1,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**3,x)","\int \frac{x^{3}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x**3/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
2,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**2,x)","\int \frac{x^{2}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x**2/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
3,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x,x)","\int \frac{x}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
4,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2),x)","\int \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
5,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/x,x)","\int \frac{1}{x \sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
6,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/x**2,x)","\int \frac{1}{x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x**2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
7,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/x**3,x)","\int \frac{1}{x^{3} \sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x**3*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
8,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/x**4,x)","\int \frac{1}{x^{4} \sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x**4*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
9,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/x**5,x)","\int \frac{1}{x^{5} \sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x**5*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
10,1,37,0,0.093101," ","integrate(1/(a*x-1)*(a*x+1)*x**3,x)","\frac{x^{4}}{4} + \frac{2 x^{3}}{3 a} + \frac{x^{2}}{a^{2}} + \frac{2 x}{a^{3}} + \frac{2 \log{\left(a x - 1 \right)}}{a^{4}}"," ",0,"x**4/4 + 2*x**3/(3*a) + x**2/a**2 + 2*x/a**3 + 2*log(a*x - 1)/a**4","A",0
11,1,27,0,0.089426," ","integrate(1/(a*x-1)*(a*x+1)*x**2,x)","\frac{x^{3}}{3} + \frac{x^{2}}{a} + \frac{2 x}{a^{2}} + \frac{2 \log{\left(a x - 1 \right)}}{a^{3}}"," ",0,"x**3/3 + x**2/a + 2*x/a**2 + 2*log(a*x - 1)/a**3","A",0
12,1,20,0,0.083251," ","integrate(1/(a*x-1)*(a*x+1)*x,x)","\frac{x^{2}}{2} + \frac{2 x}{a} + \frac{2 \log{\left(a x - 1 \right)}}{a^{2}}"," ",0,"x**2/2 + 2*x/a + 2*log(a*x - 1)/a**2","A",0
13,1,10,0,0.072619," ","integrate(1/(a*x-1)*(a*x+1),x)","x + \frac{2 \log{\left(a x - 1 \right)}}{a}"," ",0,"x + 2*log(a*x - 1)/a","A",0
14,1,10,0,0.113829," ","integrate(1/(a*x-1)*(a*x+1)/x,x)","- \log{\left(x \right)} + 2 \log{\left(x - \frac{1}{a} \right)}"," ",0,"-log(x) + 2*log(x - 1/a)","A",0
15,1,15,0,0.131778," ","integrate(1/(a*x-1)*(a*x+1)/x**2,x)","2 a \left(- \log{\left(x \right)} + \log{\left(x - \frac{1}{a} \right)}\right) + \frac{1}{x}"," ",0,"2*a*(-log(x) + log(x - 1/a)) + 1/x","A",0
16,1,26,0,0.149805," ","integrate(1/(a*x-1)*(a*x+1)/x**3,x)","2 a^{2} \left(- \log{\left(x \right)} + \log{\left(x - \frac{1}{a} \right)}\right) + \frac{4 a x + 1}{2 x^{2}}"," ",0,"2*a**2*(-log(x) + log(x - 1/a)) + (4*a*x + 1)/(2*x**2)","A",0
17,1,34,0,0.166869," ","integrate(1/(a*x-1)*(a*x+1)/x**4,x)","2 a^{3} \left(- \log{\left(x \right)} + \log{\left(x - \frac{1}{a} \right)}\right) + \frac{6 a^{2} x^{2} + 3 a x + 1}{3 x^{3}}"," ",0,"2*a**3*(-log(x) + log(x - 1/a)) + (6*a**2*x**2 + 3*a*x + 1)/(3*x**3)","A",0
18,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**2,x)","\int \frac{x^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
19,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x,x)","\int \frac{x}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
20,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2),x)","\int \frac{1}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(-3/2), x)","F",0
21,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/x,x)","\int \frac{1}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*((a*x - 1)/(a*x + 1))**(3/2)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/x**2,x)","\int \frac{1}{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*((a*x - 1)/(a*x + 1))**(3/2)), x)","F",0
23,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/x**3,x)","\int \frac{1}{x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*((a*x - 1)/(a*x + 1))**(3/2)), x)","F",0
24,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/x**4,x)","\int \frac{1}{x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**4*((a*x - 1)/(a*x + 1))**(3/2)), x)","F",0
25,1,49,0,0.154648," ","integrate(1/(a*x-1)**2*(a*x+1)**2*x**3,x)","\frac{x^{4}}{4} - \frac{4}{a^{5} x - a^{4}} + \frac{4 x^{3}}{3 a} + \frac{4 x^{2}}{a^{2}} + \frac{12 x}{a^{3}} + \frac{16 \log{\left(a x - 1 \right)}}{a^{4}}"," ",0,"x**4/4 - 4/(a**5*x - a**4) + 4*x**3/(3*a) + 4*x**2/a**2 + 12*x/a**3 + 16*log(a*x - 1)/a**4","A",0
26,1,39,0,0.146585," ","integrate(1/(a*x-1)**2*(a*x+1)**2*x**2,x)","\frac{x^{3}}{3} - \frac{4}{a^{4} x - a^{3}} + \frac{2 x^{2}}{a} + \frac{8 x}{a^{2}} + \frac{12 \log{\left(a x - 1 \right)}}{a^{3}}"," ",0,"x**3/3 - 4/(a**4*x - a**3) + 2*x**2/a + 8*x/a**2 + 12*log(a*x - 1)/a**3","A",0
27,1,31,0,0.132932," ","integrate(1/(a*x-1)**2*(a*x+1)**2*x,x)","\frac{x^{2}}{2} - \frac{4}{a^{3} x - a^{2}} + \frac{4 x}{a} + \frac{8 \log{\left(a x - 1 \right)}}{a^{2}}"," ",0,"x**2/2 - 4/(a**3*x - a**2) + 4*x/a + 8*log(a*x - 1)/a**2","A",0
28,1,19,0,0.116821," ","integrate(1/(a*x-1)**2*(a*x+1)**2,x)","x - \frac{4}{a^{2} x - a} + \frac{4 \log{\left(a x - 1 \right)}}{a}"," ",0,"x - 4/(a**2*x - a) + 4*log(a*x - 1)/a","A",0
29,1,8,0,0.145320," ","integrate(1/(a*x-1)**2*(a*x+1)**2/x,x)","\log{\left(x \right)} - \frac{4}{a x - 1}"," ",0,"log(x) - 4/(a*x - 1)","A",0
30,1,26,0,0.211249," ","integrate(1/(a*x-1)**2*(a*x+1)**2/x**2,x)","4 a \left(\log{\left(x \right)} - \log{\left(x - \frac{1}{a} \right)}\right) + \frac{- 5 a x + 1}{a x^{2} - x}"," ",0,"4*a*(log(x) - log(x - 1/a)) + (-5*a*x + 1)/(a*x**2 - x)","A",0
31,1,41,0,0.237869," ","integrate(1/(a*x-1)**2*(a*x+1)**2/x**3,x)","8 a^{2} \left(\log{\left(x \right)} - \log{\left(x - \frac{1}{a} \right)}\right) + \frac{- 16 a^{2} x^{2} + 7 a x + 1}{2 a x^{3} - 2 x^{2}}"," ",0,"8*a**2*(log(x) - log(x - 1/a)) + (-16*a**2*x**2 + 7*a*x + 1)/(2*a*x**3 - 2*x**2)","A",0
32,1,49,0,0.263911," ","integrate(1/(a*x-1)**2*(a*x+1)**2/x**4,x)","12 a^{3} \left(\log{\left(x \right)} - \log{\left(x - \frac{1}{a} \right)}\right) + \frac{- 36 a^{3} x^{3} + 18 a^{2} x^{2} + 5 a x + 1}{3 a x^{4} - 3 x^{3}}"," ",0,"12*a**3*(log(x) - log(x - 1/a)) + (-36*a**3*x**3 + 18*a**2*x**2 + 5*a*x + 1)/(3*a*x**4 - 3*x**3)","A",0
33,0,0,0,0.000000," ","integrate(x**3*((a*x-1)/(a*x+1))**(1/2),x)","\int x^{3} \sqrt{\frac{a x - 1}{a x + 1}}\, dx"," ",0,"Integral(x**3*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
34,0,0,0,0.000000," ","integrate(x**2*((a*x-1)/(a*x+1))**(1/2),x)","\int x^{2} \sqrt{\frac{a x - 1}{a x + 1}}\, dx"," ",0,"Integral(x**2*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
35,0,0,0,0.000000," ","integrate(x*((a*x-1)/(a*x+1))**(1/2),x)","\int x \sqrt{\frac{a x - 1}{a x + 1}}\, dx"," ",0,"Integral(x*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
36,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2),x)","\int \sqrt{\frac{a x - 1}{a x + 1}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1)), x)","F",0
37,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/x,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{x}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/x, x)","F",0
38,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/x**2,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{x^{2}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/x**2, x)","F",0
39,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/x**3,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{x^{3}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/x**3, x)","F",0
40,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/x**4,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{x^{4}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/x**4, x)","F",0
41,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/x**5,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{x^{5}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/x**5, x)","F",0
42,1,37,0,0.094344," ","integrate(x**3*(a*x-1)/(a*x+1),x)","\frac{x^{4}}{4} - \frac{2 x^{3}}{3 a} + \frac{x^{2}}{a^{2}} - \frac{2 x}{a^{3}} + \frac{2 \log{\left(a x + 1 \right)}}{a^{4}}"," ",0,"x**4/4 - 2*x**3/(3*a) + x**2/a**2 - 2*x/a**3 + 2*log(a*x + 1)/a**4","A",0
43,1,27,0,0.090909," ","integrate(x**2*(a*x-1)/(a*x+1),x)","\frac{x^{3}}{3} - \frac{x^{2}}{a} + \frac{2 x}{a^{2}} - \frac{2 \log{\left(a x + 1 \right)}}{a^{3}}"," ",0,"x**3/3 - x**2/a + 2*x/a**2 - 2*log(a*x + 1)/a**3","A",0
44,1,20,0,0.083774," ","integrate(x*(a*x-1)/(a*x+1),x)","\frac{x^{2}}{2} - \frac{2 x}{a} + \frac{2 \log{\left(a x + 1 \right)}}{a^{2}}"," ",0,"x**2/2 - 2*x/a + 2*log(a*x + 1)/a**2","A",0
45,1,10,0,0.074860," ","integrate((a*x-1)/(a*x+1),x)","x - \frac{2 \log{\left(a x + 1 \right)}}{a}"," ",0,"x - 2*log(a*x + 1)/a","A",0
46,1,10,0,0.110434," ","integrate((a*x-1)/(a*x+1)/x,x)","- \log{\left(x \right)} + 2 \log{\left(x + \frac{1}{a} \right)}"," ",0,"-log(x) + 2*log(x + 1/a)","A",0
47,1,15,0,0.128284," ","integrate((a*x-1)/(a*x+1)/x**2,x)","2 a \left(\log{\left(x \right)} - \log{\left(x + \frac{1}{a} \right)}\right) + \frac{1}{x}"," ",0,"2*a*(log(x) - log(x + 1/a)) + 1/x","A",0
48,1,26,0,0.147352," ","integrate((a*x-1)/(a*x+1)/x**3,x)","2 a^{2} \left(- \log{\left(x \right)} + \log{\left(x + \frac{1}{a} \right)}\right) + \frac{- 4 a x + 1}{2 x^{2}}"," ",0,"2*a**2*(-log(x) + log(x + 1/a)) + (-4*a*x + 1)/(2*x**2)","A",0
49,1,34,0,0.167040," ","integrate((a*x-1)/(a*x+1)/x**4,x)","2 a^{3} \left(\log{\left(x \right)} - \log{\left(x + \frac{1}{a} \right)}\right) + \frac{6 a^{2} x^{2} - 3 a x + 1}{3 x^{3}}"," ",0,"2*a**3*(log(x) - log(x + 1/a)) + (6*a**2*x**2 - 3*a*x + 1)/(3*x**3)","A",0
50,0,0,0,0.000000," ","integrate(x**3*((a*x-1)/(a*x+1))**(3/2),x)","\int x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
51,0,0,0,0.000000," ","integrate(x**2*((a*x-1)/(a*x+1))**(3/2),x)","\int x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
52,0,0,0,0.000000," ","integrate(x*((a*x-1)/(a*x+1))**(3/2),x)","\int x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
53,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2),x)","\int \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
54,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/x,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/2)/x, x)","F",0
55,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/x**2,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/2)/x**2, x)","F",0
56,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/x**3,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/2)/x**3, x)","F",0
57,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/x**4,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/2)/x**4, x)","F",0
58,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/x**5,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/2)/x**5, x)","F",0
59,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/4)*x**4,x)","\int \frac{x^{4}}{\sqrt[4]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x**4/((a*x - 1)/(a*x + 1))**(1/4), x)","F",0
60,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/4)*x**3,x)","\int \frac{x^{3}}{\sqrt[4]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x**3/((a*x - 1)/(a*x + 1))**(1/4), x)","F",0
61,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/4)*x**2,x)","\int \frac{x^{2}}{\sqrt[4]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x**2/((a*x - 1)/(a*x + 1))**(1/4), x)","F",0
62,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/4)*x,x)","\int \frac{x}{\sqrt[4]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x/((a*x - 1)/(a*x + 1))**(1/4), x)","F",0
63,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/4),x)","\int \frac{1}{\sqrt[4]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(-1/4), x)","F",0
64,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/4)/x,x)","\int \frac{1}{x \sqrt[4]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x*((a*x - 1)/(a*x + 1))**(1/4)), x)","F",0
65,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/4)/x**2,x)","\int \frac{1}{x^{2} \sqrt[4]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x**2*((a*x - 1)/(a*x + 1))**(1/4)), x)","F",0
66,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/4)/x**3,x)","\int \frac{1}{x^{3} \sqrt[4]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x**3*((a*x - 1)/(a*x + 1))**(1/4)), x)","F",0
67,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/4)/x**4,x)","\int \frac{1}{x^{4} \sqrt[4]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x**4*((a*x - 1)/(a*x + 1))**(1/4)), x)","F",0
68,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/4)*x**4,x)","\int \frac{x^{4}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**4/((a*x - 1)/(a*x + 1))**(3/4), x)","F",0
69,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/4)*x**3,x)","\int \frac{x^{3}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**3/((a*x - 1)/(a*x + 1))**(3/4), x)","F",0
70,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/4)*x**2,x)","\int \frac{x^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**2/((a*x - 1)/(a*x + 1))**(3/4), x)","F",0
71,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/4)*x,x)","\int \frac{x}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x/((a*x - 1)/(a*x + 1))**(3/4), x)","F",0
72,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/4),x)","\int \frac{1}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(-3/4), x)","F",0
73,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/4)/x,x)","\int \frac{1}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/(x*((a*x - 1)/(a*x + 1))**(3/4)), x)","F",0
74,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/4)/x**2,x)","\int \frac{1}{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/(x**2*((a*x - 1)/(a*x + 1))**(3/4)), x)","F",0
75,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/4)/x**3,x)","\int \frac{1}{x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/(x**3*((a*x - 1)/(a*x + 1))**(3/4)), x)","F",0
76,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/4)/x**4,x)","\int \frac{1}{x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/(x**4*((a*x - 1)/(a*x + 1))**(3/4)), x)","F",0
77,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(5/4)*x**4,x)","\int \frac{x^{4}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(x**4/((a*x - 1)/(a*x + 1))**(5/4), x)","F",0
78,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(5/4)*x**3,x)","\int \frac{x^{3}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(x**3/((a*x - 1)/(a*x + 1))**(5/4), x)","F",0
79,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(5/4)*x**2,x)","\int \frac{x^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(x**2/((a*x - 1)/(a*x + 1))**(5/4), x)","F",0
80,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(5/4)*x,x)","\int \frac{x}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(x/((a*x - 1)/(a*x + 1))**(5/4), x)","F",0
81,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(5/4),x)","\int \frac{1}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(-5/4), x)","F",0
82,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(5/4)/x,x)","\int \frac{1}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/(x*((a*x - 1)/(a*x + 1))**(5/4)), x)","F",0
83,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(5/4)/x**2,x)","\int \frac{1}{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/(x**2*((a*x - 1)/(a*x + 1))**(5/4)), x)","F",0
84,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(5/4)/x**3,x)","\int \frac{1}{x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/(x**3*((a*x - 1)/(a*x + 1))**(5/4)), x)","F",0
85,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(5/4)/x**4,x)","\int \frac{1}{x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/(x**4*((a*x - 1)/(a*x + 1))**(5/4)), x)","F",0
86,0,0,0,0.000000," ","integrate(x**4*((a*x-1)/(a*x+1))**(1/4),x)","\int x^{4} \sqrt[4]{\frac{a x - 1}{a x + 1}}\, dx"," ",0,"Integral(x**4*((a*x - 1)/(a*x + 1))**(1/4), x)","F",0
87,0,0,0,0.000000," ","integrate(x**3*((a*x-1)/(a*x+1))**(1/4),x)","\int x^{3} \sqrt[4]{\frac{a x - 1}{a x + 1}}\, dx"," ",0,"Integral(x**3*((a*x - 1)/(a*x + 1))**(1/4), x)","F",0
88,0,0,0,0.000000," ","integrate(x**2*((a*x-1)/(a*x+1))**(1/4),x)","\int x^{2} \sqrt[4]{\frac{a x - 1}{a x + 1}}\, dx"," ",0,"Integral(x**2*((a*x - 1)/(a*x + 1))**(1/4), x)","F",0
89,0,0,0,0.000000," ","integrate(x*((a*x-1)/(a*x+1))**(1/4),x)","\int x \sqrt[4]{\frac{a x - 1}{a x + 1}}\, dx"," ",0,"Integral(x*((a*x - 1)/(a*x + 1))**(1/4), x)","F",0
90,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/4),x)","\int \sqrt[4]{\frac{a x - 1}{a x + 1}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(1/4), x)","F",0
91,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/4)/x,x)","\int \frac{\sqrt[4]{\frac{a x - 1}{a x + 1}}}{x}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(1/4)/x, x)","F",0
92,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/4)/x**2,x)","\int \frac{\sqrt[4]{\frac{a x - 1}{a x + 1}}}{x^{2}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(1/4)/x**2, x)","F",0
93,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/4)/x**3,x)","\int \frac{\sqrt[4]{\frac{a x - 1}{a x + 1}}}{x^{3}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(1/4)/x**3, x)","F",0
94,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/4)/x**4,x)","\int \frac{\sqrt[4]{\frac{a x - 1}{a x + 1}}}{x^{4}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(1/4)/x**4, x)","F",0
95,-1,0,0,0.000000," ","integrate(x**4*((a*x-1)/(a*x+1))**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,0,0,0,0.000000," ","integrate(x**3*((a*x-1)/(a*x+1))**(3/4),x)","\int x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\, dx"," ",0,"Integral(x**3*((a*x - 1)/(a*x + 1))**(3/4), x)","F",0
97,0,0,0,0.000000," ","integrate(x**2*((a*x-1)/(a*x+1))**(3/4),x)","\int x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\, dx"," ",0,"Integral(x**2*((a*x - 1)/(a*x + 1))**(3/4), x)","F",0
98,0,0,0,0.000000," ","integrate(x*((a*x-1)/(a*x+1))**(3/4),x)","\int x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\, dx"," ",0,"Integral(x*((a*x - 1)/(a*x + 1))**(3/4), x)","F",0
99,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/4),x)","\int \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/4), x)","F",0
100,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/4)/x,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{x}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/4)/x, x)","F",0
101,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/4)/x**2,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{x^{2}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/4)/x**2, x)","F",0
102,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/4)/x**3,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{x^{3}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/4)/x**3, x)","F",0
103,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/4)/x**4,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{x^{4}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/4)/x**4, x)","F",0
104,-1,0,0,0.000000," ","integrate(x**4*((a*x-1)/(a*x+1))**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate(x**3*((a*x-1)/(a*x+1))**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(x**2*((a*x-1)/(a*x+1))**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate(x*((a*x-1)/(a*x+1))**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(5/4),x)","\int \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(5/4), x)","F",0
109,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(5/4)/x,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}{x}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(5/4)/x, x)","F",0
110,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(5/4)/x**2,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}{x^{2}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(5/4)/x**2, x)","F",0
111,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(5/4)/x**3,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}{x^{3}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(5/4)/x**3, x)","F",0
112,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(5/4)/x**4,x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}{x^{4}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(5/4)/x**4, x)","F",0
113,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/6)*x**2,x)","\int \frac{x^{2}}{\sqrt[6]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(x**2/((x - 1)/(x + 1))**(1/6), x)","F",0
114,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/6)*x,x)","\int \frac{x}{\sqrt[6]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(x/((x - 1)/(x + 1))**(1/6), x)","F",0
115,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/6),x)","\int \frac{1}{\sqrt[6]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(((x - 1)/(x + 1))**(-1/6), x)","F",0
116,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/6)/x,x)","\int \frac{1}{x \sqrt[6]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(1/(x*((x - 1)/(x + 1))**(1/6)), x)","F",0
117,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/6)/x**2,x)","\int \frac{1}{x^{2} \sqrt[6]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(1/(x**2*((x - 1)/(x + 1))**(1/6)), x)","F",0
118,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/6)/x**3,x)","\int \frac{1}{x^{3} \sqrt[6]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(1/(x**3*((x - 1)/(x + 1))**(1/6)), x)","F",0
119,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/6)/x**4,x)","\int \frac{1}{x^{4} \sqrt[6]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(1/(x**4*((x - 1)/(x + 1))**(1/6)), x)","F",0
120,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/3)*x**2,x)","\int \frac{x^{2}}{\sqrt[3]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(x**2/((x - 1)/(x + 1))**(1/3), x)","F",0
121,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/3)*x,x)","\int \frac{x}{\sqrt[3]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(x/((x - 1)/(x + 1))**(1/3), x)","F",0
122,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/3),x)","\int \frac{1}{\sqrt[3]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(((x - 1)/(x + 1))**(-1/3), x)","F",0
123,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/3)/x,x)","\int \frac{1}{x \sqrt[3]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(1/(x*((x - 1)/(x + 1))**(1/3)), x)","F",0
124,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/3)/x**2,x)","\int \frac{1}{x^{2} \sqrt[3]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(1/(x**2*((x - 1)/(x + 1))**(1/3)), x)","F",0
125,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/3)/x**3,x)","\int \frac{1}{x^{3} \sqrt[3]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(1/(x**3*((x - 1)/(x + 1))**(1/3)), x)","F",0
126,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/8)*x**2,x)","\int \frac{x^{2}}{\sqrt[8]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x**2/((a*x - 1)/(a*x + 1))**(1/8), x)","F",0
127,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/8)*x,x)","\int \frac{x}{\sqrt[8]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x/((a*x - 1)/(a*x + 1))**(1/8), x)","F",0
128,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/8),x)","\int \frac{1}{\sqrt[8]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(-1/8), x)","F",0
129,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/8)/x,x)","\int \frac{1}{x \sqrt[8]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x*((a*x - 1)/(a*x + 1))**(1/8)), x)","F",0
130,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/8)/x**2,x)","\int \frac{1}{x^{2} \sqrt[8]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x**2*((a*x - 1)/(a*x + 1))**(1/8)), x)","F",0
131,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/8)/x**3,x)","\int \frac{1}{x^{3} \sqrt[8]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(1/(x**3*((a*x - 1)/(a*x + 1))**(1/8)), x)","F",0
132,0,0,0,0.000000," ","integrate(1/(a*x-1)**2*(a*x+1)**2*x**m,x)","\int \frac{x^{m} \left(a x + 1\right)^{2}}{\left(a x - 1\right)^{2}}\, dx"," ",0,"Integral(x**m*(a*x + 1)**2/(a*x - 1)**2, x)","F",0
133,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**m,x)","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
134,1,100,0,2.708732," ","integrate(1/(a*x-1)*(a*x+1)*x**m,x)","- \frac{a m x^{2} x^{m} \Phi\left(a x, 1, m + 2\right) \Gamma\left(m + 2\right)}{\Gamma\left(m + 3\right)} - \frac{2 a x^{2} x^{m} \Phi\left(a x, 1, m + 2\right) \Gamma\left(m + 2\right)}{\Gamma\left(m + 3\right)} - \frac{m x x^{m} \Phi\left(a x, 1, m + 1\right) \Gamma\left(m + 1\right)}{\Gamma\left(m + 2\right)} - \frac{x x^{m} \Phi\left(a x, 1, m + 1\right) \Gamma\left(m + 1\right)}{\Gamma\left(m + 2\right)}"," ",0,"-a*m*x**2*x**m*lerchphi(a*x, 1, m + 2)*gamma(m + 2)/gamma(m + 3) - 2*a*x**2*x**m*lerchphi(a*x, 1, m + 2)*gamma(m + 2)/gamma(m + 3) - m*x*x**m*lerchphi(a*x, 1, m + 1)*gamma(m + 1)/gamma(m + 2) - x*x**m*lerchphi(a*x, 1, m + 1)*gamma(m + 1)/gamma(m + 2)","B",0
135,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**m,x)","\int \frac{x^{m}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x**m/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
136,0,0,0,0.000000," ","integrate(x**m*((a*x-1)/(a*x+1))**(1/2),x)","\int x^{m} \sqrt{\frac{a x - 1}{a x + 1}}\, dx"," ",0,"Integral(x**m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
137,1,119,0,2.689987," ","integrate(x**m*(a*x-1)/(a*x+1),x)","\frac{a m x^{2} x^{m} \Phi\left(a x e^{i \pi}, 1, m + 2\right) \Gamma\left(m + 2\right)}{\Gamma\left(m + 3\right)} + \frac{2 a x^{2} x^{m} \Phi\left(a x e^{i \pi}, 1, m + 2\right) \Gamma\left(m + 2\right)}{\Gamma\left(m + 3\right)} - \frac{m x x^{m} \Phi\left(a x e^{i \pi}, 1, m + 1\right) \Gamma\left(m + 1\right)}{\Gamma\left(m + 2\right)} - \frac{x x^{m} \Phi\left(a x e^{i \pi}, 1, m + 1\right) \Gamma\left(m + 1\right)}{\Gamma\left(m + 2\right)}"," ",0,"a*m*x**2*x**m*lerchphi(a*x*exp_polar(I*pi), 1, m + 2)*gamma(m + 2)/gamma(m + 3) + 2*a*x**2*x**m*lerchphi(a*x*exp_polar(I*pi), 1, m + 2)*gamma(m + 2)/gamma(m + 3) - m*x*x**m*lerchphi(a*x*exp_polar(I*pi), 1, m + 1)*gamma(m + 1)/gamma(m + 2) - x*x**m*lerchphi(a*x*exp_polar(I*pi), 1, m + 1)*gamma(m + 1)/gamma(m + 2)","C",0
138,-1,0,0,0.000000," ","integrate(x**m*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(5/4)*x**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/4)*x**m,x)","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**m/((a*x - 1)/(a*x + 1))**(3/4), x)","F",0
141,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/4)*x**m,x)","\int \frac{x^{m}}{\sqrt[4]{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x**m/((a*x - 1)/(a*x + 1))**(1/4), x)","F",0
142,-1,0,0,0.000000," ","integrate(x**m*((a*x-1)/(a*x+1))**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate(x**m*((a*x-1)/(a*x+1))**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate(x**m*((a*x-1)/(a*x+1))**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/3)*x**m,x)","\int \frac{x^{m}}{\sqrt[3]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(x**m/((x - 1)/(x + 1))**(1/3), x)","F",0
146,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/6)*x**m,x)","\int \frac{x^{m}}{\sqrt[6]{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(x**m/((x - 1)/(x + 1))**(1/6), x)","F",0
147,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/8)*x**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*x**m,x)","\int x^{m} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m*exp(n*acoth(a*x)), x)","F",0
149,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*x**2,x)","\int x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2*exp(n*acoth(a*x)), x)","F",0
150,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*x,x)","\int x e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral(x*exp(n*acoth(a*x)), x)","F",0
151,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x)),x)","\int e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral(exp(n*acoth(a*x)), x)","F",0
152,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/x,x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{x}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/x, x)","F",0
153,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/x**2,x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{x^{2}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/x**2, x)","F",0
154,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/x**3,x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{x^{3}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/x**3, x)","F",0
155,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/x**4,x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{x^{4}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/x**4, x)","F",0
156,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/x**5,x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{x^{5}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/x**5, x)","F",0
157,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**p,x)","\int \frac{\left(- c \left(a x - 1\right)\right)^{p}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral((-c*(a*x - 1))**p/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
158,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**4,x)","c^{4} \left(\int \left(- \frac{4 a x}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{6 a^{2} x^{2}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{4 a^{3} x^{3}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{a^{4} x^{4}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \frac{1}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx\right)"," ",0,"c**4*(Integral(-4*a*x/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(6*a**2*x**2/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-4*a**3*x**3/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**4*x**4/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(1/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
159,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**3,x)","- c^{3} \left(\int \frac{3 a x}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{3 a^{2} x^{2}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{a^{3} x^{3}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{1}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)"," ",0,"-c**3*(Integral(3*a*x/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-3*a**2*x**2/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**3*x**3/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-1/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
160,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**2,x)","c^{2} \left(\int \left(- \frac{2 a x}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{a^{2} x^{2}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \frac{1}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx\right)"," ",0,"c**2*(Integral(-2*a*x/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**2*x**2/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(1/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
161,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c),x)","- c \left(\int \frac{a x}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{1}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)"," ",0,"-c*(Integral(a*x/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-1/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
162,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c),x)","- \frac{\int \frac{1}{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c}"," ",0,"-Integral(1/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c","F",0
163,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**2,x)","\frac{\int \frac{1}{a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 2 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 2*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**2","F",0
164,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**3,x)","- \frac{\int \frac{1}{a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + 3 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{3}}"," ",0,"-Integral(1/(a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + 3*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**3","F",0
165,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**4,x)","\frac{\int \frac{1}{a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 4 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + 6 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 4 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{4}}"," ",0,"Integral(1/(a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 4*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + 6*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 4*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**4","F",0
166,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**5,x)","- \frac{\int \frac{1}{a^{5} x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 5 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + 10 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 10 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + 5 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{5}}"," ",0,"-Integral(1/(a**5*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 5*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + 10*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 10*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + 5*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**5","F",0
167,1,124,0,0.647899," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**p,x)","\begin{cases} - c^{p} x & \text{for}\: a = 0 \\- \frac{a x \log{\left(x - \frac{1}{a} \right)}}{a^{2} c x - a c} + \frac{\log{\left(x - \frac{1}{a} \right)}}{a^{2} c x - a c} + \frac{2}{a^{2} c x - a c} & \text{for}\: p = -1 \\x + \frac{2 \log{\left(x - \frac{1}{a} \right)}}{a} & \text{for}\: p = 0 \\\frac{a p x \left(- a c x + c\right)^{p}}{a p^{2} + a p} + \frac{p \left(- a c x + c\right)^{p}}{a p^{2} + a p} + \frac{2 \left(- a c x + c\right)^{p}}{a p^{2} + a p} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**p*x, Eq(a, 0)), (-a*x*log(x - 1/a)/(a**2*c*x - a*c) + log(x - 1/a)/(a**2*c*x - a*c) + 2/(a**2*c*x - a*c), Eq(p, -1)), (x + 2*log(x - 1/a)/a, Eq(p, 0)), (a*p*x*(-a*c*x + c)**p/(a*p**2 + a*p) + p*(-a*c*x + c)**p/(a*p**2 + a*p) + 2*(-a*c*x + c)**p/(a*p**2 + a*p), True))","A",0
168,1,66,0,0.078330," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**5,x)","- \frac{a^{5} c^{5} x^{6}}{6} + \frac{3 a^{4} c^{5} x^{5}}{5} - \frac{a^{3} c^{5} x^{4}}{2} - \frac{2 a^{2} c^{5} x^{3}}{3} + \frac{3 a c^{5} x^{2}}{2} - c^{5} x"," ",0,"-a**5*c**5*x**6/6 + 3*a**4*c**5*x**5/5 - a**3*c**5*x**4/2 - 2*a**2*c**5*x**3/3 + 3*a*c**5*x**2/2 - c**5*x","B",0
169,1,36,0,0.071820," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**4,x)","\frac{a^{4} c^{4} x^{5}}{5} - \frac{a^{3} c^{4} x^{4}}{2} + a c^{4} x^{2} - c^{4} x"," ",0,"a**4*c**4*x**5/5 - a**3*c**4*x**4/2 + a*c**4*x**2 - c**4*x","A",0
170,1,37,0,0.069854," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**3,x)","- \frac{a^{3} c^{3} x^{4}}{4} + \frac{a^{2} c^{3} x^{3}}{3} + \frac{a c^{3} x^{2}}{2} - c^{3} x"," ",0,"-a**3*c**3*x**4/4 + a**2*c**3*x**3/3 + a*c**3*x**2/2 - c**3*x","A",0
171,1,15,0,0.063210," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**2,x)","\frac{a^{2} c^{2} x^{3}}{3} - c^{2} x"," ",0,"a**2*c**2*x**3/3 - c**2*x","A",0
172,1,12,0,0.054726," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c),x)","- \frac{a c x^{2}}{2} - c x"," ",0,"-a*c*x**2/2 - c*x","A",0
173,1,20,0,0.133458," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c),x)","\frac{2}{a^{2} c x - a c} - \frac{\log{\left(a x - 1 \right)}}{a c}"," ",0,"2/(a**2*c*x - a*c) - log(a*x - 1)/(a*c)","A",0
174,1,24,0,0.162039," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)**2,x)","- \frac{x}{a^{2} c^{2} x^{2} - 2 a c^{2} x + c^{2}}"," ",0,"-x/(a**2*c**2*x**2 - 2*a*c**2*x + c**2)","A",0
175,1,49,0,0.224833," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)**3,x)","- \frac{- 3 a x - 1}{6 a^{4} c^{3} x^{3} - 18 a^{3} c^{3} x^{2} + 18 a^{2} c^{3} x - 6 a c^{3}}"," ",0,"-(-3*a*x - 1)/(6*a**4*c**3*x**3 - 18*a**3*c**3*x**2 + 18*a**2*c**3*x - 6*a*c**3)","A",0
176,1,60,0,0.275602," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)**4,x)","\frac{- 2 a x - 1}{6 a^{5} c^{4} x^{4} - 24 a^{4} c^{4} x^{3} + 36 a^{3} c^{4} x^{2} - 24 a^{2} c^{4} x + 6 a c^{4}}"," ",0,"(-2*a*x - 1)/(6*a**5*c**4*x**4 - 24*a**4*c**4*x**3 + 36*a**3*c**4*x**2 - 24*a**2*c**4*x + 6*a*c**4)","B",0
177,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**p,x)","\int \frac{\left(- c \left(a x - 1\right)\right)^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-c*(a*x - 1))**p/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
178,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**4,x)","c^{4} \left(\int \left(- \frac{4 a x}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{6 a^{2} x^{2}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{4 a^{3} x^{3}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{4} x^{4}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \frac{1}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx\right)"," ",0,"c**4*(Integral(-4*a*x/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(6*a**2*x**2/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-4*a**3*x**3/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**4*x**4/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(1/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))","F",0
179,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**3,x)","- c^{3} \left(\int \frac{3 a x}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{3 a^{2} x^{2}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{3} x^{3}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{1}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx\right)"," ",0,"-c**3*(Integral(3*a*x/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-3*a**2*x**2/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**3*x**3/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-1/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))","F",0
180,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**2,x)","c^{2} \left(\int \left(- \frac{2 a x}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{2} x^{2}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \frac{1}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx\right)"," ",0,"c**2*(Integral(-2*a*x/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**2*x**2/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(1/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))","F",0
181,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c),x)","- c \left(\int \frac{a x}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{1}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx\right)"," ",0,"-c*(Integral(a*x/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-1/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))","F",0
182,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c),x)","- \frac{\int \frac{1}{\frac{a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{2 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c}"," ",0,"-Integral(1/(a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 2*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c","F",0
183,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**2,x)","\frac{\int \frac{1}{\frac{a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{3 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 3*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**2","F",0
184,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**3,x)","- \frac{\int \frac{1}{\frac{a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{4 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{6 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{4 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{3}}"," ",0,"-Integral(1/(a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 4*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 6*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 4*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**3","F",0
185,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**4,x)","\frac{\int \frac{1}{\frac{a^{5} x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{5 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{10 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{10 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{5 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{4}}"," ",0,"Integral(1/(a**5*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 5*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 10*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 10*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 5*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**4","F",0
186,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**5,x)","- \frac{\int \frac{1}{\frac{a^{6} x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{6 a^{5} x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{15 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{20 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{15 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{6 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{5}}"," ",0,"-Integral(1/(a**6*x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 6*a**5*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 15*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 20*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 15*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 6*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**5","F",0
187,1,530,0,1.181158," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a*c*x+c)**p,x)","\begin{cases} c^{p} x & \text{for}\: a = 0 \\- \frac{a^{2} x^{2} \log{\left(x - \frac{1}{a} \right)}}{a^{3} c x^{2} - 2 a^{2} c x + a c} + \frac{2 a x \log{\left(x - \frac{1}{a} \right)}}{a^{3} c x^{2} - 2 a^{2} c x + a c} + \frac{4 a x}{a^{3} c x^{2} - 2 a^{2} c x + a c} - \frac{\log{\left(x - \frac{1}{a} \right)}}{a^{3} c x^{2} - 2 a^{2} c x + a c} - \frac{2}{a^{3} c x^{2} - 2 a^{2} c x + a c} & \text{for}\: p = -1 \\\frac{a^{2} x^{2}}{a^{2} x - a} + \frac{4 a x \log{\left(x - \frac{1}{a} \right)}}{a^{2} x - a} - \frac{4 \log{\left(x - \frac{1}{a} \right)}}{a^{2} x - a} - \frac{5}{a^{2} x - a} & \text{for}\: p = 0 \\- \frac{a c x^{2}}{2} - 3 c x - \frac{4 c \log{\left(x - \frac{1}{a} \right)}}{a} & \text{for}\: p = 1 \\\frac{a^{2} p^{2} x^{2} \left(- a c x + c\right)^{p}}{a^{2} p^{3} x - a^{2} p x - a p^{3} + a p} - \frac{a^{2} p x^{2} \left(- a c x + c\right)^{p}}{a^{2} p^{3} x - a^{2} p x - a p^{3} + a p} + \frac{2 a p^{2} x \left(- a c x + c\right)^{p}}{a^{2} p^{3} x - a^{2} p x - a p^{3} + a p} + \frac{2 a p x \left(- a c x + c\right)^{p}}{a^{2} p^{3} x - a^{2} p x - a p^{3} + a p} - \frac{4 a x \left(- a c x + c\right)^{p}}{a^{2} p^{3} x - a^{2} p x - a p^{3} + a p} + \frac{p^{2} \left(- a c x + c\right)^{p}}{a^{2} p^{3} x - a^{2} p x - a p^{3} + a p} + \frac{3 p \left(- a c x + c\right)^{p}}{a^{2} p^{3} x - a^{2} p x - a p^{3} + a p} + \frac{4 \left(- a c x + c\right)^{p}}{a^{2} p^{3} x - a^{2} p x - a p^{3} + a p} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**p*x, Eq(a, 0)), (-a**2*x**2*log(x - 1/a)/(a**3*c*x**2 - 2*a**2*c*x + a*c) + 2*a*x*log(x - 1/a)/(a**3*c*x**2 - 2*a**2*c*x + a*c) + 4*a*x/(a**3*c*x**2 - 2*a**2*c*x + a*c) - log(x - 1/a)/(a**3*c*x**2 - 2*a**2*c*x + a*c) - 2/(a**3*c*x**2 - 2*a**2*c*x + a*c), Eq(p, -1)), (a**2*x**2/(a**2*x - a) + 4*a*x*log(x - 1/a)/(a**2*x - a) - 4*log(x - 1/a)/(a**2*x - a) - 5/(a**2*x - a), Eq(p, 0)), (-a*c*x**2/2 - 3*c*x - 4*c*log(x - 1/a)/a, Eq(p, 1)), (a**2*p**2*x**2*(-a*c*x + c)**p/(a**2*p**3*x - a**2*p*x - a*p**3 + a*p) - a**2*p*x**2*(-a*c*x + c)**p/(a**2*p**3*x - a**2*p*x - a*p**3 + a*p) + 2*a*p**2*x*(-a*c*x + c)**p/(a**2*p**3*x - a**2*p*x - a*p**3 + a*p) + 2*a*p*x*(-a*c*x + c)**p/(a**2*p**3*x - a**2*p*x - a*p**3 + a*p) - 4*a*x*(-a*c*x + c)**p/(a**2*p**3*x - a**2*p*x - a*p**3 + a*p) + p**2*(-a*c*x + c)**p/(a**2*p**3*x - a**2*p*x - a*p**3 + a*p) + 3*p*(-a*c*x + c)**p/(a**2*p**3*x - a**2*p*x - a*p**3 + a*p) + 4*(-a*c*x + c)**p/(a**2*p**3*x - a**2*p*x - a*p**3 + a*p), True))","A",0
188,1,63,0,0.088119," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a*c*x+c)**5,x)","- \frac{a^{5} c^{5} x^{6}}{6} + \frac{a^{4} c^{5} x^{5}}{5} + \frac{a^{3} c^{5} x^{4}}{2} - \frac{2 a^{2} c^{5} x^{3}}{3} - \frac{a c^{5} x^{2}}{2} + c^{5} x"," ",0,"-a**5*c**5*x**6/6 + a**4*c**5*x**5/5 + a**3*c**5*x**4/2 - 2*a**2*c**5*x**3/3 - a*c**5*x**2/2 + c**5*x","A",0
189,1,29,0,0.080097," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a*c*x+c)**4,x)","\frac{a^{4} c^{4} x^{5}}{5} - \frac{2 a^{2} c^{4} x^{3}}{3} + c^{4} x"," ",0,"a**4*c**4*x**5/5 - 2*a**2*c**4*x**3/3 + c**4*x","A",0
190,1,37,0,0.077912," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a*c*x+c)**3,x)","- \frac{a^{3} c^{3} x^{4}}{4} - \frac{a^{2} c^{3} x^{3}}{3} + \frac{a c^{3} x^{2}}{2} + c^{3} x"," ",0,"-a**3*c**3*x**4/4 - a**2*c**3*x**3/3 + a*c**3*x**2/2 + c**3*x","A",0
191,1,24,0,0.070451," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a*c*x+c)**2,x)","\frac{a^{2} c^{2} x^{3}}{3} + a c^{2} x^{2} + c^{2} x"," ",0,"a**2*c**2*x**3/3 + a*c**2*x**2 + c**2*x","A",0
192,1,26,0,0.114749," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a*c*x+c),x)","- \frac{a c x^{2}}{2} - 3 c x - \frac{4 c \log{\left(a x - 1 \right)}}{a}"," ",0,"-a*c*x**2/2 - 3*c*x - 4*c*log(a*x - 1)/a","A",0
193,1,37,0,0.207760," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(-a*c*x+c),x)","- \frac{- 4 a x + 2}{a^{3} c x^{2} - 2 a^{2} c x + a c} - \frac{\log{\left(a x - 1 \right)}}{a c}"," ",0,"-(-4*a*x + 2)/(a**3*c*x**2 - 2*a**2*c*x + a*c) - log(a*x - 1)/(a*c)","A",0
194,1,51,0,0.244450," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(-a*c*x+c)**2,x)","\frac{- 3 a^{2} x^{2} - 1}{3 a^{4} c^{2} x^{3} - 9 a^{3} c^{2} x^{2} + 9 a^{2} c^{2} x - 3 a c^{2}}"," ",0,"(-3*a**2*x**2 - 1)/(3*a**4*c**2*x**3 - 9*a**3*c**2*x**2 + 9*a**2*c**2*x - 3*a*c**2)","B",0
195,1,70,0,0.312909," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(-a*c*x+c)**3,x)","- \frac{- 3 a^{2} x^{2} - 2 a x - 1}{6 a^{5} c^{3} x^{4} - 24 a^{4} c^{3} x^{3} + 36 a^{3} c^{3} x^{2} - 24 a^{2} c^{3} x + 6 a c^{3}}"," ",0,"-(-3*a**2*x**2 - 2*a*x - 1)/(6*a**5*c**3*x**4 - 24*a**4*c**3*x**3 + 36*a**3*c**3*x**2 - 24*a**2*c**3*x + 6*a*c**3)","A",0
196,1,80,0,0.351138," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(-a*c*x+c)**4,x)","\frac{- 5 a^{2} x^{2} - 5 a x - 2}{15 a^{6} c^{4} x^{5} - 75 a^{5} c^{4} x^{4} + 150 a^{4} c^{4} x^{3} - 150 a^{3} c^{4} x^{2} + 75 a^{2} c^{4} x - 15 a c^{4}}"," ",0,"(-5*a**2*x**2 - 5*a*x - 2)/(15*a**6*c**4*x**5 - 75*a**5*c**4*x**4 + 150*a**4*c**4*x**3 - 150*a**3*c**4*x**2 + 75*a**2*c**4*x - 15*a*c**4)","A",0
197,0,0,0,0.000000," ","integrate((-a*c*x+c)**p*((a*x-1)/(a*x+1))**(1/2),x)","\int \sqrt{\frac{a x - 1}{a x + 1}} \left(- c \left(a x - 1\right)\right)^{p}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*(-c*(a*x - 1))**p, x)","F",0
198,0,0,0,0.000000," ","integrate((-a*c*x+c)**3*((a*x-1)/(a*x+1))**(1/2),x)","- c^{3} \left(\int 3 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- 3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\right)\, dx + \int a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\right)\, dx\right)"," ",0,"-c**3*(Integral(3*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
199,0,0,0,0.000000," ","integrate((-a*c*x+c)**2*((a*x-1)/(a*x+1))**(1/2),x)","c^{2} \left(\int \left(- 2 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\right)\, dx + \int a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx\right)"," ",0,"c**2*(Integral(-2*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
200,0,0,0,0.000000," ","integrate((-a*c*x+c)*((a*x-1)/(a*x+1))**(1/2),x)","- c \left(\int a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\right)\, dx\right)"," ",0,"-c*(Integral(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
201,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c),x)","- \frac{\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x - 1}\, dx}{c}"," ",0,"-Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x - 1), x)/c","F",0
202,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**2,x)","\frac{\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{2} x^{2} - 2 a x + 1}\, dx}{c^{2}}"," ",0,"Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**2*x**2 - 2*a*x + 1), x)/c**2","F",0
203,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**3,x)","- \frac{\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{3} x^{3} - 3 a^{2} x^{2} + 3 a x - 1}\, dx}{c^{3}}"," ",0,"-Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**3*x**3 - 3*a**2*x**2 + 3*a*x - 1), x)/c**3","F",0
204,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**4,x)","\frac{\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{4} x^{4} - 4 a^{3} x^{3} + 6 a^{2} x^{2} - 4 a x + 1}\, dx}{c^{4}}"," ",0,"Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**4*x**4 - 4*a**3*x**3 + 6*a**2*x**2 - 4*a*x + 1), x)/c**4","F",0
205,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**5,x)","- \frac{\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{5} x^{5} - 5 a^{4} x^{4} + 10 a^{3} x^{3} - 10 a^{2} x^{2} + 5 a x - 1}\, dx}{c^{5}}"," ",0,"-Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**5*x**5 - 5*a**4*x**4 + 10*a**3*x**3 - 10*a**2*x**2 + 5*a*x - 1), x)/c**5","F",0
206,0,0,0,0.000000," ","integrate((-a*c*x+c)**p*(a*x-1)/(a*x+1),x)","\int \frac{\left(- c \left(a x - 1\right)\right)^{p} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral((-c*(a*x - 1))**p*(a*x - 1)/(a*x + 1), x)","F",0
207,1,68,0,0.161958," ","integrate((-a*c*x+c)**4*(a*x-1)/(a*x+1),x)","\frac{a^{4} c^{4} x^{5}}{5} - \frac{3 a^{3} c^{4} x^{4}}{2} + \frac{16 a^{2} c^{4} x^{3}}{3} - 13 a c^{4} x^{2} + 31 c^{4} x - \frac{32 c^{4} \log{\left(a x + 1 \right)}}{a}"," ",0,"a**4*c**4*x**5/5 - 3*a**3*c**4*x**4/2 + 16*a**2*c**4*x**3/3 - 13*a*c**4*x**2 + 31*c**4*x - 32*c**4*log(a*x + 1)/a","A",0
208,1,56,0,0.141324," ","integrate((-a*c*x+c)**3*(a*x-1)/(a*x+1),x)","- \frac{a^{3} c^{3} x^{4}}{4} + \frac{5 a^{2} c^{3} x^{3}}{3} - \frac{11 a c^{3} x^{2}}{2} + 15 c^{3} x - \frac{16 c^{3} \log{\left(a x + 1 \right)}}{a}"," ",0,"-a**3*c**3*x**4/4 + 5*a**2*c**3*x**3/3 - 11*a*c**3*x**2/2 + 15*c**3*x - 16*c**3*log(a*x + 1)/a","A",0
209,1,41,0,0.122464," ","integrate((-a*c*x+c)**2*(a*x-1)/(a*x+1),x)","\frac{a^{2} c^{2} x^{3}}{3} - 2 a c^{2} x^{2} + 7 c^{2} x - \frac{8 c^{2} \log{\left(a x + 1 \right)}}{a}"," ",0,"a**2*c**2*x**3/3 - 2*a*c**2*x**2 + 7*c**2*x - 8*c**2*log(a*x + 1)/a","A",0
210,1,24,0,0.105720," ","integrate((-a*c*x+c)*(a*x-1)/(a*x+1),x)","- \frac{a c x^{2}}{2} + 3 c x - \frac{4 c \log{\left(a x + 1 \right)}}{a}"," ",0,"-a*c*x**2/2 + 3*c*x - 4*c*log(a*x + 1)/a","A",0
211,1,12,0,0.062014," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c),x)","- \frac{\log{\left(a c x + c \right)}}{a c}"," ",0,"-log(a*c*x + c)/(a*c)","A",0
212,1,20,0,0.137562," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)**2,x)","\frac{\frac{\log{\left(x - \frac{1}{a} \right)}}{2} - \frac{\log{\left(x + \frac{1}{a} \right)}}{2}}{a c^{2}}"," ",0,"(log(x - 1/a)/2 - log(x + 1/a)/2)/(a*c**2)","A",0
213,1,39,0,0.217277," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)**3,x)","\frac{1}{2 a^{2} c^{3} x - 2 a c^{3}} - \frac{- \frac{\log{\left(x - \frac{1}{a} \right)}}{4} + \frac{\log{\left(x + \frac{1}{a} \right)}}{4}}{a c^{3}}"," ",0,"1/(2*a**2*c**3*x - 2*a*c**3) - (-log(x - 1/a)/4 + log(x + 1/a)/4)/(a*c**3)","A",0
214,1,54,0,0.275820," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)**4,x)","\frac{a x - 2}{4 a^{3} c^{4} x^{2} - 8 a^{2} c^{4} x + 4 a c^{4}} + \frac{\frac{\log{\left(x - \frac{1}{a} \right)}}{8} - \frac{\log{\left(x + \frac{1}{a} \right)}}{8}}{a c^{4}}"," ",0,"(a*x - 2)/(4*a**3*c**4*x**2 - 8*a**2*c**4*x + 4*a*c**4) + (log(x - 1/a)/8 - log(x + 1/a)/8)/(a*c**4)","A",0
215,1,78,0,0.364086," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)**5,x)","- \frac{- 3 a^{2} x^{2} + 9 a x - 10}{24 a^{4} c^{5} x^{3} - 72 a^{3} c^{5} x^{2} + 72 a^{2} c^{5} x - 24 a c^{5}} - \frac{- \frac{\log{\left(x - \frac{1}{a} \right)}}{16} + \frac{\log{\left(x + \frac{1}{a} \right)}}{16}}{a c^{5}}"," ",0,"-(-3*a**2*x**2 + 9*a*x - 10)/(24*a**4*c**5*x**3 - 72*a**3*c**5*x**2 + 72*a**2*c**5*x - 24*a*c**5) - (-log(x - 1/a)/16 + log(x + 1/a)/16)/(a*c**5)","A",0
216,-1,0,0,0.000000," ","integrate((-a*c*x+c)**p*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,0,0,0,0.000000," ","integrate((-a*c*x+c)**3*((a*x-1)/(a*x+1))**(3/2),x)","- c^{3} \left(\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx + \int \left(- \frac{4 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{6 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx + \int \left(- \frac{4 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)"," ",0,"-c**3*(Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(-4*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(6*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(-4*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))","F",0
218,0,0,0,0.000000," ","integrate((-a*c*x+c)**2*((a*x-1)/(a*x+1))**(3/2),x)","c^{2} \left(\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{3 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx + \int \left(- \frac{3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)"," ",0,"c**2*(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(3*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(-3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))","F",0
219,0,0,0,0.000000," ","integrate((-a*c*x+c)*((a*x-1)/(a*x+1))**(3/2),x)","- c \left(\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx + \int \left(- \frac{2 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)"," ",0,"-c*(Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(-2*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))","F",0
220,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c),x)","- \frac{\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{2} x^{2} - 1}\right)\, dx + \int \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{2} x^{2} - 1}\, dx}{c}"," ",0,"-(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**2*x**2 - 1), x) + Integral(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**2*x**2 - 1), x))/c","F",0
221,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**2,x)","\frac{\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{3} x^{3} - a^{2} x^{2} - a x + 1}\right)\, dx + \int \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{3} x^{3} - a^{2} x^{2} - a x + 1}\, dx}{c^{2}}"," ",0,"(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**3*x**3 - a**2*x**2 - a*x + 1), x) + Integral(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**3*x**3 - a**2*x**2 - a*x + 1), x))/c**2","F",0
222,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**3,x)","- \frac{\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{4} x^{4} - 2 a^{3} x^{3} + 2 a x - 1}\right)\, dx + \int \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{4} x^{4} - 2 a^{3} x^{3} + 2 a x - 1}\, dx}{c^{3}}"," ",0,"-(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**4*x**4 - 2*a**3*x**3 + 2*a*x - 1), x) + Integral(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**4*x**4 - 2*a**3*x**3 + 2*a*x - 1), x))/c**3","F",0
223,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**4,x)","\frac{\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{5} x^{5} - 3 a^{4} x^{4} + 2 a^{3} x^{3} + 2 a^{2} x^{2} - 3 a x + 1}\right)\, dx + \int \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{5} x^{5} - 3 a^{4} x^{4} + 2 a^{3} x^{3} + 2 a^{2} x^{2} - 3 a x + 1}\, dx}{c^{4}}"," ",0,"(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**5*x**5 - 3*a**4*x**4 + 2*a**3*x**3 + 2*a**2*x**2 - 3*a*x + 1), x) + Integral(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**5*x**5 - 3*a**4*x**4 + 2*a**3*x**3 + 2*a**2*x**2 - 3*a*x + 1), x))/c**4","F",0
224,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**5,x)","- \frac{\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{6} x^{6} - 4 a^{5} x^{5} + 5 a^{4} x^{4} - 5 a^{2} x^{2} + 4 a x - 1}\right)\, dx + \int \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{6} x^{6} - 4 a^{5} x^{5} + 5 a^{4} x^{4} - 5 a^{2} x^{2} + 4 a x - 1}\, dx}{c^{5}}"," ",0,"-(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**6*x**6 - 4*a**5*x**5 + 5*a**4*x**4 - 5*a**2*x**2 + 4*a*x - 1), x) + Integral(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**6*x**6 - 4*a**5*x**5 + 5*a**4*x**4 - 5*a**2*x**2 + 4*a*x - 1), x))/c**5","F",0
225,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**6,x)","\frac{\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{7} x^{7} - 5 a^{6} x^{6} + 9 a^{5} x^{5} - 5 a^{4} x^{4} - 5 a^{3} x^{3} + 9 a^{2} x^{2} - 5 a x + 1}\right)\, dx + \int \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{7} x^{7} - 5 a^{6} x^{6} + 9 a^{5} x^{5} - 5 a^{4} x^{4} - 5 a^{3} x^{3} + 9 a^{2} x^{2} - 5 a x + 1}\, dx}{c^{6}}"," ",0,"(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**7*x**7 - 5*a**6*x**6 + 9*a**5*x**5 - 5*a**4*x**4 - 5*a**3*x**3 + 9*a**2*x**2 - 5*a*x + 1), x) + Integral(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**7*x**7 - 5*a**6*x**6 + 9*a**5*x**5 - 5*a**4*x**4 - 5*a**3*x**3 + 9*a**2*x**2 - 5*a*x + 1), x))/c**6","F",0
226,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
231,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**(1/2),x)","\int \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(a x - 1\right)}}\, dx"," ",0,"Integral(1/(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(a*x - 1))), x)","F",0
232,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**(3/2),x)","\int \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}} \left(- c \left(a x - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt((a*x - 1)/(a*x + 1))*(-c*(a*x - 1))**(3/2)), x)","F",0
233,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,1,170,0,11.839924," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**(7/2),x)","\begin{cases} \frac{- c^{3} \left(\begin{cases} 0 & \text{for}\: c = 0 \\- \frac{2 \left(- a c x + c\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) - \frac{2 c^{2} \left(- a c x + c\right)^{\frac{3}{2}}}{3} + 2 c \left(- \frac{c \left(- a c x + c\right)^{\frac{3}{2}}}{3} + \frac{\left(- a c x + c\right)^{\frac{5}{2}}}{5}\right) + \frac{4 c \left(- a c x + c\right)^{\frac{5}{2}}}{5} - \frac{2 \left(- a c x + c\right)^{\frac{7}{2}}}{7} - \frac{2 \left(- \frac{c^{3} \left(- a c x + c\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(- a c x + c\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(- a c x + c\right)^{\frac{7}{2}}}{7} + \frac{\left(- a c x + c\right)^{\frac{9}{2}}}{9}\right)}{c}}{a} & \text{for}\: a \neq 0 \\- c^{\frac{7}{2}} x & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-c**3*Piecewise((0, Eq(c, 0)), (-2*(-a*c*x + c)**(3/2)/(3*c), True)) - 2*c**2*(-a*c*x + c)**(3/2)/3 + 2*c*(-c*(-a*c*x + c)**(3/2)/3 + (-a*c*x + c)**(5/2)/5) + 4*c*(-a*c*x + c)**(5/2)/5 - 2*(-a*c*x + c)**(7/2)/7 - 2*(-c**3*(-a*c*x + c)**(3/2)/3 + 3*c**2*(-a*c*x + c)**(5/2)/5 - 3*c*(-a*c*x + c)**(7/2)/7 + (-a*c*x + c)**(9/2)/9)/c)/a, Ne(a, 0)), (-c**(7/2)*x, True))","A",0
236,1,80,0,7.829390," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**(5/2),x)","\begin{cases} \frac{- c^{2} \left(\begin{cases} 0 & \text{for}\: c = 0 \\- \frac{2 \left(- a c x + c\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) - \frac{2 \left(\frac{c^{2} \left(- a c x + c\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(- a c x + c\right)^{\frac{5}{2}}}{5} + \frac{\left(- a c x + c\right)^{\frac{7}{2}}}{7}\right)}{c}}{a} & \text{for}\: a \neq 0 \\- c^{\frac{5}{2}} x & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-c**2*Piecewise((0, Eq(c, 0)), (-2*(-a*c*x + c)**(3/2)/(3*c), True)) - 2*(c**2*(-a*c*x + c)**(3/2)/3 - 2*c*(-a*c*x + c)**(5/2)/5 + (-a*c*x + c)**(7/2)/7)/c)/a, Ne(a, 0)), (-c**(5/2)*x, True))","A",0
237,1,61,0,5.433350," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**(3/2),x)","\begin{cases} \frac{- c \left(\begin{cases} 0 & \text{for}\: c = 0 \\- \frac{2 \left(- a c x + c\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) - \frac{2 \left(- \frac{c \left(- a c x + c\right)^{\frac{3}{2}}}{3} + \frac{\left(- a c x + c\right)^{\frac{5}{2}}}{5}\right)}{c}}{a} & \text{for}\: a \neq 0 \\- c^{\frac{3}{2}} x & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-c*Piecewise((0, Eq(c, 0)), (-2*(-a*c*x + c)**(3/2)/(3*c), True)) - 2*(-c*(-a*c*x + c)**(3/2)/3 + (-a*c*x + c)**(5/2)/5)/c)/a, Ne(a, 0)), (-c**(3/2)*x, True))","A",0
238,1,31,0,2.886140," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**(1/2),x)","- \frac{2 \left(- 2 c \sqrt{- a c x + c} + \frac{\left(- a c x + c\right)^{\frac{3}{2}}}{3}\right)}{a c}"," ",0,"-2*(-2*c*sqrt(-a*c*x + c) + (-a*c*x + c)**(3/2)/3)/(a*c)","A",0
239,1,49,0,14.069309," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)**(1/2),x)","\begin{cases} \frac{- \frac{2}{\sqrt{- a c x + c}} + \frac{2 \left(- \frac{c}{\sqrt{- a c x + c}} - \sqrt{- a c x + c}\right)}{c}}{a} & \text{for}\: a \neq 0 \\- \frac{x}{\sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2/sqrt(-a*c*x + c) + 2*(-c/sqrt(-a*c*x + c) - sqrt(-a*c*x + c))/c)/a, Ne(a, 0)), (-x/sqrt(c), True))","A",0
240,1,29,0,29.050032," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)**(3/2),x)","- \frac{4}{3 a \left(- a c x + c\right)^{\frac{3}{2}}} + \frac{2}{a c \sqrt{- a c x + c}}"," ",0,"-4/(3*a*(-a*c*x + c)**(3/2)) + 2/(a*c*sqrt(-a*c*x + c))","A",0
241,1,31,0,21.487107," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)**(5/2),x)","- \frac{4}{5 a \left(- a c x + c\right)^{\frac{5}{2}}} + \frac{2}{3 a c \left(- a c x + c\right)^{\frac{3}{2}}}"," ",0,"-4/(5*a*(-a*c*x + c)**(5/2)) + 2/(3*a*c*(-a*c*x + c)**(3/2))","A",0
242,1,31,0,40.688452," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)**(7/2),x)","- \frac{4}{7 a \left(- a c x + c\right)^{\frac{7}{2}}} + \frac{2}{5 a c \left(- a c x + c\right)^{\frac{5}{2}}}"," ",0,"-4/(7*a*(-a*c*x + c)**(7/2)) + 2/(5*a*c*(-a*c*x + c)**(5/2))","A",0
243,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1))/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
248,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(9/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(7/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(5/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(3/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,1,66,0,42.839630," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\frac{4 i c x \sqrt{\frac{1}{a c x + c}}}{3} + \frac{4 i c \sqrt{\frac{1}{a c x + c}}}{a} - \frac{2 i \left(- a c x + c\right)^{2} \sqrt{\frac{1}{a c x + c}}}{3 a c}"," ",0,"4*I*c*x*sqrt(1/(a*c*x + c))/3 + 4*I*c*sqrt(1/(a*c*x + c))/a - 2*I*(-a*c*x + c)**2*sqrt(1/(a*c*x + c))/(3*a*c)","C",0
257,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**(1/2),x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\sqrt{- c \left(a x - 1\right)}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/sqrt(-c*(a*x - 1)), x)","F",0
258,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**(3/2),x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\left(- c \left(a x - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/(-c*(a*x - 1))**(3/2), x)","F",0
259,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a*c*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,1,129,0,76.388875," ","integrate((-a*c*x+c)**(7/2)*(a*x-1)/(a*x+1),x)","- \frac{32 \sqrt{2} c^{4} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{a \sqrt{- c}} - \frac{32 c^{3} \sqrt{- a c x + c}}{a} - \frac{16 c^{2} \left(- a c x + c\right)^{\frac{3}{2}}}{3 a} - \frac{8 c \left(- a c x + c\right)^{\frac{5}{2}}}{5 a} - \frac{4 \left(- a c x + c\right)^{\frac{7}{2}}}{7 a} - \frac{2 \left(- a c x + c\right)^{\frac{9}{2}}}{9 a c}"," ",0,"-32*sqrt(2)*c**4*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/(a*sqrt(-c)) - 32*c**3*sqrt(-a*c*x + c)/a - 16*c**2*(-a*c*x + c)**(3/2)/(3*a) - 8*c*(-a*c*x + c)**(5/2)/(5*a) - 4*(-a*c*x + c)**(7/2)/(7*a) - 2*(-a*c*x + c)**(9/2)/(9*a*c)","A",0
262,1,110,0,51.780195," ","integrate((-a*c*x+c)**(5/2)*(a*x-1)/(a*x+1),x)","- \frac{16 \sqrt{2} c^{3} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{a \sqrt{- c}} - \frac{16 c^{2} \sqrt{- a c x + c}}{a} - \frac{8 c \left(- a c x + c\right)^{\frac{3}{2}}}{3 a} - \frac{4 \left(- a c x + c\right)^{\frac{5}{2}}}{5 a} - \frac{2 \left(- a c x + c\right)^{\frac{7}{2}}}{7 a c}"," ",0,"-16*sqrt(2)*c**3*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/(a*sqrt(-c)) - 16*c**2*sqrt(-a*c*x + c)/a - 8*c*(-a*c*x + c)**(3/2)/(3*a) - 4*(-a*c*x + c)**(5/2)/(5*a) - 2*(-a*c*x + c)**(7/2)/(7*a*c)","A",0
263,1,92,0,32.540295," ","integrate((-a*c*x+c)**(3/2)*(a*x-1)/(a*x+1),x)","- \frac{8 \sqrt{2} c^{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{a \sqrt{- c}} - \frac{8 c \sqrt{- a c x + c}}{a} - \frac{4 \left(- a c x + c\right)^{\frac{3}{2}}}{3 a} - \frac{2 \left(- a c x + c\right)^{\frac{5}{2}}}{5 a c}"," ",0,"-8*sqrt(2)*c**2*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/(a*sqrt(-c)) - 8*c*sqrt(-a*c*x + c)/a - 4*(-a*c*x + c)**(3/2)/(3*a) - 2*(-a*c*x + c)**(5/2)/(5*a*c)","A",0
264,1,73,0,3.922875," ","integrate((-a*c*x+c)**(1/2)*(a*x-1)/(a*x+1),x)","- \frac{2 \left(\frac{2 \sqrt{2} c^{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} + 2 c \sqrt{- a c x + c} + \frac{\left(- a c x + c\right)^{\frac{3}{2}}}{3}\right)}{a c}"," ",0,"-2*(2*sqrt(2)*c**2*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/sqrt(-c) + 2*c*sqrt(-a*c*x + c) + (-a*c*x + c)**(3/2)/3)/(a*c)","A",0
265,1,60,0,18.118428," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)**(1/2),x)","- \frac{2 \sqrt{- a c x + c}}{a c} - \frac{2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{- \frac{1}{c}} \sqrt{- a c x + c}} \right)}}{a c \sqrt{- \frac{1}{c}}}"," ",0,"-2*sqrt(-a*c*x + c)/(a*c) - 2*sqrt(2)*atan(sqrt(2)/(sqrt(-1/c)*sqrt(-a*c*x + c)))/(a*c*sqrt(-1/c))","A",0
266,1,41,0,15.745632," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)**(3/2),x)","- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{a c \sqrt{- c}}"," ",0,"-sqrt(2)*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/(a*c*sqrt(-c))","A",0
267,1,61,0,14.832023," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)**(5/2),x)","- \frac{1}{a c^{2} \sqrt{- a c x + c}} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{2 a c^{2} \sqrt{- c}}"," ",0,"-1/(a*c**2*sqrt(-a*c*x + c)) - sqrt(2)*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/(2*a*c**2*sqrt(-c))","A",0
268,1,82,0,28.535522," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)**(7/2),x)","- \frac{1}{3 a c^{2} \left(- a c x + c\right)^{\frac{3}{2}}} - \frac{1}{2 a c^{3} \sqrt{- a c x + c}} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{4 a c^{3} \sqrt{- c}}"," ",0,"-1/(3*a*c**2*(-a*c*x + c)**(3/2)) - 1/(2*a*c**3*sqrt(-a*c*x + c)) - sqrt(2)*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/(4*a*c**3*sqrt(-c))","A",0
269,1,100,0,21.752754," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)**(9/2),x)","- \frac{1}{5 a c^{2} \left(- a c x + c\right)^{\frac{5}{2}}} - \frac{1}{6 a c^{3} \left(- a c x + c\right)^{\frac{3}{2}}} - \frac{1}{4 a c^{4} \sqrt{- a c x + c}} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{8 a c^{4} \sqrt{- c}}"," ",0,"-1/(5*a*c**2*(-a*c*x + c)**(5/2)) - 1/(6*a*c**3*(-a*c*x + c)**(3/2)) - 1/(4*a*c**4*sqrt(-a*c*x + c)) - sqrt(2)*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/(8*a*c**4*sqrt(-c))","A",0
270,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(9/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(7/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(5/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(3/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
277,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
278,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a*c*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*x*(1+x),x)","\int \frac{x \left(x + 1\right)}{\sqrt{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(x*(x + 1)/sqrt((x - 1)/(x + 1)), x)","F",0
280,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1+x),x)","\int \frac{x + 1}{\sqrt{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral((x + 1)/sqrt((x - 1)/(x + 1)), x)","F",0
281,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1-x)*x,x)","- \int \left(- \frac{x}{\sqrt{\frac{x}{x + 1} - \frac{1}{x + 1}}}\right)\, dx - \int \frac{x^{2}}{\sqrt{\frac{x}{x + 1} - \frac{1}{x + 1}}}\, dx"," ",0,"-Integral(-x/sqrt(x/(x + 1) - 1/(x + 1)), x) - Integral(x**2/sqrt(x/(x + 1) - 1/(x + 1)), x)","F",0
282,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1-x),x)","- \int \frac{x}{\sqrt{\frac{x}{x + 1} - \frac{1}{x + 1}}}\, dx - \int \left(- \frac{1}{\sqrt{\frac{x}{x + 1} - \frac{1}{x + 1}}}\right)\, dx"," ",0,"-Integral(x/sqrt(x/(x + 1) - 1/(x + 1)), x) - Integral(-1/sqrt(x/(x + 1) - 1/(x + 1)), x)","F",0
283,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*x*(1+x)**2,x)","\int \frac{x \left(x + 1\right)^{2}}{\sqrt{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(x*(x + 1)**2/sqrt((x - 1)/(x + 1)), x)","F",0
284,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1+x)**2,x)","\int \frac{\left(x + 1\right)^{2}}{\sqrt{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral((x + 1)**2/sqrt((x - 1)/(x + 1)), x)","F",0
285,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1-x)**2*x,x)","\int \frac{x \left(x - 1\right)^{2}}{\sqrt{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral(x*(x - 1)**2/sqrt((x - 1)/(x + 1)), x)","F",0
286,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1-x)**2,x)","\int \frac{\left(x - 1\right)^{2}}{\sqrt{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral((x - 1)**2/sqrt((x - 1)/(x + 1)), x)","F",0
287,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*x/(1+x),x)","\int \frac{x}{\sqrt{\frac{x - 1}{x + 1}} \left(x + 1\right)}\, dx"," ",0,"Integral(x/(sqrt((x - 1)/(x + 1))*(x + 1)), x)","F",0
288,1,29,0,4.033135," ","integrate(1/((-1+x)/(1+x))**(1/2)/(1+x),x)","- \log{\left(-1 + \frac{1}{\sqrt{1 - \frac{2}{x + 1}}} \right)} + \log{\left(1 + \frac{1}{\sqrt{1 - \frac{2}{x + 1}}} \right)}"," ",0,"-log(-1 + 1/sqrt(1 - 2/(x + 1))) + log(1 + 1/sqrt(1 - 2/(x + 1)))","A",0
289,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*x/(1-x),x)","- \int \frac{x}{x \sqrt{\frac{x}{x + 1} - \frac{1}{x + 1}} - \sqrt{\frac{x}{x + 1} - \frac{1}{x + 1}}}\, dx"," ",0,"-Integral(x/(x*sqrt(x/(x + 1) - 1/(x + 1)) - sqrt(x/(x + 1) - 1/(x + 1))), x)","F",0
290,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)/(1-x),x)","- \int \frac{1}{x \sqrt{\frac{x}{x + 1} - \frac{1}{x + 1}} - \sqrt{\frac{x}{x + 1} - \frac{1}{x + 1}}}\, dx"," ",0,"-Integral(1/(x*sqrt(x/(x + 1) - 1/(x + 1)) - sqrt(x/(x + 1) - 1/(x + 1))), x)","F",0
291,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*x/(1+x)**2,x)","\int \frac{x}{\sqrt{\frac{x - 1}{x + 1}} \left(x + 1\right)^{2}}\, dx"," ",0,"Integral(x/(sqrt((x - 1)/(x + 1))*(x + 1)**2), x)","F",0
292,1,8,0,5.383963," ","integrate(1/((-1+x)/(1+x))**(1/2)/(1+x)**2,x)","\sqrt{\frac{x - 1}{x + 1}}"," ",0,"sqrt((x - 1)/(x + 1))","A",0
293,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*x/(1-x)**2,x)","\int \frac{x}{\sqrt{\frac{x - 1}{x + 1}} \left(x - 1\right)^{2}}\, dx"," ",0,"Integral(x/(sqrt((x - 1)/(x + 1))*(x - 1)**2), x)","F",0
294,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)/(1-x)**2,x)","\int \frac{1}{\sqrt{\frac{x - 1}{x + 1}} \left(x - 1\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)/(x + 1))*(x - 1)**2), x)","F",0
295,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**m*(-a*c*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,1,105,0,50.078367," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**2*(-a*c*x+c)**(1/2),x)","- \frac{94 i x}{105 a^{2} \sqrt{\frac{1}{a c x + c}}} + \frac{10 i}{21 a^{3} \sqrt{\frac{1}{a c x + c}}} - \frac{32 i \left(- a c x + c\right)^{2}}{35 a^{3} c^{2} \sqrt{\frac{1}{a c x + c}}} + \frac{2 i \left(- a c x + c\right)^{3}}{7 a^{3} c^{3} \sqrt{\frac{1}{a c x + c}}}"," ",0,"-94*I*x/(105*a**2*sqrt(1/(a*c*x + c))) + 10*I/(21*a**3*sqrt(1/(a*c*x + c))) - 32*I*(-a*c*x + c)**2/(35*a**3*c**2*sqrt(1/(a*c*x + c))) + 2*I*(-a*c*x + c)**3/(7*a**3*c**3*sqrt(1/(a*c*x + c)))","C",0
297,1,71,0,28.092157," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x*(-a*c*x+c)**(1/2),x)","- \frac{14 i x}{15 a \sqrt{\frac{1}{a c x + c}}} + \frac{2 i}{3 a^{2} \sqrt{\frac{1}{a c x + c}}} - \frac{2 i \left(- a c x + c\right)^{2}}{5 a^{2} c^{2} \sqrt{\frac{1}{a c x + c}}}"," ",0,"-14*I*x/(15*a*sqrt(1/(a*c*x + c))) + 2*I/(3*a**2*sqrt(1/(a*c*x + c))) - 2*I*(-a*c*x + c)**2/(5*a**2*c**2*sqrt(1/(a*c*x + c)))","C",0
298,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
299,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**(1/2)/x,x)","\int \frac{\sqrt{- c \left(a x - 1\right)}}{x \sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1))/(x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
300,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a*c*x+c)**(1/2)/x**2,x)","\int \frac{\sqrt{- c \left(a x - 1\right)}}{x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1))/(x**2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
301,1,83,0,3.534582," ","integrate(1/(a*x-1)*(a*x+1)*x**3*(-a*c*x+c)**(1/2),x)","\frac{2 \left(2 c^{4} \sqrt{- a c x + c} - \frac{7 c^{3} \left(- a c x + c\right)^{\frac{3}{2}}}{3} + \frac{9 c^{2} \left(- a c x + c\right)^{\frac{5}{2}}}{5} - \frac{5 c \left(- a c x + c\right)^{\frac{7}{2}}}{7} + \frac{\left(- a c x + c\right)^{\frac{9}{2}}}{9}\right)}{a^{4} c^{4}}"," ",0,"2*(2*c**4*sqrt(-a*c*x + c) - 7*c**3*(-a*c*x + c)**(3/2)/3 + 9*c**2*(-a*c*x + c)**(5/2)/5 - 5*c*(-a*c*x + c)**(7/2)/7 + (-a*c*x + c)**(9/2)/9)/(a**4*c**4)","A",0
302,1,68,0,3.305361," ","integrate(1/(a*x-1)*(a*x+1)*x**2*(-a*c*x+c)**(1/2),x)","- \frac{2 \left(- 2 c^{3} \sqrt{- a c x + c} + \frac{5 c^{2} \left(- a c x + c\right)^{\frac{3}{2}}}{3} - \frac{4 c \left(- a c x + c\right)^{\frac{5}{2}}}{5} + \frac{\left(- a c x + c\right)^{\frac{7}{2}}}{7}\right)}{a^{3} c^{3}}"," ",0,"-2*(-2*c**3*sqrt(-a*c*x + c) + 5*c**2*(-a*c*x + c)**(3/2)/3 - 4*c*(-a*c*x + c)**(5/2)/5 + (-a*c*x + c)**(7/2)/7)/(a**3*c**3)","A",0
303,1,48,0,3.894146," ","integrate(1/(a*x-1)*(a*x+1)*x*(-a*c*x+c)**(1/2),x)","\frac{2 \left(2 c^{2} \sqrt{- a c x + c} - c \left(- a c x + c\right)^{\frac{3}{2}} + \frac{\left(- a c x + c\right)^{\frac{5}{2}}}{5}\right)}{a^{2} c^{2}}"," ",0,"2*(2*c**2*sqrt(-a*c*x + c) - c*(-a*c*x + c)**(3/2) + (-a*c*x + c)**(5/2)/5)/(a**2*c**2)","A",0
304,1,31,0,2.895654," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**(1/2),x)","- \frac{2 \left(- 2 c \sqrt{- a c x + c} + \frac{\left(- a c x + c\right)^{\frac{3}{2}}}{3}\right)}{a c}"," ",0,"-2*(-2*c*sqrt(-a*c*x + c) + (-a*c*x + c)**(3/2)/3)/(a*c)","A",0
305,1,39,0,4.094589," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**(1/2)/x,x)","- \frac{2 c \operatorname{atan}{\left(\frac{\sqrt{- a c x + c}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + 2 \sqrt{- a c x + c}"," ",0,"-2*c*atan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + 2*sqrt(-a*c*x + c)","A",0
306,1,119,0,8.452553," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**(1/2)/x**2,x)","- \frac{a c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(- c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)}}{2} + \frac{a c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)}}{2} - \frac{2 a c \operatorname{atan}{\left(\frac{\sqrt{- a c x + c}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + \frac{\sqrt{- a c x + c}}{x}"," ",0,"-a*c**2*sqrt(c**(-3))*log(-c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c))/2 + a*c**2*sqrt(c**(-3))*log(c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c))/2 - 2*a*c*atan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + sqrt(-a*c*x + c)/x","B",0
307,1,270,0,18.116279," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**(1/2)/x**3,x)","\frac{10 a^{2} c^{4} \sqrt{- a c x + c}}{16 a c^{4} x - 8 c^{4} + 8 c^{2} \left(- a c x + c\right)^{2}} - \frac{6 a^{2} c^{3} \left(- a c x + c\right)^{\frac{3}{2}}}{16 a c^{4} x - 8 c^{4} + 8 c^{2} \left(- a c x + c\right)^{2}} - \frac{3 a^{2} c^{3} \sqrt{\frac{1}{c^{5}}} \log{\left(- c^{3} \sqrt{\frac{1}{c^{5}}} + \sqrt{- a c x + c} \right)}}{8} + \frac{3 a^{2} c^{3} \sqrt{\frac{1}{c^{5}}} \log{\left(c^{3} \sqrt{\frac{1}{c^{5}}} + \sqrt{- a c x + c} \right)}}{8} - \frac{a^{2} c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(- c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)}}{2} + \frac{a^{2} c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)}}{2} + \frac{a \sqrt{- a c x + c}}{x}"," ",0,"10*a**2*c**4*sqrt(-a*c*x + c)/(16*a*c**4*x - 8*c**4 + 8*c**2*(-a*c*x + c)**2) - 6*a**2*c**3*(-a*c*x + c)**(3/2)/(16*a*c**4*x - 8*c**4 + 8*c**2*(-a*c*x + c)**2) - 3*a**2*c**3*sqrt(c**(-5))*log(-c**3*sqrt(c**(-5)) + sqrt(-a*c*x + c))/8 + 3*a**2*c**3*sqrt(c**(-5))*log(c**3*sqrt(c**(-5)) + sqrt(-a*c*x + c))/8 - a**2*c**2*sqrt(c**(-3))*log(-c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c))/2 + a**2*c**2*sqrt(c**(-3))*log(c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c))/2 + a*sqrt(-a*c*x + c)/x","B",0
308,1,439,0,17.810799," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**(1/2)/x**4,x)","- \frac{66 a^{3} c^{6} \sqrt{- a c x + c}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} + \frac{80 a^{3} c^{5} \left(- a c x + c\right)^{\frac{3}{2}}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} - \frac{30 a^{3} c^{4} \left(- a c x + c\right)^{\frac{5}{2}}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} + \frac{10 a^{3} c^{4} \sqrt{- a c x + c}}{16 a c^{4} x - 8 c^{4} + 8 c^{2} \left(- a c x + c\right)^{2}} - \frac{5 a^{3} c^{4} \sqrt{\frac{1}{c^{7}}} \log{\left(- c^{4} \sqrt{\frac{1}{c^{7}}} + \sqrt{- a c x + c} \right)}}{16} + \frac{5 a^{3} c^{4} \sqrt{\frac{1}{c^{7}}} \log{\left(c^{4} \sqrt{\frac{1}{c^{7}}} + \sqrt{- a c x + c} \right)}}{16} - \frac{6 a^{3} c^{3} \left(- a c x + c\right)^{\frac{3}{2}}}{16 a c^{4} x - 8 c^{4} + 8 c^{2} \left(- a c x + c\right)^{2}} - \frac{3 a^{3} c^{3} \sqrt{\frac{1}{c^{5}}} \log{\left(- c^{3} \sqrt{\frac{1}{c^{5}}} + \sqrt{- a c x + c} \right)}}{8} + \frac{3 a^{3} c^{3} \sqrt{\frac{1}{c^{5}}} \log{\left(c^{3} \sqrt{\frac{1}{c^{5}}} + \sqrt{- a c x + c} \right)}}{8}"," ",0,"-66*a**3*c**6*sqrt(-a*c*x + c)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) + 80*a**3*c**5*(-a*c*x + c)**(3/2)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) - 30*a**3*c**4*(-a*c*x + c)**(5/2)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) + 10*a**3*c**4*sqrt(-a*c*x + c)/(16*a*c**4*x - 8*c**4 + 8*c**2*(-a*c*x + c)**2) - 5*a**3*c**4*sqrt(c**(-7))*log(-c**4*sqrt(c**(-7)) + sqrt(-a*c*x + c))/16 + 5*a**3*c**4*sqrt(c**(-7))*log(c**4*sqrt(c**(-7)) + sqrt(-a*c*x + c))/16 - 6*a**3*c**3*(-a*c*x + c)**(3/2)/(16*a*c**4*x - 8*c**4 + 8*c**2*(-a*c*x + c)**2) - 3*a**3*c**3*sqrt(c**(-5))*log(-c**3*sqrt(c**(-5)) + sqrt(-a*c*x + c))/8 + 3*a**3*c**3*sqrt(c**(-5))*log(c**3*sqrt(c**(-5)) + sqrt(-a*c*x + c))/8","B",0
309,1,639,0,28.189684," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)**(1/2)/x**5,x)","\frac{558 a^{4} c^{8} \sqrt{- a c x + c}}{1536 a c^{8} x - 1152 c^{8} + 2304 c^{6} \left(- a c x + c\right)^{2} - 1536 c^{5} \left(- a c x + c\right)^{3} + 384 c^{4} \left(- a c x + c\right)^{4}} - \frac{1022 a^{4} c^{7} \left(- a c x + c\right)^{\frac{3}{2}}}{1536 a c^{8} x - 1152 c^{8} + 2304 c^{6} \left(- a c x + c\right)^{2} - 1536 c^{5} \left(- a c x + c\right)^{3} + 384 c^{4} \left(- a c x + c\right)^{4}} + \frac{770 a^{4} c^{6} \left(- a c x + c\right)^{\frac{5}{2}}}{1536 a c^{8} x - 1152 c^{8} + 2304 c^{6} \left(- a c x + c\right)^{2} - 1536 c^{5} \left(- a c x + c\right)^{3} + 384 c^{4} \left(- a c x + c\right)^{4}} - \frac{66 a^{4} c^{6} \sqrt{- a c x + c}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} - \frac{210 a^{4} c^{5} \left(- a c x + c\right)^{\frac{7}{2}}}{1536 a c^{8} x - 1152 c^{8} + 2304 c^{6} \left(- a c x + c\right)^{2} - 1536 c^{5} \left(- a c x + c\right)^{3} + 384 c^{4} \left(- a c x + c\right)^{4}} + \frac{80 a^{4} c^{5} \left(- a c x + c\right)^{\frac{3}{2}}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} - \frac{35 a^{4} c^{5} \sqrt{\frac{1}{c^{9}}} \log{\left(- c^{5} \sqrt{\frac{1}{c^{9}}} + \sqrt{- a c x + c} \right)}}{128} + \frac{35 a^{4} c^{5} \sqrt{\frac{1}{c^{9}}} \log{\left(c^{5} \sqrt{\frac{1}{c^{9}}} + \sqrt{- a c x + c} \right)}}{128} - \frac{30 a^{4} c^{4} \left(- a c x + c\right)^{\frac{5}{2}}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} - \frac{5 a^{4} c^{4} \sqrt{\frac{1}{c^{7}}} \log{\left(- c^{4} \sqrt{\frac{1}{c^{7}}} + \sqrt{- a c x + c} \right)}}{16} + \frac{5 a^{4} c^{4} \sqrt{\frac{1}{c^{7}}} \log{\left(c^{4} \sqrt{\frac{1}{c^{7}}} + \sqrt{- a c x + c} \right)}}{16}"," ",0,"558*a**4*c**8*sqrt(-a*c*x + c)/(1536*a*c**8*x - 1152*c**8 + 2304*c**6*(-a*c*x + c)**2 - 1536*c**5*(-a*c*x + c)**3 + 384*c**4*(-a*c*x + c)**4) - 1022*a**4*c**7*(-a*c*x + c)**(3/2)/(1536*a*c**8*x - 1152*c**8 + 2304*c**6*(-a*c*x + c)**2 - 1536*c**5*(-a*c*x + c)**3 + 384*c**4*(-a*c*x + c)**4) + 770*a**4*c**6*(-a*c*x + c)**(5/2)/(1536*a*c**8*x - 1152*c**8 + 2304*c**6*(-a*c*x + c)**2 - 1536*c**5*(-a*c*x + c)**3 + 384*c**4*(-a*c*x + c)**4) - 66*a**4*c**6*sqrt(-a*c*x + c)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) - 210*a**4*c**5*(-a*c*x + c)**(7/2)/(1536*a*c**8*x - 1152*c**8 + 2304*c**6*(-a*c*x + c)**2 - 1536*c**5*(-a*c*x + c)**3 + 384*c**4*(-a*c*x + c)**4) + 80*a**4*c**5*(-a*c*x + c)**(3/2)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) - 35*a**4*c**5*sqrt(c**(-9))*log(-c**5*sqrt(c**(-9)) + sqrt(-a*c*x + c))/128 + 35*a**4*c**5*sqrt(c**(-9))*log(c**5*sqrt(c**(-9)) + sqrt(-a*c*x + c))/128 - 30*a**4*c**4*(-a*c*x + c)**(5/2)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) - 5*a**4*c**4*sqrt(c**(-7))*log(-c**4*sqrt(c**(-7)) + sqrt(-a*c*x + c))/16 + 5*a**4*c**4*sqrt(c**(-7))*log(c**4*sqrt(c**(-7)) + sqrt(-a*c*x + c))/16","B",0
310,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**3*(-a*c*x+c)**(1/2),x)","\int \frac{x^{3} \sqrt{- c \left(a x - 1\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*sqrt(-c*(a*x - 1))/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
311,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**2*(-a*c*x+c)**(1/2),x)","\int \frac{x^{2} \sqrt{- c \left(a x - 1\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*sqrt(-c*(a*x - 1))/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
312,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x*(-a*c*x+c)**(1/2),x)","\int \frac{x \sqrt{- c \left(a x - 1\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*sqrt(-c*(a*x - 1))/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
313,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1))/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
314,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(1/2)/x,x)","\int \frac{\sqrt{- c \left(a x - 1\right)}}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1))/(x*((a*x - 1)/(a*x + 1))**(3/2)), x)","F",0
315,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(1/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(1/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a*c*x+c)**(1/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,1,197,0,91.982374," ","integrate(1/((-1+x)/(1+x))**(1/2)*x*(1+x)**(3/2),x)","- 2 \left(\begin{cases} \frac{8 x \sqrt{x - 1}}{15} + \frac{\sqrt{x - 1} \left(x + 1\right)^{2}}{5} + \frac{8 \sqrt{x - 1}}{3} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{8 i x \sqrt{1 - x}}{15} + \frac{i \sqrt{1 - x} \left(x + 1\right)^{2}}{5} + \frac{8 i \sqrt{1 - x}}{3} & \text{otherwise} \end{cases}\right) + 2 \left(\begin{cases} \frac{32 x \sqrt{x - 1}}{35} + \frac{\sqrt{x - 1} \left(x + 1\right)^{3}}{7} + \frac{12 \sqrt{x - 1} \left(x + 1\right)^{2}}{35} + \frac{32 \sqrt{x - 1}}{7} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{32 i x \sqrt{1 - x}}{35} + \frac{i \sqrt{1 - x} \left(x + 1\right)^{3}}{7} + \frac{12 i \sqrt{1 - x} \left(x + 1\right)^{2}}{35} + \frac{32 i \sqrt{1 - x}}{7} & \text{otherwise} \end{cases}\right)"," ",0,"-2*Piecewise((8*x*sqrt(x - 1)/15 + sqrt(x - 1)*(x + 1)**2/5 + 8*sqrt(x - 1)/3, Abs(x + 1)/2 > 1), (8*I*x*sqrt(1 - x)/15 + I*sqrt(1 - x)*(x + 1)**2/5 + 8*I*sqrt(1 - x)/3, True)) + 2*Piecewise((32*x*sqrt(x - 1)/35 + sqrt(x - 1)*(x + 1)**3/7 + 12*sqrt(x - 1)*(x + 1)**2/35 + 32*sqrt(x - 1)/7, Abs(x + 1)/2 > 1), (32*I*x*sqrt(1 - x)/35 + I*sqrt(1 - x)*(x + 1)**3/7 + 12*I*sqrt(1 - x)*(x + 1)**2/35 + 32*I*sqrt(1 - x)/7, True))","C",0
320,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1+x)**(3/2),x)","\int \frac{\left(x + 1\right)^{\frac{3}{2}}}{\sqrt{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral((x + 1)**(3/2)/sqrt((x - 1)/(x + 1)), x)","F",0
321,-1,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1-x)**(3/2)*x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1-x)**(3/2),x)","\int \frac{\left(1 - x\right)^{\frac{3}{2}}}{\sqrt{\frac{x - 1}{x + 1}}}\, dx"," ",0,"Integral((1 - x)**(3/2)/sqrt((x - 1)/(x + 1)), x)","F",0
323,1,133,0,7.925996," ","integrate(1/((-1+x)/(1+x))**(1/2)*x*(1+x)**(1/2),x)","- 2 \left(\begin{cases} \frac{x \sqrt{x - 1}}{3} + \frac{5 \sqrt{x - 1}}{3} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{i x \sqrt{1 - x}}{3} + \frac{5 i \sqrt{1 - x}}{3} & \text{otherwise} \end{cases}\right) + 2 \left(\begin{cases} \frac{8 x \sqrt{x - 1}}{15} + \frac{\sqrt{x - 1} \left(x + 1\right)^{2}}{5} + \frac{8 \sqrt{x - 1}}{3} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{8 i x \sqrt{1 - x}}{15} + \frac{i \sqrt{1 - x} \left(x + 1\right)^{2}}{5} + \frac{8 i \sqrt{1 - x}}{3} & \text{otherwise} \end{cases}\right)"," ",0,"-2*Piecewise((x*sqrt(x - 1)/3 + 5*sqrt(x - 1)/3, Abs(x + 1)/2 > 1), (I*x*sqrt(1 - x)/3 + 5*I*sqrt(1 - x)/3, True)) + 2*Piecewise((8*x*sqrt(x - 1)/15 + sqrt(x - 1)*(x + 1)**2/5 + 8*sqrt(x - 1)/3, Abs(x + 1)/2 > 1), (8*I*x*sqrt(1 - x)/15 + I*sqrt(1 - x)*(x + 1)**2/5 + 8*I*sqrt(1 - x)/3, True))","C",0
324,1,39,0,4.831507," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1+x)**(1/2),x)","2 \left(\begin{cases} 2 \sqrt{2} \left(\frac{\sqrt{2} \left(x - 1\right)^{\frac{3}{2}}}{12} + \frac{\sqrt{2} \sqrt{x - 1}}{2}\right) & \text{for}\: x \geq -1 \wedge x < 1 \end{cases}\right)"," ",0,"2*Piecewise((2*sqrt(2)*(sqrt(2)*(x - 1)**(3/2)/12 + sqrt(2)*sqrt(x - 1)/2), (x >= -1) & (x < 1)))","A",0
325,1,46,0,16.154878," ","integrate(1/((-1+x)/(1+x))**(1/2)*x*(1-x)**(1/2),x)","- \frac{14 i x}{15 \sqrt{\frac{1}{x + 1}}} - \frac{2 i \left(1 - x\right)^{2}}{5 \sqrt{\frac{1}{x + 1}}} + \frac{2 i}{3 \sqrt{\frac{1}{x + 1}}}"," ",0,"-14*I*x/(15*sqrt(1/(x + 1))) - 2*I*(1 - x)**2/(5*sqrt(1/(x + 1))) + 2*I/(3*sqrt(1/(x + 1)))","C",0
326,1,29,0,6.800557," ","integrate(1/((-1+x)/(1+x))**(1/2)*(1-x)**(1/2),x)","- \frac{2 i x}{3 \sqrt{\frac{1}{x + 1}}} - \frac{2 i}{3 \sqrt{\frac{1}{x + 1}}}"," ",0,"-2*I*x/(3*sqrt(1/(x + 1))) - 2*I/(3*sqrt(1/(x + 1)))","C",0
327,1,48,0,7.822715," ","integrate(1/((-1+x)/(1+x))**(1/2)*x/(1+x)**(1/2),x)","\begin{cases} \frac{2 x \sqrt{x - 1}}{3} + \frac{4 \sqrt{x - 1}}{3} & \text{for}\: \left|{x}\right| > 1 \\\frac{2 i x \sqrt{1 - x}}{3} + \frac{4 i \sqrt{1 - x}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x*sqrt(x - 1)/3 + 4*sqrt(x - 1)/3, Abs(x) > 1), (2*I*x*sqrt(1 - x)/3 + 4*I*sqrt(1 - x)/3, True))","A",0
328,1,19,0,7.493429," ","integrate(1/((-1+x)/(1+x))**(1/2)/(1+x)**(1/2),x)","\begin{cases} 2 \sqrt{x - 1} & \text{for}\: \left|{x}\right| > 1 \\2 i \sqrt{1 - x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(x - 1), Abs(x) > 1), (2*I*sqrt(1 - x), True))","A",0
329,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*x/(1-x)**(1/2),x)","\int \frac{x}{\sqrt{\frac{x - 1}{x + 1}} \sqrt{1 - x}}\, dx"," ",0,"Integral(x/(sqrt((x - 1)/(x + 1))*sqrt(1 - x)), x)","F",0
330,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)/(1-x)**(1/2),x)","\int \frac{1}{\sqrt{\frac{x - 1}{x + 1}} \sqrt{1 - x}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)/(x + 1))*sqrt(1 - x)), x)","F",0
331,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*x/(1+x)**(3/2),x)","\int \frac{x}{\sqrt{\frac{x - 1}{x + 1}} \left(x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(sqrt((x - 1)/(x + 1))*(x + 1)**(3/2)), x)","F",0
332,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)/(1+x)**(3/2),x)","\int \frac{1}{\sqrt{\frac{x - 1}{x + 1}} \left(x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)/(x + 1))*(x + 1)**(3/2)), x)","F",0
333,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)*x/(1-x)**(3/2),x)","\int \frac{x}{\sqrt{\frac{x - 1}{x + 1}} \left(1 - x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(sqrt((x - 1)/(x + 1))*(1 - x)**(3/2)), x)","F",0
334,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))**(1/2)/(1-x)**(3/2),x)","\int \frac{1}{\sqrt{\frac{x - 1}{x + 1}} \left(1 - x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)/(x + 1))*(1 - x)**(3/2)), x)","F",0
335,-1,0,0,0.000000," ","integrate(x**m*(-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate(x**2*(-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,1,105,0,90.917072," ","integrate(x*(-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","- \frac{4 i c x \sqrt{\frac{1}{a c x + c}}}{5 a} - \frac{12 i c \sqrt{\frac{1}{a c x + c}}}{5 a^{2}} - \frac{2 i \left(- a c x + c\right)^{2} \sqrt{\frac{1}{a c x + c}}}{5 a^{2} c} + \frac{2 i \left(- a c x + c\right)^{3} \sqrt{\frac{1}{a c x + c}}}{5 a^{2} c^{2}}"," ",0,"-4*I*c*x*sqrt(1/(a*c*x + c))/(5*a) - 12*I*c*sqrt(1/(a*c*x + c))/(5*a**2) - 2*I*(-a*c*x + c)**2*sqrt(1/(a*c*x + c))/(5*a**2*c) + 2*I*(-a*c*x + c)**3*sqrt(1/(a*c*x + c))/(5*a**2*c**2)","C",0
338,1,66,0,43.137450," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\frac{4 i c x \sqrt{\frac{1}{a c x + c}}}{3} + \frac{4 i c \sqrt{\frac{1}{a c x + c}}}{a} - \frac{2 i \left(- a c x + c\right)^{2} \sqrt{\frac{1}{a c x + c}}}{3 a c}"," ",0,"4*I*c*x*sqrt(1/(a*c*x + c))/3 + 4*I*c*sqrt(1/(a*c*x + c))/a - 2*I*(-a*c*x + c)**2*sqrt(1/(a*c*x + c))/(3*a*c)","C",0
339,0,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2)/x,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(a x - 1\right)}}{x}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(a*x - 1))/x, x)","F",0
340,0,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2)/x**2,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(a x - 1\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(a*x - 1))/x**2, x)","F",0
341,1,126,0,7.534963," ","integrate(x**3*(-a*c*x+c)**(1/2)*(a*x-1)/(a*x+1),x)","\frac{2 \left(\frac{2 \sqrt{2} c^{5} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} + 2 c^{4} \sqrt{- a c x + c} + \frac{c^{3} \left(- a c x + c\right)^{\frac{3}{2}}}{3} + \frac{c^{2} \left(- a c x + c\right)^{\frac{5}{2}}}{5} - \frac{c \left(- a c x + c\right)^{\frac{7}{2}}}{7} + \frac{\left(- a c x + c\right)^{\frac{9}{2}}}{9}\right)}{a^{4} c^{4}}"," ",0,"2*(2*sqrt(2)*c**5*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/sqrt(-c) + 2*c**4*sqrt(-a*c*x + c) + c**3*(-a*c*x + c)**(3/2)/3 + c**2*(-a*c*x + c)**(5/2)/5 - c*(-a*c*x + c)**(7/2)/7 + (-a*c*x + c)**(9/2)/9)/(a**4*c**4)","A",0
342,1,95,0,6.248442," ","integrate(x**2*(-a*c*x+c)**(1/2)*(a*x-1)/(a*x+1),x)","- \frac{2 \left(\frac{2 \sqrt{2} c^{4} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} + 2 c^{3} \sqrt{- a c x + c} + \frac{c^{2} \left(- a c x + c\right)^{\frac{3}{2}}}{3} + \frac{\left(- a c x + c\right)^{\frac{7}{2}}}{7}\right)}{a^{3} c^{3}}"," ",0,"-2*(2*sqrt(2)*c**4*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/sqrt(-c) + 2*c**3*sqrt(-a*c*x + c) + c**2*(-a*c*x + c)**(3/2)/3 + (-a*c*x + c)**(7/2)/7)/(a**3*c**3)","A",0
343,1,92,0,5.290515," ","integrate(x*(-a*c*x+c)**(1/2)*(a*x-1)/(a*x+1),x)","\frac{2 \left(\frac{2 \sqrt{2} c^{3} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} + 2 c^{2} \sqrt{- a c x + c} + \frac{c \left(- a c x + c\right)^{\frac{3}{2}}}{3} + \frac{\left(- a c x + c\right)^{\frac{5}{2}}}{5}\right)}{a^{2} c^{2}}"," ",0,"2*(2*sqrt(2)*c**3*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/sqrt(-c) + 2*c**2*sqrt(-a*c*x + c) + c*(-a*c*x + c)**(3/2)/3 + (-a*c*x + c)**(5/2)/5)/(a**2*c**2)","A",0
344,1,73,0,3.852286," ","integrate((-a*c*x+c)**(1/2)*(a*x-1)/(a*x+1),x)","- \frac{2 \left(\frac{2 \sqrt{2} c^{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} + 2 c \sqrt{- a c x + c} + \frac{\left(- a c x + c\right)^{\frac{3}{2}}}{3}\right)}{a c}"," ",0,"-2*(2*sqrt(2)*c**2*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/sqrt(-c) + 2*c*sqrt(-a*c*x + c) + (-a*c*x + c)**(3/2)/3)/(a*c)","A",0
345,1,80,0,5.491397," ","integrate((-a*c*x+c)**(1/2)*(a*x-1)/(a*x+1)/x,x)","- \frac{2 c \operatorname{atan}{\left(\frac{\sqrt{- a c x + c}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + \frac{4 \sqrt{2} c \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} + 2 \sqrt{- a c x + c}"," ",0,"-2*c*atan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + 4*sqrt(2)*c*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/sqrt(-c) + 2*sqrt(-a*c*x + c)","A",0
346,1,162,0,8.102740," ","integrate((-a*c*x+c)**(1/2)*(a*x-1)/(a*x+1)/x**2,x)","- \frac{a c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(- c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)}}{2} + \frac{a c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)}}{2} + \frac{6 a c \operatorname{atan}{\left(\frac{\sqrt{- a c x + c}}{\sqrt{- c}} \right)}}{\sqrt{- c}} - \frac{4 \sqrt{2} a c \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} + \frac{\sqrt{- a c x + c}}{x}"," ",0,"-a*c**2*sqrt(c**(-3))*log(-c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c))/2 + a*c**2*sqrt(c**(-3))*log(c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c))/2 + 6*a*c*atan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) - 4*sqrt(2)*a*c*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/sqrt(-c) + sqrt(-a*c*x + c)/x","B",0
347,1,352,0,14.856844," ","integrate((-a*c*x+c)**(1/2)*(a*x-1)/(a*x+1)/x**3,x)","\frac{10 a^{2} c^{4} \sqrt{- a c x + c}}{16 a c^{4} x - 8 c^{4} + 8 c^{2} \left(- a c x + c\right)^{2}} - \frac{6 a^{2} c^{3} \left(- a c x + c\right)^{\frac{3}{2}}}{16 a c^{4} x - 8 c^{4} + 8 c^{2} \left(- a c x + c\right)^{2}} - \frac{3 a^{2} c^{3} \sqrt{\frac{1}{c^{5}}} \log{\left(- c^{3} \sqrt{\frac{1}{c^{5}}} + \sqrt{- a c x + c} \right)}}{8} + \frac{3 a^{2} c^{3} \sqrt{\frac{1}{c^{5}}} \log{\left(c^{3} \sqrt{\frac{1}{c^{5}}} + \sqrt{- a c x + c} \right)}}{8} + \frac{3 a^{2} c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(- c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)}}{2} - \frac{3 a^{2} c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)}}{2} - \frac{8 a^{2} c \operatorname{atan}{\left(\frac{\sqrt{- a c x + c}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + \frac{4 \sqrt{2} a^{2} c \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} - \frac{3 a \sqrt{- a c x + c}}{x}"," ",0,"10*a**2*c**4*sqrt(-a*c*x + c)/(16*a*c**4*x - 8*c**4 + 8*c**2*(-a*c*x + c)**2) - 6*a**2*c**3*(-a*c*x + c)**(3/2)/(16*a*c**4*x - 8*c**4 + 8*c**2*(-a*c*x + c)**2) - 3*a**2*c**3*sqrt(c**(-5))*log(-c**3*sqrt(c**(-5)) + sqrt(-a*c*x + c))/8 + 3*a**2*c**3*sqrt(c**(-5))*log(c**3*sqrt(c**(-5)) + sqrt(-a*c*x + c))/8 + 3*a**2*c**2*sqrt(c**(-3))*log(-c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c))/2 - 3*a**2*c**2*sqrt(c**(-3))*log(c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c))/2 - 8*a**2*c*atan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + 4*sqrt(2)*a**2*c*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/sqrt(-c) - 3*a*sqrt(-a*c*x + c)/x","B",0
348,1,614,0,18.383729," ","integrate((-a*c*x+c)**(1/2)*(a*x-1)/(a*x+1)/x**4,x)","- \frac{66 a^{3} c^{6} \sqrt{- a c x + c}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} + \frac{80 a^{3} c^{5} \left(- a c x + c\right)^{\frac{3}{2}}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} - \frac{30 a^{3} c^{4} \left(- a c x + c\right)^{\frac{5}{2}}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} - \frac{30 a^{3} c^{4} \sqrt{- a c x + c}}{16 a c^{4} x - 8 c^{4} + 8 c^{2} \left(- a c x + c\right)^{2}} - \frac{5 a^{3} c^{4} \sqrt{\frac{1}{c^{7}}} \log{\left(- c^{4} \sqrt{\frac{1}{c^{7}}} + \sqrt{- a c x + c} \right)}}{16} + \frac{5 a^{3} c^{4} \sqrt{\frac{1}{c^{7}}} \log{\left(c^{4} \sqrt{\frac{1}{c^{7}}} + \sqrt{- a c x + c} \right)}}{16} + \frac{18 a^{3} c^{3} \left(- a c x + c\right)^{\frac{3}{2}}}{16 a c^{4} x - 8 c^{4} + 8 c^{2} \left(- a c x + c\right)^{2}} + \frac{9 a^{3} c^{3} \sqrt{\frac{1}{c^{5}}} \log{\left(- c^{3} \sqrt{\frac{1}{c^{5}}} + \sqrt{- a c x + c} \right)}}{8} - \frac{9 a^{3} c^{3} \sqrt{\frac{1}{c^{5}}} \log{\left(c^{3} \sqrt{\frac{1}{c^{5}}} + \sqrt{- a c x + c} \right)}}{8} - 2 a^{3} c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(- c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)} + 2 a^{3} c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)} + \frac{8 a^{3} c \operatorname{atan}{\left(\frac{\sqrt{- a c x + c}}{\sqrt{- c}} \right)}}{\sqrt{- c}} - \frac{4 \sqrt{2} a^{3} c \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} + \frac{4 a^{2} \sqrt{- a c x + c}}{x}"," ",0,"-66*a**3*c**6*sqrt(-a*c*x + c)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) + 80*a**3*c**5*(-a*c*x + c)**(3/2)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) - 30*a**3*c**4*(-a*c*x + c)**(5/2)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) - 30*a**3*c**4*sqrt(-a*c*x + c)/(16*a*c**4*x - 8*c**4 + 8*c**2*(-a*c*x + c)**2) - 5*a**3*c**4*sqrt(c**(-7))*log(-c**4*sqrt(c**(-7)) + sqrt(-a*c*x + c))/16 + 5*a**3*c**4*sqrt(c**(-7))*log(c**4*sqrt(c**(-7)) + sqrt(-a*c*x + c))/16 + 18*a**3*c**3*(-a*c*x + c)**(3/2)/(16*a*c**4*x - 8*c**4 + 8*c**2*(-a*c*x + c)**2) + 9*a**3*c**3*sqrt(c**(-5))*log(-c**3*sqrt(c**(-5)) + sqrt(-a*c*x + c))/8 - 9*a**3*c**3*sqrt(c**(-5))*log(c**3*sqrt(c**(-5)) + sqrt(-a*c*x + c))/8 - 2*a**3*c**2*sqrt(c**(-3))*log(-c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c)) + 2*a**3*c**2*sqrt(c**(-3))*log(c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c)) + 8*a**3*c*atan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) - 4*sqrt(2)*a**3*c*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/sqrt(-c) + 4*a**2*sqrt(-a*c*x + c)/x","B",0
349,1,991,0,32.761069," ","integrate((-a*c*x+c)**(1/2)*(a*x-1)/(a*x+1)/x**5,x)","\frac{558 a^{4} c^{8} \sqrt{- a c x + c}}{1536 a c^{8} x - 1152 c^{8} + 2304 c^{6} \left(- a c x + c\right)^{2} - 1536 c^{5} \left(- a c x + c\right)^{3} + 384 c^{4} \left(- a c x + c\right)^{4}} - \frac{1022 a^{4} c^{7} \left(- a c x + c\right)^{\frac{3}{2}}}{1536 a c^{8} x - 1152 c^{8} + 2304 c^{6} \left(- a c x + c\right)^{2} - 1536 c^{5} \left(- a c x + c\right)^{3} + 384 c^{4} \left(- a c x + c\right)^{4}} + \frac{770 a^{4} c^{6} \left(- a c x + c\right)^{\frac{5}{2}}}{1536 a c^{8} x - 1152 c^{8} + 2304 c^{6} \left(- a c x + c\right)^{2} - 1536 c^{5} \left(- a c x + c\right)^{3} + 384 c^{4} \left(- a c x + c\right)^{4}} + \frac{198 a^{4} c^{6} \sqrt{- a c x + c}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} - \frac{210 a^{4} c^{5} \left(- a c x + c\right)^{\frac{7}{2}}}{1536 a c^{8} x - 1152 c^{8} + 2304 c^{6} \left(- a c x + c\right)^{2} - 1536 c^{5} \left(- a c x + c\right)^{3} + 384 c^{4} \left(- a c x + c\right)^{4}} - \frac{240 a^{4} c^{5} \left(- a c x + c\right)^{\frac{3}{2}}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} - \frac{35 a^{4} c^{5} \sqrt{\frac{1}{c^{9}}} \log{\left(- c^{5} \sqrt{\frac{1}{c^{9}}} + \sqrt{- a c x + c} \right)}}{128} + \frac{35 a^{4} c^{5} \sqrt{\frac{1}{c^{9}}} \log{\left(c^{5} \sqrt{\frac{1}{c^{9}}} + \sqrt{- a c x + c} \right)}}{128} + \frac{90 a^{4} c^{4} \left(- a c x + c\right)^{\frac{5}{2}}}{- 144 a c^{6} x + 96 c^{6} - 144 c^{4} \left(- a c x + c\right)^{2} + 48 c^{3} \left(- a c x + c\right)^{3}} + \frac{40 a^{4} c^{4} \sqrt{- a c x + c}}{16 a c^{4} x - 8 c^{4} + 8 c^{2} \left(- a c x + c\right)^{2}} + \frac{15 a^{4} c^{4} \sqrt{\frac{1}{c^{7}}} \log{\left(- c^{4} \sqrt{\frac{1}{c^{7}}} + \sqrt{- a c x + c} \right)}}{16} - \frac{15 a^{4} c^{4} \sqrt{\frac{1}{c^{7}}} \log{\left(c^{4} \sqrt{\frac{1}{c^{7}}} + \sqrt{- a c x + c} \right)}}{16} - \frac{24 a^{4} c^{3} \left(- a c x + c\right)^{\frac{3}{2}}}{16 a c^{4} x - 8 c^{4} + 8 c^{2} \left(- a c x + c\right)^{2}} - \frac{3 a^{4} c^{3} \sqrt{\frac{1}{c^{5}}} \log{\left(- c^{3} \sqrt{\frac{1}{c^{5}}} + \sqrt{- a c x + c} \right)}}{2} + \frac{3 a^{4} c^{3} \sqrt{\frac{1}{c^{5}}} \log{\left(c^{3} \sqrt{\frac{1}{c^{5}}} + \sqrt{- a c x + c} \right)}}{2} + 2 a^{4} c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(- c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)} - 2 a^{4} c^{2} \sqrt{\frac{1}{c^{3}}} \log{\left(c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{- a c x + c} \right)} - \frac{8 a^{4} c \operatorname{atan}{\left(\frac{\sqrt{- a c x + c}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + \frac{4 \sqrt{2} a^{4} c \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{- a c x + c}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} - \frac{4 a^{3} \sqrt{- a c x + c}}{x}"," ",0,"558*a**4*c**8*sqrt(-a*c*x + c)/(1536*a*c**8*x - 1152*c**8 + 2304*c**6*(-a*c*x + c)**2 - 1536*c**5*(-a*c*x + c)**3 + 384*c**4*(-a*c*x + c)**4) - 1022*a**4*c**7*(-a*c*x + c)**(3/2)/(1536*a*c**8*x - 1152*c**8 + 2304*c**6*(-a*c*x + c)**2 - 1536*c**5*(-a*c*x + c)**3 + 384*c**4*(-a*c*x + c)**4) + 770*a**4*c**6*(-a*c*x + c)**(5/2)/(1536*a*c**8*x - 1152*c**8 + 2304*c**6*(-a*c*x + c)**2 - 1536*c**5*(-a*c*x + c)**3 + 384*c**4*(-a*c*x + c)**4) + 198*a**4*c**6*sqrt(-a*c*x + c)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) - 210*a**4*c**5*(-a*c*x + c)**(7/2)/(1536*a*c**8*x - 1152*c**8 + 2304*c**6*(-a*c*x + c)**2 - 1536*c**5*(-a*c*x + c)**3 + 384*c**4*(-a*c*x + c)**4) - 240*a**4*c**5*(-a*c*x + c)**(3/2)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) - 35*a**4*c**5*sqrt(c**(-9))*log(-c**5*sqrt(c**(-9)) + sqrt(-a*c*x + c))/128 + 35*a**4*c**5*sqrt(c**(-9))*log(c**5*sqrt(c**(-9)) + sqrt(-a*c*x + c))/128 + 90*a**4*c**4*(-a*c*x + c)**(5/2)/(-144*a*c**6*x + 96*c**6 - 144*c**4*(-a*c*x + c)**2 + 48*c**3*(-a*c*x + c)**3) + 40*a**4*c**4*sqrt(-a*c*x + c)/(16*a*c**4*x - 8*c**4 + 8*c**2*(-a*c*x + c)**2) + 15*a**4*c**4*sqrt(c**(-7))*log(-c**4*sqrt(c**(-7)) + sqrt(-a*c*x + c))/16 - 15*a**4*c**4*sqrt(c**(-7))*log(c**4*sqrt(c**(-7)) + sqrt(-a*c*x + c))/16 - 24*a**4*c**3*(-a*c*x + c)**(3/2)/(16*a*c**4*x - 8*c**4 + 8*c**2*(-a*c*x + c)**2) - 3*a**4*c**3*sqrt(c**(-5))*log(-c**3*sqrt(c**(-5)) + sqrt(-a*c*x + c))/2 + 3*a**4*c**3*sqrt(c**(-5))*log(c**3*sqrt(c**(-5)) + sqrt(-a*c*x + c))/2 + 2*a**4*c**2*sqrt(c**(-3))*log(-c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c)) - 2*a**4*c**2*sqrt(c**(-3))*log(c**2*sqrt(c**(-3)) + sqrt(-a*c*x + c)) - 8*a**4*c*atan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + 4*sqrt(2)*a**4*c*atan(sqrt(2)*sqrt(-a*c*x + c)/(2*sqrt(-c)))/sqrt(-c) - 4*a**3*sqrt(-a*c*x + c)/x","B",0
350,-1,0,0,0.000000," ","integrate(x**3*(-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate(x**2*(-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate(x*(-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**(2+1/2*n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**(1+1/2*n),x)","\begin{cases} c^{\frac{n}{2} + 1} x e^{\frac{i \pi n}{2}} & \text{for}\: a = 0 \\- \frac{\int \frac{1}{a x e^{4 \operatorname{acoth}{\left(a x \right)}} - e^{4 \operatorname{acoth}{\left(a x \right)}}}\, dx}{c} & \text{for}\: n = -4 \\\int e^{- 2 \operatorname{acoth}{\left(a x \right)}}\, dx & \text{for}\: n = -2 \\- \frac{2 a^{2} c n x^{2} \left(- a c x + c\right)^{\frac{n}{2}} e^{n \operatorname{acoth}{\left(a x \right)}}}{a n^{2} + 6 a n + 8 a} - \frac{4 a^{2} c x^{2} \left(- a c x + c\right)^{\frac{n}{2}} e^{n \operatorname{acoth}{\left(a x \right)}}}{a n^{2} + 6 a n + 8 a} + \frac{8 a c x \left(- a c x + c\right)^{\frac{n}{2}} e^{n \operatorname{acoth}{\left(a x \right)}}}{a n^{2} + 6 a n + 8 a} + \frac{2 c n \left(- a c x + c\right)^{\frac{n}{2}} e^{n \operatorname{acoth}{\left(a x \right)}}}{a n^{2} + 6 a n + 8 a} + \frac{12 c \left(- a c x + c\right)^{\frac{n}{2}} e^{n \operatorname{acoth}{\left(a x \right)}}}{a n^{2} + 6 a n + 8 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**(n/2 + 1)*x*exp(I*pi*n/2), Eq(a, 0)), (-Integral(1/(a*x*exp(4*acoth(a*x)) - exp(4*acoth(a*x))), x)/c, Eq(n, -4)), (Integral(exp(-2*acoth(a*x)), x), Eq(n, -2)), (-2*a**2*c*n*x**2*(-a*c*x + c)**(n/2)*exp(n*acoth(a*x))/(a*n**2 + 6*a*n + 8*a) - 4*a**2*c*x**2*(-a*c*x + c)**(n/2)*exp(n*acoth(a*x))/(a*n**2 + 6*a*n + 8*a) + 8*a*c*x*(-a*c*x + c)**(n/2)*exp(n*acoth(a*x))/(a*n**2 + 6*a*n + 8*a) + 2*c*n*(-a*c*x + c)**(n/2)*exp(n*acoth(a*x))/(a*n**2 + 6*a*n + 8*a) + 12*c*(-a*c*x + c)**(n/2)*exp(n*acoth(a*x))/(a*n**2 + 6*a*n + 8*a), True))","F",0
361,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**(1/2*n),x)","\begin{cases} - \frac{x}{c} & \text{for}\: a = 0 \wedge n = -2 \\c^{\frac{n}{2}} x e^{\frac{i \pi n}{2}} & \text{for}\: a = 0 \\- \frac{\int \frac{1}{a x e^{2 \operatorname{acoth}{\left(a x \right)}} - e^{2 \operatorname{acoth}{\left(a x \right)}}}\, dx}{c} & \text{for}\: n = -2 \\\frac{2 a x \left(- a c x + c\right)^{\frac{n}{2}} e^{n \operatorname{acoth}{\left(a x \right)}}}{a n + 2 a} + \frac{2 \left(- a c x + c\right)^{\frac{n}{2}} e^{n \operatorname{acoth}{\left(a x \right)}}}{a n + 2 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x/c, Eq(a, 0) & Eq(n, -2)), (c**(n/2)*x*exp(I*pi*n/2), Eq(a, 0)), (-Integral(1/(a*x*exp(2*acoth(a*x)) - exp(2*acoth(a*x))), x)/c, Eq(n, -2)), (2*a*x*(-a*c*x + c)**(n/2)*exp(n*acoth(a*x))/(a*n + 2*a) + 2*(-a*c*x + c)**(n/2)*exp(n*acoth(a*x))/(a*n + 2*a), True))","F",0
362,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**(-1+1/2*n),x)","\int \left(- c \left(a x - 1\right)\right)^{\frac{n}{2} - 1} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral((-c*(a*x - 1))**(n/2 - 1)*exp(n*acoth(a*x)), x)","F",0
363,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**(-2+1/2*n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**p,x)","\int \left(- c \left(a x - 1\right)\right)^{p} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral((-c*(a*x - 1))**p*exp(n*acoth(a*x)), x)","F",0
365,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**3,x)","- c^{3} \left(\int 3 a x e^{n \operatorname{acoth}{\left(a x \right)}}\, dx + \int \left(- 3 a^{2} x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}\right)\, dx + \int a^{3} x^{3} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx + \int \left(- e^{n \operatorname{acoth}{\left(a x \right)}}\right)\, dx\right)"," ",0,"-c**3*(Integral(3*a*x*exp(n*acoth(a*x)), x) + Integral(-3*a**2*x**2*exp(n*acoth(a*x)), x) + Integral(a**3*x**3*exp(n*acoth(a*x)), x) + Integral(-exp(n*acoth(a*x)), x))","F",0
366,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**2,x)","c^{2} \left(\int \left(- 2 a x e^{n \operatorname{acoth}{\left(a x \right)}}\right)\, dx + \int a^{2} x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx + \int e^{n \operatorname{acoth}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(-2*a*x*exp(n*acoth(a*x)), x) + Integral(a**2*x**2*exp(n*acoth(a*x)), x) + Integral(exp(n*acoth(a*x)), x))","F",0
367,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c),x)","- c \left(\int a x e^{n \operatorname{acoth}{\left(a x \right)}}\, dx + \int \left(- e^{n \operatorname{acoth}{\left(a x \right)}}\right)\, dx\right)"," ",0,"-c*(Integral(a*x*exp(n*acoth(a*x)), x) + Integral(-exp(n*acoth(a*x)), x))","F",0
368,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a*c*x+c),x)","- \frac{\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{a x - 1}\, dx}{c}"," ",0,"-Integral(exp(n*acoth(a*x))/(a*x - 1), x)/c","F",0
369,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a*c*x+c)**2,x)","\begin{cases} \text{NaN} & \text{for}\: a = \frac{1}{x} \wedge c = 0 \wedge n = -2 \\\tilde{\infty} x e^{\infty n} & \text{for}\: a = \frac{1}{x} \\\tilde{\infty} \int e^{n \operatorname{acoth}{\left(a x \right)}}\, dx & \text{for}\: c = 0 \\- \frac{a x \operatorname{acoth}{\left(a x \right)}}{a^{2} c^{2} x e^{2 \operatorname{acoth}{\left(a x \right)}} - a c^{2} e^{2 \operatorname{acoth}{\left(a x \right)}}} - \frac{\operatorname{acoth}{\left(a x \right)}}{a^{2} c^{2} x e^{2 \operatorname{acoth}{\left(a x \right)}} - a c^{2} e^{2 \operatorname{acoth}{\left(a x \right)}}} & \text{for}\: n = -2 \\- \frac{a x e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{2} c^{2} n x + 2 a^{2} c^{2} x - a c^{2} n - 2 a c^{2}} - \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{2} c^{2} n x + 2 a^{2} c^{2} x - a c^{2} n - 2 a c^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(c, 0) & Eq(n, -2) & Eq(a, 1/x)), (zoo*x*exp(oo*n), Eq(a, 1/x)), (zoo*Integral(exp(n*acoth(a*x)), x), Eq(c, 0)), (-a*x*acoth(a*x)/(a**2*c**2*x*exp(2*acoth(a*x)) - a*c**2*exp(2*acoth(a*x))) - acoth(a*x)/(a**2*c**2*x*exp(2*acoth(a*x)) - a*c**2*exp(2*acoth(a*x))), Eq(n, -2)), (-a*x*exp(n*acoth(a*x))/(a**2*c**2*n*x + 2*a**2*c**2*x - a*c**2*n - 2*a*c**2) - exp(n*acoth(a*x))/(a**2*c**2*n*x + 2*a**2*c**2*x - a*c**2*n - 2*a*c**2), True))","F",0
370,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a*c*x+c)**3,x)","\begin{cases} \tilde{\infty} \int e^{n \operatorname{acoth}{\left(a x \right)}}\, dx & \text{for}\: c = 0 \\\frac{a^{2} x^{2} \operatorname{acoth}{\left(a x \right)}}{2 a^{3} c^{3} x^{2} e^{4 \operatorname{acoth}{\left(a x \right)}} - 4 a^{2} c^{3} x e^{4 \operatorname{acoth}{\left(a x \right)}} + 2 a c^{3} e^{4 \operatorname{acoth}{\left(a x \right)}}} + \frac{2 a x \operatorname{acoth}{\left(a x \right)}}{2 a^{3} c^{3} x^{2} e^{4 \operatorname{acoth}{\left(a x \right)}} - 4 a^{2} c^{3} x e^{4 \operatorname{acoth}{\left(a x \right)}} + 2 a c^{3} e^{4 \operatorname{acoth}{\left(a x \right)}}} - \frac{a x}{2 a^{3} c^{3} x^{2} e^{4 \operatorname{acoth}{\left(a x \right)}} - 4 a^{2} c^{3} x e^{4 \operatorname{acoth}{\left(a x \right)}} + 2 a c^{3} e^{4 \operatorname{acoth}{\left(a x \right)}}} + \frac{\operatorname{acoth}{\left(a x \right)}}{2 a^{3} c^{3} x^{2} e^{4 \operatorname{acoth}{\left(a x \right)}} - 4 a^{2} c^{3} x e^{4 \operatorname{acoth}{\left(a x \right)}} + 2 a c^{3} e^{4 \operatorname{acoth}{\left(a x \right)}}} - \frac{1}{2 a^{3} c^{3} x^{2} e^{4 \operatorname{acoth}{\left(a x \right)}} - 4 a^{2} c^{3} x e^{4 \operatorname{acoth}{\left(a x \right)}} + 2 a c^{3} e^{4 \operatorname{acoth}{\left(a x \right)}}} & \text{for}\: n = -4 \\- \frac{a^{2} x^{2} \operatorname{acoth}{\left(a x \right)}}{2 a^{3} c^{3} x^{2} e^{2 \operatorname{acoth}{\left(a x \right)}} - 4 a^{2} c^{3} x e^{2 \operatorname{acoth}{\left(a x \right)}} + 2 a c^{3} e^{2 \operatorname{acoth}{\left(a x \right)}}} + \frac{a x}{2 a^{3} c^{3} x^{2} e^{2 \operatorname{acoth}{\left(a x \right)}} - 4 a^{2} c^{3} x e^{2 \operatorname{acoth}{\left(a x \right)}} + 2 a c^{3} e^{2 \operatorname{acoth}{\left(a x \right)}}} + \frac{\operatorname{acoth}{\left(a x \right)}}{2 a^{3} c^{3} x^{2} e^{2 \operatorname{acoth}{\left(a x \right)}} - 4 a^{2} c^{3} x e^{2 \operatorname{acoth}{\left(a x \right)}} + 2 a c^{3} e^{2 \operatorname{acoth}{\left(a x \right)}}} + \frac{1}{2 a^{3} c^{3} x^{2} e^{2 \operatorname{acoth}{\left(a x \right)}} - 4 a^{2} c^{3} x e^{2 \operatorname{acoth}{\left(a x \right)}} + 2 a c^{3} e^{2 \operatorname{acoth}{\left(a x \right)}}} & \text{for}\: n = -2 \\- \frac{a^{2} x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{3} c^{3} n^{2} x^{2} + 6 a^{3} c^{3} n x^{2} + 8 a^{3} c^{3} x^{2} - 2 a^{2} c^{3} n^{2} x - 12 a^{2} c^{3} n x - 16 a^{2} c^{3} x + a c^{3} n^{2} + 6 a c^{3} n + 8 a c^{3}} + \frac{a n x e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{3} c^{3} n^{2} x^{2} + 6 a^{3} c^{3} n x^{2} + 8 a^{3} c^{3} x^{2} - 2 a^{2} c^{3} n^{2} x - 12 a^{2} c^{3} n x - 16 a^{2} c^{3} x + a c^{3} n^{2} + 6 a c^{3} n + 8 a c^{3}} + \frac{2 a x e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{3} c^{3} n^{2} x^{2} + 6 a^{3} c^{3} n x^{2} + 8 a^{3} c^{3} x^{2} - 2 a^{2} c^{3} n^{2} x - 12 a^{2} c^{3} n x - 16 a^{2} c^{3} x + a c^{3} n^{2} + 6 a c^{3} n + 8 a c^{3}} + \frac{n e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{3} c^{3} n^{2} x^{2} + 6 a^{3} c^{3} n x^{2} + 8 a^{3} c^{3} x^{2} - 2 a^{2} c^{3} n^{2} x - 12 a^{2} c^{3} n x - 16 a^{2} c^{3} x + a c^{3} n^{2} + 6 a c^{3} n + 8 a c^{3}} + \frac{3 e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{3} c^{3} n^{2} x^{2} + 6 a^{3} c^{3} n x^{2} + 8 a^{3} c^{3} x^{2} - 2 a^{2} c^{3} n^{2} x - 12 a^{2} c^{3} n x - 16 a^{2} c^{3} x + a c^{3} n^{2} + 6 a c^{3} n + 8 a c^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*Integral(exp(n*acoth(a*x)), x), Eq(c, 0)), (a**2*x**2*acoth(a*x)/(2*a**3*c**3*x**2*exp(4*acoth(a*x)) - 4*a**2*c**3*x*exp(4*acoth(a*x)) + 2*a*c**3*exp(4*acoth(a*x))) + 2*a*x*acoth(a*x)/(2*a**3*c**3*x**2*exp(4*acoth(a*x)) - 4*a**2*c**3*x*exp(4*acoth(a*x)) + 2*a*c**3*exp(4*acoth(a*x))) - a*x/(2*a**3*c**3*x**2*exp(4*acoth(a*x)) - 4*a**2*c**3*x*exp(4*acoth(a*x)) + 2*a*c**3*exp(4*acoth(a*x))) + acoth(a*x)/(2*a**3*c**3*x**2*exp(4*acoth(a*x)) - 4*a**2*c**3*x*exp(4*acoth(a*x)) + 2*a*c**3*exp(4*acoth(a*x))) - 1/(2*a**3*c**3*x**2*exp(4*acoth(a*x)) - 4*a**2*c**3*x*exp(4*acoth(a*x)) + 2*a*c**3*exp(4*acoth(a*x))), Eq(n, -4)), (-a**2*x**2*acoth(a*x)/(2*a**3*c**3*x**2*exp(2*acoth(a*x)) - 4*a**2*c**3*x*exp(2*acoth(a*x)) + 2*a*c**3*exp(2*acoth(a*x))) + a*x/(2*a**3*c**3*x**2*exp(2*acoth(a*x)) - 4*a**2*c**3*x*exp(2*acoth(a*x)) + 2*a*c**3*exp(2*acoth(a*x))) + acoth(a*x)/(2*a**3*c**3*x**2*exp(2*acoth(a*x)) - 4*a**2*c**3*x*exp(2*acoth(a*x)) + 2*a*c**3*exp(2*acoth(a*x))) + 1/(2*a**3*c**3*x**2*exp(2*acoth(a*x)) - 4*a**2*c**3*x*exp(2*acoth(a*x)) + 2*a*c**3*exp(2*acoth(a*x))), Eq(n, -2)), (-a**2*x**2*exp(n*acoth(a*x))/(a**3*c**3*n**2*x**2 + 6*a**3*c**3*n*x**2 + 8*a**3*c**3*x**2 - 2*a**2*c**3*n**2*x - 12*a**2*c**3*n*x - 16*a**2*c**3*x + a*c**3*n**2 + 6*a*c**3*n + 8*a*c**3) + a*n*x*exp(n*acoth(a*x))/(a**3*c**3*n**2*x**2 + 6*a**3*c**3*n*x**2 + 8*a**3*c**3*x**2 - 2*a**2*c**3*n**2*x - 12*a**2*c**3*n*x - 16*a**2*c**3*x + a*c**3*n**2 + 6*a*c**3*n + 8*a*c**3) + 2*a*x*exp(n*acoth(a*x))/(a**3*c**3*n**2*x**2 + 6*a**3*c**3*n*x**2 + 8*a**3*c**3*x**2 - 2*a**2*c**3*n**2*x - 12*a**2*c**3*n*x - 16*a**2*c**3*x + a*c**3*n**2 + 6*a*c**3*n + 8*a*c**3) + n*exp(n*acoth(a*x))/(a**3*c**3*n**2*x**2 + 6*a**3*c**3*n*x**2 + 8*a**3*c**3*x**2 - 2*a**2*c**3*n**2*x - 12*a**2*c**3*n*x - 16*a**2*c**3*x + a*c**3*n**2 + 6*a*c**3*n + 8*a*c**3) + 3*exp(n*acoth(a*x))/(a**3*c**3*n**2*x**2 + 6*a**3*c**3*n*x**2 + 8*a**3*c**3*x**2 - 2*a**2*c**3*n**2*x - 12*a**2*c**3*n*x - 16*a**2*c**3*x + a*c**3*n**2 + 6*a*c**3*n + 8*a*c**3), True))","F",0
371,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a*c*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-2,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**(5/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
373,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a*c*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a*c*x+c)**(1/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\sqrt{- c \left(a x - 1\right)}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/sqrt(-c*(a*x - 1)), x)","F",0
376,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a*c*x+c)**(3/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/(-c*(a*x - 1))**(3/2), x)","F",0
377,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a*c*x+c)**(5/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/(-c*(a*x - 1))**(5/2), x)","F",0
378,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a*c*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**4,x)","\frac{c^{4} \left(\int \frac{a^{4}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \frac{1}{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{4 a}{x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{6 a^{2}}{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{4 a^{3}}{x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)}{a^{4}}"," ",0,"c**4*(Integral(a**4/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(1/(x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(-4*a/(x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(6*a**2/(x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(-4*a**3/(x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x))/a**4","F",0
380,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**3,x)","\frac{c^{3} \left(\int \frac{a^{3}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{1}{x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{3 a}{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{3 a^{2}}{x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)}{a^{3}}"," ",0,"c**3*(Integral(a**3/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-1/(x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(3*a/(x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(-3*a**2/(x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x))/a**3","F",0
381,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**2,x)","\frac{c^{2} \left(\int \frac{a^{2}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \frac{1}{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{2 a}{x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)}{a^{2}}"," ",0,"c**2*(Integral(a**2/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(1/(x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(-2*a/(x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x))/a**2","F",0
382,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x),x)","\frac{c \left(\int \frac{a}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{1}{x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)}{a}"," ",0,"c*(Integral(a/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-1/(x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x))/a","F",0
383,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x),x)","\frac{a \int \frac{x}{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c}"," ",0,"a*Integral(x/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c","F",0
384,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**2,x)","\frac{a^{2} \int \frac{x^{2}}{a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 2 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{2}}"," ",0,"a**2*Integral(x**2/(a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 2*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**2","F",0
385,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**3,x)","\frac{a^{3} \int \frac{x^{3}}{a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + 3 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{3}}"," ",0,"a**3*Integral(x**3/(a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + 3*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**3","F",0
386,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**4,x)","\frac{a^{4} \int \frac{x^{4}}{a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 4 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + 6 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 4 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{4}}"," ",0,"a**4*Integral(x**4/(a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 4*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + 6*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 4*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**4","F",0
387,1,63,0,0.269899," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**5,x)","\frac{a^{5} c^{5} x - 3 a^{4} c^{5} \log{\left(x \right)} + \frac{- 8 a^{3} c^{5} x^{3} - 4 a^{2} c^{5} x^{2} + 4 a c^{5} x - c^{5}}{4 x^{4}}}{a^{5}}"," ",0,"(a**5*c**5*x - 3*a**4*c**5*log(x) + (-8*a**3*c**5*x**3 - 4*a**2*c**5*x**2 + 4*a*c**5*x - c**5)/(4*x**4))/a**5","A",0
388,1,39,0,0.184134," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**4,x)","\frac{a^{4} c^{4} x - 2 a^{3} c^{4} \log{\left(x \right)} + \frac{- 3 a c^{4} x + c^{4}}{3 x^{3}}}{a^{4}}"," ",0,"(a**4*c**4*x - 2*a**3*c**4*log(x) + (-3*a*c**4*x + c**4)/(3*x**3))/a**4","A",0
389,1,37,0,0.157081," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**3,x)","\frac{a^{3} c^{3} x - a^{2} c^{3} \log{\left(x \right)} + \frac{2 a c^{3} x - c^{3}}{2 x^{2}}}{a^{3}}"," ",0,"(a**3*c**3*x - a**2*c**3*log(x) + (2*a*c**3*x - c**3)/(2*x**2))/a**3","A",0
390,1,15,0,0.091314," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**2,x)","\frac{a^{2} c^{2} x + \frac{c^{2}}{x}}{a^{2}}"," ",0,"(a**2*c**2*x + c**2/x)/a**2","A",0
391,1,10,0,0.077130," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x),x)","\frac{a c x + c \log{\left(x \right)}}{a}"," ",0,"(a*c*x + c*log(x))/a","A",0
392,1,26,0,0.147764," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x),x)","- \frac{2}{a^{2} c x - a c} + \frac{x}{c} + \frac{3 \log{\left(a x - 1 \right)}}{a c}"," ",0,"-2/(a**2*c*x - a*c) + x/c + 3*log(a*x - 1)/(a*c)","A",0
393,1,49,0,0.232309," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)**2,x)","\frac{- 5 a x + 4}{a^{3} c^{2} x^{2} - 2 a^{2} c^{2} x + a c^{2}} + \frac{x}{c^{2}} + \frac{4 \log{\left(a x - 1 \right)}}{a c^{2}}"," ",0,"(-5*a*x + 4)/(a**3*c**2*x**2 - 2*a**2*c**2*x + a*c**2) + x/c**2 + 4*log(a*x - 1)/(a*c**2)","A",0
394,1,73,0,0.328325," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)**3,x)","\frac{- 54 a^{2} x^{2} + 87 a x - 37}{6 a^{4} c^{3} x^{3} - 18 a^{3} c^{3} x^{2} + 18 a^{2} c^{3} x - 6 a c^{3}} + \frac{x}{c^{3}} + \frac{5 \log{\left(a x - 1 \right)}}{a c^{3}}"," ",0,"(-54*a**2*x**2 + 87*a*x - 37)/(6*a**4*c**3*x**3 - 18*a**3*c**3*x**2 + 18*a**2*c**3*x - 6*a*c**3) + x/c**3 + 5*log(a*x - 1)/(a*c**3)","A",0
395,1,94,0,0.419763," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)**4,x)","\frac{- 28 a^{3} x^{3} + 68 a^{2} x^{2} - 58 a x + 17}{2 a^{5} c^{4} x^{4} - 8 a^{4} c^{4} x^{3} + 12 a^{3} c^{4} x^{2} - 8 a^{2} c^{4} x + 2 a c^{4}} + \frac{x}{c^{4}} + \frac{6 \log{\left(a x - 1 \right)}}{a c^{4}}"," ",0,"(-28*a**3*x**3 + 68*a**2*x**2 - 58*a*x + 17)/(2*a**5*c**4*x**4 - 8*a**4*c**4*x**3 + 12*a**3*c**4*x**2 - 8*a**2*c**4*x + 2*a*c**4) + x/c**4 + 6*log(a*x - 1)/(a*c**4)","A",0
396,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**4,x)","\frac{c^{4} \left(\int \left(- \frac{4 a}{\frac{a x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{6 a^{2}}{\frac{a x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{4 a^{3}}{\frac{a x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{4}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \frac{1}{\frac{a x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx\right)}{a^{4}}"," ",0,"c**4*(Integral(-4*a/(a*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(6*a**2/(a*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-4*a**3/(a*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**4/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(1/(a*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))/a**4","F",0
397,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**3,x)","\frac{c^{3} \left(\int \frac{3 a}{\frac{a x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{3 a^{2}}{\frac{a x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{3}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{1}{\frac{a x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx\right)}{a^{3}}"," ",0,"c**3*(Integral(3*a/(a*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-3*a**2/(a*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**3/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-1/(a*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))/a**3","F",0
398,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**2,x)","\frac{c^{2} \left(\int \left(- \frac{2 a}{\frac{a x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{2}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \frac{1}{\frac{a x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx\right)}{a^{2}}"," ",0,"c**2*(Integral(-2*a/(a*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**2/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(1/(a*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))/a**2","F",0
399,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x),x)","\frac{c \left(\int \frac{a}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{1}{\frac{a x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx\right)}{a}"," ",0,"c*(Integral(a/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-1/(a*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))/a","F",0
400,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x),x)","\frac{a \int \frac{x}{\frac{a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{2 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c}"," ",0,"a*Integral(x/(a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 2*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c","F",0
401,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**2,x)","\frac{a^{2} \int \frac{x^{2}}{\frac{a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{3 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{2}}"," ",0,"a**2*Integral(x**2/(a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 3*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**2","F",0
402,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**3,x)","\frac{a^{3} \int \frac{x^{3}}{\frac{a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{4 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{6 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{4 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{3}}"," ",0,"a**3*Integral(x**3/(a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 4*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 6*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 4*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**3","F",0
403,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**4,x)","\frac{a^{4} \int \frac{x^{4}}{\frac{a^{5} x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{5 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{10 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{10 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{5 a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{4}}"," ",0,"a**4*Integral(x**4/(a**5*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 5*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 10*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 10*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 5*a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**4","F",0
404,1,63,0,0.275848," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(c-c/a/x)**5,x)","\frac{a^{5} c^{5} x - a^{4} c^{5} \log{\left(x \right)} + \frac{24 a^{3} c^{5} x^{3} - 12 a^{2} c^{5} x^{2} - 4 a c^{5} x + 3 c^{5}}{12 x^{4}}}{a^{5}}"," ",0,"(a**5*c**5*x - a**4*c**5*log(x) + (24*a**3*c**5*x**3 - 12*a**2*c**5*x**2 - 4*a*c**5*x + 3*c**5)/(12*x**4))/a**5","A",0
405,1,31,0,0.153724," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(c-c/a/x)**4,x)","\frac{a^{4} c^{4} x + \frac{6 a^{2} c^{4} x^{2} - c^{4}}{3 x^{3}}}{a^{4}}"," ",0,"(a**4*c**4*x + (6*a**2*c**4*x**2 - c**4)/(3*x**3))/a**4","A",0
406,1,37,0,0.161316," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(c-c/a/x)**3,x)","\frac{a^{3} c^{3} x + a^{2} c^{3} \log{\left(x \right)} + \frac{2 a c^{3} x + c^{3}}{2 x^{2}}}{a^{3}}"," ",0,"(a**3*c**3*x + a**2*c**3*log(x) + (2*a*c**3*x + c**3)/(2*x**2))/a**3","A",0
407,1,26,0,0.115682," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(c-c/a/x)**2,x)","\frac{a^{2} c^{2} x + 2 a c^{2} \log{\left(x \right)} - \frac{c^{2}}{x}}{a^{2}}"," ",0,"(a**2*c**2*x + 2*a*c**2*log(x) - c**2/x)/a**2","A",0
408,1,17,0,0.213892," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(c-c/a/x),x)","c x + \frac{c \left(- \log{\left(x \right)} + 4 \log{\left(x - \frac{1}{a} \right)}\right)}{a}"," ",0,"c*x + c*(-log(x) + 4*log(x - 1/a))/a","A",0
409,1,41,0,0.232569," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(c-c/a/x),x)","\frac{- 8 a x + 6}{a^{3} c x^{2} - 2 a^{2} c x + a c} + \frac{x}{c} + \frac{5 \log{\left(a x - 1 \right)}}{a c}"," ",0,"(-8*a*x + 6)/(a**3*c*x**2 - 2*a**2*c*x + a*c) + x/c + 5*log(a*x - 1)/(a*c)","A",0
410,1,73,0,0.326227," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(c-c/a/x)**2,x)","\frac{- 39 a^{2} x^{2} + 60 a x - 25}{3 a^{4} c^{2} x^{3} - 9 a^{3} c^{2} x^{2} + 9 a^{2} c^{2} x - 3 a c^{2}} + \frac{x}{c^{2}} + \frac{6 \log{\left(a x - 1 \right)}}{a c^{2}}"," ",0,"(-39*a**2*x**2 + 60*a*x - 25)/(3*a**4*c**2*x**3 - 9*a**3*c**2*x**2 + 9*a**2*c**2*x - 3*a*c**2) + x/c**2 + 6*log(a*x - 1)/(a*c**2)","A",0
411,1,94,0,0.423262," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(c-c/a/x)**3,x)","\frac{- 114 a^{3} x^{3} + 267 a^{2} x^{2} - 224 a x + 65}{6 a^{5} c^{3} x^{4} - 24 a^{4} c^{3} x^{3} + 36 a^{3} c^{3} x^{2} - 24 a^{2} c^{3} x + 6 a c^{3}} + \frac{x}{c^{3}} + \frac{7 \log{\left(a x - 1 \right)}}{a c^{3}}"," ",0,"(-114*a**3*x**3 + 267*a**2*x**2 - 224*a*x + 65)/(6*a**5*c**3*x**4 - 24*a**4*c**3*x**3 + 36*a**3*c**3*x**2 - 24*a**2*c**3*x + 6*a*c**3) + x/c**3 + 7*log(a*x - 1)/(a*c**3)","A",0
412,1,114,0,0.531141," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(c-c/a/x)**4,x)","\frac{- 390 a^{4} x^{4} + 1230 a^{3} x^{3} - 1555 a^{2} x^{2} + 905 a x - 202}{15 a^{6} c^{4} x^{5} - 75 a^{5} c^{4} x^{4} + 150 a^{4} c^{4} x^{3} - 150 a^{3} c^{4} x^{2} + 75 a^{2} c^{4} x - 15 a c^{4}} + \frac{x}{c^{4}} + \frac{8 \log{\left(a x - 1 \right)}}{a c^{4}}"," ",0,"(-390*a**4*x**4 + 1230*a**3*x**3 - 1555*a**2*x**2 + 905*a*x - 202)/(15*a**6*c**4*x**5 - 75*a**5*c**4*x**4 + 150*a**4*c**4*x**3 - 150*a**3*c**4*x**2 + 75*a**2*c**4*x - 15*a*c**4) + x/c**4 + 8*log(a*x - 1)/(a*c**4)","A",0
413,0,0,0,0.000000," ","integrate((c-c/a/x)**4*((a*x-1)/(a*x+1))**(1/2),x)","\frac{c^{4} \left(\int a^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{4}}\, dx + \int \left(- \frac{4 a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{3}}\right)\, dx + \int \frac{6 a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{2}}\, dx + \int \left(- \frac{4 a^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x}\right)\, dx\right)}{a^{4}}"," ",0,"c**4*(Integral(a**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**4, x) + Integral(-4*a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**3, x) + Integral(6*a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**2, x) + Integral(-4*a**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x, x))/a**4","F",0
414,0,0,0,0.000000," ","integrate((c-c/a/x)**3*((a*x-1)/(a*x+1))**(1/2),x)","\frac{c^{3} \left(\int a^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{3}}\right)\, dx + \int \frac{3 a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{2}}\, dx + \int \left(- \frac{3 a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x}\right)\, dx\right)}{a^{3}}"," ",0,"c**3*(Integral(a**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**3, x) + Integral(3*a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**2, x) + Integral(-3*a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x, x))/a**3","F",0
415,0,0,0,0.000000," ","integrate((c-c/a/x)**2*((a*x-1)/(a*x+1))**(1/2),x)","\frac{c^{2} \left(\int a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{2}}\, dx + \int \left(- \frac{2 a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x}\right)\, dx\right)}{a^{2}}"," ",0,"c**2*(Integral(a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**2, x) + Integral(-2*a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x, x))/a**2","F",0
416,0,0,0,0.000000," ","integrate((c-c/a/x)*((a*x-1)/(a*x+1))**(1/2),x)","\frac{c \left(\int a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x}\right)\, dx\right)}{a}"," ",0,"c*(Integral(a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x, x))/a","F",0
417,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x),x)","\frac{a \int \frac{x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x - 1}\, dx}{c}"," ",0,"a*Integral(x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x - 1), x)/c","F",0
418,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**2,x)","\frac{a^{2} \int \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{2} x^{2} - 2 a x + 1}\, dx}{c^{2}}"," ",0,"a**2*Integral(x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**2*x**2 - 2*a*x + 1), x)/c**2","F",0
419,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**3,x)","\frac{a^{3} \int \frac{x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{3} x^{3} - 3 a^{2} x^{2} + 3 a x - 1}\, dx}{c^{3}}"," ",0,"a**3*Integral(x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**3*x**3 - 3*a**2*x**2 + 3*a*x - 1), x)/c**3","F",0
420,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**4,x)","\frac{a^{4} \int \frac{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{4} x^{4} - 4 a^{3} x^{3} + 6 a^{2} x^{2} - 4 a x + 1}\, dx}{c^{4}}"," ",0,"a**4*Integral(x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**4*x**4 - 4*a**3*x**3 + 6*a**2*x**2 - 4*a*x + 1), x)/c**4","F",0
421,1,56,0,0.421668," ","integrate((c-c/a/x)**4*(a*x-1)/(a*x+1),x)","c^{4} x + \frac{2 c^{4} \left(13 \log{\left(x \right)} - 16 \log{\left(x + \frac{1}{a} \right)}\right)}{a} + \frac{48 a^{2} c^{4} x^{2} - 9 a c^{4} x + c^{4}}{3 a^{4} x^{3}}"," ",0,"c**4*x + 2*c**4*(13*log(x) - 16*log(x + 1/a))/a + (48*a**2*c**4*x**2 - 9*a*c**4*x + c**4)/(3*a**4*x**3)","A",0
422,1,42,0,0.349138," ","integrate((c-c/a/x)**3*(a*x-1)/(a*x+1),x)","c^{3} x + \frac{c^{3} \left(11 \log{\left(x \right)} - 16 \log{\left(x + \frac{1}{a} \right)}\right)}{a} + \frac{10 a c^{3} x - c^{3}}{2 a^{3} x^{2}}"," ",0,"c**3*x + c**3*(11*log(x) - 16*log(x + 1/a))/a + (10*a*c**3*x - c**3)/(2*a**3*x**2)","A",0
423,1,31,0,0.273661," ","integrate((c-c/a/x)**2*(a*x-1)/(a*x+1),x)","c^{2} x + \frac{4 c^{2} \left(\log{\left(x \right)} - 2 \log{\left(x + \frac{1}{a} \right)}\right)}{a} + \frac{c^{2}}{a^{2} x}"," ",0,"c**2*x + 4*c**2*(log(x) - 2*log(x + 1/a))/a + c**2/(a**2*x)","A",0
424,1,17,0,0.206535," ","integrate((c-c/a/x)*(a*x-1)/(a*x+1),x)","c x + \frac{c \left(\log{\left(x \right)} - 4 \log{\left(x + \frac{1}{a} \right)}\right)}{a}"," ",0,"c*x + c*(log(x) - 4*log(x + 1/a))/a","A",0
425,1,17,0,0.098720," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x),x)","a \left(\frac{x}{a c} - \frac{\log{\left(a x + 1 \right)}}{a^{2} c}\right)"," ",0,"a*(x/(a*c) - log(a*x + 1)/(a**2*c))","A",0
426,1,34,0,0.153521," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)**2,x)","a^{2} \left(\frac{x}{a^{2} c^{2}} + \frac{\frac{\log{\left(x - \frac{1}{a} \right)}}{2} - \frac{\log{\left(x + \frac{1}{a} \right)}}{2}}{a^{3} c^{2}}\right)"," ",0,"a**2*(x/(a**2*c**2) + (log(x - 1/a)/2 - log(x + 1/a)/2)/(a**3*c**2))","B",0
427,1,56,0,0.304678," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)**3,x)","a^{3} \left(- \frac{1}{2 a^{5} c^{3} x - 2 a^{4} c^{3}} + \frac{x}{a^{3} c^{3}} + \frac{\frac{5 \log{\left(x - \frac{1}{a} \right)}}{4} - \frac{\log{\left(x + \frac{1}{a} \right)}}{4}}{a^{4} c^{3}}\right)"," ",0,"a**3*(-1/(2*a**5*c**3*x - 2*a**4*c**3) + x/(a**3*c**3) + (5*log(x - 1/a)/4 - log(x + 1/a)/4)/(a**4*c**3))","A",0
428,1,73,0,0.384727," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)**4,x)","a^{4} \left(\frac{- 7 a x + 6}{4 a^{7} c^{4} x^{2} - 8 a^{6} c^{4} x + 4 a^{5} c^{4}} + \frac{x}{a^{4} c^{4}} + \frac{\frac{17 \log{\left(x - \frac{1}{a} \right)}}{8} - \frac{\log{\left(x + \frac{1}{a} \right)}}{8}}{a^{5} c^{4}}\right)"," ",0,"a**4*((-7*a*x + 6)/(4*a**7*c**4*x**2 - 8*a**6*c**4*x + 4*a**5*c**4) + x/(a**4*c**4) + (17*log(x - 1/a)/8 - log(x + 1/a)/8)/(a**5*c**4))","A",0
429,0,0,0,0.000000," ","integrate((c-c/a/x)**4*((a*x-1)/(a*x+1))**(3/2),x)","\frac{c^{4} \left(\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{5} + x^{4}}\right)\, dx + \int \frac{5 a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{4} + x^{3}}\, dx + \int \left(- \frac{10 a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{3} + x^{2}}\right)\, dx + \int \frac{10 a^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{2} + x}\, dx + \int \left(- \frac{5 a^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{5} x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)}{a^{4}}"," ",0,"c**4*(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**5 + x**4), x) + Integral(5*a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**4 + x**3), x) + Integral(-10*a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**3 + x**2), x) + Integral(10*a**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**2 + x), x) + Integral(-5*a**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**5*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))/a**4","F",0
430,0,0,0,0.000000," ","integrate((c-c/a/x)**3*((a*x-1)/(a*x+1))**(3/2),x)","\frac{c^{3} \left(\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{4} + x^{3}}\, dx + \int \left(- \frac{4 a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{3} + x^{2}}\right)\, dx + \int \frac{6 a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{2} + x}\, dx + \int \left(- \frac{4 a^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{4} x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)}{a^{3}}"," ",0,"c**3*(Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**4 + x**3), x) + Integral(-4*a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**3 + x**2), x) + Integral(6*a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**2 + x), x) + Integral(-4*a**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**4*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))/a**3","F",0
431,0,0,0,0.000000," ","integrate((c-c/a/x)**2*((a*x-1)/(a*x+1))**(3/2),x)","\frac{c^{2} \left(\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{3} + x^{2}}\right)\, dx + \int \frac{3 a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{2} + x}\, dx + \int \left(- \frac{3 a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{3} x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)}{a^{2}}"," ",0,"c**2*(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**3 + x**2), x) + Integral(3*a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**2 + x), x) + Integral(-3*a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**3*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))/a**2","F",0
432,0,0,0,0.000000," ","integrate((c-c/a/x)*((a*x-1)/(a*x+1))**(3/2),x)","\frac{c \left(\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{2} + x}\, dx + \int \left(- \frac{2 a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{2} x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)}{a}"," ",0,"c*(Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**2 + x), x) + Integral(-2*a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**2*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))/a","F",0
433,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x),x)","\frac{a \left(\int \left(- \frac{x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{2} x^{2} - 1}\right)\, dx + \int \frac{a x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{2} x^{2} - 1}\, dx\right)}{c}"," ",0,"a*(Integral(-x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**2*x**2 - 1), x) + Integral(a*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**2*x**2 - 1), x))/c","F",0
434,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**2,x)","\frac{a^{2} \left(\int \left(- \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{3} x^{3} - a^{2} x^{2} - a x + 1}\right)\, dx + \int \frac{a x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{3} x^{3} - a^{2} x^{2} - a x + 1}\, dx\right)}{c^{2}}"," ",0,"a**2*(Integral(-x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**3*x**3 - a**2*x**2 - a*x + 1), x) + Integral(a*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**3*x**3 - a**2*x**2 - a*x + 1), x))/c**2","F",0
435,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**3,x)","\frac{a^{3} \left(\int \left(- \frac{x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{4} x^{4} - 2 a^{3} x^{3} + 2 a x - 1}\right)\, dx + \int \frac{a x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{4} x^{4} - 2 a^{3} x^{3} + 2 a x - 1}\, dx\right)}{c^{3}}"," ",0,"a**3*(Integral(-x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**4*x**4 - 2*a**3*x**3 + 2*a*x - 1), x) + Integral(a*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**4*x**4 - 2*a**3*x**3 + 2*a*x - 1), x))/c**3","F",0
436,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**4,x)","\frac{a^{4} \left(\int \left(- \frac{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{5} x^{5} - 3 a^{4} x^{4} + 2 a^{3} x^{3} + 2 a^{2} x^{2} - 3 a x + 1}\right)\, dx + \int \frac{a x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{5} x^{5} - 3 a^{4} x^{4} + 2 a^{3} x^{3} + 2 a^{2} x^{2} - 3 a x + 1}\, dx\right)}{c^{4}}"," ",0,"a**4*(Integral(-x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**5*x**5 - 3*a**4*x**4 + 2*a**3*x**3 + 2*a**2*x**2 - 3*a*x + 1), x) + Integral(a*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**5*x**5 - 3*a**4*x**4 + 2*a**3*x**3 + 2*a**2*x**2 - 3*a*x + 1), x))/c**4","F",0
437,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(1/2),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
443,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**(1/2),x)","\int \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(-1 + \frac{1}{a x}\right)}}\, dx"," ",0,"Integral(1/(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(-1 + 1/(a*x)))), x)","F",0
444,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
445,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(9/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
447,1,777,0,14.123094," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(7/2),x)","c^{3} \left(\begin{cases} \frac{\sqrt{a} \sqrt{c} x^{\frac{3}{2}}}{\sqrt{a x - 1}} - \frac{\sqrt{c} \operatorname{acosh}{\left(\sqrt{a} \sqrt{x} \right)}}{a} - \frac{\sqrt{c} \sqrt{x}}{\sqrt{a} \sqrt{a x - 1}} & \text{for}\: \left|{a x}\right| > 1 \\\frac{i \sqrt{c} \operatorname{asin}{\left(\sqrt{a} \sqrt{x} \right)}}{a} + \frac{i \sqrt{c} \sqrt{x} \sqrt{- a x + 1}}{\sqrt{a}} & \text{otherwise} \end{cases}\right) + \frac{2 c^{4} \operatorname{atan}{\left(\frac{\sqrt{c - \frac{c}{a x}}}{\sqrt{- c}} \right)}}{a \sqrt{- c}} + \frac{2 c^{3} \sqrt{c - \frac{c}{a x}}}{a} - \frac{c^{3} \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{2 a \left(c - \frac{c}{a x}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right)}{a^{2}} + \frac{c^{3} \left(\begin{cases} \frac{4 i a^{\frac{11}{2}} \sqrt{c} x^{\frac{7}{2}}}{- 15 i a^{\frac{7}{2}} x^{\frac{7}{2}} + 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} - \frac{4 i a^{\frac{9}{2}} \sqrt{c} x^{\frac{5}{2}}}{- 15 i a^{\frac{7}{2}} x^{\frac{7}{2}} + 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} - \frac{4 i a^{5} \sqrt{c} x^{3} \sqrt{a x - 1}}{- 15 i a^{\frac{7}{2}} x^{\frac{7}{2}} + 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} + \frac{2 i a^{4} \sqrt{c} x^{2} \sqrt{a x - 1}}{- 15 i a^{\frac{7}{2}} x^{\frac{7}{2}} + 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} + \frac{8 i a^{3} \sqrt{c} x \sqrt{a x - 1}}{- 15 i a^{\frac{7}{2}} x^{\frac{7}{2}} + 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} - \frac{6 i a^{2} \sqrt{c} \sqrt{a x - 1}}{- 15 i a^{\frac{7}{2}} x^{\frac{7}{2}} + 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} & \text{for}\: \left|{a x}\right| > 1 \\- \frac{4 i a^{\frac{11}{2}} \sqrt{c} x^{\frac{7}{2}}}{15 i a^{\frac{7}{2}} x^{\frac{7}{2}} - 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} + \frac{4 i a^{\frac{9}{2}} \sqrt{c} x^{\frac{5}{2}}}{15 i a^{\frac{7}{2}} x^{\frac{7}{2}} - 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} - \frac{4 a^{5} \sqrt{c} x^{3} \sqrt{- a x + 1}}{15 i a^{\frac{7}{2}} x^{\frac{7}{2}} - 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} + \frac{2 a^{4} \sqrt{c} x^{2} \sqrt{- a x + 1}}{15 i a^{\frac{7}{2}} x^{\frac{7}{2}} - 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} + \frac{8 a^{3} \sqrt{c} x \sqrt{- a x + 1}}{15 i a^{\frac{7}{2}} x^{\frac{7}{2}} - 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} - \frac{6 a^{2} \sqrt{c} \sqrt{- a x + 1}}{15 i a^{\frac{7}{2}} x^{\frac{7}{2}} - 15 i a^{\frac{5}{2}} x^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right)}{a^{3}}"," ",0,"c**3*Piecewise((sqrt(a)*sqrt(c)*x**(3/2)/sqrt(a*x - 1) - sqrt(c)*acosh(sqrt(a)*sqrt(x))/a - sqrt(c)*sqrt(x)/(sqrt(a)*sqrt(a*x - 1)), Abs(a*x) > 1), (I*sqrt(c)*asin(sqrt(a)*sqrt(x))/a + I*sqrt(c)*sqrt(x)*sqrt(-a*x + 1)/sqrt(a), True)) + 2*c**4*atan(sqrt(c - c/(a*x))/sqrt(-c))/(a*sqrt(-c)) + 2*c**3*sqrt(c - c/(a*x))/a - c**3*Piecewise((0, Eq(c, 0)), (2*a*(c - c/(a*x))**(3/2)/(3*c), True))/a**2 + c**3*Piecewise((4*I*a**(11/2)*sqrt(c)*x**(7/2)/(-15*I*a**(7/2)*x**(7/2) + 15*I*a**(5/2)*x**(5/2)) - 4*I*a**(9/2)*sqrt(c)*x**(5/2)/(-15*I*a**(7/2)*x**(7/2) + 15*I*a**(5/2)*x**(5/2)) - 4*I*a**5*sqrt(c)*x**3*sqrt(a*x - 1)/(-15*I*a**(7/2)*x**(7/2) + 15*I*a**(5/2)*x**(5/2)) + 2*I*a**4*sqrt(c)*x**2*sqrt(a*x - 1)/(-15*I*a**(7/2)*x**(7/2) + 15*I*a**(5/2)*x**(5/2)) + 8*I*a**3*sqrt(c)*x*sqrt(a*x - 1)/(-15*I*a**(7/2)*x**(7/2) + 15*I*a**(5/2)*x**(5/2)) - 6*I*a**2*sqrt(c)*sqrt(a*x - 1)/(-15*I*a**(7/2)*x**(7/2) + 15*I*a**(5/2)*x**(5/2)), Abs(a*x) > 1), (-4*I*a**(11/2)*sqrt(c)*x**(7/2)/(15*I*a**(7/2)*x**(7/2) - 15*I*a**(5/2)*x**(5/2)) + 4*I*a**(9/2)*sqrt(c)*x**(5/2)/(15*I*a**(7/2)*x**(7/2) - 15*I*a**(5/2)*x**(5/2)) - 4*a**5*sqrt(c)*x**3*sqrt(-a*x + 1)/(15*I*a**(7/2)*x**(7/2) - 15*I*a**(5/2)*x**(5/2)) + 2*a**4*sqrt(c)*x**2*sqrt(-a*x + 1)/(15*I*a**(7/2)*x**(7/2) - 15*I*a**(5/2)*x**(5/2)) + 8*a**3*sqrt(c)*x*sqrt(-a*x + 1)/(15*I*a**(7/2)*x**(7/2) - 15*I*a**(5/2)*x**(5/2)) - 6*a**2*sqrt(c)*sqrt(-a*x + 1)/(15*I*a**(7/2)*x**(7/2) - 15*I*a**(5/2)*x**(5/2)), True))/a**3","C",0
448,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(5/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
449,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
450,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(1/2),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x + 1)/(a*x - 1), x)","F",0
451,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)**(1/2),x)","\int \frac{a x + 1}{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/(sqrt(-c*(-1 + 1/(a*x)))*(a*x - 1)), x)","F",0
452,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)**(3/2),x)","\int \frac{a x + 1}{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{3}{2}} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/((-c*(-1 + 1/(a*x)))**(3/2)*(a*x - 1)), x)","F",0
453,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)**(5/2),x)","\int \frac{a x + 1}{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{5}{2}} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/((-c*(-1 + 1/(a*x)))**(5/2)*(a*x - 1)), x)","F",0
454,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)**(7/2),x)","\int \frac{a x + 1}{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{7}{2}} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/((-c*(-1 + 1/(a*x)))**(7/2)*(a*x - 1)), x)","F",0
455,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
461,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,-1,0,0,0.000000," ","integrate((c-c/a/x)**(7/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,-1,0,0,0.000000," ","integrate((c-c/a/x)**(5/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
465,-1,0,0,0.000000," ","integrate((c-c/a/x)**(3/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**(1/2),x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\sqrt{- c \left(-1 + \frac{1}{a x}\right)}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/sqrt(-c*(-1 + 1/(a*x))), x)","F",0
468,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a/x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,0,0,0,0.000000," ","integrate((c-c/a/x)**(7/2)*(a*x-1)/(a*x+1),x)","\int \frac{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{7}{2}} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x)))**(7/2)*(a*x - 1)/(a*x + 1), x)","F",0
472,0,0,0,0.000000," ","integrate((c-c/a/x)**(5/2)*(a*x-1)/(a*x+1),x)","\int \frac{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{5}{2}} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x)))**(5/2)*(a*x - 1)/(a*x + 1), x)","F",0
473,0,0,0,0.000000," ","integrate((c-c/a/x)**(3/2)*(a*x-1)/(a*x+1),x)","\int \frac{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{3}{2}} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x)))**(3/2)*(a*x - 1)/(a*x + 1), x)","F",0
474,0,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x - 1)/(a*x + 1), x)","F",0
475,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)**(1/2),x)","\int \frac{a x - 1}{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/(sqrt(-c*(-1 + 1/(a*x)))*(a*x + 1)), x)","F",0
476,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)**(3/2),x)","\int \frac{a x - 1}{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{3}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(-1 + 1/(a*x)))**(3/2)*(a*x + 1)), x)","F",0
477,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)**(5/2),x)","\int \frac{a x - 1}{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{5}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(-1 + 1/(a*x)))**(5/2)*(a*x + 1)), x)","F",0
478,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)**(7/2),x)","\int \frac{a x - 1}{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{7}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(-1 + 1/(a*x)))**(7/2)*(a*x + 1)), x)","F",0
479,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)**(9/2),x)","\int \frac{a x - 1}{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{9}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(-1 + 1/(a*x)))**(9/2)*(a*x + 1)), x)","F",0
480,-1,0,0,0.000000," ","integrate((c-c/a/x)**(9/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,-1,0,0,0.000000," ","integrate((c-c/a/x)**(7/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate((c-c/a/x)**(5/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate((c-c/a/x)**(3/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a/x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**m*(c-c/a/x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**2*(c-c/a/x)**(1/2),x)","\int \frac{x^{2} \sqrt{- c \left(-1 + \frac{1}{a x}\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x**2*sqrt(-c*(-1 + 1/(a*x)))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
491,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x*(c-c/a/x)**(1/2),x)","\int \frac{x \sqrt{- c \left(-1 + \frac{1}{a x}\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x*sqrt(-c*(-1 + 1/(a*x)))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
492,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(1/2),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
493,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(1/2)/x,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)}}{x \sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))/(x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
494,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(1/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(1/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**(1/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x**3*(c-c/a/x)**(1/2),x)","\int \frac{x^{3} \sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(x**3*sqrt(-c*(-1 + 1/(a*x)))*(a*x + 1)/(a*x - 1), x)","F",0
499,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x**2*(c-c/a/x)**(1/2),x)","\int \frac{x^{2} \sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(x**2*sqrt(-c*(-1 + 1/(a*x)))*(a*x + 1)/(a*x - 1), x)","F",0
500,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x*(c-c/a/x)**(1/2),x)","\int \frac{x \sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(x*sqrt(-c*(-1 + 1/(a*x)))*(a*x + 1)/(a*x - 1), x)","F",0
501,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(1/2),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x + 1)/(a*x - 1), x)","F",0
502,1,39,0,10.693566," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(1/2)/x,x)","- \frac{2 c \operatorname{atan}{\left(\frac{\sqrt{c - \frac{c}{a x}}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + 2 \sqrt{c - \frac{c}{a x}}"," ",0,"-2*c*atan(sqrt(c - c/(a*x))/sqrt(-c))/sqrt(-c) + 2*sqrt(c - c/(a*x))","A",0
503,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(1/2)/x**2,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{x^{2} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x + 1)/(x**2*(a*x - 1)), x)","F",0
504,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(1/2)/x**3,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{x^{3} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x + 1)/(x**3*(a*x - 1)), x)","F",0
505,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(1/2)/x**4,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{x^{4} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x + 1)/(x**4*(a*x - 1)), x)","F",0
506,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**(1/2)/x**5,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{x^{5} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x + 1)/(x**5*(a*x - 1)), x)","F",0
507,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**3*(c-c/a/x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**2*(c-c/a/x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x*(c-c/a/x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(1/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
512,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
513,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(1/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
514,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(1/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a/x)**(1/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,-1,0,0,0.000000," ","integrate(x**m*(c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,-1,0,0,0.000000," ","integrate(x**2*(c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,-1,0,0,0.000000," ","integrate(x*(c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,0,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\int \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(-1 + \frac{1}{a x}\right)}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(-1 + 1/(a*x))), x)","F",0
520,0,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(1/2)/x,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(-1 + \frac{1}{a x}\right)}}{x}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(-1 + 1/(a*x)))/x, x)","F",0
521,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(1/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
523,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(1/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,0,0,0,0.000000," ","integrate(x**3*(c-c/a/x)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{x^{3} \sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(x**3*sqrt(-c*(-1 + 1/(a*x)))*(a*x - 1)/(a*x + 1), x)","F",0
525,0,0,0,0.000000," ","integrate(x**2*(c-c/a/x)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{x^{2} \sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(x**2*sqrt(-c*(-1 + 1/(a*x)))*(a*x - 1)/(a*x + 1), x)","F",0
526,0,0,0,0.000000," ","integrate(x*(c-c/a/x)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{x \sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(x*sqrt(-c*(-1 + 1/(a*x)))*(a*x - 1)/(a*x + 1), x)","F",0
527,0,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x - 1)/(a*x + 1), x)","F",0
528,1,80,0,12.749144," ","integrate((c-c/a/x)**(1/2)*(a*x-1)/(a*x+1)/x,x)","- \frac{2 c \operatorname{atan}{\left(\frac{\sqrt{c - \frac{c}{a x}}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + \frac{4 \sqrt{2} c \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{c - \frac{c}{a x}}}{2 \sqrt{- c}} \right)}}{\sqrt{- c}} + 2 \sqrt{c - \frac{c}{a x}}"," ",0,"-2*c*atan(sqrt(c - c/(a*x))/sqrt(-c))/sqrt(-c) + 4*sqrt(2)*c*atan(sqrt(2)*sqrt(c - c/(a*x))/(2*sqrt(-c)))/sqrt(-c) + 2*sqrt(c - c/(a*x))","A",0
529,0,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*(a*x-1)/(a*x+1)/x**2,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{x^{2} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x - 1)/(x**2*(a*x + 1)), x)","F",0
530,0,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*(a*x-1)/(a*x+1)/x**3,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{x^{3} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x - 1)/(x**3*(a*x + 1)), x)","F",0
531,0,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*(a*x-1)/(a*x+1)/x**4,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{x^{4} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x - 1)/(x**4*(a*x + 1)), x)","F",0
532,0,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*(a*x-1)/(a*x+1)/x**5,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{x^{5} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*(a*x - 1)/(x**5*(a*x + 1)), x)","F",0
533,-1,0,0,0.000000," ","integrate(x**3*(c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,-1,0,0,0.000000," ","integrate(x**2*(c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,-1,0,0,0.000000," ","integrate(x*(c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate((c-c/a/x)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(c-c/a/x),x)","\frac{c \left(\int a e^{n \operatorname{acoth}{\left(a x \right)}}\, dx + \int \left(- \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{x}\right)\, dx\right)}{a}"," ",0,"c*(Integral(a*exp(n*acoth(a*x)), x) + Integral(-exp(n*acoth(a*x))/x, x))/a","F",0
543,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(c-c/a/x),x)","\frac{a \int \frac{x e^{n \operatorname{acoth}{\left(a x \right)}}}{a x - 1}\, dx}{c}"," ",0,"a*Integral(x*exp(n*acoth(a*x))/(a*x - 1), x)/c","F",0
544,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(c-c/a/x)**2,x)","\frac{a^{2} \int \frac{x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{2} x^{2} - 2 a x + 1}\, dx}{c^{2}}"," ",0,"a**2*Integral(x**2*exp(n*acoth(a*x))/(a**2*x**2 - 2*a*x + 1), x)/c**2","F",0
545,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(c-c/a/x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(c-c/a/x)**(1/2),x)","\int \sqrt{- c \left(-1 + \frac{1}{a x}\right)} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x)))*exp(n*acoth(a*x)), x)","F",0
547,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(c-c/a/x)**(1/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\sqrt{- c \left(-1 + \frac{1}{a x}\right)}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/sqrt(-c*(-1 + 1/(a*x))), x)","F",0
548,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(c-c/a/x)**(3/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/(-c*(-1 + 1/(a*x)))**(3/2), x)","F",0
549,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(c-c/a/x)**p,x)","\int \left(- c \left(-1 + \frac{1}{a x}\right)\right)^{p} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x)))**p*exp(n*acoth(a*x)), x)","F",0
550,0,0,0,0.000000," ","integrate(exp(2*p*acoth(a*x))*(c-c/a/x)**p,x)","\int \left(- c \left(-1 + \frac{1}{a x}\right)\right)^{p} e^{2 p \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x)))**p*exp(2*p*acoth(a*x)), x)","F",0
551,0,0,0,0.000000," ","integrate((c-c/a/x)**p/exp(2*p*acoth(a*x)),x)","\int \left(- c \left(-1 + \frac{1}{a x}\right)\right)^{p} e^{- 2 p \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x)))**p*exp(-2*p*acoth(a*x)), x)","F",0
552,1,272,0,7.830307," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)**p,x)","a \left(\begin{cases} \frac{0^{p} x}{a} + \frac{0^{p} \log{\left(a x - 1 \right)}}{a^{2}} - \frac{a^{- p} c^{p} p x^{2} x^{- p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(2 - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, 2 - p \\ 3 - p \end{matrix}\middle| {a x} \right)}}{\Gamma\left(3 - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{a x}\right| > 1 \\\frac{0^{p} x}{a} + \frac{0^{p} \log{\left(- a x + 1 \right)}}{a^{2}} - \frac{a^{- p} c^{p} p x^{2} x^{- p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(2 - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, 2 - p \\ 3 - p \end{matrix}\middle| {a x} \right)}}{\Gamma\left(3 - p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}\right) + \begin{cases} \frac{0^{p} \log{\left(a x - 1 \right)}}{a} - \frac{a^{- p} c^{p} p x x^{- p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, 1 - p \\ 2 - p \end{matrix}\middle| {a x} \right)}}{\Gamma\left(2 - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{a x}\right| > 1 \\\frac{0^{p} \log{\left(- a x + 1 \right)}}{a} - \frac{a^{- p} c^{p} p x x^{- p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, 1 - p \\ 2 - p \end{matrix}\middle| {a x} \right)}}{\Gamma\left(2 - p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"a*Piecewise((0**p*x/a + 0**p*log(a*x - 1)/a**2 - a**(-p)*c**p*p*x**2*x**(-p)*exp(I*pi*p)*gamma(p)*gamma(2 - p)*hyper((1 - p, 2 - p), (3 - p,), a*x)/(gamma(3 - p)*gamma(p + 1)), Abs(a*x) > 1), (0**p*x/a + 0**p*log(-a*x + 1)/a**2 - a**(-p)*c**p*p*x**2*x**(-p)*exp(I*pi*p)*gamma(p)*gamma(2 - p)*hyper((1 - p, 2 - p), (3 - p,), a*x)/(gamma(3 - p)*gamma(p + 1)), True)) + Piecewise((0**p*log(a*x - 1)/a - a**(-p)*c**p*p*x*x**(-p)*exp(I*pi*p)*gamma(p)*gamma(1 - p)*hyper((1 - p, 1 - p), (2 - p,), a*x)/(gamma(2 - p)*gamma(p + 1)), Abs(a*x) > 1), (0**p*log(-a*x + 1)/a - a**(-p)*c**p*p*x*x**(-p)*exp(I*pi*p)*gamma(p)*gamma(1 - p)*hyper((1 - p, 1 - p), (2 - p,), a*x)/(gamma(2 - p)*gamma(p + 1)), True))","C",0
553,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a/x)**p,x)","\int \frac{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{p}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x)))**p/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
554,0,0,0,0.000000," ","integrate((c-c/a/x)**p*((a*x-1)/(a*x+1))**(1/2),x)","\int \sqrt{\frac{a x - 1}{a x + 1}} \left(- c \left(-1 + \frac{1}{a x}\right)\right)^{p}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*(-c*(-1 + 1/(a*x)))**p, x)","F",0
555,0,0,0,0.000000," ","integrate((c-c/a/x)**p*(a*x-1)/(a*x+1),x)","\int \frac{\left(- c \left(-1 + \frac{1}{a x}\right)\right)^{p} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x)))**p*(a*x - 1)/(a*x + 1), x)","F",0
556,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**4,x)","c^{4} \left(\int \left(- \frac{4 a^{2} x^{2}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{6 a^{4} x^{4}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{4 a^{6} x^{6}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{a^{8} x^{8}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \frac{1}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx\right)"," ",0,"c**4*(Integral(-4*a**2*x**2/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(6*a**4*x**4/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-4*a**6*x**6/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**8*x**8/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(1/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
557,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**3,x)","- c^{3} \left(\int \frac{3 a^{2} x^{2}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{3 a^{4} x^{4}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{a^{6} x^{6}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{1}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)"," ",0,"-c**3*(Integral(3*a**2*x**2/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-3*a**4*x**4/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**6*x**6/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-1/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
558,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**2,x)","c^{2} \left(\int \left(- \frac{2 a^{2} x^{2}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{a^{4} x^{4}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \frac{1}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx\right)"," ",0,"c**2*(Integral(-2*a**2*x**2/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**4*x**4/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(1/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
559,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c),x)","- c \left(\int \frac{a^{2} x^{2}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{1}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)"," ",0,"-c*(Integral(a**2*x**2/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-1/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
560,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c),x)","- \frac{\int \frac{1}{a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c}"," ",0,"-Integral(1/(a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c","F",0
561,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**2,x)","\frac{\int \frac{1}{a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 2 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 2*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**2","F",0
562,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**3,x)","- \frac{\int \frac{1}{a^{6} x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 3 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + 3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{3}}"," ",0,"-Integral(1/(a**6*x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 3*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + 3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**3","F",0
563,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**4,x)","\frac{\int \frac{1}{a^{8} x^{8} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 4 a^{6} x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + 6 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 4 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{4}}"," ",0,"Integral(1/(a**8*x**8*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 4*a**6*x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + 6*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 4*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**4","F",0
564,1,119,0,0.097894," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**5,x)","- \frac{a^{10} c^{5} x^{11}}{11} - \frac{a^{9} c^{5} x^{10}}{5} + \frac{a^{8} c^{5} x^{9}}{3} + a^{7} c^{5} x^{8} - \frac{2 a^{6} c^{5} x^{7}}{7} - 2 a^{5} c^{5} x^{6} - \frac{2 a^{4} c^{5} x^{5}}{5} + 2 a^{3} c^{5} x^{4} + a^{2} c^{5} x^{3} - a c^{5} x^{2} - c^{5} x"," ",0,"-a**10*c**5*x**11/11 - a**9*c**5*x**10/5 + a**8*c**5*x**9/3 + a**7*c**5*x**8 - 2*a**6*c**5*x**7/7 - 2*a**5*c**5*x**6 - 2*a**4*c**5*x**5/5 + 2*a**3*c**5*x**4 + a**2*c**5*x**3 - a*c**5*x**2 - c**5*x","A",0
565,1,87,0,0.087537," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**4,x)","\frac{a^{8} c^{4} x^{9}}{9} + \frac{a^{7} c^{4} x^{8}}{4} - \frac{2 a^{6} c^{4} x^{7}}{7} - a^{5} c^{4} x^{6} + \frac{3 a^{3} c^{4} x^{4}}{2} + \frac{2 a^{2} c^{4} x^{3}}{3} - a c^{4} x^{2} - c^{4} x"," ",0,"a**8*c**4*x**9/9 + a**7*c**4*x**8/4 - 2*a**6*c**4*x**7/7 - a**5*c**4*x**6 + 3*a**3*c**4*x**4/2 + 2*a**2*c**4*x**3/3 - a*c**4*x**2 - c**4*x","A",0
566,1,70,0,0.080544," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**3,x)","- \frac{a^{6} c^{3} x^{7}}{7} - \frac{a^{5} c^{3} x^{6}}{3} + \frac{a^{4} c^{3} x^{5}}{5} + a^{3} c^{3} x^{4} + \frac{a^{2} c^{3} x^{3}}{3} - a c^{3} x^{2} - c^{3} x"," ",0,"-a**6*c**3*x**7/7 - a**5*c**3*x**6/3 + a**4*c**3*x**5/5 + a**3*c**3*x**4 + a**2*c**3*x**3/3 - a*c**3*x**2 - c**3*x","A",0
567,1,36,0,0.070776," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**2,x)","\frac{a^{4} c^{2} x^{5}}{5} + \frac{a^{3} c^{2} x^{4}}{2} - a c^{2} x^{2} - c^{2} x"," ",0,"a**4*c**2*x**5/5 + a**3*c**2*x**4/2 - a*c**2*x**2 - c**2*x","A",0
568,1,20,0,0.058872," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c),x)","- \frac{a^{2} c x^{3}}{3} - a c x^{2} - c x"," ",0,"-a**2*c*x**3/3 - a*c*x**2 - c*x","A",0
569,1,10,0,0.118675," ","integrate(1/(a*x-1)*(a*x+1)/(-a**2*c*x**2+c),x)","\frac{1}{a^{2} c x - a c}"," ",0,"1/(a**2*c*x - a*c)","A",0
570,1,54,0,0.269210," ","integrate(1/(a*x-1)*(a*x+1)/(-a**2*c*x**2+c)**2,x)","\frac{a x - 2}{4 a^{3} c^{2} x^{2} - 8 a^{2} c^{2} x + 4 a c^{2}} + \frac{\frac{\log{\left(x - \frac{1}{a} \right)}}{8} - \frac{\log{\left(x + \frac{1}{a} \right)}}{8}}{a c^{2}}"," ",0,"(a*x - 2)/(4*a**3*c**2*x**2 - 8*a**2*c**2*x + 4*a*c**2) + (log(x - 1/a)/8 - log(x + 1/a)/8)/(a*c**2)","A",0
571,1,85,0,0.403676," ","integrate(1/(a*x-1)*(a*x+1)/(-a**2*c*x**2+c)**3,x)","- \frac{- 3 a^{3} x^{3} + 6 a^{2} x^{2} - a x - 4}{12 a^{5} c^{3} x^{4} - 24 a^{4} c^{3} x^{3} + 24 a^{2} c^{3} x - 12 a c^{3}} - \frac{- \frac{\log{\left(x - \frac{1}{a} \right)}}{8} + \frac{\log{\left(x + \frac{1}{a} \right)}}{8}}{a c^{3}}"," ",0,"-(-3*a**3*x**3 + 6*a**2*x**2 - a*x - 4)/(12*a**5*c**3*x**4 - 24*a**4*c**3*x**3 + 24*a**2*c**3*x - 12*a*c**3) - (-log(x - 1/a)/8 + log(x + 1/a)/8)/(a*c**3)","A",0
572,1,141,0,0.562832," ","integrate(1/(a*x-1)*(a*x+1)/(-a**2*c*x**2+c)**4,x)","\frac{15 a^{5} x^{5} - 30 a^{4} x^{4} - 10 a^{3} x^{3} + 50 a^{2} x^{2} - 17 a x - 16}{64 a^{7} c^{4} x^{6} - 128 a^{6} c^{4} x^{5} - 64 a^{5} c^{4} x^{4} + 256 a^{4} c^{4} x^{3} - 64 a^{3} c^{4} x^{2} - 128 a^{2} c^{4} x + 64 a c^{4}} + \frac{\frac{15 \log{\left(x - \frac{1}{a} \right)}}{128} - \frac{15 \log{\left(x + \frac{1}{a} \right)}}{128}}{a c^{4}}"," ",0,"(15*a**5*x**5 - 30*a**4*x**4 - 10*a**3*x**3 + 50*a**2*x**2 - 17*a*x - 16)/(64*a**7*c**4*x**6 - 128*a**6*c**4*x**5 - 64*a**5*c**4*x**4 + 256*a**4*c**4*x**3 - 64*a**3*c**4*x**2 - 128*a**2*c**4*x + 64*a*c**4) + (15*log(x - 1/a)/128 - 15*log(x + 1/a)/128)/(a*c**4)","A",0
573,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**4,x)","c^{4} \left(\int \left(- \frac{4 a^{2} x^{2}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{6 a^{4} x^{4}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{4 a^{6} x^{6}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{8} x^{8}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \frac{1}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx\right)"," ",0,"c**4*(Integral(-4*a**2*x**2/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(6*a**4*x**4/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-4*a**6*x**6/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**8*x**8/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(1/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))","F",0
574,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**3,x)","- c^{3} \left(\int \frac{3 a^{2} x^{2}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{3 a^{4} x^{4}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{6} x^{6}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{1}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx\right)"," ",0,"-c**3*(Integral(3*a**2*x**2/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-3*a**4*x**4/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**6*x**6/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-1/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))","F",0
575,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**2,x)","c^{2} \left(\int \left(- \frac{2 a^{2} x^{2}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{4} x^{4}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \frac{1}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx\right)"," ",0,"c**2*(Integral(-2*a**2*x**2/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**4*x**4/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(1/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))","F",0
576,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c),x)","- c \left(\int \frac{a^{2} x^{2}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{1}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx\right)"," ",0,"-c*(Integral(a**2*x**2/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-1/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))","F",0
577,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c),x)","- \frac{\int \frac{1}{\frac{a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c}"," ",0,"-Integral(1/(a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c","F",0
578,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**2,x)","\frac{\int \frac{1}{\frac{a^{5} x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{2 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{2 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**5*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 2*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 2*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**2","F",0
579,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**3,x)","- \frac{\int \frac{1}{\frac{a^{7} x^{7} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{a^{6} x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{3 a^{5} x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{3 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{3 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{3}}"," ",0,"-Integral(1/(a**7*x**7*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - a**6*x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 3*a**5*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 3*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 3*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**3","F",0
580,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,1,109,0,0.898984," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a**2*c*x**2+c)**5,x)","- \frac{a^{10} c^{5} x^{11}}{11} - \frac{2 a^{9} c^{5} x^{10}}{5} - \frac{a^{8} c^{5} x^{9}}{3} + a^{7} c^{5} x^{8} + 2 a^{6} c^{5} x^{7} - \frac{14 a^{4} c^{5} x^{5}}{5} - 2 a^{3} c^{5} x^{4} + a^{2} c^{5} x^{3} + 2 a c^{5} x^{2} + c^{5} x"," ",0,"-a**10*c**5*x**11/11 - 2*a**9*c**5*x**10/5 - a**8*c**5*x**9/3 + a**7*c**5*x**8 + 2*a**6*c**5*x**7 - 14*a**4*c**5*x**5/5 - 2*a**3*c**5*x**4 + a**2*c**5*x**3 + 2*a*c**5*x**2 + c**5*x","B",0
582,1,100,0,0.107344," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a**2*c*x**2+c)**4,x)","\frac{a^{8} c^{4} x^{9}}{9} + \frac{a^{7} c^{4} x^{8}}{2} + \frac{4 a^{6} c^{4} x^{7}}{7} - \frac{2 a^{5} c^{4} x^{6}}{3} - 2 a^{4} c^{4} x^{5} - a^{3} c^{4} x^{4} + \frac{4 a^{2} c^{4} x^{3}}{3} + 2 a c^{4} x^{2} + c^{4} x"," ",0,"a**8*c**4*x**9/9 + a**7*c**4*x**8/2 + 4*a**6*c**4*x**7/7 - 2*a**5*c**4*x**6/3 - 2*a**4*c**4*x**5 - a**3*c**4*x**4 + 4*a**2*c**4*x**3/3 + 2*a*c**4*x**2 + c**4*x","B",0
583,1,63,0,0.091855," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a**2*c*x**2+c)**3,x)","- \frac{a^{6} c^{3} x^{7}}{7} - \frac{2 a^{5} c^{3} x^{6}}{3} - a^{4} c^{3} x^{5} + \frac{5 a^{2} c^{3} x^{3}}{3} + 2 a c^{3} x^{2} + c^{3} x"," ",0,"-a**6*c**3*x**7/7 - 2*a**5*c**3*x**6/3 - a**4*c**3*x**5 + 5*a**2*c**3*x**3/3 + 2*a*c**3*x**2 + c**3*x","B",0
584,1,48,0,0.089104," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a**2*c*x**2+c)**2,x)","\frac{a^{4} c^{2} x^{5}}{5} + a^{3} c^{2} x^{4} + 2 a^{2} c^{2} x^{3} + 2 a c^{2} x^{2} + c^{2} x"," ",0,"a**4*c**2*x**5/5 + a**3*c**2*x**4 + 2*a**2*c**2*x**3 + 2*a*c**2*x**2 + c**2*x","B",0
585,1,36,0,0.170804," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a**2*c*x**2+c),x)","- \frac{a^{2} c x^{3}}{3} - 2 a c x^{2} - 7 c x - \frac{8 c \log{\left(a x - 1 \right)}}{a}"," ",0,"-a**2*c*x**3/3 - 2*a*c*x**2 - 7*c*x - 8*c*log(a*x - 1)/a","A",0
586,1,17,0,0.184670," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(-a**2*c*x**2+c),x)","\frac{x}{a^{2} c x^{2} - 2 a c x + c}"," ",0,"x/(a**2*c*x**2 - 2*a*c*x + c)","B",0
587,1,42,0,0.229391," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(-a**2*c*x**2+c)**2,x)","- \frac{1}{3 a^{4} c^{2} x^{3} - 9 a^{3} c^{2} x^{2} + 9 a^{2} c^{2} x - 3 a c^{2}}"," ",0,"-1/(3*a**4*c**2*x**3 - 9*a**3*c**2*x**2 + 9*a**2*c**2*x - 3*a*c**2)","B",0
588,1,99,0,0.500154," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(-a**2*c*x**2+c)**3,x)","- \frac{3 a^{3} x^{3} - 12 a^{2} x^{2} + 19 a x - 16}{48 a^{5} c^{3} x^{4} - 192 a^{4} c^{3} x^{3} + 288 a^{3} c^{3} x^{2} - 192 a^{2} c^{3} x + 48 a c^{3}} - \frac{\frac{\log{\left(x - \frac{1}{a} \right)}}{32} - \frac{\log{\left(x + \frac{1}{a} \right)}}{32}}{a c^{3}}"," ",0,"-(3*a**3*x**3 - 12*a**2*x**2 + 19*a*x - 16)/(48*a**5*c**3*x**4 - 192*a**4*c**3*x**3 + 288*a**3*c**3*x**2 - 192*a**2*c**3*x + 48*a*c**3) - (log(x - 1/a)/32 - log(x + 1/a)/32)/(a*c**3)","A",0
589,1,129,0,0.595580," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(-a**2*c*x**2+c)**4,x)","\frac{- 15 a^{5} x^{5} + 60 a^{4} x^{4} - 80 a^{3} x^{3} + 20 a^{2} x^{2} + 47 a x - 48}{160 a^{7} c^{4} x^{6} - 640 a^{6} c^{4} x^{5} + 800 a^{5} c^{4} x^{4} - 800 a^{3} c^{4} x^{2} + 640 a^{2} c^{4} x - 160 a c^{4}} + \frac{- \frac{3 \log{\left(x - \frac{1}{a} \right)}}{64} + \frac{3 \log{\left(x + \frac{1}{a} \right)}}{64}}{a c^{4}}"," ",0,"(-15*a**5*x**5 + 60*a**4*x**4 - 80*a**3*x**3 + 20*a**2*x**2 + 47*a*x - 48)/(160*a**7*c**4*x**6 - 640*a**6*c**4*x**5 + 800*a**5*c**4*x**4 - 800*a**3*c**4*x**2 + 640*a**2*c**4*x - 160*a*c**4) + (-3*log(x - 1/a)/64 + 3*log(x + 1/a)/64)/(a*c**4)","A",0
590,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**4*((a*x-1)/(a*x+1))**(1/2),x)","c^{4} \left(\int \left(- 4 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\right)\, dx + \int 6 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- 4 a^{6} x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\right)\, dx + \int a^{8} x^{8} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx\right)"," ",0,"c**4*(Integral(-4*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(6*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-4*a**6*x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**8*x**8*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
591,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**3*((a*x-1)/(a*x+1))**(1/2),x)","- c^{3} \left(\int 3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- 3 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\right)\, dx + \int a^{6} x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\right)\, dx\right)"," ",0,"-c**3*(Integral(3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-3*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**6*x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
592,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**2*((a*x-1)/(a*x+1))**(1/2),x)","c^{2} \left(\int \left(- 2 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\right)\, dx + \int a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx\right)"," ",0,"c**2*(Integral(-2*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
593,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)*((a*x-1)/(a*x+1))**(1/2),x)","- c \left(\int a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\right)\, dx\right)"," ",0,"-c*(Integral(a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x))","F",0
594,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c),x)","- \frac{\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{2} x^{2} - 1}\, dx}{c}"," ",0,"-Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**2*x**2 - 1), x)/c","F",0
595,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**2,x)","\frac{\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{4} x^{4} - 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**4*x**4 - 2*a**2*x**2 + 1), x)/c**2","F",0
596,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**3,x)","- \frac{\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx}{c^{3}}"," ",0,"-Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)/c**3","F",0
597,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,1,87,0,0.306645," ","integrate((-a**2*c*x**2+c)**4*(a*x-1)/(a*x+1),x)","\frac{a^{8} c^{4} x^{9}}{9} - \frac{a^{7} c^{4} x^{8}}{4} - \frac{2 a^{6} c^{4} x^{7}}{7} + a^{5} c^{4} x^{6} - \frac{3 a^{3} c^{4} x^{4}}{2} + \frac{2 a^{2} c^{4} x^{3}}{3} + a c^{4} x^{2} - c^{4} x"," ",0,"a**8*c**4*x**9/9 - a**7*c**4*x**8/4 - 2*a**6*c**4*x**7/7 + a**5*c**4*x**6 - 3*a**3*c**4*x**4/2 + 2*a**2*c**4*x**3/3 + a*c**4*x**2 - c**4*x","A",0
599,1,70,0,0.088852," ","integrate((-a**2*c*x**2+c)**3*(a*x-1)/(a*x+1),x)","- \frac{a^{6} c^{3} x^{7}}{7} + \frac{a^{5} c^{3} x^{6}}{3} + \frac{a^{4} c^{3} x^{5}}{5} - a^{3} c^{3} x^{4} + \frac{a^{2} c^{3} x^{3}}{3} + a c^{3} x^{2} - c^{3} x"," ",0,"-a**6*c**3*x**7/7 + a**5*c**3*x**6/3 + a**4*c**3*x**5/5 - a**3*c**3*x**4 + a**2*c**3*x**3/3 + a*c**3*x**2 - c**3*x","A",0
600,1,36,0,0.077837," ","integrate((-a**2*c*x**2+c)**2*(a*x-1)/(a*x+1),x)","\frac{a^{4} c^{2} x^{5}}{5} - \frac{a^{3} c^{2} x^{4}}{2} + a c^{2} x^{2} - c^{2} x"," ",0,"a**4*c**2*x**5/5 - a**3*c**2*x**4/2 + a*c**2*x**2 - c**2*x","A",0
601,1,19,0,0.067725," ","integrate((-a**2*c*x**2+c)*(a*x-1)/(a*x+1),x)","- \frac{a^{2} c x^{3}}{3} + a c x^{2} - c x"," ",0,"-a**2*c*x**3/3 + a*c*x**2 - c*x","A",0
602,1,10,0,0.124470," ","integrate((a*x-1)/(a*x+1)/(-a**2*c*x**2+c),x)","\frac{1}{a^{2} c x + a c}"," ",0,"1/(a**2*c*x + a*c)","A",0
603,1,54,0,0.280180," ","integrate((a*x-1)/(a*x+1)/(-a**2*c*x**2+c)**2,x)","\frac{a x + 2}{4 a^{3} c^{2} x^{2} + 8 a^{2} c^{2} x + 4 a c^{2}} + \frac{\frac{\log{\left(x - \frac{1}{a} \right)}}{8} - \frac{\log{\left(x + \frac{1}{a} \right)}}{8}}{a c^{2}}"," ",0,"(a*x + 2)/(4*a**3*c**2*x**2 + 8*a**2*c**2*x + 4*a*c**2) + (log(x - 1/a)/8 - log(x + 1/a)/8)/(a*c**2)","A",0
604,1,85,0,0.418108," ","integrate((a*x-1)/(a*x+1)/(-a**2*c*x**2+c)**3,x)","- \frac{- 3 a^{3} x^{3} - 6 a^{2} x^{2} - a x + 4}{12 a^{5} c^{3} x^{4} + 24 a^{4} c^{3} x^{3} - 24 a^{2} c^{3} x - 12 a c^{3}} - \frac{- \frac{\log{\left(x - \frac{1}{a} \right)}}{8} + \frac{\log{\left(x + \frac{1}{a} \right)}}{8}}{a c^{3}}"," ",0,"-(-3*a**3*x**3 - 6*a**2*x**2 - a*x + 4)/(12*a**5*c**3*x**4 + 24*a**4*c**3*x**3 - 24*a**2*c**3*x - 12*a*c**3) - (-log(x - 1/a)/8 + log(x + 1/a)/8)/(a*c**3)","A",0
605,1,141,0,0.595022," ","integrate((a*x-1)/(a*x+1)/(-a**2*c*x**2+c)**4,x)","\frac{15 a^{5} x^{5} + 30 a^{4} x^{4} - 10 a^{3} x^{3} - 50 a^{2} x^{2} - 17 a x + 16}{64 a^{7} c^{4} x^{6} + 128 a^{6} c^{4} x^{5} - 64 a^{5} c^{4} x^{4} - 256 a^{4} c^{4} x^{3} - 64 a^{3} c^{4} x^{2} + 128 a^{2} c^{4} x + 64 a c^{4}} + \frac{\frac{15 \log{\left(x - \frac{1}{a} \right)}}{128} - \frac{15 \log{\left(x + \frac{1}{a} \right)}}{128}}{a c^{4}}"," ",0,"(15*a**5*x**5 + 30*a**4*x**4 - 10*a**3*x**3 - 50*a**2*x**2 - 17*a*x + 16)/(64*a**7*c**4*x**6 + 128*a**6*c**4*x**5 - 64*a**5*c**4*x**4 - 256*a**4*c**4*x**3 - 64*a**3*c**4*x**2 + 128*a**2*c**4*x + 64*a*c**4) + (15*log(x - 1/a)/128 - 15*log(x + 1/a)/128)/(a*c**4)","A",0
606,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**4*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**3*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
608,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**2*((a*x-1)/(a*x+1))**(3/2),x)","c^{2} \left(\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx + \int \frac{2 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx + \int \left(- \frac{2 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \left(- \frac{a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{5} x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)"," ",0,"c**2*(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(2*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(-2*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(-a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**5*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))","F",0
609,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)*((a*x-1)/(a*x+1))**(3/2),x)","- c \left(\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx + \int \left(- \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \left(- \frac{a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)"," ",0,"-c*(Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(-a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(-a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))","F",0
610,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c),x)","- \frac{\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{3} x^{3} + a^{2} x^{2} - a x - 1}\right)\, dx + \int \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{3} x^{3} + a^{2} x^{2} - a x - 1}\, dx}{c}"," ",0,"-(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**3*x**3 + a**2*x**2 - a*x - 1), x) + Integral(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**3*x**3 + a**2*x**2 - a*x - 1), x))/c","F",0
611,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
619,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(1/(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(a*x - 1)*(a*x + 1))), x)","F",0
620,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,1,1341,0,36.346756," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(9/2),x)","a^{8} c^{4} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{11}}{10 \sqrt{a^{2} x^{2} - 1}} - \frac{9 i \sqrt{c} x^{9}}{80 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x^{7}}{480 a^{2} \sqrt{a^{2} x^{2} - 1}} - \frac{7 i \sqrt{c} x^{5}}{1920 a^{4} \sqrt{a^{2} x^{2} - 1}} - \frac{7 i \sqrt{c} x^{3}}{768 a^{6} \sqrt{a^{2} x^{2} - 1}} + \frac{7 i \sqrt{c} x}{256 a^{8} \sqrt{a^{2} x^{2} - 1}} - \frac{7 i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{256 a^{9}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\- \frac{a^{2} \sqrt{c} x^{11}}{10 \sqrt{- a^{2} x^{2} + 1}} + \frac{9 \sqrt{c} x^{9}}{80 \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} x^{7}}{480 a^{2} \sqrt{- a^{2} x^{2} + 1}} + \frac{7 \sqrt{c} x^{5}}{1920 a^{4} \sqrt{- a^{2} x^{2} + 1}} + \frac{7 \sqrt{c} x^{3}}{768 a^{6} \sqrt{- a^{2} x^{2} + 1}} - \frac{7 \sqrt{c} x}{256 a^{8} \sqrt{- a^{2} x^{2} + 1}} + \frac{7 \sqrt{c} \operatorname{asin}{\left(a x \right)}}{256 a^{9}} & \text{otherwise} \end{cases}\right) + 2 a^{7} c^{4} \left(\begin{cases} \frac{x^{8} \sqrt{- a^{2} c x^{2} + c}}{9} - \frac{x^{6} \sqrt{- a^{2} c x^{2} + c}}{63 a^{2}} - \frac{2 x^{4} \sqrt{- a^{2} c x^{2} + c}}{105 a^{4}} - \frac{8 x^{2} \sqrt{- a^{2} c x^{2} + c}}{315 a^{6}} - \frac{16 \sqrt{- a^{2} c x^{2} + c}}{315 a^{8}} & \text{for}\: a \neq 0 \\\frac{\sqrt{c} x^{8}}{8} & \text{otherwise} \end{cases}\right) - 2 a^{6} c^{4} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{9}}{8 \sqrt{a^{2} x^{2} - 1}} - \frac{7 i \sqrt{c} x^{7}}{48 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x^{5}}{192 a^{2} \sqrt{a^{2} x^{2} - 1}} - \frac{5 i \sqrt{c} x^{3}}{384 a^{4} \sqrt{a^{2} x^{2} - 1}} + \frac{5 i \sqrt{c} x}{128 a^{6} \sqrt{a^{2} x^{2} - 1}} - \frac{5 i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{128 a^{7}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\- \frac{a^{2} \sqrt{c} x^{9}}{8 \sqrt{- a^{2} x^{2} + 1}} + \frac{7 \sqrt{c} x^{7}}{48 \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} x^{5}}{192 a^{2} \sqrt{- a^{2} x^{2} + 1}} + \frac{5 \sqrt{c} x^{3}}{384 a^{4} \sqrt{- a^{2} x^{2} + 1}} - \frac{5 \sqrt{c} x}{128 a^{6} \sqrt{- a^{2} x^{2} + 1}} + \frac{5 \sqrt{c} \operatorname{asin}{\left(a x \right)}}{128 a^{7}} & \text{otherwise} \end{cases}\right) - 6 a^{5} c^{4} \left(\begin{cases} \frac{x^{6} \sqrt{- a^{2} c x^{2} + c}}{7} - \frac{x^{4} \sqrt{- a^{2} c x^{2} + c}}{35 a^{2}} - \frac{4 x^{2} \sqrt{- a^{2} c x^{2} + c}}{105 a^{4}} - \frac{8 \sqrt{- a^{2} c x^{2} + c}}{105 a^{6}} & \text{for}\: a \neq 0 \\\frac{\sqrt{c} x^{6}}{6} & \text{otherwise} \end{cases}\right) + 6 a^{3} c^{4} \left(\begin{cases} \frac{x^{4} \sqrt{- a^{2} c x^{2} + c}}{5} - \frac{x^{2} \sqrt{- a^{2} c x^{2} + c}}{15 a^{2}} - \frac{2 \sqrt{- a^{2} c x^{2} + c}}{15 a^{4}} & \text{for}\: a \neq 0 \\\frac{\sqrt{c} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 2 a^{2} c^{4} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{5}}{4 \sqrt{a^{2} x^{2} - 1}} - \frac{3 i \sqrt{c} x^{3}}{8 \sqrt{a^{2} x^{2} - 1}} + \frac{i \sqrt{c} x}{8 a^{2} \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{8 a^{3}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\- \frac{a^{2} \sqrt{c} x^{5}}{4 \sqrt{- a^{2} x^{2} + 1}} + \frac{3 \sqrt{c} x^{3}}{8 \sqrt{- a^{2} x^{2} + 1}} - \frac{\sqrt{c} x}{8 a^{2} \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{8 a^{3}} & \text{otherwise} \end{cases}\right) - 2 a c^{4} \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{\sqrt{c} x^{2}}{2} & \text{for}\: a^{2} = 0 \\- \frac{\left(- a^{2} c x^{2} + c\right)^{\frac{3}{2}}}{3 a^{2} c} & \text{otherwise} \end{cases}\right) - c^{4} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{3}}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{2 a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{\sqrt{c} x \sqrt{- a^{2} x^{2} + 1}}{2} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{2 a} & \text{otherwise} \end{cases}\right)"," ",0,"a**8*c**4*Piecewise((I*a**2*sqrt(c)*x**11/(10*sqrt(a**2*x**2 - 1)) - 9*I*sqrt(c)*x**9/(80*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x**7/(480*a**2*sqrt(a**2*x**2 - 1)) - 7*I*sqrt(c)*x**5/(1920*a**4*sqrt(a**2*x**2 - 1)) - 7*I*sqrt(c)*x**3/(768*a**6*sqrt(a**2*x**2 - 1)) + 7*I*sqrt(c)*x/(256*a**8*sqrt(a**2*x**2 - 1)) - 7*I*sqrt(c)*acosh(a*x)/(256*a**9), Abs(a**2*x**2) > 1), (-a**2*sqrt(c)*x**11/(10*sqrt(-a**2*x**2 + 1)) + 9*sqrt(c)*x**9/(80*sqrt(-a**2*x**2 + 1)) + sqrt(c)*x**7/(480*a**2*sqrt(-a**2*x**2 + 1)) + 7*sqrt(c)*x**5/(1920*a**4*sqrt(-a**2*x**2 + 1)) + 7*sqrt(c)*x**3/(768*a**6*sqrt(-a**2*x**2 + 1)) - 7*sqrt(c)*x/(256*a**8*sqrt(-a**2*x**2 + 1)) + 7*sqrt(c)*asin(a*x)/(256*a**9), True)) + 2*a**7*c**4*Piecewise((x**8*sqrt(-a**2*c*x**2 + c)/9 - x**6*sqrt(-a**2*c*x**2 + c)/(63*a**2) - 2*x**4*sqrt(-a**2*c*x**2 + c)/(105*a**4) - 8*x**2*sqrt(-a**2*c*x**2 + c)/(315*a**6) - 16*sqrt(-a**2*c*x**2 + c)/(315*a**8), Ne(a, 0)), (sqrt(c)*x**8/8, True)) - 2*a**6*c**4*Piecewise((I*a**2*sqrt(c)*x**9/(8*sqrt(a**2*x**2 - 1)) - 7*I*sqrt(c)*x**7/(48*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x**5/(192*a**2*sqrt(a**2*x**2 - 1)) - 5*I*sqrt(c)*x**3/(384*a**4*sqrt(a**2*x**2 - 1)) + 5*I*sqrt(c)*x/(128*a**6*sqrt(a**2*x**2 - 1)) - 5*I*sqrt(c)*acosh(a*x)/(128*a**7), Abs(a**2*x**2) > 1), (-a**2*sqrt(c)*x**9/(8*sqrt(-a**2*x**2 + 1)) + 7*sqrt(c)*x**7/(48*sqrt(-a**2*x**2 + 1)) + sqrt(c)*x**5/(192*a**2*sqrt(-a**2*x**2 + 1)) + 5*sqrt(c)*x**3/(384*a**4*sqrt(-a**2*x**2 + 1)) - 5*sqrt(c)*x/(128*a**6*sqrt(-a**2*x**2 + 1)) + 5*sqrt(c)*asin(a*x)/(128*a**7), True)) - 6*a**5*c**4*Piecewise((x**6*sqrt(-a**2*c*x**2 + c)/7 - x**4*sqrt(-a**2*c*x**2 + c)/(35*a**2) - 4*x**2*sqrt(-a**2*c*x**2 + c)/(105*a**4) - 8*sqrt(-a**2*c*x**2 + c)/(105*a**6), Ne(a, 0)), (sqrt(c)*x**6/6, True)) + 6*a**3*c**4*Piecewise((x**4*sqrt(-a**2*c*x**2 + c)/5 - x**2*sqrt(-a**2*c*x**2 + c)/(15*a**2) - 2*sqrt(-a**2*c*x**2 + c)/(15*a**4), Ne(a, 0)), (sqrt(c)*x**4/4, True)) + 2*a**2*c**4*Piecewise((I*a**2*sqrt(c)*x**5/(4*sqrt(a**2*x**2 - 1)) - 3*I*sqrt(c)*x**3/(8*sqrt(a**2*x**2 - 1)) + I*sqrt(c)*x/(8*a**2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(8*a**3), Abs(a**2*x**2) > 1), (-a**2*sqrt(c)*x**5/(4*sqrt(-a**2*x**2 + 1)) + 3*sqrt(c)*x**3/(8*sqrt(-a**2*x**2 + 1)) - sqrt(c)*x/(8*a**2*sqrt(-a**2*x**2 + 1)) + sqrt(c)*asin(a*x)/(8*a**3), True)) - 2*a*c**4*Piecewise((0, Eq(c, 0)), (sqrt(c)*x**2/2, Eq(a**2, 0)), (-(-a**2*c*x**2 + c)**(3/2)/(3*a**2*c), True)) - c**4*Piecewise((I*a**2*sqrt(c)*x**3/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(2*a), Abs(a**2*x**2) > 1), (sqrt(c)*x*sqrt(-a**2*x**2 + 1)/2 + sqrt(c)*asin(a*x)/(2*a), True))","C",0
624,1,1091,0,21.832576," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(7/2),x)","- a^{6} c^{3} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{9}}{8 \sqrt{a^{2} x^{2} - 1}} - \frac{7 i \sqrt{c} x^{7}}{48 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x^{5}}{192 a^{2} \sqrt{a^{2} x^{2} - 1}} - \frac{5 i \sqrt{c} x^{3}}{384 a^{4} \sqrt{a^{2} x^{2} - 1}} + \frac{5 i \sqrt{c} x}{128 a^{6} \sqrt{a^{2} x^{2} - 1}} - \frac{5 i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{128 a^{7}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\- \frac{a^{2} \sqrt{c} x^{9}}{8 \sqrt{- a^{2} x^{2} + 1}} + \frac{7 \sqrt{c} x^{7}}{48 \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} x^{5}}{192 a^{2} \sqrt{- a^{2} x^{2} + 1}} + \frac{5 \sqrt{c} x^{3}}{384 a^{4} \sqrt{- a^{2} x^{2} + 1}} - \frac{5 \sqrt{c} x}{128 a^{6} \sqrt{- a^{2} x^{2} + 1}} + \frac{5 \sqrt{c} \operatorname{asin}{\left(a x \right)}}{128 a^{7}} & \text{otherwise} \end{cases}\right) - 2 a^{5} c^{3} \left(\begin{cases} \frac{x^{6} \sqrt{- a^{2} c x^{2} + c}}{7} - \frac{x^{4} \sqrt{- a^{2} c x^{2} + c}}{35 a^{2}} - \frac{4 x^{2} \sqrt{- a^{2} c x^{2} + c}}{105 a^{4}} - \frac{8 \sqrt{- a^{2} c x^{2} + c}}{105 a^{6}} & \text{for}\: a \neq 0 \\\frac{\sqrt{c} x^{6}}{6} & \text{otherwise} \end{cases}\right) + a^{4} c^{3} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{7}}{6 \sqrt{a^{2} x^{2} - 1}} - \frac{5 i \sqrt{c} x^{5}}{24 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x^{3}}{48 a^{2} \sqrt{a^{2} x^{2} - 1}} + \frac{i \sqrt{c} x}{16 a^{4} \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{16 a^{5}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\- \frac{a^{2} \sqrt{c} x^{7}}{6 \sqrt{- a^{2} x^{2} + 1}} + \frac{5 \sqrt{c} x^{5}}{24 \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} x^{3}}{48 a^{2} \sqrt{- a^{2} x^{2} + 1}} - \frac{\sqrt{c} x}{16 a^{4} \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{16 a^{5}} & \text{otherwise} \end{cases}\right) + 4 a^{3} c^{3} \left(\begin{cases} \frac{x^{4} \sqrt{- a^{2} c x^{2} + c}}{5} - \frac{x^{2} \sqrt{- a^{2} c x^{2} + c}}{15 a^{2}} - \frac{2 \sqrt{- a^{2} c x^{2} + c}}{15 a^{4}} & \text{for}\: a \neq 0 \\\frac{\sqrt{c} x^{4}}{4} & \text{otherwise} \end{cases}\right) + a^{2} c^{3} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{5}}{4 \sqrt{a^{2} x^{2} - 1}} - \frac{3 i \sqrt{c} x^{3}}{8 \sqrt{a^{2} x^{2} - 1}} + \frac{i \sqrt{c} x}{8 a^{2} \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{8 a^{3}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\- \frac{a^{2} \sqrt{c} x^{5}}{4 \sqrt{- a^{2} x^{2} + 1}} + \frac{3 \sqrt{c} x^{3}}{8 \sqrt{- a^{2} x^{2} + 1}} - \frac{\sqrt{c} x}{8 a^{2} \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{8 a^{3}} & \text{otherwise} \end{cases}\right) - 2 a c^{3} \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{\sqrt{c} x^{2}}{2} & \text{for}\: a^{2} = 0 \\- \frac{\left(- a^{2} c x^{2} + c\right)^{\frac{3}{2}}}{3 a^{2} c} & \text{otherwise} \end{cases}\right) - c^{3} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{3}}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{2 a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{\sqrt{c} x \sqrt{- a^{2} x^{2} + 1}}{2} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{2 a} & \text{otherwise} \end{cases}\right)"," ",0,"-a**6*c**3*Piecewise((I*a**2*sqrt(c)*x**9/(8*sqrt(a**2*x**2 - 1)) - 7*I*sqrt(c)*x**7/(48*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x**5/(192*a**2*sqrt(a**2*x**2 - 1)) - 5*I*sqrt(c)*x**3/(384*a**4*sqrt(a**2*x**2 - 1)) + 5*I*sqrt(c)*x/(128*a**6*sqrt(a**2*x**2 - 1)) - 5*I*sqrt(c)*acosh(a*x)/(128*a**7), Abs(a**2*x**2) > 1), (-a**2*sqrt(c)*x**9/(8*sqrt(-a**2*x**2 + 1)) + 7*sqrt(c)*x**7/(48*sqrt(-a**2*x**2 + 1)) + sqrt(c)*x**5/(192*a**2*sqrt(-a**2*x**2 + 1)) + 5*sqrt(c)*x**3/(384*a**4*sqrt(-a**2*x**2 + 1)) - 5*sqrt(c)*x/(128*a**6*sqrt(-a**2*x**2 + 1)) + 5*sqrt(c)*asin(a*x)/(128*a**7), True)) - 2*a**5*c**3*Piecewise((x**6*sqrt(-a**2*c*x**2 + c)/7 - x**4*sqrt(-a**2*c*x**2 + c)/(35*a**2) - 4*x**2*sqrt(-a**2*c*x**2 + c)/(105*a**4) - 8*sqrt(-a**2*c*x**2 + c)/(105*a**6), Ne(a, 0)), (sqrt(c)*x**6/6, True)) + a**4*c**3*Piecewise((I*a**2*sqrt(c)*x**7/(6*sqrt(a**2*x**2 - 1)) - 5*I*sqrt(c)*x**5/(24*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x**3/(48*a**2*sqrt(a**2*x**2 - 1)) + I*sqrt(c)*x/(16*a**4*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(16*a**5), Abs(a**2*x**2) > 1), (-a**2*sqrt(c)*x**7/(6*sqrt(-a**2*x**2 + 1)) + 5*sqrt(c)*x**5/(24*sqrt(-a**2*x**2 + 1)) + sqrt(c)*x**3/(48*a**2*sqrt(-a**2*x**2 + 1)) - sqrt(c)*x/(16*a**4*sqrt(-a**2*x**2 + 1)) + sqrt(c)*asin(a*x)/(16*a**5), True)) + 4*a**3*c**3*Piecewise((x**4*sqrt(-a**2*c*x**2 + c)/5 - x**2*sqrt(-a**2*c*x**2 + c)/(15*a**2) - 2*sqrt(-a**2*c*x**2 + c)/(15*a**4), Ne(a, 0)), (sqrt(c)*x**4/4, True)) + a**2*c**3*Piecewise((I*a**2*sqrt(c)*x**5/(4*sqrt(a**2*x**2 - 1)) - 3*I*sqrt(c)*x**3/(8*sqrt(a**2*x**2 - 1)) + I*sqrt(c)*x/(8*a**2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(8*a**3), Abs(a**2*x**2) > 1), (-a**2*sqrt(c)*x**5/(4*sqrt(-a**2*x**2 + 1)) + 3*sqrt(c)*x**3/(8*sqrt(-a**2*x**2 + 1)) - sqrt(c)*x/(8*a**2*sqrt(-a**2*x**2 + 1)) + sqrt(c)*asin(a*x)/(8*a**3), True)) - 2*a*c**3*Piecewise((0, Eq(c, 0)), (sqrt(c)*x**2/2, Eq(a**2, 0)), (-(-a**2*c*x**2 + c)**(3/2)/(3*a**2*c), True)) - c**3*Piecewise((I*a**2*sqrt(c)*x**3/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(2*a), Abs(a**2*x**2) > 1), (sqrt(c)*x*sqrt(-a**2*x**2 + 1)/2 + sqrt(c)*asin(a*x)/(2*a), True))","C",0
625,1,478,0,12.015771," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(5/2),x)","a^{4} c^{2} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{7}}{6 \sqrt{a^{2} x^{2} - 1}} - \frac{5 i \sqrt{c} x^{5}}{24 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x^{3}}{48 a^{2} \sqrt{a^{2} x^{2} - 1}} + \frac{i \sqrt{c} x}{16 a^{4} \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{16 a^{5}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\- \frac{a^{2} \sqrt{c} x^{7}}{6 \sqrt{- a^{2} x^{2} + 1}} + \frac{5 \sqrt{c} x^{5}}{24 \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} x^{3}}{48 a^{2} \sqrt{- a^{2} x^{2} + 1}} - \frac{\sqrt{c} x}{16 a^{4} \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{16 a^{5}} & \text{otherwise} \end{cases}\right) + 2 a^{3} c^{2} \left(\begin{cases} \frac{x^{4} \sqrt{- a^{2} c x^{2} + c}}{5} - \frac{x^{2} \sqrt{- a^{2} c x^{2} + c}}{15 a^{2}} - \frac{2 \sqrt{- a^{2} c x^{2} + c}}{15 a^{4}} & \text{for}\: a \neq 0 \\\frac{\sqrt{c} x^{4}}{4} & \text{otherwise} \end{cases}\right) - 2 a c^{2} \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{\sqrt{c} x^{2}}{2} & \text{for}\: a^{2} = 0 \\- \frac{\left(- a^{2} c x^{2} + c\right)^{\frac{3}{2}}}{3 a^{2} c} & \text{otherwise} \end{cases}\right) - c^{2} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{3}}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{2 a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{\sqrt{c} x \sqrt{- a^{2} x^{2} + 1}}{2} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{2 a} & \text{otherwise} \end{cases}\right)"," ",0,"a**4*c**2*Piecewise((I*a**2*sqrt(c)*x**7/(6*sqrt(a**2*x**2 - 1)) - 5*I*sqrt(c)*x**5/(24*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x**3/(48*a**2*sqrt(a**2*x**2 - 1)) + I*sqrt(c)*x/(16*a**4*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(16*a**5), Abs(a**2*x**2) > 1), (-a**2*sqrt(c)*x**7/(6*sqrt(-a**2*x**2 + 1)) + 5*sqrt(c)*x**5/(24*sqrt(-a**2*x**2 + 1)) + sqrt(c)*x**3/(48*a**2*sqrt(-a**2*x**2 + 1)) - sqrt(c)*x/(16*a**4*sqrt(-a**2*x**2 + 1)) + sqrt(c)*asin(a*x)/(16*a**5), True)) + 2*a**3*c**2*Piecewise((x**4*sqrt(-a**2*c*x**2 + c)/5 - x**2*sqrt(-a**2*c*x**2 + c)/(15*a**2) - 2*sqrt(-a**2*c*x**2 + c)/(15*a**4), Ne(a, 0)), (sqrt(c)*x**4/4, True)) - 2*a*c**2*Piecewise((0, Eq(c, 0)), (sqrt(c)*x**2/2, Eq(a**2, 0)), (-(-a**2*c*x**2 + c)**(3/2)/(3*a**2*c), True)) - c**2*Piecewise((I*a**2*sqrt(c)*x**3/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(2*a), Abs(a**2*x**2) > 1), (sqrt(c)*x*sqrt(-a**2*x**2 + 1)/2 + sqrt(c)*asin(a*x)/(2*a), True))","C",0
626,1,342,0,7.799863," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(3/2),x)","- a^{2} c \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{5}}{4 \sqrt{a^{2} x^{2} - 1}} - \frac{3 i \sqrt{c} x^{3}}{8 \sqrt{a^{2} x^{2} - 1}} + \frac{i \sqrt{c} x}{8 a^{2} \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{8 a^{3}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\- \frac{a^{2} \sqrt{c} x^{5}}{4 \sqrt{- a^{2} x^{2} + 1}} + \frac{3 \sqrt{c} x^{3}}{8 \sqrt{- a^{2} x^{2} + 1}} - \frac{\sqrt{c} x}{8 a^{2} \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{8 a^{3}} & \text{otherwise} \end{cases}\right) - 2 a c \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{\sqrt{c} x^{2}}{2} & \text{for}\: a^{2} = 0 \\- \frac{\left(- a^{2} c x^{2} + c\right)^{\frac{3}{2}}}{3 a^{2} c} & \text{otherwise} \end{cases}\right) - c \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{3}}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{2 a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{\sqrt{c} x \sqrt{- a^{2} x^{2} + 1}}{2} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{2 a} & \text{otherwise} \end{cases}\right)"," ",0,"-a**2*c*Piecewise((I*a**2*sqrt(c)*x**5/(4*sqrt(a**2*x**2 - 1)) - 3*I*sqrt(c)*x**3/(8*sqrt(a**2*x**2 - 1)) + I*sqrt(c)*x/(8*a**2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(8*a**3), Abs(a**2*x**2) > 1), (-a**2*sqrt(c)*x**5/(4*sqrt(-a**2*x**2 + 1)) + 3*sqrt(c)*x**3/(8*sqrt(-a**2*x**2 + 1)) - sqrt(c)*x/(8*a**2*sqrt(-a**2*x**2 + 1)) + sqrt(c)*asin(a*x)/(8*a**3), True)) - 2*a*c*Piecewise((0, Eq(c, 0)), (sqrt(c)*x**2/2, Eq(a**2, 0)), (-(-a**2*c*x**2 + c)**(3/2)/(3*a**2*c), True)) - c*Piecewise((I*a**2*sqrt(c)*x**3/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(2*a), Abs(a**2*x**2) > 1), (sqrt(c)*x*sqrt(-a**2*x**2 + 1)/2 + sqrt(c)*asin(a*x)/(2*a), True))","C",0
627,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(a*x - 1), x)","F",0
628,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(-a**2*c*x**2+c)**(1/2),x)","\int \frac{a x + 1}{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)), x)","F",0
629,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(-a**2*c*x**2+c)**(3/2),x)","\int \frac{a x + 1}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/((-c*(a*x - 1)*(a*x + 1))**(3/2)*(a*x - 1)), x)","F",0
630,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(-a**2*c*x**2+c)**(5/2),x)","\int \frac{a x + 1}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/((-c*(a*x - 1)*(a*x + 1))**(5/2)*(a*x - 1)), x)","F",0
631,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(-a**2*c*x**2+c)**(7/2),x)","\int \frac{a x + 1}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{7}{2}} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/((-c*(a*x - 1)*(a*x + 1))**(7/2)*(a*x - 1)), x)","F",0
632,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(-a**2*c*x**2+c)**(9/2),x)","\int \frac{a x + 1}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{9}{2}} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/((-c*(a*x - 1)*(a*x + 1))**(9/2)*(a*x - 1)), x)","F",0
633,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
638,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(1/(((a*x - 1)/(a*x + 1))**(3/2)*sqrt(-c*(a*x - 1)*(a*x + 1))), x)","F",0
639,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
640,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
642,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(9/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(7/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(5/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
645,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(3/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
646,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\int \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(a*x - 1)*(a*x + 1)), x)","F",0
647,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/sqrt(-c*(a*x - 1)*(a*x + 1)), x)","F",0
648,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**(3/2),x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/(-c*(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
649,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
650,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
651,1,478,0,10.879100," ","integrate((-a**2*c*x**2+c)**(5/2)*(a*x-1)/(a*x+1),x)","a^{4} c^{2} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{7}}{6 \sqrt{a^{2} x^{2} - 1}} - \frac{5 i \sqrt{c} x^{5}}{24 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x^{3}}{48 a^{2} \sqrt{a^{2} x^{2} - 1}} + \frac{i \sqrt{c} x}{16 a^{4} \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{16 a^{5}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\- \frac{a^{2} \sqrt{c} x^{7}}{6 \sqrt{- a^{2} x^{2} + 1}} + \frac{5 \sqrt{c} x^{5}}{24 \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} x^{3}}{48 a^{2} \sqrt{- a^{2} x^{2} + 1}} - \frac{\sqrt{c} x}{16 a^{4} \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{16 a^{5}} & \text{otherwise} \end{cases}\right) - 2 a^{3} c^{2} \left(\begin{cases} \frac{x^{4} \sqrt{- a^{2} c x^{2} + c}}{5} - \frac{x^{2} \sqrt{- a^{2} c x^{2} + c}}{15 a^{2}} - \frac{2 \sqrt{- a^{2} c x^{2} + c}}{15 a^{4}} & \text{for}\: a \neq 0 \\\frac{\sqrt{c} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 2 a c^{2} \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{\sqrt{c} x^{2}}{2} & \text{for}\: a^{2} = 0 \\- \frac{\left(- a^{2} c x^{2} + c\right)^{\frac{3}{2}}}{3 a^{2} c} & \text{otherwise} \end{cases}\right) - c^{2} \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{3}}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{2 a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{\sqrt{c} x \sqrt{- a^{2} x^{2} + 1}}{2} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{2 a} & \text{otherwise} \end{cases}\right)"," ",0,"a**4*c**2*Piecewise((I*a**2*sqrt(c)*x**7/(6*sqrt(a**2*x**2 - 1)) - 5*I*sqrt(c)*x**5/(24*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x**3/(48*a**2*sqrt(a**2*x**2 - 1)) + I*sqrt(c)*x/(16*a**4*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(16*a**5), Abs(a**2*x**2) > 1), (-a**2*sqrt(c)*x**7/(6*sqrt(-a**2*x**2 + 1)) + 5*sqrt(c)*x**5/(24*sqrt(-a**2*x**2 + 1)) + sqrt(c)*x**3/(48*a**2*sqrt(-a**2*x**2 + 1)) - sqrt(c)*x/(16*a**4*sqrt(-a**2*x**2 + 1)) + sqrt(c)*asin(a*x)/(16*a**5), True)) - 2*a**3*c**2*Piecewise((x**4*sqrt(-a**2*c*x**2 + c)/5 - x**2*sqrt(-a**2*c*x**2 + c)/(15*a**2) - 2*sqrt(-a**2*c*x**2 + c)/(15*a**4), Ne(a, 0)), (sqrt(c)*x**4/4, True)) + 2*a*c**2*Piecewise((0, Eq(c, 0)), (sqrt(c)*x**2/2, Eq(a**2, 0)), (-(-a**2*c*x**2 + c)**(3/2)/(3*a**2*c), True)) - c**2*Piecewise((I*a**2*sqrt(c)*x**3/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(2*a), Abs(a**2*x**2) > 1), (sqrt(c)*x*sqrt(-a**2*x**2 + 1)/2 + sqrt(c)*asin(a*x)/(2*a), True))","C",0
652,1,340,0,8.160254," ","integrate((-a**2*c*x**2+c)**(3/2)*(a*x-1)/(a*x+1),x)","- a^{2} c \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{5}}{4 \sqrt{a^{2} x^{2} - 1}} - \frac{3 i \sqrt{c} x^{3}}{8 \sqrt{a^{2} x^{2} - 1}} + \frac{i \sqrt{c} x}{8 a^{2} \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{8 a^{3}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\- \frac{a^{2} \sqrt{c} x^{5}}{4 \sqrt{- a^{2} x^{2} + 1}} + \frac{3 \sqrt{c} x^{3}}{8 \sqrt{- a^{2} x^{2} + 1}} - \frac{\sqrt{c} x}{8 a^{2} \sqrt{- a^{2} x^{2} + 1}} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{8 a^{3}} & \text{otherwise} \end{cases}\right) + 2 a c \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{\sqrt{c} x^{2}}{2} & \text{for}\: a^{2} = 0 \\- \frac{\left(- a^{2} c x^{2} + c\right)^{\frac{3}{2}}}{3 a^{2} c} & \text{otherwise} \end{cases}\right) - c \left(\begin{cases} \frac{i a^{2} \sqrt{c} x^{3}}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} x}{2 \sqrt{a^{2} x^{2} - 1}} - \frac{i \sqrt{c} \operatorname{acosh}{\left(a x \right)}}{2 a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{\sqrt{c} x \sqrt{- a^{2} x^{2} + 1}}{2} + \frac{\sqrt{c} \operatorname{asin}{\left(a x \right)}}{2 a} & \text{otherwise} \end{cases}\right)"," ",0,"-a**2*c*Piecewise((I*a**2*sqrt(c)*x**5/(4*sqrt(a**2*x**2 - 1)) - 3*I*sqrt(c)*x**3/(8*sqrt(a**2*x**2 - 1)) + I*sqrt(c)*x/(8*a**2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(8*a**3), Abs(a**2*x**2) > 1), (-a**2*sqrt(c)*x**5/(4*sqrt(-a**2*x**2 + 1)) + 3*sqrt(c)*x**3/(8*sqrt(-a**2*x**2 + 1)) - sqrt(c)*x/(8*a**2*sqrt(-a**2*x**2 + 1)) + sqrt(c)*asin(a*x)/(8*a**3), True)) + 2*a*c*Piecewise((0, Eq(c, 0)), (sqrt(c)*x**2/2, Eq(a**2, 0)), (-(-a**2*c*x**2 + c)**(3/2)/(3*a**2*c), True)) - c*Piecewise((I*a**2*sqrt(c)*x**3/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*x/(2*sqrt(a**2*x**2 - 1)) - I*sqrt(c)*acosh(a*x)/(2*a), Abs(a**2*x**2) > 1), (sqrt(c)*x*sqrt(-a**2*x**2 + 1)/2 + sqrt(c)*asin(a*x)/(2*a), True))","C",0
653,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(a*x + 1), x)","F",0
654,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(-a**2*c*x**2+c)**(1/2),x)","\int \frac{a x - 1}{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)), x)","F",0
655,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(-a**2*c*x**2+c)**(3/2),x)","\int \frac{a x - 1}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(a*x - 1)*(a*x + 1))**(3/2)*(a*x + 1)), x)","F",0
656,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(-a**2*c*x**2+c)**(5/2),x)","\int \frac{a x - 1}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(a*x - 1)*(a*x + 1))**(5/2)*(a*x + 1)), x)","F",0
657,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(-a**2*c*x**2+c)**(7/2),x)","\int \frac{a x - 1}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{7}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(a*x - 1)*(a*x + 1))**(7/2)*(a*x + 1)), x)","F",0
658,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(-a**2*c*x**2+c)**(9/2),x)","\int \frac{a x - 1}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{9}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(a*x - 1)*(a*x + 1))**(9/2)*(a*x + 1)), x)","F",0
659,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(9/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
660,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(7/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
661,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(5/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
662,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(3/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
663,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
664,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**(1/2),x)","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(((a*x - 1)/(a*x + 1))**(3/2)/sqrt(-c*(a*x - 1)*(a*x + 1)), x)","F",0
665,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
666,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
667,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(-a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
668,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**2*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{2} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x**2*sqrt(-c*(a*x - 1)*(a*x + 1))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
669,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{x \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(x*sqrt(-c*(a*x - 1)*(a*x + 1))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
670,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
671,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**(1/2)/x,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{x \sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))/(x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
672,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**(1/2)/x**2,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))/(x**2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
673,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x**3*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{3} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(x**3*sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(a*x - 1), x)","F",0
674,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x**2*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{2} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(x**2*sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(a*x - 1), x)","F",0
675,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{x \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(x*sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(a*x - 1), x)","F",0
676,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(a*x - 1), x)","F",0
677,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(1/2)/x,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{x \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(x*(a*x - 1)), x)","F",0
678,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(1/2)/x**2,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{x^{2} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(x**2*(a*x - 1)), x)","F",0
679,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(1/2)/x**3,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{x^{3} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(x**3*(a*x - 1)), x)","F",0
680,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(1/2)/x**4,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{x^{4} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(x**4*(a*x - 1)), x)","F",0
681,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**(1/2)/x**5,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{x^{5} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(x**5*(a*x - 1)), x)","F",0
682,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**3*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{3} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*sqrt(-c*(a*x - 1)*(a*x + 1))/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
683,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**2*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{2} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*sqrt(-c*(a*x - 1)*(a*x + 1))/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
684,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{x \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*sqrt(-c*(a*x - 1)*(a*x + 1))/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
685,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
686,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(1/2)/x,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))/(x*((a*x - 1)/(a*x + 1))**(3/2)), x)","F",0
687,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
688,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(1/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
689,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(1/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
690,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**(1/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
691,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**4/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**3/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
693,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**2/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
694,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
695,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
696,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/x/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
697,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/x**2/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
698,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/x**3/(-a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
699,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**5/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
700,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**4/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
701,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**3/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
702,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**2/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
703,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
704,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/x/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
706,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/x**2/(-a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
707,-1,0,0,0.000000," ","integrate(x**2*(-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
708,0,0,0,0.000000," ","integrate(x*(-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\int x \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}\, dx"," ",0,"Integral(x*sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(a*x - 1)*(a*x + 1)), x)","F",0
709,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\int \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(a*x - 1)*(a*x + 1)), x)","F",0
710,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2)/x,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{x}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(a*x - 1)*(a*x + 1))/x, x)","F",0
711,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2)/x**2,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(a*x - 1)*(a*x + 1))/x**2, x)","F",0
712,0,0,0,0.000000," ","integrate(x**3*(-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{x^{3} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(x**3*sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(a*x + 1), x)","F",0
713,0,0,0,0.000000," ","integrate(x**2*(-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{x^{2} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(x**2*sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(a*x + 1), x)","F",0
714,0,0,0,0.000000," ","integrate(x*(-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{x \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(x*sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(a*x + 1), x)","F",0
715,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(a*x + 1), x)","F",0
716,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1)/x,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{x \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(x*(a*x + 1)), x)","F",0
717,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1)/x**2,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{x^{2} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(x**2*(a*x + 1)), x)","F",0
718,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1)/x**3,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{x^{3} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(x**3*(a*x + 1)), x)","F",0
719,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1)/x**4,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{x^{4} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(x**4*(a*x + 1)), x)","F",0
720,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1)/x**5,x)","\int \frac{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{x^{5} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(x**5*(a*x + 1)), x)","F",0
721,-1,0,0,0.000000," ","integrate(x**3*(-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
722,-1,0,0,0.000000," ","integrate(x**2*(-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
723,-1,0,0,0.000000," ","integrate(x*(-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
724,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
728,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
729,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**m*(-a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
731,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x**m*(-a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{m} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(x**m*sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x + 1)/(a*x - 1), x)","F",0
732,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**m*(-a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
733,-1,0,0,0.000000," ","integrate(x**m*(-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
734,0,0,0,0.000000," ","integrate(x**m*(-a**2*c*x**2+c)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{x^{m} \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(x**m*sqrt(-c*(a*x - 1)*(a*x + 1))*(a*x - 1)/(a*x + 1), x)","F",0
735,-1,0,0,0.000000," ","integrate(x**m*(-a**2*c*x**2+c)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
736,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a**2*c*x**2+c)**3,x)","- c^{3} \left(\int 3 a^{2} x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx + \int \left(- 3 a^{4} x^{4} e^{n \operatorname{acoth}{\left(a x \right)}}\right)\, dx + \int a^{6} x^{6} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx + \int \left(- e^{n \operatorname{acoth}{\left(a x \right)}}\right)\, dx\right)"," ",0,"-c**3*(Integral(3*a**2*x**2*exp(n*acoth(a*x)), x) + Integral(-3*a**4*x**4*exp(n*acoth(a*x)), x) + Integral(a**6*x**6*exp(n*acoth(a*x)), x) + Integral(-exp(n*acoth(a*x)), x))","F",0
737,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a**2*c*x**2+c)**2,x)","c^{2} \left(\int \left(- 2 a^{2} x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}\right)\, dx + \int a^{4} x^{4} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx + \int e^{n \operatorname{acoth}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(-2*a**2*x**2*exp(n*acoth(a*x)), x) + Integral(a**4*x**4*exp(n*acoth(a*x)), x) + Integral(exp(n*acoth(a*x)), x))","F",0
738,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a**2*c*x**2+c),x)","- c \left(\int a^{2} x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx + \int \left(- e^{n \operatorname{acoth}{\left(a x \right)}}\right)\, dx\right)"," ",0,"-c*(Integral(a**2*x**2*exp(n*acoth(a*x)), x) + Integral(-exp(n*acoth(a*x)), x))","F",0
739,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x)),x)","\int e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral(exp(n*acoth(a*x)), x)","F",0
740,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c),x)","\begin{cases} \tilde{\infty} x & \text{for}\: c = 0 \wedge n = 0 \\\tilde{\infty} \int e^{n \operatorname{acoth}{\left(a x \right)}}\, dx & \text{for}\: c = 0 \\- \frac{\log{\left(x - \frac{1}{a} \right)}}{2 a c} + \frac{\log{\left(x + \frac{1}{a} \right)}}{2 a c} & \text{for}\: n = 0 \\\frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{a c n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(c, 0) & Eq(n, 0)), (zoo*Integral(exp(n*acoth(a*x)), x), Eq(c, 0)), (-log(x - 1/a)/(2*a*c) + log(x + 1/a)/(2*a*c), Eq(n, 0)), (exp(n*acoth(a*x))/(a*c*n), True))","F",0
741,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c)**2,x)","\begin{cases} \tilde{\infty} x e^{- \infty n} & \text{for}\: a = - \frac{1}{x} \\\tilde{\infty} x e^{\infty n} & \text{for}\: a = \frac{1}{x} \\\tilde{\infty} \int e^{n \operatorname{acoth}{\left(a x \right)}}\, dx & \text{for}\: c = 0 \\- \frac{a^{2} x^{2} \operatorname{acoth}{\left(a x \right)}}{4 a^{3} c^{2} x^{2} e^{2 \operatorname{acoth}{\left(a x \right)}} - 4 a c^{2} e^{2 \operatorname{acoth}{\left(a x \right)}}} - \frac{2 a x \operatorname{acoth}{\left(a x \right)}}{4 a^{3} c^{2} x^{2} e^{2 \operatorname{acoth}{\left(a x \right)}} - 4 a c^{2} e^{2 \operatorname{acoth}{\left(a x \right)}}} + \frac{a x}{4 a^{3} c^{2} x^{2} e^{2 \operatorname{acoth}{\left(a x \right)}} - 4 a c^{2} e^{2 \operatorname{acoth}{\left(a x \right)}}} - \frac{\operatorname{acoth}{\left(a x \right)}}{4 a^{3} c^{2} x^{2} e^{2 \operatorname{acoth}{\left(a x \right)}} - 4 a c^{2} e^{2 \operatorname{acoth}{\left(a x \right)}}} + \frac{2}{4 a^{3} c^{2} x^{2} e^{2 \operatorname{acoth}{\left(a x \right)}} - 4 a c^{2} e^{2 \operatorname{acoth}{\left(a x \right)}}} & \text{for}\: n = -2 \\- \frac{a^{2} x^{2} \log{\left(x - \frac{1}{a} \right)}}{4 a^{3} c^{2} x^{2} - 4 a c^{2}} + \frac{a^{2} x^{2} \log{\left(x + \frac{1}{a} \right)}}{4 a^{3} c^{2} x^{2} - 4 a c^{2}} - \frac{2 a x}{4 a^{3} c^{2} x^{2} - 4 a c^{2}} + \frac{\log{\left(x - \frac{1}{a} \right)}}{4 a^{3} c^{2} x^{2} - 4 a c^{2}} - \frac{\log{\left(x + \frac{1}{a} \right)}}{4 a^{3} c^{2} x^{2} - 4 a c^{2}} & \text{for}\: n = 0 \\\frac{\int \frac{e^{2 \operatorname{acoth}{\left(a x \right)}}}{a^{4} x^{4} - 2 a^{2} x^{2} + 1}\, dx}{c^{2}} & \text{for}\: n = 2 \\- \frac{2 a^{2} x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{3} c^{2} n^{3} x^{2} - 4 a^{3} c^{2} n x^{2} - a c^{2} n^{3} + 4 a c^{2} n} + \frac{2 a n x e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{3} c^{2} n^{3} x^{2} - 4 a^{3} c^{2} n x^{2} - a c^{2} n^{3} + 4 a c^{2} n} - \frac{n^{2} e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{3} c^{2} n^{3} x^{2} - 4 a^{3} c^{2} n x^{2} - a c^{2} n^{3} + 4 a c^{2} n} + \frac{2 e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{3} c^{2} n^{3} x^{2} - 4 a^{3} c^{2} n x^{2} - a c^{2} n^{3} + 4 a c^{2} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*exp(-oo*n), Eq(a, -1/x)), (zoo*x*exp(oo*n), Eq(a, 1/x)), (zoo*Integral(exp(n*acoth(a*x)), x), Eq(c, 0)), (-a**2*x**2*acoth(a*x)/(4*a**3*c**2*x**2*exp(2*acoth(a*x)) - 4*a*c**2*exp(2*acoth(a*x))) - 2*a*x*acoth(a*x)/(4*a**3*c**2*x**2*exp(2*acoth(a*x)) - 4*a*c**2*exp(2*acoth(a*x))) + a*x/(4*a**3*c**2*x**2*exp(2*acoth(a*x)) - 4*a*c**2*exp(2*acoth(a*x))) - acoth(a*x)/(4*a**3*c**2*x**2*exp(2*acoth(a*x)) - 4*a*c**2*exp(2*acoth(a*x))) + 2/(4*a**3*c**2*x**2*exp(2*acoth(a*x)) - 4*a*c**2*exp(2*acoth(a*x))), Eq(n, -2)), (-a**2*x**2*log(x - 1/a)/(4*a**3*c**2*x**2 - 4*a*c**2) + a**2*x**2*log(x + 1/a)/(4*a**3*c**2*x**2 - 4*a*c**2) - 2*a*x/(4*a**3*c**2*x**2 - 4*a*c**2) + log(x - 1/a)/(4*a**3*c**2*x**2 - 4*a*c**2) - log(x + 1/a)/(4*a**3*c**2*x**2 - 4*a*c**2), Eq(n, 0)), (Integral(exp(2*acoth(a*x))/(a**4*x**4 - 2*a**2*x**2 + 1), x)/c**2, Eq(n, 2)), (-2*a**2*x**2*exp(n*acoth(a*x))/(a**3*c**2*n**3*x**2 - 4*a**3*c**2*n*x**2 - a*c**2*n**3 + 4*a*c**2*n) + 2*a*n*x*exp(n*acoth(a*x))/(a**3*c**2*n**3*x**2 - 4*a**3*c**2*n*x**2 - a*c**2*n**3 + 4*a*c**2*n) - n**2*exp(n*acoth(a*x))/(a**3*c**2*n**3*x**2 - 4*a**3*c**2*n*x**2 - a*c**2*n**3 + 4*a*c**2*n) + 2*exp(n*acoth(a*x))/(a**3*c**2*n**3*x**2 - 4*a**3*c**2*n*x**2 - a*c**2*n**3 + 4*a*c**2*n), True))","F",0
742,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a**2*c*x**2+c)**(3/2),x)","\int \left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral((-c*(a*x - 1)*(a*x + 1))**(3/2)*exp(n*acoth(a*x)), x)","F",0
745,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a**2*c*x**2+c)**(1/2),x)","\int \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*exp(n*acoth(a*x)), x)","F",0
746,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c)**(1/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/sqrt(-c*(a*x - 1)*(a*x + 1)), x)","F",0
747,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c)**(3/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
748,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c)**(5/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
749,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,-1,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*x**3/(-a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{3} e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
752,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*x**2/(-a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
753,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*x/(-a**2*c*x**2+c)**(3/2),x)","\int \frac{x e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
754,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c)**(3/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
755,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/x/(-a**2*c*x**2+c)**(3/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{x \left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/(x*(-c*(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
756,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*x**4/(-a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{4} e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
757,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*x**3/(-a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{3} e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
758,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*x**2/(-a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
759,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*x/(-a**2*c*x**2+c)**(5/2),x)","\int \frac{x e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
760,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(-a**2*c*x**2+c)**(5/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/(-c*(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
761,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/x/(-a**2*c*x**2+c)**(5/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{x \left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/(x*(-c*(a*x - 1)*(a*x + 1))**(5/2)), x)","F",0
762,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(-a**2*c*x**2+c)**p,x)","\int \left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{p} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral((-c*(a*x - 1)*(a*x + 1))**p*exp(n*acoth(a*x)), x)","F",0
763,0,0,0,0.000000," ","integrate(exp(2*p*acoth(a*x))*(-a**2*c*x**2+c)**p,x)","\begin{cases} - \frac{i x}{\sqrt{c}} & \text{for}\: a = 0 \wedge p = - \frac{1}{2} \\c^{p} x e^{i \pi p} & \text{for}\: a = 0 \\\int \frac{e^{- \operatorname{acoth}{\left(a x \right)}}}{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{a x \left(- a^{2} c x^{2} + c\right)^{p} e^{2 p \operatorname{acoth}{\left(a x \right)}}}{2 a p + a} + \frac{\left(- a^{2} c x^{2} + c\right)^{p} e^{2 p \operatorname{acoth}{\left(a x \right)}}}{2 a p + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*x/sqrt(c), Eq(a, 0) & Eq(p, -1/2)), (c**p*x*exp(I*pi*p), Eq(a, 0)), (Integral(exp(-acoth(a*x))/sqrt(-c*(a*x - 1)*(a*x + 1)), x), Eq(p, -1/2)), (a*x*(-a**2*c*x**2 + c)**p*exp(2*p*acoth(a*x))/(2*a*p + a) + (-a**2*c*x**2 + c)**p*exp(2*p*acoth(a*x))/(2*a*p + a), True))","F",0
764,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**p/exp(2*p*acoth(a*x)),x)","\begin{cases} \frac{i x}{\sqrt{c}} & \text{for}\: a = 0 \wedge p = - \frac{1}{2} \\c^{p} x e^{- i \pi p} & \text{for}\: a = 0 \\\int \frac{e^{\operatorname{acoth}{\left(a x \right)}}}{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{a x \left(- a^{2} c x^{2} + c\right)^{p}}{2 a p e^{2 p \operatorname{acoth}{\left(a x \right)}} + a e^{2 p \operatorname{acoth}{\left(a x \right)}}} - \frac{\left(- a^{2} c x^{2} + c\right)^{p}}{2 a p e^{2 p \operatorname{acoth}{\left(a x \right)}} + a e^{2 p \operatorname{acoth}{\left(a x \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x/sqrt(c), Eq(a, 0) & Eq(p, -1/2)), (c**p*x*exp(-I*pi*p), Eq(a, 0)), (Integral(exp(acoth(a*x))/sqrt(-c*(a*x - 1)*(a*x + 1)), x), Eq(p, -1/2)), (a*x*(-a**2*c*x**2 + c)**p/(2*a*p*exp(2*p*acoth(a*x)) + a*exp(2*p*acoth(a*x))) - (-a**2*c*x**2 + c)**p/(2*a*p*exp(2*p*acoth(a*x)) + a*exp(2*p*acoth(a*x))), True))","F",0
765,0,0,0,0.000000," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(-a**2*c*x**2+c)**p,x)","\int \frac{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{p} \left(a x + 1\right)^{2}}{\left(a x - 1\right)^{2}}\, dx"," ",0,"Integral((-c*(a*x - 1)*(a*x + 1))**p*(a*x + 1)**2/(a*x - 1)**2, x)","F",0
766,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(-a**2*c*x**2+c)**p,x)","\int \frac{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-c*(a*x - 1)*(a*x + 1))**p/((a*x - 1)/(a*x + 1))**(3/2), x)","F",0
767,1,651,0,19.966324," ","integrate(1/(a*x-1)*(a*x+1)*(-a**2*c*x**2+c)**p,x)","a \left(\begin{cases} \frac{0^{p} x}{a} - \frac{0^{p} \log{\left(\frac{1}{a^{2} x^{2}} \right)}}{2 a^{2}} + \frac{0^{p} \log{\left(-1 + \frac{1}{a^{2} x^{2}} \right)}}{2 a^{2}} - \frac{0^{p} \operatorname{acoth}{\left(\frac{1}{a x} \right)}}{a^{2}} + \frac{c^{p} x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {a^{2} x^{2} e^{2 i \pi}} \right)}}{2 \Gamma\left(- p\right) \Gamma\left(p + 1\right)} - \frac{a^{2 p} c^{p} p x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{1}{a^{2} x^{2}}} \right)}}{2 a \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\\frac{0^{p} x}{a} - \frac{0^{p} \log{\left(\frac{1}{a^{2} x^{2}} \right)}}{2 a^{2}} + \frac{0^{p} \log{\left(1 - \frac{1}{a^{2} x^{2}} \right)}}{2 a^{2}} - \frac{0^{p} \operatorname{atanh}{\left(\frac{1}{a x} \right)}}{a^{2}} + \frac{c^{p} x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {a^{2} x^{2} e^{2 i \pi}} \right)}}{2 \Gamma\left(- p\right) \Gamma\left(p + 1\right)} - \frac{a^{2 p} c^{p} p x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{1}{a^{2} x^{2}}} \right)}}{2 a \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}\right) + \begin{cases} \frac{0^{p} \log{\left(a^{2} x^{2} - 1 \right)}}{2 a} - \frac{0^{p} \operatorname{acoth}{\left(a x \right)}}{a} + \frac{a c^{p} x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {a^{2} x^{2} e^{2 i \pi}} \right)}}{2 \Gamma\left(- p\right) \Gamma\left(p + 1\right)} - \frac{a^{2 p} c^{p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{1}{2} - p \\ \frac{3}{2} - p \end{matrix}\middle| {\frac{1}{a^{2} x^{2}}} \right)}}{2 a^{2} x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{0^{p} \log{\left(- a^{2} x^{2} + 1 \right)}}{2 a} - \frac{0^{p} \operatorname{atanh}{\left(a x \right)}}{a} + \frac{a c^{p} x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {a^{2} x^{2} e^{2 i \pi}} \right)}}{2 \Gamma\left(- p\right) \Gamma\left(p + 1\right)} - \frac{a^{2 p} c^{p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{1}{2} - p \\ \frac{3}{2} - p \end{matrix}\middle| {\frac{1}{a^{2} x^{2}}} \right)}}{2 a^{2} x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"a*Piecewise((0**p*x/a - 0**p*log(1/(a**2*x**2))/(2*a**2) + 0**p*log(-1 + 1/(a**2*x**2))/(2*a**2) - 0**p*acoth(1/(a*x))/a**2 + c**p*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), a**2*x**2*exp_polar(2*I*pi))/(2*gamma(-p)*gamma(p + 1)) - a**(2*p)*c**p*p*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), 1/(a**2*x**2))/(2*a*gamma(1/2 - p)*gamma(p + 1)), 1/Abs(a**2*x**2) > 1), (0**p*x/a - 0**p*log(1/(a**2*x**2))/(2*a**2) + 0**p*log(1 - 1/(a**2*x**2))/(2*a**2) - 0**p*atanh(1/(a*x))/a**2 + c**p*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), a**2*x**2*exp_polar(2*I*pi))/(2*gamma(-p)*gamma(p + 1)) - a**(2*p)*c**p*p*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), 1/(a**2*x**2))/(2*a*gamma(1/2 - p)*gamma(p + 1)), True)) + Piecewise((0**p*log(a**2*x**2 - 1)/(2*a) - 0**p*acoth(a*x)/a + a*c**p*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), a**2*x**2*exp_polar(2*I*pi))/(2*gamma(-p)*gamma(p + 1)) - a**(2*p)*c**p*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), 1/(a**2*x**2))/(2*a**2*x*gamma(3/2 - p)*gamma(p + 1)), Abs(a**2*x**2) > 1), (0**p*log(-a**2*x**2 + 1)/(2*a) - 0**p*atanh(a*x)/a + a*c**p*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), a**2*x**2*exp_polar(2*I*pi))/(2*gamma(-p)*gamma(p + 1)) - a**(2*p)*c**p*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), 1/(a**2*x**2))/(2*a**2*x*gamma(3/2 - p)*gamma(p + 1)), True))","C",0
768,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(-a**2*c*x**2+c)**p,x)","\int \frac{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{p}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral((-c*(a*x - 1)*(a*x + 1))**p/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
769,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**p*((a*x-1)/(a*x+1))**(1/2),x)","\int \sqrt{\frac{a x - 1}{a x + 1}} \left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{p}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*(-c*(a*x - 1)*(a*x + 1))**p, x)","F",0
770,1,651,0,17.796566," ","integrate((-a**2*c*x**2+c)**p*(a*x-1)/(a*x+1),x)","a \left(\begin{cases} \frac{0^{p} x}{a} + \frac{0^{p} \log{\left(\frac{1}{a^{2} x^{2}} \right)}}{2 a^{2}} - \frac{0^{p} \log{\left(-1 + \frac{1}{a^{2} x^{2}} \right)}}{2 a^{2}} - \frac{0^{p} \operatorname{acoth}{\left(\frac{1}{a x} \right)}}{a^{2}} - \frac{c^{p} x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {a^{2} x^{2} e^{2 i \pi}} \right)}}{2 \Gamma\left(- p\right) \Gamma\left(p + 1\right)} - \frac{a^{2 p} c^{p} p x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{1}{a^{2} x^{2}}} \right)}}{2 a \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\\frac{0^{p} x}{a} + \frac{0^{p} \log{\left(\frac{1}{a^{2} x^{2}} \right)}}{2 a^{2}} - \frac{0^{p} \log{\left(1 - \frac{1}{a^{2} x^{2}} \right)}}{2 a^{2}} - \frac{0^{p} \operatorname{atanh}{\left(\frac{1}{a x} \right)}}{a^{2}} - \frac{c^{p} x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {a^{2} x^{2} e^{2 i \pi}} \right)}}{2 \Gamma\left(- p\right) \Gamma\left(p + 1\right)} - \frac{a^{2 p} c^{p} p x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{1}{a^{2} x^{2}}} \right)}}{2 a \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{0^{p} \log{\left(a^{2} x^{2} - 1 \right)}}{2 a} + \frac{0^{p} \operatorname{acoth}{\left(a x \right)}}{a} + \frac{a c^{p} x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {a^{2} x^{2} e^{2 i \pi}} \right)}}{2 \Gamma\left(- p\right) \Gamma\left(p + 1\right)} + \frac{a^{2 p} c^{p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{1}{2} - p \\ \frac{3}{2} - p \end{matrix}\middle| {\frac{1}{a^{2} x^{2}}} \right)}}{2 a^{2} x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{0^{p} \log{\left(- a^{2} x^{2} + 1 \right)}}{2 a} + \frac{0^{p} \operatorname{atanh}{\left(a x \right)}}{a} + \frac{a c^{p} x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {a^{2} x^{2} e^{2 i \pi}} \right)}}{2 \Gamma\left(- p\right) \Gamma\left(p + 1\right)} + \frac{a^{2 p} c^{p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{1}{2} - p \\ \frac{3}{2} - p \end{matrix}\middle| {\frac{1}{a^{2} x^{2}}} \right)}}{2 a^{2} x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"a*Piecewise((0**p*x/a + 0**p*log(1/(a**2*x**2))/(2*a**2) - 0**p*log(-1 + 1/(a**2*x**2))/(2*a**2) - 0**p*acoth(1/(a*x))/a**2 - c**p*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), a**2*x**2*exp_polar(2*I*pi))/(2*gamma(-p)*gamma(p + 1)) - a**(2*p)*c**p*p*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), 1/(a**2*x**2))/(2*a*gamma(1/2 - p)*gamma(p + 1)), 1/Abs(a**2*x**2) > 1), (0**p*x/a + 0**p*log(1/(a**2*x**2))/(2*a**2) - 0**p*log(1 - 1/(a**2*x**2))/(2*a**2) - 0**p*atanh(1/(a*x))/a**2 - c**p*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), a**2*x**2*exp_polar(2*I*pi))/(2*gamma(-p)*gamma(p + 1)) - a**(2*p)*c**p*p*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), 1/(a**2*x**2))/(2*a*gamma(1/2 - p)*gamma(p + 1)), True)) - Piecewise((0**p*log(a**2*x**2 - 1)/(2*a) + 0**p*acoth(a*x)/a + a*c**p*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), a**2*x**2*exp_polar(2*I*pi))/(2*gamma(-p)*gamma(p + 1)) + a**(2*p)*c**p*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), 1/(a**2*x**2))/(2*a**2*x*gamma(3/2 - p)*gamma(p + 1)), Abs(a**2*x**2) > 1), (0**p*log(-a**2*x**2 + 1)/(2*a) + 0**p*atanh(a*x)/a + a*c**p*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), a**2*x**2*exp_polar(2*I*pi))/(2*gamma(-p)*gamma(p + 1)) + a**(2*p)*c**p*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), 1/(a**2*x**2))/(2*a**2*x*gamma(3/2 - p)*gamma(p + 1)), True))","C",0
771,-1,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**p*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
772,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2)**4,x)","\frac{c^{4} \left(\int \frac{a^{8}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \frac{1}{x^{8} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{4 a^{2}}{x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{6 a^{4}}{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{4 a^{6}}{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)}{a^{8}}"," ",0,"c**4*(Integral(a**8/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(1/(x**8*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(-4*a**2/(x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(6*a**4/(x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(-4*a**6/(x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x))/a**8","F",0
773,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2)**3,x)","\frac{c^{3} \left(\int \frac{a^{6}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{1}{x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx + \int \frac{3 a^{2}}{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{3 a^{4}}{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)}{a^{6}}"," ",0,"c**3*(Integral(a**6/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-1/(x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(3*a**2/(x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(-3*a**4/(x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x))/a**6","F",0
774,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2)**2,x)","\frac{c^{2} \left(\int \frac{a^{4}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \frac{1}{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{2 a^{2}}{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)}{a^{4}}"," ",0,"c**2*(Integral(a**4/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(1/(x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x) + Integral(-2*a**2/(x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x))/a**4","F",0
775,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2),x)","\frac{c \left(\int \frac{a^{2}}{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx + \int \left(- \frac{1}{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\right)\, dx\right)}{a^{2}}"," ",0,"c*(Integral(a**2/sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-1/(x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x))/a**2","F",0
776,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2),x)","\frac{a^{2} \int \frac{x^{2}}{a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c}"," ",0,"a**2*Integral(x**2/(a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c","F",0
777,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**2,x)","\frac{a^{4} \int \frac{x^{4}}{a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 2 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{2}}"," ",0,"a**4*Integral(x**4/(a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 2*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**2","F",0
778,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**3,x)","\frac{a^{6} \int \frac{x^{6}}{a^{6} x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 3 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + 3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{3}}"," ",0,"a**6*Integral(x**6/(a**6*x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 3*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + 3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**3","F",0
779,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**4,x)","\frac{a^{8} \int \frac{x^{8}}{a^{8} x^{8} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 4 a^{6} x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + 6 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} - 4 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}} + \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}\, dx}{c^{4}}"," ",0,"a**8*Integral(x**8/(a**8*x**8*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 4*a**6*x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + 6*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) - 4*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))), x)/c**4","F",0
780,1,124,0,0.657524," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**5,x)","\frac{a^{10} c^{5} x + 2 a^{9} c^{5} \log{\left(x \right)} + \frac{3780 a^{8} c^{5} x^{8} + 5040 a^{7} c^{5} x^{7} - 840 a^{6} c^{5} x^{6} - 3780 a^{5} c^{5} x^{5} - 504 a^{4} c^{5} x^{4} + 1680 a^{3} c^{5} x^{3} + 540 a^{2} c^{5} x^{2} - 315 a c^{5} x - 140 c^{5}}{1260 x^{9}}}{a^{10}}"," ",0,"(a**10*c**5*x + 2*a**9*c**5*log(x) + (3780*a**8*c**5*x**8 + 5040*a**7*c**5*x**7 - 840*a**6*c**5*x**6 - 3780*a**5*c**5*x**5 - 504*a**4*c**5*x**4 + 1680*a**3*c**5*x**3 + 540*a**2*c**5*x**2 - 315*a*c**5*x - 140*c**5)/(1260*x**9))/a**10","A",0
781,1,88,0,0.440538," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**4,x)","\frac{a^{8} c^{4} x + 2 a^{7} c^{4} \log{\left(x \right)} + \frac{420 a^{6} c^{4} x^{6} + 630 a^{5} c^{4} x^{5} - 315 a^{3} c^{4} x^{3} - 84 a^{2} c^{4} x^{2} + 70 a c^{4} x + 30 c^{4}}{210 x^{7}}}{a^{8}}"," ",0,"(a**8*c**4*x + 2*a**7*c**4*log(x) + (420*a**6*c**4*x**6 + 630*a**5*c**4*x**5 - 315*a**3*c**4*x**3 - 84*a**2*c**4*x**2 + 70*a*c**4*x + 30*c**4)/(210*x**7))/a**8","A",0
782,1,76,0,0.326990," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**3,x)","\frac{a^{6} c^{3} x + 2 a^{5} c^{3} \log{\left(x \right)} + \frac{30 a^{4} c^{3} x^{4} + 60 a^{3} c^{3} x^{3} + 10 a^{2} c^{3} x^{2} - 15 a c^{3} x - 6 c^{3}}{30 x^{5}}}{a^{6}}"," ",0,"(a**6*c**3*x + 2*a**5*c**3*log(x) + (30*a**4*c**3*x**4 + 60*a**3*c**3*x**3 + 10*a**2*c**3*x**2 - 15*a*c**3*x - 6*c**3)/(30*x**5))/a**6","A",0
783,1,39,0,0.178015," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**2,x)","\frac{a^{4} c^{2} x + 2 a^{3} c^{2} \log{\left(x \right)} + \frac{3 a c^{2} x + c^{2}}{3 x^{3}}}{a^{4}}"," ",0,"(a**4*c**2*x + 2*a**3*c**2*log(x) + (3*a*c**2*x + c**2)/(3*x**3))/a**4","A",0
784,1,20,0,0.105637," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2),x)","\frac{a^{2} c x + 2 a c \log{\left(x \right)} - \frac{c}{x}}{a^{2}}"," ",0,"(a**2*c*x + 2*a*c*log(x) - c/x)/a**2","A",0
785,1,36,0,0.144838," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a**2/x**2),x)","a^{2} \left(- \frac{1}{a^{4} c x - a^{3} c} + \frac{x}{a^{2} c} + \frac{2 \log{\left(a x - 1 \right)}}{a^{3} c}\right)"," ",0,"a**2*(-1/(a**4*c*x - a**3*c) + x/(a**2*c) + 2*log(a*x - 1)/(a**3*c))","A",0
786,1,73,0,0.368720," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a**2/x**2)**2,x)","a^{4} \left(\frac{- 7 a x + 6}{4 a^{7} c^{2} x^{2} - 8 a^{6} c^{2} x + 4 a^{5} c^{2}} + \frac{x}{a^{4} c^{2}} + \frac{\frac{17 \log{\left(x - \frac{1}{a} \right)}}{8} - \frac{\log{\left(x + \frac{1}{a} \right)}}{8}}{a^{5} c^{2}}\right)"," ",0,"a**4*((-7*a*x + 6)/(4*a**7*c**2*x**2 - 8*a**6*c**2*x + 4*a**5*c**2) + x/(a**4*c**2) + (17*log(x - 1/a)/8 - log(x + 1/a)/8)/(a**5*c**2))","A",0
787,1,102,0,0.591658," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a**2/x**2)**3,x)","a^{6} \left(\frac{- 15 a^{3} x^{3} + 12 a^{2} x^{2} + 13 a x - 11}{6 a^{11} c^{3} x^{4} - 12 a^{10} c^{3} x^{3} + 12 a^{8} c^{3} x - 6 a^{7} c^{3}} + \frac{x}{a^{6} c^{3}} + \frac{\frac{9 \log{\left(x - \frac{1}{a} \right)}}{4} - \frac{\log{\left(x + \frac{1}{a} \right)}}{4}}{a^{7} c^{3}}\right)"," ",0,"a**6*((-15*a**3*x**3 + 12*a**2*x**2 + 13*a*x - 11)/(6*a**11*c**3*x**4 - 12*a**10*c**3*x**3 + 12*a**8*c**3*x - 6*a**7*c**3) + x/(a**6*c**3) + (9*log(x - 1/a)/4 - log(x + 1/a)/4)/(a**7*c**3))","A",0
788,1,156,0,0.841502," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a**2/x**2)**4,x)","a^{8} \left(\frac{- 627 a^{5} x^{5} + 486 a^{4} x^{4} + 1058 a^{3} x^{3} - 874 a^{2} x^{2} - 467 a x + 400}{192 a^{15} c^{4} x^{6} - 384 a^{14} c^{4} x^{5} - 192 a^{13} c^{4} x^{4} + 768 a^{12} c^{4} x^{3} - 192 a^{11} c^{4} x^{2} - 384 a^{10} c^{4} x + 192 a^{9} c^{4}} + \frac{x}{a^{8} c^{4}} + \frac{\frac{303 \log{\left(x - \frac{1}{a} \right)}}{128} - \frac{47 \log{\left(x + \frac{1}{a} \right)}}{128}}{a^{9} c^{4}}\right)"," ",0,"a**8*((-627*a**5*x**5 + 486*a**4*x**4 + 1058*a**3*x**3 - 874*a**2*x**2 - 467*a*x + 400)/(192*a**15*c**4*x**6 - 384*a**14*c**4*x**5 - 192*a**13*c**4*x**4 + 768*a**12*c**4*x**3 - 192*a**11*c**4*x**2 - 384*a**10*c**4*x + 192*a**9*c**4) + x/(a**8*c**4) + (303*log(x - 1/a)/128 - 47*log(x + 1/a)/128)/(a**9*c**4))","A",0
789,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**4,x)","\frac{c^{4} \left(\int \left(- \frac{4 a^{2}}{\frac{a x^{7} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{6 a^{4}}{\frac{a x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{4 a^{6}}{\frac{a x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{8}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \frac{1}{\frac{a x^{9} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{8} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx\right)}{a^{8}}"," ",0,"c**4*(Integral(-4*a**2/(a*x**7*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(6*a**4/(a*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-4*a**6/(a*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**8/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(1/(a*x**9*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**8*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))/a**8","F",0
790,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**3,x)","\frac{c^{3} \left(\int \frac{3 a^{2}}{\frac{a x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{3 a^{4}}{\frac{a x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{6}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{1}{\frac{a x^{7} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx\right)}{a^{6}}"," ",0,"c**3*(Integral(3*a**2/(a*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-3*a**4/(a*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**6/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-1/(a*x**7*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))/a**6","F",0
791,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**2,x)","\frac{c^{2} \left(\int \left(- \frac{2 a^{2}}{\frac{a x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx + \int \frac{a^{4}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \frac{1}{\frac{a x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx\right)}{a^{4}}"," ",0,"c**2*(Integral(-2*a**2/(a*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(a**4/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(1/(a*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))/a**4","F",0
792,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2),x)","\frac{c \left(\int \frac{a^{2}}{\frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx + \int \left(- \frac{1}{\frac{a x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\right)\, dx\right)}{a^{2}}"," ",0,"c*(Integral(a**2/(a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x) + Integral(-1/(a*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x))/a**2","F",0
793,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2),x)","\frac{a^{2} \int \frac{x^{2}}{\frac{a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c}"," ",0,"a**2*Integral(x**2/(a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c","F",0
794,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**2,x)","\frac{a^{4} \int \frac{x^{4}}{\frac{a^{5} x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{2 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{2 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{2}}"," ",0,"a**4*Integral(x**4/(a**5*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 2*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 2*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**2","F",0
795,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**3,x)","\frac{a^{6} \int \frac{x^{6}}{\frac{a^{7} x^{7} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{a^{6} x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{3 a^{5} x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{3 a^{4} x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{3 a^{3} x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{3 a^{2} x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} - \frac{a x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1} + \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}}\, dx}{c^{3}}"," ",0,"a**6*Integral(x**6/(a**7*x**7*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - a**6*x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 3*a**5*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 3*a**4*x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + 3*a**3*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - 3*a**2*x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) - a*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1) + sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1)), x)/c**3","F",0
796,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
797,1,112,0,0.619896," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(c-c/a**2/x**2)**5,x)","\frac{a^{10} c^{5} x + 4 a^{9} c^{5} \log{\left(x \right)} + \frac{- 1890 a^{8} c^{5} x^{8} + 2520 a^{7} c^{5} x^{7} + 2940 a^{6} c^{5} x^{6} - 1764 a^{4} c^{5} x^{4} - 840 a^{3} c^{5} x^{3} + 270 a^{2} c^{5} x^{2} + 315 a c^{5} x + 70 c^{5}}{630 x^{9}}}{a^{10}}"," ",0,"(a**10*c**5*x + 4*a**9*c**5*log(x) + (-1890*a**8*c**5*x**8 + 2520*a**7*c**5*x**7 + 2940*a**6*c**5*x**6 - 1764*a**4*c**5*x**4 - 840*a**3*c**5*x**3 + 270*a**2*c**5*x**2 + 315*a*c**5*x + 70*c**5)/(630*x**9))/a**10","A",0
798,1,100,0,0.476228," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(c-c/a**2/x**2)**4,x)","\frac{a^{8} c^{4} x + 4 a^{7} c^{4} \log{\left(x \right)} + \frac{- 420 a^{6} c^{4} x^{6} + 210 a^{5} c^{4} x^{5} + 350 a^{4} c^{4} x^{4} + 105 a^{3} c^{4} x^{3} - 84 a^{2} c^{4} x^{2} - 70 a c^{4} x - 15 c^{4}}{105 x^{7}}}{a^{8}}"," ",0,"(a**8*c**4*x + 4*a**7*c**4*log(x) + (-420*a**6*c**4*x**6 + 210*a**5*c**4*x**5 + 350*a**4*c**4*x**4 + 105*a**3*c**4*x**3 - 84*a**2*c**4*x**2 - 70*a*c**4*x - 15*c**4)/(105*x**7))/a**8","A",0
799,1,65,0,0.294459," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(c-c/a**2/x**2)**3,x)","\frac{a^{6} c^{3} x + 4 a^{5} c^{3} \log{\left(x \right)} + \frac{- 75 a^{4} c^{3} x^{4} + 25 a^{2} c^{3} x^{2} + 15 a c^{3} x + 3 c^{3}}{15 x^{5}}}{a^{6}}"," ",0,"(a**6*c**3*x + 4*a**5*c**3*log(x) + (-75*a**4*c**3*x**4 + 25*a**2*c**3*x**2 + 15*a*c**3*x + 3*c**3)/(15*x**5))/a**6","A",0
800,1,53,0,0.205335," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(c-c/a**2/x**2)**2,x)","\frac{a^{4} c^{2} x + 4 a^{3} c^{2} \log{\left(x \right)} + \frac{- 18 a^{2} c^{2} x^{2} - 6 a c^{2} x - c^{2}}{3 x^{3}}}{a^{4}}"," ",0,"(a**4*c**2*x + 4*a**3*c**2*log(x) + (-18*a**2*c**2*x**2 - 6*a*c**2*x - c**2)/(3*x**3))/a**4","A",0
801,1,26,0,0.265449," ","integrate(1/(a*x-1)**2*(a*x+1)**2*(c-c/a**2/x**2),x)","c x + \frac{4 c \left(- \log{\left(x \right)} + 2 \log{\left(x - \frac{1}{a} \right)}\right)}{a} + \frac{c}{a^{2} x}"," ",0,"c*x + 4*c*(-log(x) + 2*log(x - 1/a))/a + c/(a**2*x)","A",0
802,1,41,0,0.231038," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(c-c/a**2/x**2),x)","\frac{- 5 a x + 4}{a^{3} c x^{2} - 2 a^{2} c x + a c} + \frac{x}{c} + \frac{4 \log{\left(a x - 1 \right)}}{a c}"," ",0,"(-5*a*x + 4)/(a**3*c*x**2 - 2*a**2*c*x + a*c) + x/c + 4*log(a*x - 1)/(a*c)","A",0
803,1,83,0,0.322532," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(c-c/a**2/x**2)**2,x)","a^{4} \left(\frac{- 18 a^{2} x^{2} + 30 a x - 13}{3 a^{8} c^{2} x^{3} - 9 a^{7} c^{2} x^{2} + 9 a^{6} c^{2} x - 3 a^{5} c^{2}} + \frac{x}{a^{4} c^{2}} + \frac{4 \log{\left(a x - 1 \right)}}{a^{5} c^{2}}\right)"," ",0,"a**4*((-18*a**2*x**2 + 30*a*x - 13)/(3*a**8*c**2*x**3 - 9*a**7*c**2*x**2 + 9*a**6*c**2*x - 3*a**5*c**2) + x/(a**4*c**2) + 4*log(a*x - 1)/(a**5*c**2))","A",0
804,1,114,0,0.614429," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(c-c/a**2/x**2)**3,x)","a^{6} \left(\frac{- 333 a^{3} x^{3} + 852 a^{2} x^{2} - 749 a x + 224}{48 a^{11} c^{3} x^{4} - 192 a^{10} c^{3} x^{3} + 288 a^{9} c^{3} x^{2} - 192 a^{8} c^{3} x + 48 a^{7} c^{3}} + \frac{x}{a^{6} c^{3}} + \frac{\frac{129 \log{\left(x - \frac{1}{a} \right)}}{32} - \frac{\log{\left(x + \frac{1}{a} \right)}}{32}}{a^{7} c^{3}}\right)"," ",0,"a**6*((-333*a**3*x**3 + 852*a**2*x**2 - 749*a*x + 224)/(48*a**11*c**3*x**4 - 192*a**10*c**3*x**3 + 288*a**9*c**3*x**2 - 192*a**8*c**3*x + 48*a**7*c**3) + x/(a**6*c**3) + (129*log(x - 1/a)/32 - log(x + 1/a)/32)/(a**7*c**3))","A",0
805,1,144,0,0.919918," ","integrate(1/(a*x-1)**2*(a*x+1)**2/(c-c/a**2/x**2)**4,x)","a^{8} \left(\frac{- 3765 a^{5} x^{5} + 9300 a^{4} x^{4} - 4400 a^{3} x^{3} - 6820 a^{2} x^{2} + 8021 a x - 2384}{480 a^{15} c^{4} x^{6} - 1920 a^{14} c^{4} x^{5} + 2400 a^{13} c^{4} x^{4} - 2400 a^{11} c^{4} x^{2} + 1920 a^{10} c^{4} x - 480 a^{9} c^{4}} + \frac{x}{a^{8} c^{4}} + \frac{\frac{261 \log{\left(x - \frac{1}{a} \right)}}{64} - \frac{5 \log{\left(x + \frac{1}{a} \right)}}{64}}{a^{9} c^{4}}\right)"," ",0,"a**8*((-3765*a**5*x**5 + 9300*a**4*x**4 - 4400*a**3*x**3 - 6820*a**2*x**2 + 8021*a*x - 2384)/(480*a**15*c**4*x**6 - 1920*a**14*c**4*x**5 + 2400*a**13*c**4*x**4 - 2400*a**11*c**4*x**2 + 1920*a**10*c**4*x - 480*a**9*c**4) + x/(a**8*c**4) + (261*log(x - 1/a)/64 - 5*log(x + 1/a)/64)/(a**9*c**4))","A",0
806,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**4*((a*x-1)/(a*x+1))**(1/2),x)","\frac{c^{4} \left(\int a^{8} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{8}}\, dx + \int \left(- \frac{4 a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{6}}\right)\, dx + \int \frac{6 a^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{4}}\, dx + \int \left(- \frac{4 a^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{2}}\right)\, dx\right)}{a^{8}}"," ",0,"c**4*(Integral(a**8*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**8, x) + Integral(-4*a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**6, x) + Integral(6*a**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**4, x) + Integral(-4*a**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**2, x))/a**8","F",0
807,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**3*((a*x-1)/(a*x+1))**(1/2),x)","\frac{c^{3} \left(\int a^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{6}}\right)\, dx + \int \frac{3 a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{4}}\, dx + \int \left(- \frac{3 a^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{2}}\right)\, dx\right)}{a^{6}}"," ",0,"c**3*(Integral(a**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**6, x) + Integral(3*a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**4, x) + Integral(-3*a**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**2, x))/a**6","F",0
808,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**2*((a*x-1)/(a*x+1))**(1/2),x)","\frac{c^{2} \left(\int a^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{4}}\, dx + \int \left(- \frac{2 a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{2}}\right)\, dx\right)}{a^{4}}"," ",0,"c**2*(Integral(a**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**4, x) + Integral(-2*a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**2, x))/a**4","F",0
809,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)*((a*x-1)/(a*x+1))**(1/2),x)","\frac{c \left(\int a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}\, dx + \int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{x^{2}}\right)\, dx\right)}{a^{2}}"," ",0,"c*(Integral(a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1)), x) + Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/x**2, x))/a**2","F",0
810,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2),x)","\frac{a^{2} \int \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{2} x^{2} - 1}\, dx}{c}"," ",0,"a**2*Integral(x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**2*x**2 - 1), x)/c","F",0
811,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**2,x)","\frac{a^{4} \int \frac{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{4} x^{4} - 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"a**4*Integral(x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**4*x**4 - 2*a**2*x**2 + 1), x)/c**2","F",0
812,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**3,x)","\frac{a^{6} \int \frac{x^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx}{c^{3}}"," ",0,"a**6*Integral(x**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)/c**3","F",0
813,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**4,x)","\frac{a^{8} \int \frac{x^{8} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{8} x^{8} - 4 a^{6} x^{6} + 6 a^{4} x^{4} - 4 a^{2} x^{2} + 1}\, dx}{c^{4}}"," ",0,"a**8*Integral(x**8*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**8*x**8 - 4*a**6*x**6 + 6*a**4*x**4 - 4*a**2*x**2 + 1), x)/c**4","F",0
814,1,88,0,0.457573," ","integrate((c-c/a**2/x**2)**4*(a*x-1)/(a*x+1),x)","\frac{a^{8} c^{4} x - 2 a^{7} c^{4} \log{\left(x \right)} + \frac{420 a^{6} c^{4} x^{6} - 630 a^{5} c^{4} x^{5} + 315 a^{3} c^{4} x^{3} - 84 a^{2} c^{4} x^{2} - 70 a c^{4} x + 30 c^{4}}{210 x^{7}}}{a^{8}}"," ",0,"(a**8*c**4*x - 2*a**7*c**4*log(x) + (420*a**6*c**4*x**6 - 630*a**5*c**4*x**5 + 315*a**3*c**4*x**3 - 84*a**2*c**4*x**2 - 70*a*c**4*x + 30*c**4)/(210*x**7))/a**8","A",0
815,1,76,0,0.325746," ","integrate((c-c/a**2/x**2)**3*(a*x-1)/(a*x+1),x)","\frac{a^{6} c^{3} x - 2 a^{5} c^{3} \log{\left(x \right)} + \frac{30 a^{4} c^{3} x^{4} - 60 a^{3} c^{3} x^{3} + 10 a^{2} c^{3} x^{2} + 15 a c^{3} x - 6 c^{3}}{30 x^{5}}}{a^{6}}"," ",0,"(a**6*c**3*x - 2*a**5*c**3*log(x) + (30*a**4*c**3*x**4 - 60*a**3*c**3*x**3 + 10*a**2*c**3*x**2 + 15*a*c**3*x - 6*c**3)/(30*x**5))/a**6","A",0
816,1,39,0,0.182507," ","integrate((c-c/a**2/x**2)**2*(a*x-1)/(a*x+1),x)","\frac{a^{4} c^{2} x - 2 a^{3} c^{2} \log{\left(x \right)} + \frac{- 3 a c^{2} x + c^{2}}{3 x^{3}}}{a^{4}}"," ",0,"(a**4*c**2*x - 2*a**3*c**2*log(x) + (-3*a*c**2*x + c**2)/(3*x**3))/a**4","A",0
817,1,20,0,0.106586," ","integrate((c-c/a**2/x**2)*(a*x-1)/(a*x+1),x)","\frac{a^{2} c x - 2 a c \log{\left(x \right)} - \frac{c}{x}}{a^{2}}"," ",0,"(a**2*c*x - 2*a*c*log(x) - c/x)/a**2","A",0
818,1,36,0,0.147954," ","integrate((a*x-1)/(a*x+1)/(c-c/a**2/x**2),x)","a^{2} \left(- \frac{1}{a^{4} c x + a^{3} c} + \frac{x}{a^{2} c} - \frac{2 \log{\left(a x + 1 \right)}}{a^{3} c}\right)"," ",0,"a**2*(-1/(a**4*c*x + a**3*c) + x/(a**2*c) - 2*log(a*x + 1)/(a**3*c))","A",0
819,1,75,0,0.378764," ","integrate((a*x-1)/(a*x+1)/(c-c/a**2/x**2)**2,x)","a^{4} \left(\frac{- 7 a x - 6}{4 a^{7} c^{2} x^{2} + 8 a^{6} c^{2} x + 4 a^{5} c^{2}} + \frac{x}{a^{4} c^{2}} + \frac{\frac{\log{\left(x - \frac{1}{a} \right)}}{8} - \frac{17 \log{\left(x + \frac{1}{a} \right)}}{8}}{a^{5} c^{2}}\right)"," ",0,"a**4*((-7*a*x - 6)/(4*a**7*c**2*x**2 + 8*a**6*c**2*x + 4*a**5*c**2) + x/(a**4*c**2) + (log(x - 1/a)/8 - 17*log(x + 1/a)/8)/(a**5*c**2))","A",0
820,1,102,0,0.610217," ","integrate((a*x-1)/(a*x+1)/(c-c/a**2/x**2)**3,x)","a^{6} \left(\frac{- 15 a^{3} x^{3} - 12 a^{2} x^{2} + 13 a x + 11}{6 a^{11} c^{3} x^{4} + 12 a^{10} c^{3} x^{3} - 12 a^{8} c^{3} x - 6 a^{7} c^{3}} + \frac{x}{a^{6} c^{3}} + \frac{\frac{\log{\left(x - \frac{1}{a} \right)}}{4} - \frac{9 \log{\left(x + \frac{1}{a} \right)}}{4}}{a^{7} c^{3}}\right)"," ",0,"a**6*((-15*a**3*x**3 - 12*a**2*x**2 + 13*a*x + 11)/(6*a**11*c**3*x**4 + 12*a**10*c**3*x**3 - 12*a**8*c**3*x - 6*a**7*c**3) + x/(a**6*c**3) + (log(x - 1/a)/4 - 9*log(x + 1/a)/4)/(a**7*c**3))","A",0
821,1,156,0,0.846394," ","integrate((a*x-1)/(a*x+1)/(c-c/a**2/x**2)**4,x)","a^{8} \left(\frac{- 627 a^{5} x^{5} - 486 a^{4} x^{4} + 1058 a^{3} x^{3} + 874 a^{2} x^{2} - 467 a x - 400}{192 a^{15} c^{4} x^{6} + 384 a^{14} c^{4} x^{5} - 192 a^{13} c^{4} x^{4} - 768 a^{12} c^{4} x^{3} - 192 a^{11} c^{4} x^{2} + 384 a^{10} c^{4} x + 192 a^{9} c^{4}} + \frac{x}{a^{8} c^{4}} + \frac{\frac{47 \log{\left(x - \frac{1}{a} \right)}}{128} - \frac{303 \log{\left(x + \frac{1}{a} \right)}}{128}}{a^{9} c^{4}}\right)"," ",0,"a**8*((-627*a**5*x**5 - 486*a**4*x**4 + 1058*a**3*x**3 + 874*a**2*x**2 - 467*a*x - 400)/(192*a**15*c**4*x**6 + 384*a**14*c**4*x**5 - 192*a**13*c**4*x**4 - 768*a**12*c**4*x**3 - 192*a**11*c**4*x**2 + 384*a**10*c**4*x + 192*a**9*c**4) + x/(a**8*c**4) + (47*log(x - 1/a)/128 - 303*log(x + 1/a)/128)/(a**9*c**4))","A",0
822,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**4*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
823,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**3*((a*x-1)/(a*x+1))**(3/2),x)","\frac{c^{3} \left(\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{7} + x^{6}}\, dx + \int \left(- \frac{a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{6} + x^{5}}\right)\, dx + \int \left(- \frac{3 a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{5} + x^{4}}\right)\, dx + \int \frac{3 a^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{4} + x^{3}}\, dx + \int \frac{3 a^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{3} + x^{2}}\, dx + \int \left(- \frac{3 a^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{2} + x}\right)\, dx + \int \left(- \frac{a^{6} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{7} x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)}{a^{6}}"," ",0,"c**3*(Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**7 + x**6), x) + Integral(-a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**6 + x**5), x) + Integral(-3*a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**5 + x**4), x) + Integral(3*a**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**4 + x**3), x) + Integral(3*a**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**3 + x**2), x) + Integral(-3*a**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**2 + x), x) + Integral(-a**6*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**7*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))/a**6","F",0
824,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**2*((a*x-1)/(a*x+1))**(3/2),x)","\frac{c^{2} \left(\int \left(- \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{5} + x^{4}}\right)\, dx + \int \frac{a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{4} + x^{3}}\, dx + \int \frac{2 a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{3} + x^{2}}\, dx + \int \left(- \frac{2 a^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{2} + x}\right)\, dx + \int \left(- \frac{a^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{5} x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)}{a^{4}}"," ",0,"c**2*(Integral(-sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**5 + x**4), x) + Integral(a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**4 + x**3), x) + Integral(2*a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**3 + x**2), x) + Integral(-2*a**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**2 + x), x) + Integral(-a**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**5*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))/a**4","F",0
825,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)*((a*x-1)/(a*x+1))**(3/2),x)","\frac{c \left(\int \frac{\sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{3} + x^{2}}\, dx + \int \left(- \frac{a \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x^{2} + x}\right)\, dx + \int \left(- \frac{a^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\right)\, dx + \int \frac{a^{3} x \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a x + 1}\, dx\right)}{a^{2}}"," ",0,"c*(Integral(sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**3 + x**2), x) + Integral(-a*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x**2 + x), x) + Integral(-a**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x) + Integral(a**3*x*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a*x + 1), x))/a**2","F",0
826,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2),x)","\frac{a^{2} \left(\int \left(- \frac{x^{2} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{3} x^{3} + a^{2} x^{2} - a x - 1}\right)\, dx + \int \frac{a x^{3} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{3} x^{3} + a^{2} x^{2} - a x - 1}\, dx\right)}{c}"," ",0,"a**2*(Integral(-x**2*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**3*x**3 + a**2*x**2 - a*x - 1), x) + Integral(a*x**3*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**3*x**3 + a**2*x**2 - a*x - 1), x))/c","F",0
827,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**2,x)","\frac{a^{4} \left(\int \left(- \frac{x^{4} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{5} x^{5} + a^{4} x^{4} - 2 a^{3} x^{3} - 2 a^{2} x^{2} + a x + 1}\right)\, dx + \int \frac{a x^{5} \sqrt{\frac{a x}{a x + 1} - \frac{1}{a x + 1}}}{a^{5} x^{5} + a^{4} x^{4} - 2 a^{3} x^{3} - 2 a^{2} x^{2} + a x + 1}\, dx\right)}{c^{2}}"," ",0,"a**4*(Integral(-x**4*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**5*x**5 + a**4*x**4 - 2*a**3*x**3 - 2*a**2*x**2 + a*x + 1), x) + Integral(a*x**5*sqrt(a*x/(a*x + 1) - 1/(a*x + 1))/(a**5*x**5 + a**4*x**4 - 2*a**3*x**3 - 2*a**2*x**2 + a*x + 1), x))/c**2","F",0
828,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
829,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
830,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
831,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
832,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
833,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2)**(1/2),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
834,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
835,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
836,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
837,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
838,1,1059,0,33.428250," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**(7/2),x)","c^{3} \left(\begin{cases} \frac{\sqrt{c} \sqrt{a^{2} x^{2} - 1}}{a} - \frac{i \sqrt{c} \log{\left(a x \right)}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} + \frac{\sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} - \frac{i \sqrt{c} \log{\left(\sqrt{- a^{2} x^{2} + 1} + 1 \right)}}{a} & \text{otherwise} \end{cases}\right) + \frac{2 c^{3} \left(\begin{cases} - \frac{a \sqrt{c} x}{\sqrt{a^{2} x^{2} - 1}} + \sqrt{c} \operatorname{acosh}{\left(a x \right)} + \frac{\sqrt{c}}{a x \sqrt{a^{2} x^{2} - 1}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i a \sqrt{c} x}{\sqrt{- a^{2} x^{2} + 1}} - i \sqrt{c} \operatorname{asin}{\left(a x \right)} - \frac{i \sqrt{c}}{a x \sqrt{- a^{2} x^{2} + 1}} & \text{otherwise} \end{cases}\right)}{a} - \frac{c^{3} \left(\begin{cases} \frac{i a \sqrt{c} \operatorname{acosh}{\left(\frac{1}{a x} \right)}}{2} + \frac{i \sqrt{c}}{2 x \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} - \frac{i \sqrt{c}}{2 a^{2} x^{3} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\- \frac{a \sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{2} - \frac{\sqrt{c} \sqrt{1 - \frac{1}{a^{2} x^{2}}}}{2 x} & \text{otherwise} \end{cases}\right)}{a^{2}} - \frac{4 c^{3} \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{a^{2} \left(c - \frac{c}{a^{2} x^{2}}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right)}{a^{3}} - \frac{c^{3} \left(\begin{cases} \frac{i a^{3} \sqrt{c} \operatorname{acosh}{\left(\frac{1}{a x} \right)}}{8} - \frac{i a^{2} \sqrt{c}}{8 x \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} + \frac{3 i \sqrt{c}}{8 x^{3} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} - \frac{i \sqrt{c}}{4 a^{2} x^{5} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\- \frac{a^{3} \sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{8} + \frac{a^{2} \sqrt{c}}{8 x \sqrt{1 - \frac{1}{a^{2} x^{2}}}} - \frac{3 \sqrt{c}}{8 x^{3} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} + \frac{\sqrt{c}}{4 a^{2} x^{5} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} & \text{otherwise} \end{cases}\right)}{a^{4}} + \frac{2 c^{3} \left(\begin{cases} \frac{2 a^{3} \sqrt{c} \sqrt{a^{2} x^{2} - 1}}{15 x} + \frac{a \sqrt{c} \sqrt{a^{2} x^{2} - 1}}{15 x^{3}} - \frac{\sqrt{c} \sqrt{a^{2} x^{2} - 1}}{5 a x^{5}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{2 i a^{3} \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{15 x} + \frac{i a \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{15 x^{3}} - \frac{i \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{5 a x^{5}} & \text{otherwise} \end{cases}\right)}{a^{5}} + \frac{c^{3} \left(\begin{cases} \frac{i a^{5} \sqrt{c} \operatorname{acosh}{\left(\frac{1}{a x} \right)}}{16} - \frac{i a^{4} \sqrt{c}}{16 x \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} + \frac{i a^{2} \sqrt{c}}{48 x^{3} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} + \frac{5 i \sqrt{c}}{24 x^{5} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} - \frac{i \sqrt{c}}{6 a^{2} x^{7} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\- \frac{a^{5} \sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{16} + \frac{a^{4} \sqrt{c}}{16 x \sqrt{1 - \frac{1}{a^{2} x^{2}}}} - \frac{a^{2} \sqrt{c}}{48 x^{3} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} - \frac{5 \sqrt{c}}{24 x^{5} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} + \frac{\sqrt{c}}{6 a^{2} x^{7} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} & \text{otherwise} \end{cases}\right)}{a^{6}}"," ",0,"c**3*Piecewise((sqrt(c)*sqrt(a**2*x**2 - 1)/a - I*sqrt(c)*log(a*x)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) + sqrt(c)*asin(1/(a*x))/a, Abs(a**2*x**2) > 1), (I*sqrt(c)*sqrt(-a**2*x**2 + 1)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) - I*sqrt(c)*log(sqrt(-a**2*x**2 + 1) + 1)/a, True)) + 2*c**3*Piecewise((-a*sqrt(c)*x/sqrt(a**2*x**2 - 1) + sqrt(c)*acosh(a*x) + sqrt(c)/(a*x*sqrt(a**2*x**2 - 1)), Abs(a**2*x**2) > 1), (I*a*sqrt(c)*x/sqrt(-a**2*x**2 + 1) - I*sqrt(c)*asin(a*x) - I*sqrt(c)/(a*x*sqrt(-a**2*x**2 + 1)), True))/a - c**3*Piecewise((I*a*sqrt(c)*acosh(1/(a*x))/2 + I*sqrt(c)/(2*x*sqrt(-1 + 1/(a**2*x**2))) - I*sqrt(c)/(2*a**2*x**3*sqrt(-1 + 1/(a**2*x**2))), 1/Abs(a**2*x**2) > 1), (-a*sqrt(c)*asin(1/(a*x))/2 - sqrt(c)*sqrt(1 - 1/(a**2*x**2))/(2*x), True))/a**2 - 4*c**3*Piecewise((0, Eq(c, 0)), (a**2*(c - c/(a**2*x**2))**(3/2)/(3*c), True))/a**3 - c**3*Piecewise((I*a**3*sqrt(c)*acosh(1/(a*x))/8 - I*a**2*sqrt(c)/(8*x*sqrt(-1 + 1/(a**2*x**2))) + 3*I*sqrt(c)/(8*x**3*sqrt(-1 + 1/(a**2*x**2))) - I*sqrt(c)/(4*a**2*x**5*sqrt(-1 + 1/(a**2*x**2))), 1/Abs(a**2*x**2) > 1), (-a**3*sqrt(c)*asin(1/(a*x))/8 + a**2*sqrt(c)/(8*x*sqrt(1 - 1/(a**2*x**2))) - 3*sqrt(c)/(8*x**3*sqrt(1 - 1/(a**2*x**2))) + sqrt(c)/(4*a**2*x**5*sqrt(1 - 1/(a**2*x**2))), True))/a**4 + 2*c**3*Piecewise((2*a**3*sqrt(c)*sqrt(a**2*x**2 - 1)/(15*x) + a*sqrt(c)*sqrt(a**2*x**2 - 1)/(15*x**3) - sqrt(c)*sqrt(a**2*x**2 - 1)/(5*a*x**5), Abs(a**2*x**2) > 1), (2*I*a**3*sqrt(c)*sqrt(-a**2*x**2 + 1)/(15*x) + I*a*sqrt(c)*sqrt(-a**2*x**2 + 1)/(15*x**3) - I*sqrt(c)*sqrt(-a**2*x**2 + 1)/(5*a*x**5), True))/a**5 + c**3*Piecewise((I*a**5*sqrt(c)*acosh(1/(a*x))/16 - I*a**4*sqrt(c)/(16*x*sqrt(-1 + 1/(a**2*x**2))) + I*a**2*sqrt(c)/(48*x**3*sqrt(-1 + 1/(a**2*x**2))) + 5*I*sqrt(c)/(24*x**5*sqrt(-1 + 1/(a**2*x**2))) - I*sqrt(c)/(6*a**2*x**7*sqrt(-1 + 1/(a**2*x**2))), 1/Abs(a**2*x**2) > 1), (-a**5*sqrt(c)*asin(1/(a*x))/16 + a**4*sqrt(c)/(16*x*sqrt(1 - 1/(a**2*x**2))) - a**2*sqrt(c)/(48*x**3*sqrt(1 - 1/(a**2*x**2))) - 5*sqrt(c)/(24*x**5*sqrt(1 - 1/(a**2*x**2))) + sqrt(c)/(6*a**2*x**7*sqrt(1 - 1/(a**2*x**2))), True))/a**6","C",0
839,1,500,0,20.073418," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**(5/2),x)","c^{2} \left(\begin{cases} \frac{\sqrt{c} \sqrt{a^{2} x^{2} - 1}}{a} - \frac{i \sqrt{c} \log{\left(a x \right)}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} + \frac{\sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} - \frac{i \sqrt{c} \log{\left(\sqrt{- a^{2} x^{2} + 1} + 1 \right)}}{a} & \text{otherwise} \end{cases}\right) + \frac{2 c^{2} \left(\begin{cases} - \frac{a \sqrt{c} x}{\sqrt{a^{2} x^{2} - 1}} + \sqrt{c} \operatorname{acosh}{\left(a x \right)} + \frac{\sqrt{c}}{a x \sqrt{a^{2} x^{2} - 1}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i a \sqrt{c} x}{\sqrt{- a^{2} x^{2} + 1}} - i \sqrt{c} \operatorname{asin}{\left(a x \right)} - \frac{i \sqrt{c}}{a x \sqrt{- a^{2} x^{2} + 1}} & \text{otherwise} \end{cases}\right)}{a} - \frac{2 c^{2} \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{a^{2} \left(c - \frac{c}{a^{2} x^{2}}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right)}{a^{3}} - \frac{c^{2} \left(\begin{cases} \frac{i a^{3} \sqrt{c} \operatorname{acosh}{\left(\frac{1}{a x} \right)}}{8} - \frac{i a^{2} \sqrt{c}}{8 x \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} + \frac{3 i \sqrt{c}}{8 x^{3} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} - \frac{i \sqrt{c}}{4 a^{2} x^{5} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\- \frac{a^{3} \sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{8} + \frac{a^{2} \sqrt{c}}{8 x \sqrt{1 - \frac{1}{a^{2} x^{2}}}} - \frac{3 \sqrt{c}}{8 x^{3} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} + \frac{\sqrt{c}}{4 a^{2} x^{5} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} & \text{otherwise} \end{cases}\right)}{a^{4}}"," ",0,"c**2*Piecewise((sqrt(c)*sqrt(a**2*x**2 - 1)/a - I*sqrt(c)*log(a*x)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) + sqrt(c)*asin(1/(a*x))/a, Abs(a**2*x**2) > 1), (I*sqrt(c)*sqrt(-a**2*x**2 + 1)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) - I*sqrt(c)*log(sqrt(-a**2*x**2 + 1) + 1)/a, True)) + 2*c**2*Piecewise((-a*sqrt(c)*x/sqrt(a**2*x**2 - 1) + sqrt(c)*acosh(a*x) + sqrt(c)/(a*x*sqrt(a**2*x**2 - 1)), Abs(a**2*x**2) > 1), (I*a*sqrt(c)*x/sqrt(-a**2*x**2 + 1) - I*sqrt(c)*asin(a*x) - I*sqrt(c)/(a*x*sqrt(-a**2*x**2 + 1)), True))/a - 2*c**2*Piecewise((0, Eq(c, 0)), (a**2*(c - c/(a**2*x**2))**(3/2)/(3*c), True))/a**3 - c**2*Piecewise((I*a**3*sqrt(c)*acosh(1/(a*x))/8 - I*a**2*sqrt(c)/(8*x*sqrt(-1 + 1/(a**2*x**2))) + 3*I*sqrt(c)/(8*x**3*sqrt(-1 + 1/(a**2*x**2))) - I*sqrt(c)/(4*a**2*x**5*sqrt(-1 + 1/(a**2*x**2))), 1/Abs(a**2*x**2) > 1), (-a**3*sqrt(c)*asin(1/(a*x))/8 + a**2*sqrt(c)/(8*x*sqrt(1 - 1/(a**2*x**2))) - 3*sqrt(c)/(8*x**3*sqrt(1 - 1/(a**2*x**2))) + sqrt(c)/(4*a**2*x**5*sqrt(1 - 1/(a**2*x**2))), True))/a**4","C",0
840,1,376,0,14.141185," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**(3/2),x)","c \left(\begin{cases} \frac{\sqrt{c} \sqrt{a^{2} x^{2} - 1}}{a} - \frac{i \sqrt{c} \log{\left(a x \right)}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} + \frac{\sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} - \frac{i \sqrt{c} \log{\left(\sqrt{- a^{2} x^{2} + 1} + 1 \right)}}{a} & \text{otherwise} \end{cases}\right) + \frac{2 c \left(\begin{cases} - \frac{a \sqrt{c} x}{\sqrt{a^{2} x^{2} - 1}} + \sqrt{c} \operatorname{acosh}{\left(a x \right)} + \frac{\sqrt{c}}{a x \sqrt{a^{2} x^{2} - 1}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i a \sqrt{c} x}{\sqrt{- a^{2} x^{2} + 1}} - i \sqrt{c} \operatorname{asin}{\left(a x \right)} - \frac{i \sqrt{c}}{a x \sqrt{- a^{2} x^{2} + 1}} & \text{otherwise} \end{cases}\right)}{a} + \frac{c \left(\begin{cases} \frac{i a \sqrt{c} \operatorname{acosh}{\left(\frac{1}{a x} \right)}}{2} + \frac{i \sqrt{c}}{2 x \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} - \frac{i \sqrt{c}}{2 a^{2} x^{3} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\- \frac{a \sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{2} - \frac{\sqrt{c} \sqrt{1 - \frac{1}{a^{2} x^{2}}}}{2 x} & \text{otherwise} \end{cases}\right)}{a^{2}}"," ",0,"c*Piecewise((sqrt(c)*sqrt(a**2*x**2 - 1)/a - I*sqrt(c)*log(a*x)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) + sqrt(c)*asin(1/(a*x))/a, Abs(a**2*x**2) > 1), (I*sqrt(c)*sqrt(-a**2*x**2 + 1)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) - I*sqrt(c)*log(sqrt(-a**2*x**2 + 1) + 1)/a, True)) + 2*c*Piecewise((-a*sqrt(c)*x/sqrt(a**2*x**2 - 1) + sqrt(c)*acosh(a*x) + sqrt(c)/(a*x*sqrt(a**2*x**2 - 1)), Abs(a**2*x**2) > 1), (I*a*sqrt(c)*x/sqrt(-a**2*x**2 + 1) - I*sqrt(c)*asin(a*x) - I*sqrt(c)/(a*x*sqrt(-a**2*x**2 + 1)), True))/a + c*Piecewise((I*a*sqrt(c)*acosh(1/(a*x))/2 + I*sqrt(c)/(2*x*sqrt(-1 + 1/(a**2*x**2))) - I*sqrt(c)/(2*a**2*x**3*sqrt(-1 + 1/(a**2*x**2))), 1/Abs(a**2*x**2) > 1), (-a*sqrt(c)*asin(1/(a*x))/2 - sqrt(c)*sqrt(1 - 1/(a**2*x**2))/(2*x), True))/a**2","C",0
841,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**(1/2),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)/(a*x - 1), x)","F",0
842,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a**2/x**2)**(1/2),x)","\int \frac{a x + 1}{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)), x)","F",0
843,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a**2/x**2)**(3/2),x)","\int \frac{a x + 1}{\left(- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)\right)^{\frac{3}{2}} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/((-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))**(3/2)*(a*x - 1)), x)","F",0
844,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a**2/x**2)**(5/2),x)","\int \frac{a x + 1}{\left(- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)\right)^{\frac{5}{2}} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/((-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))**(5/2)*(a*x - 1)), x)","F",0
845,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a**2/x**2)**(7/2),x)","\int \frac{a x + 1}{\left(- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)\right)^{\frac{7}{2}} \left(a x - 1\right)}\, dx"," ",0,"Integral((a*x + 1)/((-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))**(7/2)*(a*x - 1)), x)","F",0
846,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
847,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
849,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
852,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
854,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(7/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
856,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(5/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
857,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(3/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
858,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
859,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**(1/2),x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)}}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))/sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x))), x)","F",0
860,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
861,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
862,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(1/2)/(c-c/a**2/x**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
863,1,1059,0,32.676526," ","integrate((c-c/a**2/x**2)**(7/2)*(a*x-1)/(a*x+1),x)","c^{3} \left(\begin{cases} \frac{\sqrt{c} \sqrt{a^{2} x^{2} - 1}}{a} - \frac{i \sqrt{c} \log{\left(a x \right)}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} + \frac{\sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} - \frac{i \sqrt{c} \log{\left(\sqrt{- a^{2} x^{2} + 1} + 1 \right)}}{a} & \text{otherwise} \end{cases}\right) - \frac{2 c^{3} \left(\begin{cases} - \frac{a \sqrt{c} x}{\sqrt{a^{2} x^{2} - 1}} + \sqrt{c} \operatorname{acosh}{\left(a x \right)} + \frac{\sqrt{c}}{a x \sqrt{a^{2} x^{2} - 1}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i a \sqrt{c} x}{\sqrt{- a^{2} x^{2} + 1}} - i \sqrt{c} \operatorname{asin}{\left(a x \right)} - \frac{i \sqrt{c}}{a x \sqrt{- a^{2} x^{2} + 1}} & \text{otherwise} \end{cases}\right)}{a} - \frac{c^{3} \left(\begin{cases} \frac{i a \sqrt{c} \operatorname{acosh}{\left(\frac{1}{a x} \right)}}{2} + \frac{i \sqrt{c}}{2 x \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} - \frac{i \sqrt{c}}{2 a^{2} x^{3} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\- \frac{a \sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{2} - \frac{\sqrt{c} \sqrt{1 - \frac{1}{a^{2} x^{2}}}}{2 x} & \text{otherwise} \end{cases}\right)}{a^{2}} + \frac{4 c^{3} \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{a^{2} \left(c - \frac{c}{a^{2} x^{2}}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right)}{a^{3}} - \frac{c^{3} \left(\begin{cases} \frac{i a^{3} \sqrt{c} \operatorname{acosh}{\left(\frac{1}{a x} \right)}}{8} - \frac{i a^{2} \sqrt{c}}{8 x \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} + \frac{3 i \sqrt{c}}{8 x^{3} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} - \frac{i \sqrt{c}}{4 a^{2} x^{5} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\- \frac{a^{3} \sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{8} + \frac{a^{2} \sqrt{c}}{8 x \sqrt{1 - \frac{1}{a^{2} x^{2}}}} - \frac{3 \sqrt{c}}{8 x^{3} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} + \frac{\sqrt{c}}{4 a^{2} x^{5} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} & \text{otherwise} \end{cases}\right)}{a^{4}} - \frac{2 c^{3} \left(\begin{cases} \frac{2 a^{3} \sqrt{c} \sqrt{a^{2} x^{2} - 1}}{15 x} + \frac{a \sqrt{c} \sqrt{a^{2} x^{2} - 1}}{15 x^{3}} - \frac{\sqrt{c} \sqrt{a^{2} x^{2} - 1}}{5 a x^{5}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{2 i a^{3} \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{15 x} + \frac{i a \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{15 x^{3}} - \frac{i \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{5 a x^{5}} & \text{otherwise} \end{cases}\right)}{a^{5}} + \frac{c^{3} \left(\begin{cases} \frac{i a^{5} \sqrt{c} \operatorname{acosh}{\left(\frac{1}{a x} \right)}}{16} - \frac{i a^{4} \sqrt{c}}{16 x \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} + \frac{i a^{2} \sqrt{c}}{48 x^{3} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} + \frac{5 i \sqrt{c}}{24 x^{5} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} - \frac{i \sqrt{c}}{6 a^{2} x^{7} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\- \frac{a^{5} \sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{16} + \frac{a^{4} \sqrt{c}}{16 x \sqrt{1 - \frac{1}{a^{2} x^{2}}}} - \frac{a^{2} \sqrt{c}}{48 x^{3} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} - \frac{5 \sqrt{c}}{24 x^{5} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} + \frac{\sqrt{c}}{6 a^{2} x^{7} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} & \text{otherwise} \end{cases}\right)}{a^{6}}"," ",0,"c**3*Piecewise((sqrt(c)*sqrt(a**2*x**2 - 1)/a - I*sqrt(c)*log(a*x)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) + sqrt(c)*asin(1/(a*x))/a, Abs(a**2*x**2) > 1), (I*sqrt(c)*sqrt(-a**2*x**2 + 1)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) - I*sqrt(c)*log(sqrt(-a**2*x**2 + 1) + 1)/a, True)) - 2*c**3*Piecewise((-a*sqrt(c)*x/sqrt(a**2*x**2 - 1) + sqrt(c)*acosh(a*x) + sqrt(c)/(a*x*sqrt(a**2*x**2 - 1)), Abs(a**2*x**2) > 1), (I*a*sqrt(c)*x/sqrt(-a**2*x**2 + 1) - I*sqrt(c)*asin(a*x) - I*sqrt(c)/(a*x*sqrt(-a**2*x**2 + 1)), True))/a - c**3*Piecewise((I*a*sqrt(c)*acosh(1/(a*x))/2 + I*sqrt(c)/(2*x*sqrt(-1 + 1/(a**2*x**2))) - I*sqrt(c)/(2*a**2*x**3*sqrt(-1 + 1/(a**2*x**2))), 1/Abs(a**2*x**2) > 1), (-a*sqrt(c)*asin(1/(a*x))/2 - sqrt(c)*sqrt(1 - 1/(a**2*x**2))/(2*x), True))/a**2 + 4*c**3*Piecewise((0, Eq(c, 0)), (a**2*(c - c/(a**2*x**2))**(3/2)/(3*c), True))/a**3 - c**3*Piecewise((I*a**3*sqrt(c)*acosh(1/(a*x))/8 - I*a**2*sqrt(c)/(8*x*sqrt(-1 + 1/(a**2*x**2))) + 3*I*sqrt(c)/(8*x**3*sqrt(-1 + 1/(a**2*x**2))) - I*sqrt(c)/(4*a**2*x**5*sqrt(-1 + 1/(a**2*x**2))), 1/Abs(a**2*x**2) > 1), (-a**3*sqrt(c)*asin(1/(a*x))/8 + a**2*sqrt(c)/(8*x*sqrt(1 - 1/(a**2*x**2))) - 3*sqrt(c)/(8*x**3*sqrt(1 - 1/(a**2*x**2))) + sqrt(c)/(4*a**2*x**5*sqrt(1 - 1/(a**2*x**2))), True))/a**4 - 2*c**3*Piecewise((2*a**3*sqrt(c)*sqrt(a**2*x**2 - 1)/(15*x) + a*sqrt(c)*sqrt(a**2*x**2 - 1)/(15*x**3) - sqrt(c)*sqrt(a**2*x**2 - 1)/(5*a*x**5), Abs(a**2*x**2) > 1), (2*I*a**3*sqrt(c)*sqrt(-a**2*x**2 + 1)/(15*x) + I*a*sqrt(c)*sqrt(-a**2*x**2 + 1)/(15*x**3) - I*sqrt(c)*sqrt(-a**2*x**2 + 1)/(5*a*x**5), True))/a**5 + c**3*Piecewise((I*a**5*sqrt(c)*acosh(1/(a*x))/16 - I*a**4*sqrt(c)/(16*x*sqrt(-1 + 1/(a**2*x**2))) + I*a**2*sqrt(c)/(48*x**3*sqrt(-1 + 1/(a**2*x**2))) + 5*I*sqrt(c)/(24*x**5*sqrt(-1 + 1/(a**2*x**2))) - I*sqrt(c)/(6*a**2*x**7*sqrt(-1 + 1/(a**2*x**2))), 1/Abs(a**2*x**2) > 1), (-a**5*sqrt(c)*asin(1/(a*x))/16 + a**4*sqrt(c)/(16*x*sqrt(1 - 1/(a**2*x**2))) - a**2*sqrt(c)/(48*x**3*sqrt(1 - 1/(a**2*x**2))) - 5*sqrt(c)/(24*x**5*sqrt(1 - 1/(a**2*x**2))) + sqrt(c)/(6*a**2*x**7*sqrt(1 - 1/(a**2*x**2))), True))/a**6","C",0
864,1,500,0,19.521451," ","integrate((c-c/a**2/x**2)**(5/2)*(a*x-1)/(a*x+1),x)","c^{2} \left(\begin{cases} \frac{\sqrt{c} \sqrt{a^{2} x^{2} - 1}}{a} - \frac{i \sqrt{c} \log{\left(a x \right)}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} + \frac{\sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} - \frac{i \sqrt{c} \log{\left(\sqrt{- a^{2} x^{2} + 1} + 1 \right)}}{a} & \text{otherwise} \end{cases}\right) - \frac{2 c^{2} \left(\begin{cases} - \frac{a \sqrt{c} x}{\sqrt{a^{2} x^{2} - 1}} + \sqrt{c} \operatorname{acosh}{\left(a x \right)} + \frac{\sqrt{c}}{a x \sqrt{a^{2} x^{2} - 1}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i a \sqrt{c} x}{\sqrt{- a^{2} x^{2} + 1}} - i \sqrt{c} \operatorname{asin}{\left(a x \right)} - \frac{i \sqrt{c}}{a x \sqrt{- a^{2} x^{2} + 1}} & \text{otherwise} \end{cases}\right)}{a} + \frac{2 c^{2} \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{a^{2} \left(c - \frac{c}{a^{2} x^{2}}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right)}{a^{3}} - \frac{c^{2} \left(\begin{cases} \frac{i a^{3} \sqrt{c} \operatorname{acosh}{\left(\frac{1}{a x} \right)}}{8} - \frac{i a^{2} \sqrt{c}}{8 x \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} + \frac{3 i \sqrt{c}}{8 x^{3} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} - \frac{i \sqrt{c}}{4 a^{2} x^{5} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\- \frac{a^{3} \sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{8} + \frac{a^{2} \sqrt{c}}{8 x \sqrt{1 - \frac{1}{a^{2} x^{2}}}} - \frac{3 \sqrt{c}}{8 x^{3} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} + \frac{\sqrt{c}}{4 a^{2} x^{5} \sqrt{1 - \frac{1}{a^{2} x^{2}}}} & \text{otherwise} \end{cases}\right)}{a^{4}}"," ",0,"c**2*Piecewise((sqrt(c)*sqrt(a**2*x**2 - 1)/a - I*sqrt(c)*log(a*x)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) + sqrt(c)*asin(1/(a*x))/a, Abs(a**2*x**2) > 1), (I*sqrt(c)*sqrt(-a**2*x**2 + 1)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) - I*sqrt(c)*log(sqrt(-a**2*x**2 + 1) + 1)/a, True)) - 2*c**2*Piecewise((-a*sqrt(c)*x/sqrt(a**2*x**2 - 1) + sqrt(c)*acosh(a*x) + sqrt(c)/(a*x*sqrt(a**2*x**2 - 1)), Abs(a**2*x**2) > 1), (I*a*sqrt(c)*x/sqrt(-a**2*x**2 + 1) - I*sqrt(c)*asin(a*x) - I*sqrt(c)/(a*x*sqrt(-a**2*x**2 + 1)), True))/a + 2*c**2*Piecewise((0, Eq(c, 0)), (a**2*(c - c/(a**2*x**2))**(3/2)/(3*c), True))/a**3 - c**2*Piecewise((I*a**3*sqrt(c)*acosh(1/(a*x))/8 - I*a**2*sqrt(c)/(8*x*sqrt(-1 + 1/(a**2*x**2))) + 3*I*sqrt(c)/(8*x**3*sqrt(-1 + 1/(a**2*x**2))) - I*sqrt(c)/(4*a**2*x**5*sqrt(-1 + 1/(a**2*x**2))), 1/Abs(a**2*x**2) > 1), (-a**3*sqrt(c)*asin(1/(a*x))/8 + a**2*sqrt(c)/(8*x*sqrt(1 - 1/(a**2*x**2))) - 3*sqrt(c)/(8*x**3*sqrt(1 - 1/(a**2*x**2))) + sqrt(c)/(4*a**2*x**5*sqrt(1 - 1/(a**2*x**2))), True))/a**4","C",0
865,1,376,0,13.214815," ","integrate((c-c/a**2/x**2)**(3/2)*(a*x-1)/(a*x+1),x)","c \left(\begin{cases} \frac{\sqrt{c} \sqrt{a^{2} x^{2} - 1}}{a} - \frac{i \sqrt{c} \log{\left(a x \right)}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} + \frac{\sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{a} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{c} \sqrt{- a^{2} x^{2} + 1}}{a} + \frac{i \sqrt{c} \log{\left(a^{2} x^{2} \right)}}{2 a} - \frac{i \sqrt{c} \log{\left(\sqrt{- a^{2} x^{2} + 1} + 1 \right)}}{a} & \text{otherwise} \end{cases}\right) - \frac{2 c \left(\begin{cases} - \frac{a \sqrt{c} x}{\sqrt{a^{2} x^{2} - 1}} + \sqrt{c} \operatorname{acosh}{\left(a x \right)} + \frac{\sqrt{c}}{a x \sqrt{a^{2} x^{2} - 1}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{i a \sqrt{c} x}{\sqrt{- a^{2} x^{2} + 1}} - i \sqrt{c} \operatorname{asin}{\left(a x \right)} - \frac{i \sqrt{c}}{a x \sqrt{- a^{2} x^{2} + 1}} & \text{otherwise} \end{cases}\right)}{a} + \frac{c \left(\begin{cases} \frac{i a \sqrt{c} \operatorname{acosh}{\left(\frac{1}{a x} \right)}}{2} + \frac{i \sqrt{c}}{2 x \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} - \frac{i \sqrt{c}}{2 a^{2} x^{3} \sqrt{-1 + \frac{1}{a^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{a^{2} x^{2}}\right|} > 1 \\- \frac{a \sqrt{c} \operatorname{asin}{\left(\frac{1}{a x} \right)}}{2} - \frac{\sqrt{c} \sqrt{1 - \frac{1}{a^{2} x^{2}}}}{2 x} & \text{otherwise} \end{cases}\right)}{a^{2}}"," ",0,"c*Piecewise((sqrt(c)*sqrt(a**2*x**2 - 1)/a - I*sqrt(c)*log(a*x)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) + sqrt(c)*asin(1/(a*x))/a, Abs(a**2*x**2) > 1), (I*sqrt(c)*sqrt(-a**2*x**2 + 1)/a + I*sqrt(c)*log(a**2*x**2)/(2*a) - I*sqrt(c)*log(sqrt(-a**2*x**2 + 1) + 1)/a, True)) - 2*c*Piecewise((-a*sqrt(c)*x/sqrt(a**2*x**2 - 1) + sqrt(c)*acosh(a*x) + sqrt(c)/(a*x*sqrt(a**2*x**2 - 1)), Abs(a**2*x**2) > 1), (I*a*sqrt(c)*x/sqrt(-a**2*x**2 + 1) - I*sqrt(c)*asin(a*x) - I*sqrt(c)/(a*x*sqrt(-a**2*x**2 + 1)), True))/a + c*Piecewise((I*a*sqrt(c)*acosh(1/(a*x))/2 + I*sqrt(c)/(2*x*sqrt(-1 + 1/(a**2*x**2))) - I*sqrt(c)/(2*a**2*x**3*sqrt(-1 + 1/(a**2*x**2))), 1/Abs(a**2*x**2) > 1), (-a*sqrt(c)*asin(1/(a*x))/2 - sqrt(c)*sqrt(1 - 1/(a**2*x**2))/(2*x), True))/a**2","C",0
866,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)/(a*x + 1), x)","F",0
867,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a**2/x**2)**(1/2),x)","\int \frac{a x - 1}{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)), x)","F",0
868,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a**2/x**2)**(3/2),x)","\int \frac{a x - 1}{\left(- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)\right)^{\frac{3}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))**(3/2)*(a*x + 1)), x)","F",0
869,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a**2/x**2)**(5/2),x)","\int \frac{a x - 1}{\left(- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)\right)^{\frac{5}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))**(5/2)*(a*x + 1)), x)","F",0
870,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a**2/x**2)**(7/2),x)","\int \frac{a x - 1}{\left(- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)\right)^{\frac{7}{2}} \left(a x + 1\right)}\, dx"," ",0,"Integral((a*x - 1)/((-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))**(7/2)*(a*x + 1)), x)","F",0
871,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(9/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
872,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(7/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
873,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(5/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
874,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(3/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
875,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
876,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
877,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
878,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,-1,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))**(3/2)/(c-c/a**2/x**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**m*(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
881,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x**2*(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
882,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*x*(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
883,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2)**(1/2),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)}}{\sqrt{\frac{a x - 1}{a x + 1}}}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
884,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2)**(1/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
885,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(1/2)*(c-c/a**2/x**2)**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
886,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x**3*(c-c/a**2/x**2)**(1/2),x)","\int \frac{x^{3} \sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(x**3*sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)/(a*x - 1), x)","F",0
887,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x**2*(c-c/a**2/x**2)**(1/2),x)","\int \frac{x^{2} \sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(x**2*sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)/(a*x - 1), x)","F",0
888,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x*(c-c/a**2/x**2)**(1/2),x)","\int \frac{x \sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(x*sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)/(a*x - 1), x)","F",0
889,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**(1/2),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{a x - 1}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)/(a*x - 1), x)","F",0
890,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**(1/2)/x,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{x \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)/(x*(a*x - 1)), x)","F",0
891,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**(1/2)/x**2,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{x^{2} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)/(x**2*(a*x - 1)), x)","F",0
892,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**(1/2)/x**3,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{x^{3} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)/(x**3*(a*x - 1)), x)","F",0
893,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**(1/2)/x**4,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{x^{4} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)/(x**4*(a*x - 1)), x)","F",0
894,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a**2/x**2)**(1/2)/x**5,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x + 1\right)}{x^{5} \left(a x - 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x + 1)/(x**5*(a*x - 1)), x)","F",0
895,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**3*(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
896,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x**2*(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*x*(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
899,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(1/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
900,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
901,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(1/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
902,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(1/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
903,-1,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))**(3/2)*(c-c/a**2/x**2)**(1/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
904,-1,0,0,0.000000," ","integrate(x**m*(c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
905,-1,0,0,0.000000," ","integrate(x**2*(c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
906,-1,0,0,0.000000," ","integrate(x*(c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
908,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(1/2)/x,x)","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}} \sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)}}{x}\, dx"," ",0,"Integral(sqrt((a*x - 1)/(a*x + 1))*sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))/x, x)","F",0
909,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
910,0,0,0,0.000000," ","integrate(x**3*(c-c/a**2/x**2)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{x^{3} \sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(x**3*sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)/(a*x + 1), x)","F",0
911,0,0,0,0.000000," ","integrate(x**2*(c-c/a**2/x**2)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{x^{2} \sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(x**2*sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)/(a*x + 1), x)","F",0
912,0,0,0,0.000000," ","integrate(x*(c-c/a**2/x**2)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{x \sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(x*sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)/(a*x + 1), x)","F",0
913,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*(a*x-1)/(a*x+1),x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{a x + 1}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)/(a*x + 1), x)","F",0
914,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*(a*x-1)/(a*x+1)/x,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{x \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)/(x*(a*x + 1)), x)","F",0
915,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*(a*x-1)/(a*x+1)/x**2,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{x^{2} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)/(x**2*(a*x + 1)), x)","F",0
916,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*(a*x-1)/(a*x+1)/x**3,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{x^{3} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)/(x**3*(a*x + 1)), x)","F",0
917,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*(a*x-1)/(a*x+1)/x**4,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{x^{4} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)/(x**4*(a*x + 1)), x)","F",0
918,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*(a*x-1)/(a*x+1)/x**5,x)","\int \frac{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} \left(a x - 1\right)}{x^{5} \left(a x + 1\right)}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*(a*x - 1)/(x**5*(a*x + 1)), x)","F",0
919,-1,0,0,0.000000," ","integrate(x**3*(c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
920,-1,0,0,0.000000," ","integrate(x**2*(c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
921,-1,0,0,0.000000," ","integrate(x*(c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
922,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
923,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
924,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
925,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
926,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
927,-1,0,0,0.000000," ","integrate((c-c/a**2/x**2)**(1/2)*((a*x-1)/(a*x+1))**(3/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
928,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(c-c/a**2/x**2),x)","\frac{c \left(\int a^{2} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx + \int \left(- \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{x^{2}}\right)\, dx\right)}{a^{2}}"," ",0,"c*(Integral(a**2*exp(n*acoth(a*x)), x) + Integral(-exp(n*acoth(a*x))/x**2, x))/a**2","F",0
929,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(c-c/a**2/x**2),x)","\frac{a^{2} \int \frac{x^{2} e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{2} x^{2} - 1}\, dx}{c}"," ",0,"a**2*Integral(x**2*exp(n*acoth(a*x))/(a**2*x**2 - 1), x)/c","F",0
930,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(c-c/a**2/x**2)**2,x)","\frac{a^{4} \int \frac{x^{4} e^{n \operatorname{acoth}{\left(a x \right)}}}{a^{4} x^{4} - 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"a**4*Integral(x**4*exp(n*acoth(a*x))/(a**4*x**4 - 2*a**2*x**2 + 1), x)/c**2","F",0
931,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(c-c/a**2/x**2)**(1/2),x)","\int \sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))*exp(n*acoth(a*x)), x)","F",0
932,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))/(c-c/a**2/x**2)**(1/2),x)","\int \frac{e^{n \operatorname{acoth}{\left(a x \right)}}}{\sqrt{- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)}}\, dx"," ",0,"Integral(exp(n*acoth(a*x))/sqrt(-c*(-1 + 1/(a*x))*(1 + 1/(a*x))), x)","F",0
933,0,0,0,0.000000," ","integrate(exp(n*acoth(a*x))*(c-c/a**2/x**2)**p,x)","\int \left(- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)\right)^{p} e^{n \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))**p*exp(n*acoth(a*x)), x)","F",0
934,0,0,0,0.000000," ","integrate((c-c/a**2/x**2)**p/exp(2*p*acoth(a*x)),x)","\int \left(- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)\right)^{p} e^{- 2 p \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))**p*exp(-2*p*acoth(a*x)), x)","F",0
935,0,0,0,0.000000," ","integrate(exp(2*p*acoth(a*x))*(c-c/a**2/x**2)**p,x)","\int \left(- c \left(-1 + \frac{1}{a x}\right) \left(1 + \frac{1}{a x}\right)\right)^{p} e^{2 p \operatorname{acoth}{\left(a x \right)}}\, dx"," ",0,"Integral((-c*(-1 + 1/(a*x))*(1 + 1/(a*x)))**p*exp(2*p*acoth(a*x)), x)","F",0
