"Integral((a + b*(c*x**n)**(1/n))**p, x)","F",0
3026,0,0,0,0.000000," ","integrate((a+b*(c*x**n)**(1/n))**p/x,x)","\int \frac{\left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{p}}{x}\, dx"," ",0,"Integral((a + b*(c*x**n)**(1/n))**p/x, x)","F",0
3027,0,0,0,0.000000," ","integrate((a+b*(c*x**n)**(1/n))**p/x**2,x)","\int \frac{\left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((a + b*(c*x**n)**(1/n))**p/x**2, x)","F",0
3028,1,63,0,0.994896," ","integrate((a+b*(c*x**n)**(2/n))**3,x)","a^{3} x + a^{2} b c^{\frac{2}{n}} x \left(x^{n}\right)^{\frac{2}{n}} + \frac{3 a b^{2} c^{\frac{4}{n}} x \left(x^{n}\right)^{\frac{4}{n}}}{5} + \frac{b^{3} c^{\frac{6}{n}} x \left(x^{n}\right)^{\frac{6}{n}}}{7}"," ",0,"a**3*x + a**2*b*c**(2/n)*x*(x**n)**(2/n) + 3*a*b**2*c**(4/n)*x*(x**n)**(4/n)/5 + b**3*c**(6/n)*x*(x**n)**(6/n)/7","A",0
3029,1,42,0,0.571354," ","integrate((a+b*(c*x**n)**(2/n))**2,x)","a^{2} x + \frac{2 a b c^{\frac{2}{n}} x \left(x^{n}\right)^{\frac{2}{n}}}{3} + \frac{b^{2} c^{\frac{4}{n}} x \left(x^{n}\right)^{\frac{4}{n}}}{5}"," ",0,"a**2*x + 2*a*b*c**(2/n)*x*(x**n)**(2/n)/3 + b**2*c**(4/n)*x*(x**n)**(4/n)/5","A",0
3030,1,19,0,0.312478," ","integrate(a+b*(c*x**n)**(2/n),x)","a x + \frac{b c^{\frac{2}{n}} x \left(x^{n}\right)^{\frac{2}{n}}}{3}"," ",0,"a*x + b*c**(2/n)*x*(x**n)**(2/n)/3","A",0
3031,0,0,0,0.000000," ","integrate(1/(a+b*(c*x**n)**(2/n)),x)","\int \frac{1}{a + b \left(c x^{n}\right)^{\frac{2}{n}}}\, dx"," ",0,"Integral(1/(a + b*(c*x**n)**(2/n)), x)","F",0
3032,0,0,0,0.000000," ","integrate(1/(a+b*(c*x**n)**(2/n))**2,x)","\int \frac{1}{\left(a + b \left(c x^{n}\right)^{\frac{2}{n}}\right)^{2}}\, dx"," ",0,"Integral((a + b*(c*x**n)**(2/n))**(-2), x)","F",0
3033,0,0,0,0.000000," ","integrate(1/(a+b*(c*x**n)**(2/n))**3,x)","\int \frac{1}{\left(a + b \left(c x^{n}\right)^{\frac{2}{n}}\right)^{3}}\, dx"," ",0,"Integral((a + b*(c*x**n)**(2/n))**(-3), x)","F",0
3034,1,5,0,0.137249," ","integrate(1/(1+4*(x**4)**(1/2)),x)","\frac{\operatorname{atan}{\left(2 x \right)}}{2}"," ",0,"atan(2*x)/2","A",0
3035,1,15,0,0.145013," ","integrate(1/(1-4*(x**4)**(1/2)),x)","- \frac{\log{\left(x - \frac{1}{2} \right)}}{4} + \frac{\log{\left(x + \frac{1}{2} \right)}}{4}"," ",0,"-log(x - 1/2)/4 + log(x + 1/2)/4","A",0
3036,1,5,0,0.125931," ","integrate(1/(1+4*(x**6)**(1/3)),x)","\frac{\operatorname{atan}{\left(2 x \right)}}{2}"," ",0,"atan(2*x)/2","A",0
3037,1,15,0,0.130113," ","integrate(1/(1-4*(x**6)**(1/3)),x)","- \frac{\log{\left(x - \frac{1}{2} \right)}}{4} + \frac{\log{\left(x + \frac{1}{2} \right)}}{4}"," ",0,"-log(x - 1/2)/4 + log(x + 1/2)/4","A",0
3038,1,5,0,0.126747," ","integrate(1/(1+4*(x**(2*n))**(1/n)),x)","\frac{\operatorname{atan}{\left(2 x \right)}}{2}"," ",0,"atan(2*x)/2","A",0
3039,1,15,0,0.135203," ","integrate(1/(1-4*(x**(2*n))**(1/n)),x)","- \frac{\log{\left(x - \frac{1}{2} \right)}}{4} + \frac{\log{\left(x + \frac{1}{2} \right)}}{4}"," ",0,"-log(x - 1/2)/4 + log(x + 1/2)/4","A",0
3040,1,66,0,1.057123," ","integrate((a+b*(c*x**n)**(3/n))**3,x)","a^{3} x + \frac{3 a^{2} b c^{\frac{3}{n}} x \left(x^{n}\right)^{\frac{3}{n}}}{4} + \frac{3 a b^{2} c^{\frac{6}{n}} x \left(x^{n}\right)^{\frac{6}{n}}}{7} + \frac{b^{3} c^{\frac{9}{n}} x \left(x^{n}\right)^{\frac{9}{n}}}{10}"," ",0,"a**3*x + 3*a**2*b*c**(3/n)*x*(x**n)**(3/n)/4 + 3*a*b**2*c**(6/n)*x*(x**n)**(6/n)/7 + b**3*c**(9/n)*x*(x**n)**(9/n)/10","A",0
3041,1,41,0,0.562830," ","integrate((a+b*(c*x**n)**(3/n))**2,x)","a^{2} x + \frac{a b c^{\frac{3}{n}} x \left(x^{n}\right)^{\frac{3}{n}}}{2} + \frac{b^{2} c^{\frac{6}{n}} x \left(x^{n}\right)^{\frac{6}{n}}}{7}"," ",0,"a**2*x + a*b*c**(3/n)*x*(x**n)**(3/n)/2 + b**2*c**(6/n)*x*(x**n)**(6/n)/7","A",0
3042,1,19,0,0.296526," ","integrate(a+b*(c*x**n)**(3/n),x)","a x + \frac{b c^{\frac{3}{n}} x \left(x^{n}\right)^{\frac{3}{n}}}{4}"," ",0,"a*x + b*c**(3/n)*x*(x**n)**(3/n)/4","A",0
3043,0,0,0,0.000000," ","integrate(1/(a+b*(c*x**n)**(3/n)),x)","\int \frac{1}{a + b \left(c x^{n}\right)^{\frac{3}{n}}}\, dx"," ",0,"Integral(1/(a + b*(c*x**n)**(3/n)), x)","F",0
3044,0,0,0,0.000000," ","integrate(1/(a+b*(c*x**n)**(3/n))**2,x)","\int \frac{1}{\left(a + b \left(c x^{n}\right)^{\frac{3}{n}}\right)^{2}}\, dx"," ",0,"Integral((a + b*(c*x**n)**(3/n))**(-2), x)","F",0
3045,0,0,0,0.000000," ","integrate(1/(a+b*(c*x**n)**(3/n))**3,x)","\int \frac{1}{\left(a + b \left(c x^{n}\right)^{\frac{3}{n}}\right)^{3}}\, dx"," ",0,"Integral((a + b*(c*x**n)**(3/n))**(-3), x)","F",0
3046,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*(c*x**q)**n)**p,x)","\int \left(d x\right)^{m} \left(a + b \left(c x^{q}\right)^{n}\right)^{p}\, dx"," ",0,"Integral((d*x)**m*(a + b*(c*x**q)**n)**p, x)","F",0
3047,0,0,0,0.000000," ","integrate(x**2*(a+b*(c*x**q)**n)**p,x)","\int x^{2} \left(a + b \left(c x^{q}\right)^{n}\right)^{p}\, dx"," ",0,"Integral(x**2*(a + b*(c*x**q)**n)**p, x)","F",0
3048,0,0,0,0.000000," ","integrate(x*(a+b*(c*x**q)**n)**p,x)","\int x \left(a + b \left(c x^{q}\right)^{n}\right)^{p}\, dx"," ",0,"Integral(x*(a + b*(c*x**q)**n)**p, x)","F",0
3049,0,0,0,0.000000," ","integrate((a+b*(c*x**q)**n)**p,x)","\int \left(a + b \left(c x^{q}\right)^{n}\right)^{p}\, dx"," ",0,"Integral((a + b*(c*x**q)**n)**p, x)","F",0
3050,0,0,0,0.000000," ","integrate((a+b*(c*x**q)**n)**p/x,x)","\int \frac{\left(a + b \left(c x^{q}\right)^{n}\right)^{p}}{x}\, dx"," ",0,"Integral((a + b*(c*x**q)**n)**p/x, x)","F",0
3051,0,0,0,0.000000," ","integrate((a+b*(c*x**q)**n)**p/x**2,x)","\int \frac{\left(a + b \left(c x^{q}\right)^{n}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((a + b*(c*x**q)**n)**p/x**2, x)","F",0
3052,0,0,0,0.000000," ","integrate(x**m*(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int x^{m} \sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}\, dx"," ",0,"Integral(x**m*sqrt(a + b*sqrt(d/x) + c/x), x)","F",0
3053,0,0,0,0.000000," ","integrate(x**2*(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int x^{2} \sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*sqrt(d/x) + c/x), x)","F",0
3054,0,0,0,0.000000," ","integrate(x*(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int x \sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}\, dx"," ",0,"Integral(x*sqrt(a + b*sqrt(d/x) + c/x), x)","F",0
3055,0,0,0,0.000000," ","integrate((a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int \sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(d/x) + c/x), x)","F",0
3056,0,0,0,0.000000," ","integrate((a+c/x+b*(d/x)**(1/2))**(1/2)/x,x)","\int \frac{\sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(d/x) + c/x)/x, x)","F",0
3057,0,0,0,0.000000," ","integrate((a+c/x+b*(d/x)**(1/2))**(1/2)/x**2,x)","\int \frac{\sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(d/x) + c/x)/x**2, x)","F",0
3058,0,0,0,0.000000," ","integrate((a+c/x+b*(d/x)**(1/2))**(1/2)/x**3,x)","\int \frac{\sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(d/x) + c/x)/x**3, x)","F",0
3059,0,0,0,0.000000," ","integrate((a+c/x+b*(d/x)**(1/2))**(1/2)/x**4,x)","\int \frac{\sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(d/x) + c/x)/x**4, x)","F",0
3060,0,0,0,0.000000," ","integrate(x**m/(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int \frac{x^{m}}{\sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}\, dx"," ",0,"Integral(x**m/sqrt(a + b*sqrt(d/x) + c/x), x)","F",0
3061,0,0,0,0.000000," ","integrate(x**2/(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}\, dx"," ",0,"Integral(x**2/sqrt(a + b*sqrt(d/x) + c/x), x)","F",0
3062,0,0,0,0.000000," ","integrate(x/(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int \frac{x}{\sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}\, dx"," ",0,"Integral(x/sqrt(a + b*sqrt(d/x) + c/x), x)","F",0
3063,0,0,0,0.000000," ","integrate(1/(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sqrt(d/x) + c/x), x)","F",0
3064,0,0,0,0.000000," ","integrate(1/x/(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int \frac{1}{x \sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*sqrt(d/x) + c/x)), x)","F",0
3065,0,0,0,0.000000," ","integrate(1/x**2/(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a + b*sqrt(d/x) + c/x)), x)","F",0
3066,0,0,0,0.000000," ","integrate(1/x**3/(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int \frac{1}{x^{3} \sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(a + b*sqrt(d/x) + c/x)), x)","F",0
3067,0,0,0,0.000000," ","integrate(1/x**4/(a+c/x+b*(d/x)**(1/2))**(1/2),x)","\int \frac{1}{x^{4} \sqrt{a + b \sqrt{\frac{d}{x}} + \frac{c}{x}}}\, dx"," ",0,"Integral(1/(x**4*sqrt(a + b*sqrt(d/x) + c/x)), x)","F",0
3068,0,0,0,0.000000," ","integrate((1/x+(1/x)**(1/2))**(1/2),x)","\int \sqrt{\sqrt{\frac{1}{x}} + \frac{1}{x}}\, dx"," ",0,"Integral(sqrt(sqrt(1/x) + 1/x), x)","F",0
3069,0,0,0,0.000000," ","integrate((2+1/x+(1/x)**(1/2))**(1/2),x)","\int \sqrt{\sqrt{\frac{1}{x}} + 2 + \frac{1}{x}}\, dx"," ",0,"Integral(sqrt(sqrt(1/x) + 2 + 1/x), x)","F",0
3070,0,0,0,0.000000," ","integrate((c*x**n)**(1/n)*(a+b*(c*x**n)**(1/n))**p,x)","\int \left(c x^{n}\right)^{\frac{1}{n}} \left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{p}\, dx"," ",0,"Integral((c*x**n)**(1/n)*(a + b*(c*x**n)**(1/n))**p, x)","F",0
3071,1,76,0,1.836849," ","integrate((c*x**n)**(1/n)*(a+b*(c*x**n)**(1/n))**3,x)","\frac{a^{3} c^{\frac{1}{n}} x \left(x^{n}\right)^{\frac{1}{n}}}{2} + a^{2} b c^{\frac{2}{n}} x \left(x^{n}\right)^{\frac{2}{n}} + \frac{3 a b^{2} c^{\frac{3}{n}} x \left(x^{n}\right)^{\frac{3}{n}}}{4} + \frac{b^{3} c^{\frac{4}{n}} x \left(x^{n}\right)^{\frac{4}{n}}}{5}"," ",0,"a**3*c**(1/n)*x*(x**n)**(1/n)/2 + a**2*b*c**(2/n)*x*(x**n)**(2/n) + 3*a*b**2*c**(3/n)*x*(x**n)**(3/n)/4 + b**3*c**(4/n)*x*(x**n)**(4/n)/5","A",0
3072,1,56,0,0.997333," ","integrate((c*x**n)**(1/n)*(a+b*(c*x**n)**(1/n))**2,x)","\frac{a^{2} c^{\frac{1}{n}} x \left(x^{n}\right)^{\frac{1}{n}}}{2} + \frac{2 a b c^{\frac{2}{n}} x \left(x^{n}\right)^{\frac{2}{n}}}{3} + \frac{b^{2} c^{\frac{3}{n}} x \left(x^{n}\right)^{\frac{3}{n}}}{4}"," ",0,"a**2*c**(1/n)*x*(x**n)**(1/n)/2 + 2*a*b*c**(2/n)*x*(x**n)**(2/n)/3 + b**2*c**(3/n)*x*(x**n)**(3/n)/4","A",0
3073,1,32,0,0.498948," ","integrate((c*x**n)**(1/n)*(a+b*(c*x**n)**(1/n)),x)","\frac{a c^{\frac{1}{n}} x \left(x^{n}\right)^{\frac{1}{n}}}{2} + \frac{b c^{\frac{2}{n}} x \left(x^{n}\right)^{\frac{2}{n}}}{3}"," ",0,"a*c**(1/n)*x*(x**n)**(1/n)/2 + b*c**(2/n)*x*(x**n)**(2/n)/3","A",0
3074,0,0,0,0.000000," ","integrate((c*x**n)**(1/n)/(a+b*(c*x**n)**(1/n)),x)","\int \frac{\left(c x^{n}\right)^{\frac{1}{n}}}{a + b \left(c x^{n}\right)^{\frac{1}{n}}}\, dx"," ",0,"Integral((c*x**n)**(1/n)/(a + b*(c*x**n)**(1/n)), x)","F",0
3075,0,0,0,0.000000," ","integrate((c*x**n)**(1/n)/(a+b*(c*x**n)**(1/n))**2,x)","\int \frac{\left(c x^{n}\right)^{\frac{1}{n}}}{\left(a + b \left(c x^{n}\right)^{\frac{1}{n}}\right)^{2}}\, dx"," ",0,"Integral((c*x**n)**(1/n)/(a + b*(c*x**n)**(1/n))**2, x)","F",0
3076,1,160,0,178.512694," ","integrate((c*x**n)**(1/n)/(a+b*(c*x**n)**(1/n))**3,x)","\begin{cases} \tilde{\infty} c^{- \frac{2}{n}} x \left(x^{n}\right)^{- \frac{2}{n}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{x}{b^{3} \left(2 \cdot 0^{n} \tilde{\infty}^{n} \left(0^{n}\right)^{\frac{2}{n}} \left(x^{n}\right)^{\frac{2}{n}} - \left(0^{n}\right)^{\frac{2}{n}} \left(x^{n}\right)^{\frac{2}{n}}\right)} & \text{for}\: a = 0 \wedge c = 0^{n} \\- \frac{c^{- \frac{2}{n}} x \left(x^{n}\right)^{- \frac{2}{n}}}{b^{3}} & \text{for}\: a = 0 \\\tilde{\infty} c^{\frac{1}{n}} x \left(x^{n}\right)^{\frac{1}{n}} & \text{for}\: a = - b c^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} \\\frac{c^{\frac{1}{n}} x \left(x^{n}\right)^{\frac{1}{n}}}{2 a^{3} + 4 a^{2} b c^{\frac{1}{n}} \left(x^{n}\right)^{\frac{1}{n}} + 2 a b^{2} c^{\frac{2}{n}} \left(x^{n}\right)^{\frac{2}{n}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*c**(-2/n)*x*(x**n)**(-2/n), Eq(a, 0) & Eq(b, 0)), (-x/(b**3*(2*0**n*zoo**n*(0**n)**(2/n)*(x**n)**(2/n) - (0**n)**(2/n)*(x**n)**(2/n))), Eq(a, 0) & Eq(c, 0**n)), (-c**(-2/n)*x*(x**n)**(-2/n)/b**3, Eq(a, 0)), (zoo*c**(1/n)*x*(x**n)**(1/n), Eq(a, -b*c**(1/n)*(x**n)**(1/n))), (c**(1/n)*x*(x**n)**(1/n)/(2*a**3 + 4*a**2*b*c**(1/n)*(x**n)**(1/n) + 2*a*b**2*c**(2/n)*(x**n)**(2/n)), True))","A",0
3077,-1,0,0,0.000000," ","integrate((c*x**n)**(1/n)/(a+b*(c*x**n)**(1/n))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3078,-1,0,0,0.000000," ","integrate((c*x**n)**(1/n)/(a+b*(c*x**n)**(1/n))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
