1,0,0,0,0.000000," ","integrate(x**3*(c*x**2+b*x)**(1/2),x)","\int x^{3} \sqrt{x \left(b + c x\right)}\, dx"," ",0,"Integral(x**3*sqrt(x*(b + c*x)), x)","F",0
2,0,0,0,0.000000," ","integrate(x**2*(c*x**2+b*x)**(1/2),x)","\int x^{2} \sqrt{x \left(b + c x\right)}\, dx"," ",0,"Integral(x**2*sqrt(x*(b + c*x)), x)","F",0
3,0,0,0,0.000000," ","integrate(x*(c*x**2+b*x)**(1/2),x)","\int x \sqrt{x \left(b + c x\right)}\, dx"," ",0,"Integral(x*sqrt(x*(b + c*x)), x)","F",0
4,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2),x)","\int \sqrt{b x + c x^{2}}\, dx"," ",0,"Integral(sqrt(b*x + c*x**2), x)","F",0
5,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x, x)","F",0
6,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**2,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**2, x)","F",0
7,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**3,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**3, x)","F",0
8,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**4,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{4}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**4, x)","F",0
9,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**5,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{5}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**5, x)","F",0
10,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**6,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{6}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**6, x)","F",0
11,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**7,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{7}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**7, x)","F",0
12,0,0,0,0.000000," ","integrate(x**2*(c*x**2+b*x)**(3/2),x)","\int x^{2} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(x*(b + c*x))**(3/2), x)","F",0
13,0,0,0,0.000000," ","integrate(x*(c*x**2+b*x)**(3/2),x)","\int x \left(x \left(b + c x\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(x*(b + c*x))**(3/2), x)","F",0
14,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2),x)","\int \left(b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*x + c*x**2)**(3/2), x)","F",0
15,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x, x)","F",0
16,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**2,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**2, x)","F",0
17,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**3,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**3, x)","F",0
18,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**4,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**4, x)","F",0
19,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**5,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**5, x)","F",0
20,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**6,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**6, x)","F",0
21,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**7,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**7, x)","F",0
22,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**8,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{8}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**8, x)","F",0
23,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**9,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{9}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**9, x)","F",0
24,0,0,0,0.000000," ","integrate(x**2*(b*x**2+a*x)**(5/2),x)","\int x^{2} \left(x \left(a + b x\right)\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**2*(x*(a + b*x))**(5/2), x)","F",0
25,0,0,0,0.000000," ","integrate(x*(b*x**2+a*x)**(5/2),x)","\int x \left(x \left(a + b x\right)\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x*(x*(a + b*x))**(5/2), x)","F",0
26,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2),x)","\int \left(a x + b x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a*x + b*x**2)**(5/2), x)","F",0
27,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x, x)","F",0
28,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**2,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**2, x)","F",0
29,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**3,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{3}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**3, x)","F",0
30,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**4,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{4}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**4, x)","F",0
31,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**5,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{5}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**5, x)","F",0
32,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**6,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{6}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**6, x)","F",0
33,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**7,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{7}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**7, x)","F",0
34,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**8,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{8}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**8, x)","F",0
35,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**9,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{9}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**9, x)","F",0
36,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**10,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{10}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**10, x)","F",0
37,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**11,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{11}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**11, x)","F",0
38,0,0,0,0.000000," ","integrate((b*x**2+a*x)**(5/2)/x**12,x)","\int \frac{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}{x^{12}}\, dx"," ",0,"Integral((x*(a + b*x))**(5/2)/x**12, x)","F",0
39,0,0,0,0.000000," ","integrate(x*(-x**2+2*x)**(1/2),x)","\int x \sqrt{- x \left(x - 2\right)}\, dx"," ",0,"Integral(x*sqrt(-x*(x - 2)), x)","F",0
40,0,0,0,0.000000," ","integrate(x*(-4*x**2+3*x)**(1/2),x)","\int x \sqrt{- x \left(4 x - 3\right)}\, dx"," ",0,"Integral(x*sqrt(-x*(4*x - 3)), x)","F",0
41,0,0,0,0.000000," ","integrate(x*(x**2+x)**(1/2),x)","\int x \sqrt{x \left(x + 1\right)}\, dx"," ",0,"Integral(x*sqrt(x*(x + 1)), x)","F",0
42,0,0,0,0.000000," ","integrate(x**4/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{4}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**4/sqrt(x*(b + c*x)), x)","F",0
43,0,0,0,0.000000," ","integrate(x**3/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{3}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**3/sqrt(x*(b + c*x)), x)","F",0
44,0,0,0,0.000000," ","integrate(x**2/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{2}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**2/sqrt(x*(b + c*x)), x)","F",0
45,0,0,0,0.000000," ","integrate(x/(c*x**2+b*x)**(1/2),x)","\int \frac{x}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x/sqrt(x*(b + c*x)), x)","F",0
46,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{\sqrt{b x + c x^{2}}}\, dx"," ",0,"Integral(1/sqrt(b*x + c*x**2), x)","F",0
47,0,0,0,0.000000," ","integrate(1/x/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{x \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(x*(b + c*x))), x)","F",0
48,0,0,0,0.000000," ","integrate(1/x**2/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(1/(x**2*sqrt(x*(b + c*x))), x)","F",0
49,0,0,0,0.000000," ","integrate(1/x**3/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(1/(x**3*sqrt(x*(b + c*x))), x)","F",0
50,0,0,0,0.000000," ","integrate(1/x**4/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{x^{4} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(1/(x**4*sqrt(x*(b + c*x))), x)","F",0
51,0,0,0,0.000000," ","integrate(1/x**5/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{x^{5} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(1/(x**5*sqrt(x*(b + c*x))), x)","F",0
52,0,0,0,0.000000," ","integrate(x**4/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{4}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4/(x*(b + c*x))**(3/2), x)","F",0
53,0,0,0,0.000000," ","integrate(x**3/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{3}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/(x*(b + c*x))**(3/2), x)","F",0
54,0,0,0,0.000000," ","integrate(x**2/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{2}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/(x*(b + c*x))**(3/2), x)","F",0
55,0,0,0,0.000000," ","integrate(x/(c*x**2+b*x)**(3/2),x)","\int \frac{x}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(x*(b + c*x))**(3/2), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{\left(b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*x + c*x**2)**(-3/2), x)","F",0
57,0,0,0,0.000000," ","integrate(1/x/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{x \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(x*(b + c*x))**(3/2)), x)","F",0
58,0,0,0,0.000000," ","integrate(1/x**2/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{x^{2} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(x*(b + c*x))**(3/2)), x)","F",0
59,0,0,0,0.000000," ","integrate(1/x**3/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{x^{3} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*(x*(b + c*x))**(3/2)), x)","F",0
60,0,0,0,0.000000," ","integrate(x**6/(b*x**2+a*x)**(5/2),x)","\int \frac{x^{6}}{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**6/(x*(a + b*x))**(5/2), x)","F",0
61,0,0,0,0.000000," ","integrate(x**5/(b*x**2+a*x)**(5/2),x)","\int \frac{x^{5}}{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**5/(x*(a + b*x))**(5/2), x)","F",0
62,0,0,0,0.000000," ","integrate(x**4/(b*x**2+a*x)**(5/2),x)","\int \frac{x^{4}}{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4/(x*(a + b*x))**(5/2), x)","F",0
63,0,0,0,0.000000," ","integrate(x**3/(b*x**2+a*x)**(5/2),x)","\int \frac{x^{3}}{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3/(x*(a + b*x))**(5/2), x)","F",0
64,0,0,0,0.000000," ","integrate(x**2/(b*x**2+a*x)**(5/2),x)","\int \frac{x^{2}}{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/(x*(a + b*x))**(5/2), x)","F",0
65,0,0,0,0.000000," ","integrate(x/(b*x**2+a*x)**(5/2),x)","\int \frac{x}{\left(x \left(a + b x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/(x*(a + b*x))**(5/2), x)","F",0
66,0,0,0,0.000000," ","integrate(1/(b*x**2+a*x)**(5/2),x)","\int \frac{1}{\left(a x + b x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*x + b*x**2)**(-5/2), x)","F",0
67,0,0,0,0.000000," ","integrate(1/x/(b*x**2+a*x)**(5/2),x)","\int \frac{1}{x \left(x \left(a + b x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x*(x*(a + b*x))**(5/2)), x)","F",0
68,0,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a*x)**(5/2),x)","\int \frac{1}{x^{2} \left(x \left(a + b x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*(x*(a + b*x))**(5/2)), x)","F",0
69,0,0,0,0.000000," ","integrate(x/(-x**2+4*x)**(1/2),x)","\int \frac{x}{\sqrt{- x \left(x - 4\right)}}\, dx"," ",0,"Integral(x/sqrt(-x*(x - 4)), x)","F",0
70,0,0,0,0.000000," ","integrate(x/(x**2-4*x)**(1/2),x)","\int \frac{x}{\sqrt{x \left(x - 4\right)}}\, dx"," ",0,"Integral(x/sqrt(x*(x - 4)), x)","F",0
71,0,0,0,0.000000," ","integrate(x**2/(-x**2+2*x)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- x \left(x - 2\right)}}\, dx"," ",0,"Integral(x**2/sqrt(-x*(x - 2)), x)","F",0
72,0,0,0,0.000000," ","integrate(x**(7/2)*(c*x**2+b*x)**(1/2),x)","\int x^{\frac{7}{2}} \sqrt{x \left(b + c x\right)}\, dx"," ",0,"Integral(x**(7/2)*sqrt(x*(b + c*x)), x)","F",0
73,0,0,0,0.000000," ","integrate(x**(5/2)*(c*x**2+b*x)**(1/2),x)","\int x^{\frac{5}{2}} \sqrt{x \left(b + c x\right)}\, dx"," ",0,"Integral(x**(5/2)*sqrt(x*(b + c*x)), x)","F",0
74,0,0,0,0.000000," ","integrate(x**(3/2)*(c*x**2+b*x)**(1/2),x)","\int x^{\frac{3}{2}} \sqrt{x \left(b + c x\right)}\, dx"," ",0,"Integral(x**(3/2)*sqrt(x*(b + c*x)), x)","F",0
75,0,0,0,0.000000," ","integrate(x**(1/2)*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x} \sqrt{x \left(b + c x\right)}\, dx"," ",0,"Integral(sqrt(x)*sqrt(x*(b + c*x)), x)","F",0
76,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**(1/2),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{\sqrt{x}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/sqrt(x), x)","F",0
77,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**(3/2),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**(3/2), x)","F",0
78,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**(5/2),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**(5/2), x)","F",0
79,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**(7/2),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**(7/2), x)","F",0
80,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**(9/2),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{\frac{9}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**(9/2), x)","F",0
81,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/x**(11/2),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{x^{\frac{11}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/x**(11/2), x)","F",0
82,-1,0,0,0.000000," ","integrate(x**(7/2)*(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,0,0,0,0.000000," ","integrate(x**(5/2)*(c*x**2+b*x)**(3/2),x)","\int x^{\frac{5}{2}} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**(5/2)*(x*(b + c*x))**(3/2), x)","F",0
84,0,0,0,0.000000," ","integrate(x**(3/2)*(c*x**2+b*x)**(3/2),x)","\int x^{\frac{3}{2}} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**(3/2)*(x*(b + c*x))**(3/2), x)","F",0
85,0,0,0,0.000000," ","integrate(x**(1/2)*(c*x**2+b*x)**(3/2),x)","\int \sqrt{x} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(x)*(x*(b + c*x))**(3/2), x)","F",0
86,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**(1/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{\sqrt{x}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/sqrt(x), x)","F",0
87,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**(3/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{\frac{3}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**(3/2), x)","F",0
88,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**(5/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{\frac{5}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**(5/2), x)","F",0
89,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**(7/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{\frac{7}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**(7/2), x)","F",0
90,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**(9/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{\frac{9}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**(9/2), x)","F",0
91,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**(11/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{x^{\frac{11}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/x**(11/2), x)","F",0
92,-1,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/x**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,0,0,0,0.000000," ","integrate(x**(7/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{\frac{7}{2}}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**(7/2)/sqrt(x*(b + c*x)), x)","F",0
95,0,0,0,0.000000," ","integrate(x**(5/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{\frac{5}{2}}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**(5/2)/sqrt(x*(b + c*x)), x)","F",0
96,0,0,0,0.000000," ","integrate(x**(3/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{\frac{3}{2}}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**(3/2)/sqrt(x*(b + c*x)), x)","F",0
97,0,0,0,0.000000," ","integrate(x**(1/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{\sqrt{x}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(sqrt(x)/sqrt(x*(b + c*x)), x)","F",0
98,0,0,0,0.000000," ","integrate(1/x**(1/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{\sqrt{x} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(1/(sqrt(x)*sqrt(x*(b + c*x))), x)","F",0
99,0,0,0,0.000000," ","integrate(1/x**(3/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{x^{\frac{3}{2}} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(1/(x**(3/2)*sqrt(x*(b + c*x))), x)","F",0
100,0,0,0,0.000000," ","integrate(1/x**(5/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{x^{\frac{5}{2}} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(1/(x**(5/2)*sqrt(x*(b + c*x))), x)","F",0
101,0,0,0,0.000000," ","integrate(1/x**(7/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{x^{\frac{7}{2}} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(1/(x**(7/2)*sqrt(x*(b + c*x))), x)","F",0
102,-1,0,0,0.000000," ","integrate(x**(13/2)/(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,0,0,0,0.000000," ","integrate(x**(11/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{\frac{11}{2}}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(11/2)/(x*(b + c*x))**(3/2), x)","F",0
104,0,0,0,0.000000," ","integrate(x**(9/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{\frac{9}{2}}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(9/2)/(x*(b + c*x))**(3/2), x)","F",0
105,0,0,0,0.000000," ","integrate(x**(7/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{\frac{7}{2}}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(7/2)/(x*(b + c*x))**(3/2), x)","F",0
106,0,0,0,0.000000," ","integrate(x**(5/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{\frac{5}{2}}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(5/2)/(x*(b + c*x))**(3/2), x)","F",0
107,0,0,0,0.000000," ","integrate(x**(3/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{\frac{3}{2}}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(3/2)/(x*(b + c*x))**(3/2), x)","F",0
108,0,0,0,0.000000," ","integrate(x**(1/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{\sqrt{x}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(x)/(x*(b + c*x))**(3/2), x)","F",0
109,0,0,0,0.000000," ","integrate(1/x**(1/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{\sqrt{x} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(x)*(x*(b + c*x))**(3/2)), x)","F",0
110,0,0,0,0.000000," ","integrate(1/x**(3/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{x^{\frac{3}{2}} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**(3/2)*(x*(b + c*x))**(3/2)), x)","F",0
111,0,0,0,0.000000," ","integrate(1/x**(5/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{x^{\frac{5}{2}} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**(5/2)*(x*(b + c*x))**(3/2)), x)","F",0
112,1,738,0,1.766792," ","integrate((d*x)**m*(c*x**2+b*x)**3,x)","\begin{cases} \frac{- \frac{b^{3}}{3 x^{3}} - \frac{3 b^{2} c}{2 x^{2}} - \frac{3 b c^{2}}{x} + c^{3} \log{\left(x \right)}}{d^{7}} & \text{for}\: m = -7 \\\frac{- \frac{b^{3}}{2 x^{2}} - \frac{3 b^{2} c}{x} + 3 b c^{2} \log{\left(x \right)} + c^{3} x}{d^{6}} & \text{for}\: m = -6 \\\frac{- \frac{b^{3}}{x} + 3 b^{2} c \log{\left(x \right)} + 3 b c^{2} x + \frac{c^{3} x^{2}}{2}}{d^{5}} & \text{for}\: m = -5 \\\frac{b^{3} \log{\left(x \right)} + 3 b^{2} c x + \frac{3 b c^{2} x^{2}}{2} + \frac{c^{3} x^{3}}{3}}{d^{4}} & \text{for}\: m = -4 \\\frac{b^{3} d^{m} m^{3} x^{4} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{18 b^{3} d^{m} m^{2} x^{4} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{107 b^{3} d^{m} m x^{4} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{210 b^{3} d^{m} x^{4} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{3 b^{2} c d^{m} m^{3} x^{5} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{51 b^{2} c d^{m} m^{2} x^{5} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{282 b^{2} c d^{m} m x^{5} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{504 b^{2} c d^{m} x^{5} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{3 b c^{2} d^{m} m^{3} x^{6} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{48 b c^{2} d^{m} m^{2} x^{6} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{249 b c^{2} d^{m} m x^{6} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{420 b c^{2} d^{m} x^{6} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{c^{3} d^{m} m^{3} x^{7} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{15 c^{3} d^{m} m^{2} x^{7} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{74 c^{3} d^{m} m x^{7} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} + \frac{120 c^{3} d^{m} x^{7} x^{m}}{m^{4} + 22 m^{3} + 179 m^{2} + 638 m + 840} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-b**3/(3*x**3) - 3*b**2*c/(2*x**2) - 3*b*c**2/x + c**3*log(x))/d**7, Eq(m, -7)), ((-b**3/(2*x**2) - 3*b**2*c/x + 3*b*c**2*log(x) + c**3*x)/d**6, Eq(m, -6)), ((-b**3/x + 3*b**2*c*log(x) + 3*b*c**2*x + c**3*x**2/2)/d**5, Eq(m, -5)), ((b**3*log(x) + 3*b**2*c*x + 3*b*c**2*x**2/2 + c**3*x**3/3)/d**4, Eq(m, -4)), (b**3*d**m*m**3*x**4*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 18*b**3*d**m*m**2*x**4*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 107*b**3*d**m*m*x**4*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 210*b**3*d**m*x**4*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 3*b**2*c*d**m*m**3*x**5*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 51*b**2*c*d**m*m**2*x**5*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 282*b**2*c*d**m*m*x**5*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 504*b**2*c*d**m*x**5*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 3*b*c**2*d**m*m**3*x**6*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 48*b*c**2*d**m*m**2*x**6*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 249*b*c**2*d**m*m*x**6*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 420*b*c**2*d**m*x**6*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + c**3*d**m*m**3*x**7*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 15*c**3*d**m*m**2*x**7*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 74*c**3*d**m*m*x**7*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840) + 120*c**3*d**m*x**7*x**m/(m**4 + 22*m**3 + 179*m**2 + 638*m + 840), True))","A",0
113,1,345,0,0.991235," ","integrate((d*x)**m*(c*x**2+b*x)**2,x)","\begin{cases} \frac{- \frac{b^{2}}{2 x^{2}} - \frac{2 b c}{x} + c^{2} \log{\left(x \right)}}{d^{5}} & \text{for}\: m = -5 \\\frac{- \frac{b^{2}}{x} + 2 b c \log{\left(x \right)} + c^{2} x}{d^{4}} & \text{for}\: m = -4 \\\frac{b^{2} \log{\left(x \right)} + 2 b c x + \frac{c^{2} x^{2}}{2}}{d^{3}} & \text{for}\: m = -3 \\\frac{b^{2} d^{m} m^{2} x^{3} x^{m}}{m^{3} + 12 m^{2} + 47 m + 60} + \frac{9 b^{2} d^{m} m x^{3} x^{m}}{m^{3} + 12 m^{2} + 47 m + 60} + \frac{20 b^{2} d^{m} x^{3} x^{m}}{m^{3} + 12 m^{2} + 47 m + 60} + \frac{2 b c d^{m} m^{2} x^{4} x^{m}}{m^{3} + 12 m^{2} + 47 m + 60} + \frac{16 b c d^{m} m x^{4} x^{m}}{m^{3} + 12 m^{2} + 47 m + 60} + \frac{30 b c d^{m} x^{4} x^{m}}{m^{3} + 12 m^{2} + 47 m + 60} + \frac{c^{2} d^{m} m^{2} x^{5} x^{m}}{m^{3} + 12 m^{2} + 47 m + 60} + \frac{7 c^{2} d^{m} m x^{5} x^{m}}{m^{3} + 12 m^{2} + 47 m + 60} + \frac{12 c^{2} d^{m} x^{5} x^{m}}{m^{3} + 12 m^{2} + 47 m + 60} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-b**2/(2*x**2) - 2*b*c/x + c**2*log(x))/d**5, Eq(m, -5)), ((-b**2/x + 2*b*c*log(x) + c**2*x)/d**4, Eq(m, -4)), ((b**2*log(x) + 2*b*c*x + c**2*x**2/2)/d**3, Eq(m, -3)), (b**2*d**m*m**2*x**3*x**m/(m**3 + 12*m**2 + 47*m + 60) + 9*b**2*d**m*m*x**3*x**m/(m**3 + 12*m**2 + 47*m + 60) + 20*b**2*d**m*x**3*x**m/(m**3 + 12*m**2 + 47*m + 60) + 2*b*c*d**m*m**2*x**4*x**m/(m**3 + 12*m**2 + 47*m + 60) + 16*b*c*d**m*m*x**4*x**m/(m**3 + 12*m**2 + 47*m + 60) + 30*b*c*d**m*x**4*x**m/(m**3 + 12*m**2 + 47*m + 60) + c**2*d**m*m**2*x**5*x**m/(m**3 + 12*m**2 + 47*m + 60) + 7*c**2*d**m*m*x**5*x**m/(m**3 + 12*m**2 + 47*m + 60) + 12*c**2*d**m*x**5*x**m/(m**3 + 12*m**2 + 47*m + 60), True))","A",0
114,1,112,0,0.452629," ","integrate((d*x)**m*(c*x**2+b*x),x)","\begin{cases} \frac{- \frac{b}{x} + c \log{\left(x \right)}}{d^{3}} & \text{for}\: m = -3 \\\frac{b \log{\left(x \right)} + c x}{d^{2}} & \text{for}\: m = -2 \\\frac{b d^{m} m x^{2} x^{m}}{m^{2} + 5 m + 6} + \frac{3 b d^{m} x^{2} x^{m}}{m^{2} + 5 m + 6} + \frac{c d^{m} m x^{3} x^{m}}{m^{2} + 5 m + 6} + \frac{2 c d^{m} x^{3} x^{m}}{m^{2} + 5 m + 6} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-b/x + c*log(x))/d**3, Eq(m, -3)), ((b*log(x) + c*x)/d**2, Eq(m, -2)), (b*d**m*m*x**2*x**m/(m**2 + 5*m + 6) + 3*b*d**m*x**2*x**m/(m**2 + 5*m + 6) + c*d**m*m*x**3*x**m/(m**2 + 5*m + 6) + 2*c*d**m*x**3*x**m/(m**2 + 5*m + 6), True))","A",0
115,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**2+b*x),x)","\int \frac{\left(d x\right)^{m}}{x \left(b + c x\right)}\, dx"," ",0,"Integral((d*x)**m/(x*(b + c*x)), x)","F",0
116,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**2+b*x)**2,x)","\int \frac{\left(d x\right)^{m}}{x^{2} \left(b + c x\right)^{2}}\, dx"," ",0,"Integral((d*x)**m/(x**2*(b + c*x)**2), x)","F",0
117,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**2+b*x)**3,x)","\int \frac{\left(d x\right)^{m}}{x^{3} \left(b + c x\right)^{3}}\, dx"," ",0,"Integral((d*x)**m/(x**3*(b + c*x)**3), x)","F",0
118,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2+b*x)**(5/2),x)","\int \left(d x\right)^{m} \left(x \left(b + c x\right)\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d*x)**m*(x*(b + c*x))**(5/2), x)","F",0
119,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2+b*x)**(3/2),x)","\int \left(d x\right)^{m} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*x)**m*(x*(b + c*x))**(3/2), x)","F",0
120,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2+b*x)**(1/2),x)","\int \left(d x\right)^{m} \sqrt{x \left(b + c x\right)}\, dx"," ",0,"Integral((d*x)**m*sqrt(x*(b + c*x)), x)","F",0
121,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(d x\right)^{m}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((d*x)**m/sqrt(x*(b + c*x)), x)","F",0
122,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**2+b*x)**(3/2),x)","\int \frac{\left(d x\right)^{m}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m/(x*(b + c*x))**(3/2), x)","F",0
123,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**2+b*x)**(5/2),x)","\int \frac{\left(d x\right)^{m}}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d*x)**m/(x*(b + c*x))**(5/2), x)","F",0
124,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2+b*x)**p,x)","\int \left(d x\right)^{m} \left(x \left(b + c x\right)\right)^{p}\, dx"," ",0,"Integral((d*x)**m*(x*(b + c*x))**p, x)","F",0
125,0,0,0,0.000000," ","integrate(x**3*(c*x**2+b*x)**p,x)","\int x^{3} \left(x \left(b + c x\right)\right)^{p}\, dx"," ",0,"Integral(x**3*(x*(b + c*x))**p, x)","F",0
126,0,0,0,0.000000," ","integrate(x**2*(c*x**2+b*x)**p,x)","\int x^{2} \left(x \left(b + c x\right)\right)^{p}\, dx"," ",0,"Integral(x**2*(x*(b + c*x))**p, x)","F",0
127,0,0,0,0.000000," ","integrate(x*(c*x**2+b*x)**p,x)","\int x \left(x \left(b + c x\right)\right)^{p}\, dx"," ",0,"Integral(x*(x*(b + c*x))**p, x)","F",0
128,0,0,0,0.000000," ","integrate((c*x**2+b*x)**p/x,x)","\int \frac{\left(x \left(b + c x\right)\right)^{p}}{x}\, dx"," ",0,"Integral((x*(b + c*x))**p/x, x)","F",0
129,0,0,0,0.000000," ","integrate((c*x**2+b*x)**p/x**2,x)","\int \frac{\left(x \left(b + c x\right)\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((x*(b + c*x))**p/x**2, x)","F",0
130,0,0,0,0.000000," ","integrate((c*x**2+b*x)**p/x**3,x)","\int \frac{\left(x \left(b + c x\right)\right)^{p}}{x^{3}}\, dx"," ",0,"Integral((x*(b + c*x))**p/x**3, x)","F",0
131,0,0,0,0.000000," ","integrate((d*x)**(5/2)*(c*x**2+b*x)**p,x)","\int \left(d x\right)^{\frac{5}{2}} \left(x \left(b + c x\right)\right)^{p}\, dx"," ",0,"Integral((d*x)**(5/2)*(x*(b + c*x))**p, x)","F",0
132,0,0,0,0.000000," ","integrate((d*x)**(3/2)*(c*x**2+b*x)**p,x)","\int \left(d x\right)^{\frac{3}{2}} \left(x \left(b + c x\right)\right)^{p}\, dx"," ",0,"Integral((d*x)**(3/2)*(x*(b + c*x))**p, x)","F",0
133,0,0,0,0.000000," ","integrate((d*x)**(1/2)*(c*x**2+b*x)**p,x)","\int \sqrt{d x} \left(x \left(b + c x\right)\right)^{p}\, dx"," ",0,"Integral(sqrt(d*x)*(x*(b + c*x))**p, x)","F",0
134,0,0,0,0.000000," ","integrate((c*x**2+b*x)**p/(d*x)**(1/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{p}}{\sqrt{d x}}\, dx"," ",0,"Integral((x*(b + c*x))**p/sqrt(d*x), x)","F",0
135,0,0,0,0.000000," ","integrate((c*x**2+b*x)**p/(d*x)**(3/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{p}}{\left(d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**p/(d*x)**(3/2), x)","F",0
136,0,0,0,0.000000," ","integrate((c*x**2+b*x)**p/(d*x)**(5/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{p}}{\left(d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**p/(d*x)**(5/2), x)","F",0
137,1,12,0,0.089922," ","integrate(x**4*((b*x+a)**2)**(1/2),x)","\frac{a x^{5}}{5} + \frac{b x^{6}}{6}"," ",0,"a*x**5/5 + b*x**6/6","A",0
138,1,12,0,0.086741," ","integrate(x**3*((b*x+a)**2)**(1/2),x)","\frac{a x^{4}}{4} + \frac{b x^{5}}{5}"," ",0,"a*x**4/4 + b*x**5/5","A",0
139,1,12,0,0.088448," ","integrate(x**2*((b*x+a)**2)**(1/2),x)","\frac{a x^{3}}{3} + \frac{b x^{4}}{4}"," ",0,"a*x**3/3 + b*x**4/4","A",0
140,1,12,0,0.085331," ","integrate(x*((b*x+a)**2)**(1/2),x)","\frac{a x^{2}}{2} + \frac{b x^{3}}{3}"," ",0,"a*x**2/2 + b*x**3/3","A",0
141,1,8,0,0.082206," ","integrate(((b*x+a)**2)**(1/2),x)","a x + \frac{b x^{2}}{2}"," ",0,"a*x + b*x**2/2","A",0
142,1,7,0,0.109596," ","integrate(((b*x+a)**2)**(1/2)/x,x)","a \log{\left(x \right)} + b x"," ",0,"a*log(x) + b*x","A",0
143,1,7,0,0.121345," ","integrate(((b*x+a)**2)**(1/2)/x**2,x)","- \frac{a}{x} + b \log{\left(x \right)}"," ",0,"-a/x + b*log(x)","A",0
144,1,12,0,0.129487," ","integrate(((b*x+a)**2)**(1/2)/x**3,x)","\frac{- a - 2 b x}{2 x^{2}}"," ",0,"(-a - 2*b*x)/(2*x**2)","A",0
145,1,14,0,0.136981," ","integrate(((b*x+a)**2)**(1/2)/x**4,x)","\frac{- 2 a - 3 b x}{6 x^{3}}"," ",0,"(-2*a - 3*b*x)/(6*x**3)","A",0
146,1,14,0,0.146531," ","integrate(((b*x+a)**2)**(1/2)/x**5,x)","\frac{- 3 a - 4 b x}{12 x^{4}}"," ",0,"(-3*a - 4*b*x)/(12*x**4)","A",0
147,1,14,0,0.156784," ","integrate(((b*x+a)**2)**(1/2)/x**6,x)","\frac{- 4 a - 5 b x}{20 x^{5}}"," ",0,"(-4*a - 5*b*x)/(20*x**5)","A",0
148,0,0,0,0.000000," ","integrate(x**5*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x^{5} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**5*((a + b*x)**2)**(3/2), x)","F",0
149,0,0,0,0.000000," ","integrate(x**4*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x^{4} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**4*((a + b*x)**2)**(3/2), x)","F",0
150,0,0,0,0.000000," ","integrate(x**3*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*((a + b*x)**2)**(3/2), x)","F",0
151,0,0,0,0.000000," ","integrate(x**2*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*((a + b*x)**2)**(3/2), x)","F",0
152,0,0,0,0.000000," ","integrate(x*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*((a + b*x)**2)**(3/2), x)","F",0
153,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2)**(3/2), x)","F",0
154,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/x,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/x, x)","F",0
155,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/x**2,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/x**2, x)","F",0
156,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/x**3,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/x**3, x)","F",0
157,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/x**4,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/x**4, x)","F",0
158,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/x**5,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/x**5, x)","F",0
159,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/x**6,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/x**6, x)","F",0
160,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/x**7,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/x**7, x)","F",0
161,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/x**8,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{8}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/x**8, x)","F",0
162,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/x**9,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{9}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/x**9, x)","F",0
163,0,0,0,0.000000," ","integrate(x**5*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x^{5} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**5*((a + b*x)**2)**(5/2), x)","F",0
164,0,0,0,0.000000," ","integrate(x**4*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x^{4} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**4*((a + b*x)**2)**(5/2), x)","F",0
165,0,0,0,0.000000," ","integrate(x**3*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**3*((a + b*x)**2)**(5/2), x)","F",0
166,0,0,0,0.000000," ","integrate(x**2*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**2*((a + b*x)**2)**(5/2), x)","F",0
167,0,0,0,0.000000," ","integrate(x*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x*((a + b*x)**2)**(5/2), x)","F",0
168,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2)**(5/2), x)","F",0
169,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x, x)","F",0
170,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**2,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**2, x)","F",0
171,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**3,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{3}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**3, x)","F",0
172,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**4,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{4}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**4, x)","F",0
173,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**5,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{5}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**5, x)","F",0
174,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**6,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**6, x)","F",0
175,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**7,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{7}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**7, x)","F",0
176,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**8,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{8}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**8, x)","F",0
177,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**9,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{9}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**9, x)","F",0
178,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**10,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{10}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**10, x)","F",0
179,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**11,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{11}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**11, x)","F",0
180,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/x**12,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{12}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/x**12, x)","F",0
181,1,49,0,0.170651," ","integrate(x**4/((b*x+a)**2)**(1/2),x)","\frac{a^{4} \log{\left(a + b x \right)}}{b^{5}} - \frac{a^{3} x}{b^{4}} + \frac{a^{2} x^{2}}{2 b^{3}} - \frac{a x^{3}}{3 b^{2}} + \frac{x^{4}}{4 b}"," ",0,"a**4*log(a + b*x)/b**5 - a**3*x/b**4 + a**2*x**2/(2*b**3) - a*x**3/(3*b**2) + x**4/(4*b)","A",0
182,1,37,0,0.148579," ","integrate(x**3/((b*x+a)**2)**(1/2),x)","- \frac{a^{3} \log{\left(a + b x \right)}}{b^{4}} + \frac{a^{2} x}{b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{3}}{3 b}"," ",0,"-a**3*log(a + b*x)/b**4 + a**2*x/b**3 - a*x**2/(2*b**2) + x**3/(3*b)","A",0
183,1,26,0,0.140478," ","integrate(x**2/((b*x+a)**2)**(1/2),x)","\frac{a^{2} \log{\left(a + b x \right)}}{b^{3}} - \frac{a x}{b^{2}} + \frac{x^{2}}{2 b}"," ",0,"a**2*log(a + b*x)/b**3 - a*x/b**2 + x**2/(2*b)","A",0
184,1,14,0,0.124837," ","integrate(x/((b*x+a)**2)**(1/2),x)","- \frac{a \log{\left(a + b x \right)}}{b^{2}} + \frac{x}{b}"," ",0,"-a*log(a + b*x)/b**2 + x/b","A",0
185,1,7,0,0.087391," ","integrate(1/((b*x+a)**2)**(1/2),x)","\frac{\log{\left(a + b x \right)}}{b}"," ",0,"log(a + b*x)/b","A",0
186,1,10,0,0.173188," ","integrate(1/x/((b*x+a)**2)**(1/2),x)","\frac{\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}}{a}"," ",0,"(log(x) - log(a/b + x))/a","A",0
187,1,19,0,0.211035," ","integrate(1/x**2/((b*x+a)**2)**(1/2),x)","- \frac{1}{a x} + \frac{b \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{2}}"," ",0,"-1/(a*x) + b*(-log(x) + log(a/b + x))/a**2","A",0
188,1,31,0,0.236070," ","integrate(1/x**3/((b*x+a)**2)**(1/2),x)","\frac{- a + 2 b x}{2 a^{2} x^{2}} + \frac{b^{2} \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{3}}"," ",0,"(-a + 2*b*x)/(2*a**2*x**2) + b**2*(log(x) - log(a/b + x))/a**3","A",0
189,1,44,0,0.262711," ","integrate(1/x**4/((b*x+a)**2)**(1/2),x)","\frac{- 2 a^{2} + 3 a b x - 6 b^{2} x^{2}}{6 a^{3} x^{3}} + \frac{b^{3} \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{4}}"," ",0,"(-2*a**2 + 3*a*b*x - 6*b**2*x**2)/(6*a**3*x**3) + b**3*(-log(x) + log(a/b + x))/a**4","A",0
190,0,0,0,0.000000," ","integrate(x**4/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{x^{4}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x)**2)**(3/2), x)","F",0
191,0,0,0,0.000000," ","integrate(x**3/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{x^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x)**2)**(3/2), x)","F",0
192,0,0,0,0.000000," ","integrate(x**2/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{x^{2}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x)**2)**(3/2), x)","F",0
193,0,0,0,0.000000," ","integrate(x/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{x}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/((a + b*x)**2)**(3/2), x)","F",0
194,0,0,0,0.000000," ","integrate(1/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{\left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2)**(-3/2), x)","F",0
195,0,0,0,0.000000," ","integrate(1/x/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{x \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*((a + b*x)**2)**(3/2)), x)","F",0
196,0,0,0,0.000000," ","integrate(1/x**2/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{x^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*((a + b*x)**2)**(3/2)), x)","F",0
197,0,0,0,0.000000," ","integrate(1/x**3/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{x^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*((a + b*x)**2)**(3/2)), x)","F",0
198,0,0,0,0.000000," ","integrate(x**6/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{x^{6}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**6/((a + b*x)**2)**(5/2), x)","F",0
199,0,0,0,0.000000," ","integrate(x**5/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{x^{5}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**5/((a + b*x)**2)**(5/2), x)","F",0
200,0,0,0,0.000000," ","integrate(x**4/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{x^{4}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x)**2)**(5/2), x)","F",0
201,0,0,0,0.000000," ","integrate(x**3/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{x^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x)**2)**(5/2), x)","F",0
202,0,0,0,0.000000," ","integrate(x**2/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{x^{2}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x)**2)**(5/2), x)","F",0
203,0,0,0,0.000000," ","integrate(x/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{x}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/((a + b*x)**2)**(5/2), x)","F",0
204,0,0,0,0.000000," ","integrate(1/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{1}{\left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2)**(-5/2), x)","F",0
205,0,0,0,0.000000," ","integrate(1/x/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{1}{x \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x*((a + b*x)**2)**(5/2)), x)","F",0
206,0,0,0,0.000000," ","integrate(1/x**2/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{1}{x^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*((a + b*x)**2)**(5/2)), x)","F",0
207,0,0,0,0.000000," ","integrate(1/x**3/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{1}{x^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**3*((a + b*x)**2)**(5/2)), x)","F",0
208,0,0,0,0.000000," ","integrate(x*(4*x**2+12*x+9)**(5/2),x)","\int x \left(\left(2 x + 3\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x*((2*x + 3)**2)**(5/2), x)","F",0
209,0,0,0,0.000000," ","integrate(x*(4*x**2+12*x+9)**(3/2),x)","\int x \left(\left(2 x + 3\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*((2*x + 3)**2)**(3/2), x)","F",0
210,0,0,0,0.000000," ","integrate(x*(4*x**2+12*x+9)**(1/2),x)","\int x \sqrt{\left(2 x + 3\right)^{2}}\, dx"," ",0,"Integral(x*sqrt((2*x + 3)**2), x)","F",0
211,0,0,0,0.000000," ","integrate(x/(4*x**2+12*x+9)**(1/2),x)","\int \frac{x}{\sqrt{\left(2 x + 3\right)^{2}}}\, dx"," ",0,"Integral(x/sqrt((2*x + 3)**2), x)","F",0
212,0,0,0,0.000000," ","integrate(x/(4*x**2+12*x+9)**(3/2),x)","\int \frac{x}{\left(\left(2 x + 3\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/((2*x + 3)**2)**(3/2), x)","F",0
213,0,0,0,0.000000," ","integrate(x/(4*x**2+12*x+9)**(5/2),x)","\int \frac{x}{\left(\left(2 x + 3\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/((2*x + 3)**2)**(5/2), x)","F",0
214,0,0,0,0.000000," ","integrate(x/(4*x**2+12*x+9)**(7/2),x)","\int \frac{x}{\left(\left(2 x + 3\right)^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x/((2*x + 3)**2)**(7/2), x)","F",0
215,1,12,0,0.104939," ","integrate(x/((2+3*x)**2)**(1/2),x)","\frac{x}{3} - \frac{2 \log{\left(3 x + 2 \right)}}{9}"," ",0,"x/3 - 2*log(3*x + 2)/9","A",0
216,1,12,0,0.098500," ","integrate(x/((-2+3*x)**2)**(1/2),x)","\frac{x}{3} + \frac{2 \log{\left(3 x - 2 \right)}}{9}"," ",0,"x/3 + 2*log(3*x - 2)/9","A",0
217,0,0,0,0.000000," ","integrate(x/(-(-2+3*x)**2)**(1/2),x)","\int \frac{x}{\sqrt{- \left(3 x - 2\right)^{2}}}\, dx"," ",0,"Integral(x/sqrt(-(3*x - 2)**2), x)","F",0
218,0,0,0,0.000000," ","integrate(x/(-(2+3*x)**2)**(1/2),x)","\int \frac{x}{\sqrt{- \left(3 x + 2\right)^{2}}}\, dx"," ",0,"Integral(x/sqrt(-(3*x + 2)**2), x)","F",0
219,1,8,0,0.088542," ","integrate((1+x)/(x**2+2*x),x)","\frac{\log{\left(x^{2} + 2 x \right)}}{2}"," ",0,"log(x**2 + 2*x)/2","A",0
220,1,8,0,0.124489," ","integrate((2*b*x+a)/(b*x**2+a*x),x)","\log{\left(a x + b x^{2} \right)}"," ",0,"log(a*x + b*x**2)","A",0
221,1,107,0,0.087412," ","integrate((e*x+d)**4*(c*x**2+b*x),x)","\frac{b d^{4} x^{2}}{2} + \frac{c e^{4} x^{7}}{7} + x^{6} \left(\frac{b e^{4}}{6} + \frac{2 c d e^{3}}{3}\right) + x^{5} \left(\frac{4 b d e^{3}}{5} + \frac{6 c d^{2} e^{2}}{5}\right) + x^{4} \left(\frac{3 b d^{2} e^{2}}{2} + c d^{3} e\right) + x^{3} \left(\frac{4 b d^{3} e}{3} + \frac{c d^{4}}{3}\right)"," ",0,"b*d**4*x**2/2 + c*e**4*x**7/7 + x**6*(b*e**4/6 + 2*c*d*e**3/3) + x**5*(4*b*d*e**3/5 + 6*c*d**2*e**2/5) + x**4*(3*b*d**2*e**2/2 + c*d**3*e) + x**3*(4*b*d**3*e/3 + c*d**4/3)","B",0
222,1,80,0,0.082020," ","integrate((e*x+d)**3*(c*x**2+b*x),x)","\frac{b d^{3} x^{2}}{2} + \frac{c e^{3} x^{6}}{6} + x^{5} \left(\frac{b e^{3}}{5} + \frac{3 c d e^{2}}{5}\right) + x^{4} \left(\frac{3 b d e^{2}}{4} + \frac{3 c d^{2} e}{4}\right) + x^{3} \left(b d^{2} e + \frac{c d^{3}}{3}\right)"," ",0,"b*d**3*x**2/2 + c*e**3*x**6/6 + x**5*(b*e**3/5 + 3*c*d*e**2/5) + x**4*(3*b*d*e**2/4 + 3*c*d**2*e/4) + x**3*(b*d**2*e + c*d**3/3)","A",0
223,1,54,0,0.076675," ","integrate((e*x+d)**2*(c*x**2+b*x),x)","\frac{b d^{2} x^{2}}{2} + \frac{c e^{2} x^{5}}{5} + x^{4} \left(\frac{b e^{2}}{4} + \frac{c d e}{2}\right) + x^{3} \left(\frac{2 b d e}{3} + \frac{c d^{2}}{3}\right)"," ",0,"b*d**2*x**2/2 + c*e**2*x**5/5 + x**4*(b*e**2/4 + c*d*e/2) + x**3*(2*b*d*e/3 + c*d**2/3)","A",0
224,1,29,0,0.065520," ","integrate((e*x+d)*(c*x**2+b*x),x)","\frac{b d x^{2}}{2} + \frac{c e x^{4}}{4} + x^{3} \left(\frac{b e}{3} + \frac{c d}{3}\right)"," ",0,"b*d*x**2/2 + c*e*x**4/4 + x**3*(b*e/3 + c*d/3)","A",0
225,1,12,0,0.059713," ","integrate(c*x**2+b*x,x)","\frac{b x^{2}}{2} + \frac{c x^{3}}{3}"," ",0,"b*x**2/2 + c*x**3/3","A",0
226,1,37,0,0.186394," ","integrate((c*x**2+b*x)/(e*x+d),x)","\frac{c x^{2}}{2 e} - \frac{d \left(b e - c d\right) \log{\left(d + e x \right)}}{e^{3}} + x \left(\frac{b}{e} - \frac{c d}{e^{2}}\right)"," ",0,"c*x**2/(2*e) - d*(b*e - c*d)*log(d + e*x)/e**3 + x*(b/e - c*d/e**2)","A",0
227,1,44,0,0.283899," ","integrate((c*x**2+b*x)/(e*x+d)**2,x)","\frac{c x}{e^{2}} + \frac{b d e - c d^{2}}{d e^{3} + e^{4} x} + \frac{\left(b e - 2 c d\right) \log{\left(d + e x \right)}}{e^{3}}"," ",0,"c*x/e**2 + (b*d*e - c*d**2)/(d*e**3 + e**4*x) + (b*e - 2*c*d)*log(d + e*x)/e**3","A",0
228,1,63,0,0.361509," ","integrate((c*x**2+b*x)/(e*x+d)**3,x)","\frac{c \log{\left(d + e x \right)}}{e^{3}} + \frac{- b d e + 3 c d^{2} + x \left(- 2 b e^{2} + 4 c d e\right)}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}}"," ",0,"c*log(d + e*x)/e**3 + (-b*d*e + 3*c*d**2 + x*(-2*b*e**2 + 4*c*d*e))/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2)","A",0
229,1,75,0,0.453315," ","integrate((c*x**2+b*x)/(e*x+d)**4,x)","\frac{- b d e - 2 c d^{2} - 6 c e^{2} x^{2} + x \left(- 3 b e^{2} - 6 c d e\right)}{6 d^{3} e^{3} + 18 d^{2} e^{4} x + 18 d e^{5} x^{2} + 6 e^{6} x^{3}}"," ",0,"(-b*d*e - 2*c*d**2 - 6*c*e**2*x**2 + x*(-3*b*e**2 - 6*c*d*e))/(6*d**3*e**3 + 18*d**2*e**4*x + 18*d*e**5*x**2 + 6*e**6*x**3)","A",0
230,1,85,0,0.584198," ","integrate((c*x**2+b*x)/(e*x+d)**5,x)","\frac{- b d e - c d^{2} - 6 c e^{2} x^{2} + x \left(- 4 b e^{2} - 4 c d e\right)}{12 d^{4} e^{3} + 48 d^{3} e^{4} x + 72 d^{2} e^{5} x^{2} + 48 d e^{6} x^{3} + 12 e^{7} x^{4}}"," ",0,"(-b*d*e - c*d**2 - 6*c*e**2*x**2 + x*(-4*b*e**2 - 4*c*d*e))/(12*d**4*e**3 + 48*d**3*e**4*x + 72*d**2*e**5*x**2 + 48*d*e**6*x**3 + 12*e**7*x**4)","A",0
231,1,178,0,0.106067," ","integrate((e*x+d)**4*(c*x**2+b*x)**2,x)","\frac{b^{2} d^{4} x^{3}}{3} + \frac{c^{2} e^{4} x^{9}}{9} + x^{8} \left(\frac{b c e^{4}}{4} + \frac{c^{2} d e^{3}}{2}\right) + x^{7} \left(\frac{b^{2} e^{4}}{7} + \frac{8 b c d e^{3}}{7} + \frac{6 c^{2} d^{2} e^{2}}{7}\right) + x^{6} \left(\frac{2 b^{2} d e^{3}}{3} + 2 b c d^{2} e^{2} + \frac{2 c^{2} d^{3} e}{3}\right) + x^{5} \left(\frac{6 b^{2} d^{2} e^{2}}{5} + \frac{8 b c d^{3} e}{5} + \frac{c^{2} d^{4}}{5}\right) + x^{4} \left(b^{2} d^{3} e + \frac{b c d^{4}}{2}\right)"," ",0,"b**2*d**4*x**3/3 + c**2*e**4*x**9/9 + x**8*(b*c*e**4/4 + c**2*d*e**3/2) + x**7*(b**2*e**4/7 + 8*b*c*d*e**3/7 + 6*c**2*d**2*e**2/7) + x**6*(2*b**2*d*e**3/3 + 2*b*c*d**2*e**2 + 2*c**2*d**3*e/3) + x**5*(6*b**2*d**2*e**2/5 + 8*b*c*d**3*e/5 + c**2*d**4/5) + x**4*(b**2*d**3*e + b*c*d**4/2)","A",0
232,1,138,0,0.096278," ","integrate((e*x+d)**3*(c*x**2+b*x)**2,x)","\frac{b^{2} d^{3} x^{3}}{3} + \frac{c^{2} e^{3} x^{8}}{8} + x^{7} \left(\frac{2 b c e^{3}}{7} + \frac{3 c^{2} d e^{2}}{7}\right) + x^{6} \left(\frac{b^{2} e^{3}}{6} + b c d e^{2} + \frac{c^{2} d^{2} e}{2}\right) + x^{5} \left(\frac{3 b^{2} d e^{2}}{5} + \frac{6 b c d^{2} e}{5} + \frac{c^{2} d^{3}}{5}\right) + x^{4} \left(\frac{3 b^{2} d^{2} e}{4} + \frac{b c d^{3}}{2}\right)"," ",0,"b**2*d**3*x**3/3 + c**2*e**3*x**8/8 + x**7*(2*b*c*e**3/7 + 3*c**2*d*e**2/7) + x**6*(b**2*e**3/6 + b*c*d*e**2 + c**2*d**2*e/2) + x**5*(3*b**2*d*e**2/5 + 6*b*c*d**2*e/5 + c**2*d**3/5) + x**4*(3*b**2*d**2*e/4 + b*c*d**3/2)","A",0
233,1,94,0,0.088702," ","integrate((e*x+d)**2*(c*x**2+b*x)**2,x)","\frac{b^{2} d^{2} x^{3}}{3} + \frac{c^{2} e^{2} x^{7}}{7} + x^{6} \left(\frac{b c e^{2}}{3} + \frac{c^{2} d e}{3}\right) + x^{5} \left(\frac{b^{2} e^{2}}{5} + \frac{4 b c d e}{5} + \frac{c^{2} d^{2}}{5}\right) + x^{4} \left(\frac{b^{2} d e}{2} + \frac{b c d^{2}}{2}\right)"," ",0,"b**2*d**2*x**3/3 + c**2*e**2*x**7/7 + x**6*(b*c*e**2/3 + c**2*d*e/3) + x**5*(b**2*e**2/5 + 4*b*c*d*e/5 + c**2*d**2/5) + x**4*(b**2*d*e/2 + b*c*d**2/2)","A",0
234,1,54,0,0.078268," ","integrate((e*x+d)*(c*x**2+b*x)**2,x)","\frac{b^{2} d x^{3}}{3} + \frac{c^{2} e x^{6}}{6} + x^{5} \left(\frac{2 b c e}{5} + \frac{c^{2} d}{5}\right) + x^{4} \left(\frac{b^{2} e}{4} + \frac{b c d}{2}\right)"," ",0,"b**2*d*x**3/3 + c**2*e*x**6/6 + x**5*(2*b*c*e/5 + c**2*d/5) + x**4*(b**2*e/4 + b*c*d/2)","A",0
235,1,24,0,0.068250," ","integrate((c*x**2+b*x)**2,x)","\frac{b^{2} x^{3}}{3} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5}"," ",0,"b**2*x**3/3 + b*c*x**4/2 + c**2*x**5/5","A",0
236,1,116,0,0.324498," ","integrate((c*x**2+b*x)**2/(e*x+d),x)","\frac{c^{2} x^{4}}{4 e} + \frac{d^{2} \left(b e - c d\right)^{2} \log{\left(d + e x \right)}}{e^{5}} + x^{3} \left(\frac{2 b c}{3 e} - \frac{c^{2} d}{3 e^{2}}\right) + x^{2} \left(\frac{b^{2}}{2 e} - \frac{b c d}{e^{2}} + \frac{c^{2} d^{2}}{2 e^{3}}\right) + x \left(- \frac{b^{2} d}{e^{2}} + \frac{2 b c d^{2}}{e^{3}} - \frac{c^{2} d^{3}}{e^{4}}\right)"," ",0,"c**2*x**4/(4*e) + d**2*(b*e - c*d)**2*log(d + e*x)/e**5 + x**3*(2*b*c/(3*e) - c**2*d/(3*e**2)) + x**2*(b**2/(2*e) - b*c*d/e**2 + c**2*d**2/(2*e**3)) + x*(-b**2*d/e**2 + 2*b*c*d**2/e**3 - c**2*d**3/e**4)","A",0
237,1,126,0,0.581469," ","integrate((c*x**2+b*x)**2/(e*x+d)**2,x)","\frac{c^{2} x^{3}}{3 e^{2}} - \frac{2 d \left(b e - 2 c d\right) \left(b e - c d\right) \log{\left(d + e x \right)}}{e^{5}} + x^{2} \left(\frac{b c}{e^{2}} - \frac{c^{2} d}{e^{3}}\right) + x \left(\frac{b^{2}}{e^{2}} - \frac{4 b c d}{e^{3}} + \frac{3 c^{2} d^{2}}{e^{4}}\right) + \frac{- b^{2} d^{2} e^{2} + 2 b c d^{3} e - c^{2} d^{4}}{d e^{5} + e^{6} x}"," ",0,"c**2*x**3/(3*e**2) - 2*d*(b*e - 2*c*d)*(b*e - c*d)*log(d + e*x)/e**5 + x**2*(b*c/e**2 - c**2*d/e**3) + x*(b**2/e**2 - 4*b*c*d/e**3 + 3*c**2*d**2/e**4) + (-b**2*d**2*e**2 + 2*b*c*d**3*e - c**2*d**4)/(d*e**5 + e**6*x)","A",0
238,1,155,0,0.939517," ","integrate((c*x**2+b*x)**2/(e*x+d)**3,x)","\frac{c^{2} x^{2}}{2 e^{3}} + x \left(\frac{2 b c}{e^{3}} - \frac{3 c^{2} d}{e^{4}}\right) + \frac{3 b^{2} d^{2} e^{2} - 10 b c d^{3} e + 7 c^{2} d^{4} + x \left(4 b^{2} d e^{3} - 12 b c d^{2} e^{2} + 8 c^{2} d^{3} e\right)}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{\left(b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{5}}"," ",0,"c**2*x**2/(2*e**3) + x*(2*b*c/e**3 - 3*c**2*d/e**4) + (3*b**2*d**2*e**2 - 10*b*c*d**3*e + 7*c**2*d**4 + x*(4*b**2*d*e**3 - 12*b*c*d**2*e**2 + 8*c**2*d**3*e))/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + (b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2)*log(d + e*x)/e**5","A",0
239,1,163,0,1.453703," ","integrate((c*x**2+b*x)**2/(e*x+d)**4,x)","\frac{c^{2} x}{e^{4}} + \frac{2 c \left(b e - 2 c d\right) \log{\left(d + e x \right)}}{e^{5}} + \frac{- b^{2} d^{2} e^{2} + 11 b c d^{3} e - 13 c^{2} d^{4} + x^{2} \left(- 3 b^{2} e^{4} + 18 b c d e^{3} - 18 c^{2} d^{2} e^{2}\right) + x \left(- 3 b^{2} d e^{3} + 27 b c d^{2} e^{2} - 30 c^{2} d^{3} e\right)}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}}"," ",0,"c**2*x/e**4 + 2*c*(b*e - 2*c*d)*log(d + e*x)/e**5 + (-b**2*d**2*e**2 + 11*b*c*d**3*e - 13*c**2*d**4 + x**2*(-3*b**2*e**4 + 18*b*c*d*e**3 - 18*c**2*d**2*e**2) + x*(-3*b**2*d*e**3 + 27*b*c*d**2*e**2 - 30*c**2*d**3*e))/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3)","A",0
240,1,180,0,1.878849," ","integrate((c*x**2+b*x)**2/(e*x+d)**5,x)","\frac{c^{2} \log{\left(d + e x \right)}}{e^{5}} + \frac{- b^{2} d^{2} e^{2} - 6 b c d^{3} e + 25 c^{2} d^{4} + x^{3} \left(- 24 b c e^{4} + 48 c^{2} d e^{3}\right) + x^{2} \left(- 6 b^{2} e^{4} - 36 b c d e^{3} + 108 c^{2} d^{2} e^{2}\right) + x \left(- 4 b^{2} d e^{3} - 24 b c d^{2} e^{2} + 88 c^{2} d^{3} e\right)}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}}"," ",0,"c**2*log(d + e*x)/e**5 + (-b**2*d**2*e**2 - 6*b*c*d**3*e + 25*c**2*d**4 + x**3*(-24*b*c*e**4 + 48*c**2*d*e**3) + x**2*(-6*b**2*e**4 - 36*b*c*d*e**3 + 108*c**2*d**2*e**2) + x*(-4*b**2*d*e**3 - 24*b*c*d**2*e**2 + 88*c**2*d**3*e))/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4)","A",0
241,1,196,0,2.847346," ","integrate((c*x**2+b*x)**2/(e*x+d)**6,x)","\frac{- b^{2} d^{2} e^{2} - 3 b c d^{3} e - 6 c^{2} d^{4} - 30 c^{2} e^{4} x^{4} + x^{3} \left(- 30 b c e^{4} - 60 c^{2} d e^{3}\right) + x^{2} \left(- 10 b^{2} e^{4} - 30 b c d e^{3} - 60 c^{2} d^{2} e^{2}\right) + x \left(- 5 b^{2} d e^{3} - 15 b c d^{2} e^{2} - 30 c^{2} d^{3} e\right)}{30 d^{5} e^{5} + 150 d^{4} e^{6} x + 300 d^{3} e^{7} x^{2} + 300 d^{2} e^{8} x^{3} + 150 d e^{9} x^{4} + 30 e^{10} x^{5}}"," ",0,"(-b**2*d**2*e**2 - 3*b*c*d**3*e - 6*c**2*d**4 - 30*c**2*e**4*x**4 + x**3*(-30*b*c*e**4 - 60*c**2*d*e**3) + x**2*(-10*b**2*e**4 - 30*b*c*d*e**3 - 60*c**2*d**2*e**2) + x*(-5*b**2*d*e**3 - 15*b*c*d**2*e**2 - 30*c**2*d**3*e))/(30*d**5*e**5 + 150*d**4*e**6*x + 300*d**3*e**7*x**2 + 300*d**2*e**8*x**3 + 150*d*e**9*x**4 + 30*e**10*x**5)","A",0
242,1,207,0,4.113776," ","integrate((c*x**2+b*x)**2/(e*x+d)**7,x)","\frac{- b^{2} d^{2} e^{2} - 2 b c d^{3} e - 2 c^{2} d^{4} - 30 c^{2} e^{4} x^{4} + x^{3} \left(- 40 b c e^{4} - 40 c^{2} d e^{3}\right) + x^{2} \left(- 15 b^{2} e^{4} - 30 b c d e^{3} - 30 c^{2} d^{2} e^{2}\right) + x \left(- 6 b^{2} d e^{3} - 12 b c d^{2} e^{2} - 12 c^{2} d^{3} e\right)}{60 d^{6} e^{5} + 360 d^{5} e^{6} x + 900 d^{4} e^{7} x^{2} + 1200 d^{3} e^{8} x^{3} + 900 d^{2} e^{9} x^{4} + 360 d e^{10} x^{5} + 60 e^{11} x^{6}}"," ",0,"(-b**2*d**2*e**2 - 2*b*c*d**3*e - 2*c**2*d**4 - 30*c**2*e**4*x**4 + x**3*(-40*b*c*e**4 - 40*c**2*d*e**3) + x**2*(-15*b**2*e**4 - 30*b*c*d*e**3 - 30*c**2*d**2*e**2) + x*(-6*b**2*d*e**3 - 12*b*c*d**2*e**2 - 12*c**2*d**3*e))/(60*d**6*e**5 + 360*d**5*e**6*x + 900*d**4*e**7*x**2 + 1200*d**3*e**8*x**3 + 900*d**2*e**9*x**4 + 360*d*e**10*x**5 + 60*e**11*x**6)","A",0
243,1,221,0,7.196238," ","integrate((c*x**2+b*x)**2/(e*x+d)**8,x)","\frac{- 2 b^{2} d^{2} e^{2} - 3 b c d^{3} e - 2 c^{2} d^{4} - 70 c^{2} e^{4} x^{4} + x^{3} \left(- 105 b c e^{4} - 70 c^{2} d e^{3}\right) + x^{2} \left(- 42 b^{2} e^{4} - 63 b c d e^{3} - 42 c^{2} d^{2} e^{2}\right) + x \left(- 14 b^{2} d e^{3} - 21 b c d^{2} e^{2} - 14 c^{2} d^{3} e\right)}{210 d^{7} e^{5} + 1470 d^{6} e^{6} x + 4410 d^{5} e^{7} x^{2} + 7350 d^{4} e^{8} x^{3} + 7350 d^{3} e^{9} x^{4} + 4410 d^{2} e^{10} x^{5} + 1470 d e^{11} x^{6} + 210 e^{12} x^{7}}"," ",0,"(-2*b**2*d**2*e**2 - 3*b*c*d**3*e - 2*c**2*d**4 - 70*c**2*e**4*x**4 + x**3*(-105*b*c*e**4 - 70*c**2*d*e**3) + x**2*(-42*b**2*e**4 - 63*b*c*d*e**3 - 42*c**2*d**2*e**2) + x*(-14*b**2*d*e**3 - 21*b*c*d**2*e**2 - 14*c**2*d**3*e))/(210*d**7*e**5 + 1470*d**6*e**6*x + 4410*d**5*e**7*x**2 + 7350*d**4*e**8*x**3 + 7350*d**3*e**9*x**4 + 4410*d**2*e**10*x**5 + 1470*d*e**11*x**6 + 210*e**12*x**7)","A",0
244,1,257,0,0.122280," ","integrate((e*x+d)**4*(c*x**2+b*x)**3,x)","\frac{b^{3} d^{4} x^{4}}{4} + \frac{c^{3} e^{4} x^{11}}{11} + x^{10} \left(\frac{3 b c^{2} e^{4}}{10} + \frac{2 c^{3} d e^{3}}{5}\right) + x^{9} \left(\frac{b^{2} c e^{4}}{3} + \frac{4 b c^{2} d e^{3}}{3} + \frac{2 c^{3} d^{2} e^{2}}{3}\right) + x^{8} \left(\frac{b^{3} e^{4}}{8} + \frac{3 b^{2} c d e^{3}}{2} + \frac{9 b c^{2} d^{2} e^{2}}{4} + \frac{c^{3} d^{3} e}{2}\right) + x^{7} \left(\frac{4 b^{3} d e^{3}}{7} + \frac{18 b^{2} c d^{2} e^{2}}{7} + \frac{12 b c^{2} d^{3} e}{7} + \frac{c^{3} d^{4}}{7}\right) + x^{6} \left(b^{3} d^{2} e^{2} + 2 b^{2} c d^{3} e + \frac{b c^{2} d^{4}}{2}\right) + x^{5} \left(\frac{4 b^{3} d^{3} e}{5} + \frac{3 b^{2} c d^{4}}{5}\right)"," ",0,"b**3*d**4*x**4/4 + c**3*e**4*x**11/11 + x**10*(3*b*c**2*e**4/10 + 2*c**3*d*e**3/5) + x**9*(b**2*c*e**4/3 + 4*b*c**2*d*e**3/3 + 2*c**3*d**2*e**2/3) + x**8*(b**3*e**4/8 + 3*b**2*c*d*e**3/2 + 9*b*c**2*d**2*e**2/4 + c**3*d**3*e/2) + x**7*(4*b**3*d*e**3/7 + 18*b**2*c*d**2*e**2/7 + 12*b*c**2*d**3*e/7 + c**3*d**4/7) + x**6*(b**3*d**2*e**2 + 2*b**2*c*d**3*e + b*c**2*d**4/2) + x**5*(4*b**3*d**3*e/5 + 3*b**2*c*d**4/5)","A",0
245,1,199,0,0.110555," ","integrate((e*x+d)**3*(c*x**2+b*x)**3,x)","\frac{b^{3} d^{3} x^{4}}{4} + \frac{c^{3} e^{3} x^{10}}{10} + x^{9} \left(\frac{b c^{2} e^{3}}{3} + \frac{c^{3} d e^{2}}{3}\right) + x^{8} \left(\frac{3 b^{2} c e^{3}}{8} + \frac{9 b c^{2} d e^{2}}{8} + \frac{3 c^{3} d^{2} e}{8}\right) + x^{7} \left(\frac{b^{3} e^{3}}{7} + \frac{9 b^{2} c d e^{2}}{7} + \frac{9 b c^{2} d^{2} e}{7} + \frac{c^{3} d^{3}}{7}\right) + x^{6} \left(\frac{b^{3} d e^{2}}{2} + \frac{3 b^{2} c d^{2} e}{2} + \frac{b c^{2} d^{3}}{2}\right) + x^{5} \left(\frac{3 b^{3} d^{2} e}{5} + \frac{3 b^{2} c d^{3}}{5}\right)"," ",0,"b**3*d**3*x**4/4 + c**3*e**3*x**10/10 + x**9*(b*c**2*e**3/3 + c**3*d*e**2/3) + x**8*(3*b**2*c*e**3/8 + 9*b*c**2*d*e**2/8 + 3*c**3*d**2*e/8) + x**7*(b**3*e**3/7 + 9*b**2*c*d*e**2/7 + 9*b*c**2*d**2*e/7 + c**3*d**3/7) + x**6*(b**3*d*e**2/2 + 3*b**2*c*d**2*e/2 + b*c**2*d**3/2) + x**5*(3*b**3*d**2*e/5 + 3*b**2*c*d**3/5)","A",0
246,1,138,0,0.098062," ","integrate((e*x+d)**2*(c*x**2+b*x)**3,x)","\frac{b^{3} d^{2} x^{4}}{4} + \frac{c^{3} e^{2} x^{9}}{9} + x^{8} \left(\frac{3 b c^{2} e^{2}}{8} + \frac{c^{3} d e}{4}\right) + x^{7} \left(\frac{3 b^{2} c e^{2}}{7} + \frac{6 b c^{2} d e}{7} + \frac{c^{3} d^{2}}{7}\right) + x^{6} \left(\frac{b^{3} e^{2}}{6} + b^{2} c d e + \frac{b c^{2} d^{2}}{2}\right) + x^{5} \left(\frac{2 b^{3} d e}{5} + \frac{3 b^{2} c d^{2}}{5}\right)"," ",0,"b**3*d**2*x**4/4 + c**3*e**2*x**9/9 + x**8*(3*b*c**2*e**2/8 + c**3*d*e/4) + x**7*(3*b**2*c*e**2/7 + 6*b*c**2*d*e/7 + c**3*d**2/7) + x**6*(b**3*e**2/6 + b**2*c*d*e + b*c**2*d**2/2) + x**5*(2*b**3*d*e/5 + 3*b**2*c*d**2/5)","A",0
247,1,80,0,0.086709," ","integrate((e*x+d)*(c*x**2+b*x)**3,x)","\frac{b^{3} d x^{4}}{4} + \frac{c^{3} e x^{8}}{8} + x^{7} \left(\frac{3 b c^{2} e}{7} + \frac{c^{3} d}{7}\right) + x^{6} \left(\frac{b^{2} c e}{2} + \frac{b c^{2} d}{2}\right) + x^{5} \left(\frac{b^{3} e}{5} + \frac{3 b^{2} c d}{5}\right)"," ",0,"b**3*d*x**4/4 + c**3*e*x**8/8 + x**7*(3*b*c**2*e/7 + c**3*d/7) + x**6*(b**2*c*e/2 + b*c**2*d/2) + x**5*(b**3*e/5 + 3*b**2*c*d/5)","A",0
248,1,37,0,0.073311," ","integrate((c*x**2+b*x)**3,x)","\frac{b^{3} x^{4}}{4} + \frac{3 b^{2} c x^{5}}{5} + \frac{b c^{2} x^{6}}{2} + \frac{c^{3} x^{7}}{7}"," ",0,"b**3*x**4/4 + 3*b**2*c*x**5/5 + b*c**2*x**6/2 + c**3*x**7/7","A",0
249,1,243,0,0.483491," ","integrate((c*x**2+b*x)**3/(e*x+d),x)","\frac{c^{3} x^{6}}{6 e} - \frac{d^{3} \left(b e - c d\right)^{3} \log{\left(d + e x \right)}}{e^{7}} + x^{5} \left(\frac{3 b c^{2}}{5 e} - \frac{c^{3} d}{5 e^{2}}\right) + x^{4} \left(\frac{3 b^{2} c}{4 e} - \frac{3 b c^{2} d}{4 e^{2}} + \frac{c^{3} d^{2}}{4 e^{3}}\right) + x^{3} \left(\frac{b^{3}}{3 e} - \frac{b^{2} c d}{e^{2}} + \frac{b c^{2} d^{2}}{e^{3}} - \frac{c^{3} d^{3}}{3 e^{4}}\right) + x^{2} \left(- \frac{b^{3} d}{2 e^{2}} + \frac{3 b^{2} c d^{2}}{2 e^{3}} - \frac{3 b c^{2} d^{3}}{2 e^{4}} + \frac{c^{3} d^{4}}{2 e^{5}}\right) + x \left(\frac{b^{3} d^{2}}{e^{3}} - \frac{3 b^{2} c d^{3}}{e^{4}} + \frac{3 b c^{2} d^{4}}{e^{5}} - \frac{c^{3} d^{5}}{e^{6}}\right)"," ",0,"c**3*x**6/(6*e) - d**3*(b*e - c*d)**3*log(d + e*x)/e**7 + x**5*(3*b*c**2/(5*e) - c**3*d/(5*e**2)) + x**4*(3*b**2*c/(4*e) - 3*b*c**2*d/(4*e**2) + c**3*d**2/(4*e**3)) + x**3*(b**3/(3*e) - b**2*c*d/e**2 + b*c**2*d**2/e**3 - c**3*d**3/(3*e**4)) + x**2*(-b**3*d/(2*e**2) + 3*b**2*c*d**2/(2*e**3) - 3*b*c**2*d**3/(2*e**4) + c**3*d**4/(2*e**5)) + x*(b**3*d**2/e**3 - 3*b**2*c*d**3/e**4 + 3*b*c**2*d**4/e**5 - c**3*d**5/e**6)","A",0
250,1,257,0,0.915129," ","integrate((c*x**2+b*x)**3/(e*x+d)**2,x)","\frac{c^{3} x^{5}}{5 e^{2}} + \frac{3 d^{2} \left(b e - 2 c d\right) \left(b e - c d\right)^{2} \log{\left(d + e x \right)}}{e^{7}} + x^{4} \left(\frac{3 b c^{2}}{4 e^{2}} - \frac{c^{3} d}{2 e^{3}}\right) + x^{3} \left(\frac{b^{2} c}{e^{2}} - \frac{2 b c^{2} d}{e^{3}} + \frac{c^{3} d^{2}}{e^{4}}\right) + x^{2} \left(\frac{b^{3}}{2 e^{2}} - \frac{3 b^{2} c d}{e^{3}} + \frac{9 b c^{2} d^{2}}{2 e^{4}} - \frac{2 c^{3} d^{3}}{e^{5}}\right) + x \left(- \frac{2 b^{3} d}{e^{3}} + \frac{9 b^{2} c d^{2}}{e^{4}} - \frac{12 b c^{2} d^{3}}{e^{5}} + \frac{5 c^{3} d^{4}}{e^{6}}\right) + \frac{b^{3} d^{3} e^{3} - 3 b^{2} c d^{4} e^{2} + 3 b c^{2} d^{5} e - c^{3} d^{6}}{d e^{7} + e^{8} x}"," ",0,"c**3*x**5/(5*e**2) + 3*d**2*(b*e - 2*c*d)*(b*e - c*d)**2*log(d + e*x)/e**7 + x**4*(3*b*c**2/(4*e**2) - c**3*d/(2*e**3)) + x**3*(b**2*c/e**2 - 2*b*c**2*d/e**3 + c**3*d**2/e**4) + x**2*(b**3/(2*e**2) - 3*b**2*c*d/e**3 + 9*b*c**2*d**2/(2*e**4) - 2*c**3*d**3/e**5) + x*(-2*b**3*d/e**3 + 9*b**2*c*d**2/e**4 - 12*b*c**2*d**3/e**5 + 5*c**3*d**4/e**6) + (b**3*d**3*e**3 - 3*b**2*c*d**4*e**2 + 3*b*c**2*d**5*e - c**3*d**6)/(d*e**7 + e**8*x)","A",0
251,1,284,0,1.613404," ","integrate((c*x**2+b*x)**3/(e*x+d)**3,x)","\frac{c^{3} x^{4}}{4 e^{3}} - \frac{3 d \left(b e - c d\right) \left(b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{7}} + x^{3} \left(\frac{b c^{2}}{e^{3}} - \frac{c^{3} d}{e^{4}}\right) + x^{2} \left(\frac{3 b^{2} c}{2 e^{3}} - \frac{9 b c^{2} d}{2 e^{4}} + \frac{3 c^{3} d^{2}}{e^{5}}\right) + x \left(\frac{b^{3}}{e^{3}} - \frac{9 b^{2} c d}{e^{4}} + \frac{18 b c^{2} d^{2}}{e^{5}} - \frac{10 c^{3} d^{3}}{e^{6}}\right) + \frac{- 5 b^{3} d^{3} e^{3} + 21 b^{2} c d^{4} e^{2} - 27 b c^{2} d^{5} e + 11 c^{3} d^{6} + x \left(- 6 b^{3} d^{2} e^{4} + 24 b^{2} c d^{3} e^{3} - 30 b c^{2} d^{4} e^{2} + 12 c^{3} d^{5} e\right)}{2 d^{2} e^{7} + 4 d e^{8} x + 2 e^{9} x^{2}}"," ",0,"c**3*x**4/(4*e**3) - 3*d*(b*e - c*d)*(b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)*log(d + e*x)/e**7 + x**3*(b*c**2/e**3 - c**3*d/e**4) + x**2*(3*b**2*c/(2*e**3) - 9*b*c**2*d/(2*e**4) + 3*c**3*d**2/e**5) + x*(b**3/e**3 - 9*b**2*c*d/e**4 + 18*b*c**2*d**2/e**5 - 10*c**3*d**3/e**6) + (-5*b**3*d**3*e**3 + 21*b**2*c*d**4*e**2 - 27*b*c**2*d**5*e + 11*c**3*d**6 + x*(-6*b**3*d**2*e**4 + 24*b**2*c*d**3*e**3 - 30*b*c**2*d**4*e**2 + 12*c**3*d**5*e))/(2*d**2*e**7 + 4*d*e**8*x + 2*e**9*x**2)","A",0
252,1,301,0,2.727829," ","integrate((c*x**2+b*x)**3/(e*x+d)**4,x)","\frac{c^{3} x^{3}}{3 e^{4}} + x^{2} \left(\frac{3 b c^{2}}{2 e^{4}} - \frac{2 c^{3} d}{e^{5}}\right) + x \left(\frac{3 b^{2} c}{e^{4}} - \frac{12 b c^{2} d}{e^{5}} + \frac{10 c^{3} d^{2}}{e^{6}}\right) + \frac{11 b^{3} d^{3} e^{3} - 78 b^{2} c d^{4} e^{2} + 141 b c^{2} d^{5} e - 74 c^{3} d^{6} + x^{2} \left(18 b^{3} d e^{5} - 108 b^{2} c d^{2} e^{4} + 180 b c^{2} d^{3} e^{3} - 90 c^{3} d^{4} e^{2}\right) + x \left(27 b^{3} d^{2} e^{4} - 180 b^{2} c d^{3} e^{3} + 315 b c^{2} d^{4} e^{2} - 162 c^{3} d^{5} e\right)}{6 d^{3} e^{7} + 18 d^{2} e^{8} x + 18 d e^{9} x^{2} + 6 e^{10} x^{3}} + \frac{\left(b e - 2 c d\right) \left(b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{7}}"," ",0,"c**3*x**3/(3*e**4) + x**2*(3*b*c**2/(2*e**4) - 2*c**3*d/e**5) + x*(3*b**2*c/e**4 - 12*b*c**2*d/e**5 + 10*c**3*d**2/e**6) + (11*b**3*d**3*e**3 - 78*b**2*c*d**4*e**2 + 141*b*c**2*d**5*e - 74*c**3*d**6 + x**2*(18*b**3*d*e**5 - 108*b**2*c*d**2*e**4 + 180*b*c**2*d**3*e**3 - 90*c**3*d**4*e**2) + x*(27*b**3*d**2*e**4 - 180*b**2*c*d**3*e**3 + 315*b*c**2*d**4*e**2 - 162*c**3*d**5*e))/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + (b*e - 2*c*d)*(b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2)*log(d + e*x)/e**7","A",0
253,1,316,0,5.026470," ","integrate((c*x**2+b*x)**3/(e*x+d)**5,x)","\frac{c^{3} x^{2}}{2 e^{5}} + \frac{3 c \left(b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{7}} + x \left(\frac{3 b c^{2}}{e^{5}} - \frac{5 c^{3} d}{e^{6}}\right) + \frac{- b^{3} d^{3} e^{3} + 25 b^{2} c d^{4} e^{2} - 77 b c^{2} d^{5} e + 57 c^{3} d^{6} + x^{3} \left(- 4 b^{3} e^{6} + 48 b^{2} c d e^{5} - 120 b c^{2} d^{2} e^{4} + 80 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 6 b^{3} d e^{5} + 108 b^{2} c d^{2} e^{4} - 300 b c^{2} d^{3} e^{3} + 210 c^{3} d^{4} e^{2}\right) + x \left(- 4 b^{3} d^{2} e^{4} + 88 b^{2} c d^{3} e^{3} - 260 b c^{2} d^{4} e^{2} + 188 c^{3} d^{5} e\right)}{4 d^{4} e^{7} + 16 d^{3} e^{8} x + 24 d^{2} e^{9} x^{2} + 16 d e^{10} x^{3} + 4 e^{11} x^{4}}"," ",0,"c**3*x**2/(2*e**5) + 3*c*(b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)*log(d + e*x)/e**7 + x*(3*b*c**2/e**5 - 5*c**3*d/e**6) + (-b**3*d**3*e**3 + 25*b**2*c*d**4*e**2 - 77*b*c**2*d**5*e + 57*c**3*d**6 + x**3*(-4*b**3*e**6 + 48*b**2*c*d*e**5 - 120*b*c**2*d**2*e**4 + 80*c**3*d**3*e**3) + x**2*(-6*b**3*d*e**5 + 108*b**2*c*d**2*e**4 - 300*b*c**2*d**3*e**3 + 210*c**3*d**4*e**2) + x*(-4*b**3*d**2*e**4 + 88*b**2*c*d**3*e**3 - 260*b*c**2*d**4*e**2 + 188*c**3*d**5*e))/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4)","A",0
254,1,326,0,11.624763," ","integrate((c*x**2+b*x)**3/(e*x+d)**6,x)","\frac{c^{3} x}{e^{6}} + \frac{3 c^{2} \left(b e - 2 c d\right) \log{\left(d + e x \right)}}{e^{7}} + \frac{- b^{3} d^{3} e^{3} - 12 b^{2} c d^{4} e^{2} + 137 b c^{2} d^{5} e - 174 c^{3} d^{6} + x^{4} \left(- 60 b^{2} c e^{6} + 300 b c^{2} d e^{5} - 300 c^{3} d^{2} e^{4}\right) + x^{3} \left(- 10 b^{3} e^{6} - 120 b^{2} c d e^{5} + 900 b c^{2} d^{2} e^{4} - 1000 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 10 b^{3} d e^{5} - 120 b^{2} c d^{2} e^{4} + 1100 b c^{2} d^{3} e^{3} - 1300 c^{3} d^{4} e^{2}\right) + x \left(- 5 b^{3} d^{2} e^{4} - 60 b^{2} c d^{3} e^{3} + 625 b c^{2} d^{4} e^{2} - 770 c^{3} d^{5} e\right)}{20 d^{5} e^{7} + 100 d^{4} e^{8} x + 200 d^{3} e^{9} x^{2} + 200 d^{2} e^{10} x^{3} + 100 d e^{11} x^{4} + 20 e^{12} x^{5}}"," ",0,"c**3*x/e**6 + 3*c**2*(b*e - 2*c*d)*log(d + e*x)/e**7 + (-b**3*d**3*e**3 - 12*b**2*c*d**4*e**2 + 137*b*c**2*d**5*e - 174*c**3*d**6 + x**4*(-60*b**2*c*e**6 + 300*b*c**2*d*e**5 - 300*c**3*d**2*e**4) + x**3*(-10*b**3*e**6 - 120*b**2*c*d*e**5 + 900*b*c**2*d**2*e**4 - 1000*c**3*d**3*e**3) + x**2*(-10*b**3*d*e**5 - 120*b**2*c*d**2*e**4 + 1100*b*c**2*d**3*e**3 - 1300*c**3*d**4*e**2) + x*(-5*b**3*d**2*e**4 - 60*b**2*c*d**3*e**3 + 625*b*c**2*d**4*e**2 - 770*c**3*d**5*e))/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5)","A",0
255,1,343,0,30.821435," ","integrate((c*x**2+b*x)**3/(e*x+d)**7,x)","\frac{c^{3} \log{\left(d + e x \right)}}{e^{7}} + \frac{- b^{3} d^{3} e^{3} - 6 b^{2} c d^{4} e^{2} - 30 b c^{2} d^{5} e + 147 c^{3} d^{6} + x^{5} \left(- 180 b c^{2} e^{6} + 360 c^{3} d e^{5}\right) + x^{4} \left(- 90 b^{2} c e^{6} - 450 b c^{2} d e^{5} + 1350 c^{3} d^{2} e^{4}\right) + x^{3} \left(- 20 b^{3} e^{6} - 120 b^{2} c d e^{5} - 600 b c^{2} d^{2} e^{4} + 2200 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 15 b^{3} d e^{5} - 90 b^{2} c d^{2} e^{4} - 450 b c^{2} d^{3} e^{3} + 1875 c^{3} d^{4} e^{2}\right) + x \left(- 6 b^{3} d^{2} e^{4} - 36 b^{2} c d^{3} e^{3} - 180 b c^{2} d^{4} e^{2} + 822 c^{3} d^{5} e\right)}{60 d^{6} e^{7} + 360 d^{5} e^{8} x + 900 d^{4} e^{9} x^{2} + 1200 d^{3} e^{10} x^{3} + 900 d^{2} e^{11} x^{4} + 360 d e^{12} x^{5} + 60 e^{13} x^{6}}"," ",0,"c**3*log(d + e*x)/e**7 + (-b**3*d**3*e**3 - 6*b**2*c*d**4*e**2 - 30*b*c**2*d**5*e + 147*c**3*d**6 + x**5*(-180*b*c**2*e**6 + 360*c**3*d*e**5) + x**4*(-90*b**2*c*e**6 - 450*b*c**2*d*e**5 + 1350*c**3*d**2*e**4) + x**3*(-20*b**3*e**6 - 120*b**2*c*d*e**5 - 600*b*c**2*d**2*e**4 + 2200*c**3*d**3*e**3) + x**2*(-15*b**3*d*e**5 - 90*b**2*c*d**2*e**4 - 450*b*c**2*d**3*e**3 + 1875*c**3*d**4*e**2) + x*(-6*b**3*d**2*e**4 - 36*b**2*c*d**3*e**3 - 180*b*c**2*d**4*e**2 + 822*c**3*d**5*e))/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6)","A",0
256,1,362,0,86.181547," ","integrate((c*x**2+b*x)**3/(e*x+d)**8,x)","\frac{- b^{3} d^{3} e^{3} - 4 b^{2} c d^{4} e^{2} - 10 b c^{2} d^{5} e - 20 c^{3} d^{6} - 140 c^{3} e^{6} x^{6} + x^{5} \left(- 210 b c^{2} e^{6} - 420 c^{3} d e^{5}\right) + x^{4} \left(- 140 b^{2} c e^{6} - 350 b c^{2} d e^{5} - 700 c^{3} d^{2} e^{4}\right) + x^{3} \left(- 35 b^{3} e^{6} - 140 b^{2} c d e^{5} - 350 b c^{2} d^{2} e^{4} - 700 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 21 b^{3} d e^{5} - 84 b^{2} c d^{2} e^{4} - 210 b c^{2} d^{3} e^{3} - 420 c^{3} d^{4} e^{2}\right) + x \left(- 7 b^{3} d^{2} e^{4} - 28 b^{2} c d^{3} e^{3} - 70 b c^{2} d^{4} e^{2} - 140 c^{3} d^{5} e\right)}{140 d^{7} e^{7} + 980 d^{6} e^{8} x + 2940 d^{5} e^{9} x^{2} + 4900 d^{4} e^{10} x^{3} + 4900 d^{3} e^{11} x^{4} + 2940 d^{2} e^{12} x^{5} + 980 d e^{13} x^{6} + 140 e^{14} x^{7}}"," ",0,"(-b**3*d**3*e**3 - 4*b**2*c*d**4*e**2 - 10*b*c**2*d**5*e - 20*c**3*d**6 - 140*c**3*e**6*x**6 + x**5*(-210*b*c**2*e**6 - 420*c**3*d*e**5) + x**4*(-140*b**2*c*e**6 - 350*b*c**2*d*e**5 - 700*c**3*d**2*e**4) + x**3*(-35*b**3*e**6 - 140*b**2*c*d*e**5 - 350*b*c**2*d**2*e**4 - 700*c**3*d**3*e**3) + x**2*(-21*b**3*d*e**5 - 84*b**2*c*d**2*e**4 - 210*b*c**2*d**3*e**3 - 420*c**3*d**4*e**2) + x*(-7*b**3*d**2*e**4 - 28*b**2*c*d**3*e**3 - 70*b*c**2*d**4*e**2 - 140*c**3*d**5*e))/(140*d**7*e**7 + 980*d**6*e**8*x + 2940*d**5*e**9*x**2 + 4900*d**4*e**10*x**3 + 4900*d**3*e**11*x**4 + 2940*d**2*e**12*x**5 + 980*d*e**13*x**6 + 140*e**14*x**7)","A",0
257,-1,0,0,0.000000," ","integrate((c*x**2+b*x)**3/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate((c*x**2+b*x)**3/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,1,165,0,1.796309," ","integrate((e*x+d)**4/(c*x**2+b*x),x)","x^{2} \left(- \frac{b e^{4}}{2 c^{2}} + \frac{2 d e^{3}}{c}\right) + x \left(\frac{b^{2} e^{4}}{c^{3}} - \frac{4 b d e^{3}}{c^{2}} + \frac{6 d^{2} e^{2}}{c}\right) + \frac{e^{4} x^{3}}{3 c} + \frac{d^{4} \log{\left(x \right)}}{b} - \frac{\left(b e - c d\right)^{4} \log{\left(x + \frac{b c^{3} d^{4} + \frac{b \left(b e - c d\right)^{4}}{c}}{b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}} \right)}}{b c^{4}}"," ",0,"x**2*(-b*e**4/(2*c**2) + 2*d*e**3/c) + x*(b**2*e**4/c**3 - 4*b*d*e**3/c**2 + 6*d**2*e**2/c) + e**4*x**3/(3*c) + d**4*log(x)/b - (b*e - c*d)**4*log(x + (b*c**3*d**4 + b*(b*e - c*d)**4/c)/(b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4))/(b*c**4)","A",0
260,1,112,0,1.281201," ","integrate((e*x+d)**3/(c*x**2+b*x),x)","x \left(- \frac{b e^{3}}{c^{2}} + \frac{3 d e^{2}}{c}\right) + \frac{e^{3} x^{2}}{2 c} + \frac{d^{3} \log{\left(x \right)}}{b} + \frac{\left(b e - c d\right)^{3} \log{\left(x + \frac{- b c^{2} d^{3} + \frac{b \left(b e - c d\right)^{3}}{c}}{b^{3} e^{3} - 3 b^{2} c d e^{2} + 3 b c^{2} d^{2} e - 2 c^{3} d^{3}} \right)}}{b c^{3}}"," ",0,"x*(-b*e**3/c**2 + 3*d*e**2/c) + e**3*x**2/(2*c) + d**3*log(x)/b + (b*e - c*d)**3*log(x + (-b*c**2*d**3 + b*(b*e - c*d)**3/c)/(b**3*e**3 - 3*b**2*c*d*e**2 + 3*b*c**2*d**2*e - 2*c**3*d**3))/(b*c**3)","B",0
261,1,73,0,0.874947," ","integrate((e*x+d)**2/(c*x**2+b*x),x)","\frac{e^{2} x}{c} + \frac{d^{2} \log{\left(x \right)}}{b} - \frac{\left(b e - c d\right)^{2} \log{\left(x + \frac{b c d^{2} + \frac{b \left(b e - c d\right)^{2}}{c}}{b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}} \right)}}{b c^{2}}"," ",0,"e**2*x/c + d**2*log(x)/b - (b*e - c*d)**2*log(x + (b*c*d**2 + b*(b*e - c*d)**2/c)/(b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2))/(b*c**2)","B",0
262,1,41,0,0.439597," ","integrate((e*x+d)/(c*x**2+b*x),x)","\frac{d \log{\left(x \right)}}{b} + \frac{\left(b e - c d\right) \log{\left(x + \frac{- b d + \frac{b \left(b e - c d\right)}{c}}{b e - 2 c d} \right)}}{b c}"," ",0,"d*log(x)/b + (b*e - c*d)*log(x + (-b*d + b*(b*e - c*d)/c)/(b*e - 2*c*d))/(b*c)","A",0
263,1,10,0,0.148040," ","integrate(1/(c*x**2+b*x),x)","\frac{\log{\left(x \right)} - \log{\left(\frac{b}{c} + x \right)}}{b}"," ",0,"(log(x) - log(b/c + x))/b","A",0
264,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,-1,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,1,381,0,3.956749," ","integrate((e*x+d)**5/(c*x**2+b*x)**2,x)","x \left(- \frac{2 b e^{5}}{c^{3}} + \frac{5 d e^{4}}{c^{2}}\right) + \frac{- b c^{4} d^{5} + x \left(b^{5} e^{5} - 5 b^{4} c d e^{4} + 10 b^{3} c^{2} d^{2} e^{3} - 10 b^{2} c^{3} d^{3} e^{2} + 5 b c^{4} d^{4} e - 2 c^{5} d^{5}\right)}{b^{3} c^{4} x + b^{2} c^{5} x^{2}} + \frac{e^{5} x^{2}}{2 c^{2}} + \frac{d^{4} \left(5 b e - 2 c d\right) \log{\left(x + \frac{- 5 b^{2} c^{3} d^{4} e + 2 b c^{4} d^{5} + b c^{3} d^{4} \left(5 b e - 2 c d\right)}{3 b^{5} e^{5} - 10 b^{4} c d e^{4} + 10 b^{3} c^{2} d^{2} e^{3} - 10 b c^{4} d^{4} e + 4 c^{5} d^{5}} \right)}}{b^{3}} + \frac{\left(b e - c d\right)^{4} \left(3 b e + 2 c d\right) \log{\left(x + \frac{- 5 b^{2} c^{3} d^{4} e + 2 b c^{4} d^{5} + \frac{b \left(b e - c d\right)^{4} \left(3 b e + 2 c d\right)}{c}}{3 b^{5} e^{5} - 10 b^{4} c d e^{4} + 10 b^{3} c^{2} d^{2} e^{3} - 10 b c^{4} d^{4} e + 4 c^{5} d^{5}} \right)}}{b^{3} c^{4}}"," ",0,"x*(-2*b*e**5/c**3 + 5*d*e**4/c**2) + (-b*c**4*d**5 + x*(b**5*e**5 - 5*b**4*c*d*e**4 + 10*b**3*c**2*d**2*e**3 - 10*b**2*c**3*d**3*e**2 + 5*b*c**4*d**4*e - 2*c**5*d**5))/(b**3*c**4*x + b**2*c**5*x**2) + e**5*x**2/(2*c**2) + d**4*(5*b*e - 2*c*d)*log(x + (-5*b**2*c**3*d**4*e + 2*b*c**4*d**5 + b*c**3*d**4*(5*b*e - 2*c*d))/(3*b**5*e**5 - 10*b**4*c*d*e**4 + 10*b**3*c**2*d**2*e**3 - 10*b*c**4*d**4*e + 4*c**5*d**5))/b**3 + (b*e - c*d)**4*(3*b*e + 2*c*d)*log(x + (-5*b**2*c**3*d**4*e + 2*b*c**4*d**5 + b*(b*e - c*d)**4*(3*b*e + 2*c*d)/c)/(3*b**5*e**5 - 10*b**4*c*d*e**4 + 10*b**3*c**2*d**2*e**3 - 10*b*c**4*d**4*e + 4*c**5*d**5))/(b**3*c**4)","B",0
268,1,306,0,2.761553," ","integrate((e*x+d)**4/(c*x**2+b*x)**2,x)","\frac{- b c^{3} d^{4} + x \left(- b^{4} e^{4} + 4 b^{3} c d e^{3} - 6 b^{2} c^{2} d^{2} e^{2} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{b^{3} c^{3} x + b^{2} c^{4} x^{2}} + \frac{e^{4} x}{c^{2}} + \frac{2 d^{3} \left(2 b e - c d\right) \log{\left(x + \frac{4 b^{2} c^{2} d^{3} e - 2 b c^{3} d^{4} - 2 b c^{2} d^{3} \left(2 b e - c d\right)}{2 b^{4} e^{4} - 4 b^{3} c d e^{3} + 8 b c^{3} d^{3} e - 4 c^{4} d^{4}} \right)}}{b^{3}} - \frac{2 \left(b e - c d\right)^{3} \left(b e + c d\right) \log{\left(x + \frac{4 b^{2} c^{2} d^{3} e - 2 b c^{3} d^{4} + \frac{2 b \left(b e - c d\right)^{3} \left(b e + c d\right)}{c}}{2 b^{4} e^{4} - 4 b^{3} c d e^{3} + 8 b c^{3} d^{3} e - 4 c^{4} d^{4}} \right)}}{b^{3} c^{3}}"," ",0,"(-b*c**3*d**4 + x*(-b**4*e**4 + 4*b**3*c*d*e**3 - 6*b**2*c**2*d**2*e**2 + 4*b*c**3*d**3*e - 2*c**4*d**4))/(b**3*c**3*x + b**2*c**4*x**2) + e**4*x/c**2 + 2*d**3*(2*b*e - c*d)*log(x + (4*b**2*c**2*d**3*e - 2*b*c**3*d**4 - 2*b*c**2*d**3*(2*b*e - c*d))/(2*b**4*e**4 - 4*b**3*c*d*e**3 + 8*b*c**3*d**3*e - 4*c**4*d**4))/b**3 - 2*(b*e - c*d)**3*(b*e + c*d)*log(x + (4*b**2*c**2*d**3*e - 2*b*c**3*d**4 + 2*b*(b*e - c*d)**3*(b*e + c*d)/c)/(2*b**4*e**4 - 4*b**3*c*d*e**3 + 8*b*c**3*d**3*e - 4*c**4*d**4))/(b**3*c**3)","B",0
269,1,250,0,1.548193," ","integrate((e*x+d)**3/(c*x**2+b*x)**2,x)","\frac{- b c^{2} d^{3} + x \left(b^{3} e^{3} - 3 b^{2} c d e^{2} + 3 b c^{2} d^{2} e - 2 c^{3} d^{3}\right)}{b^{3} c^{2} x + b^{2} c^{3} x^{2}} + \frac{d^{2} \left(3 b e - 2 c d\right) \log{\left(x + \frac{- 3 b^{2} c d^{2} e + 2 b c^{2} d^{3} + b c d^{2} \left(3 b e - 2 c d\right)}{b^{3} e^{3} - 6 b c^{2} d^{2} e + 4 c^{3} d^{3}} \right)}}{b^{3}} + \frac{\left(b e - c d\right)^{2} \left(b e + 2 c d\right) \log{\left(x + \frac{- 3 b^{2} c d^{2} e + 2 b c^{2} d^{3} + \frac{b \left(b e - c d\right)^{2} \left(b e + 2 c d\right)}{c}}{b^{3} e^{3} - 6 b c^{2} d^{2} e + 4 c^{3} d^{3}} \right)}}{b^{3} c^{2}}"," ",0,"(-b*c**2*d**3 + x*(b**3*e**3 - 3*b**2*c*d*e**2 + 3*b*c**2*d**2*e - 2*c**3*d**3))/(b**3*c**2*x + b**2*c**3*x**2) + d**2*(3*b*e - 2*c*d)*log(x + (-3*b**2*c*d**2*e + 2*b*c**2*d**3 + b*c*d**2*(3*b*e - 2*c*d))/(b**3*e**3 - 6*b*c**2*d**2*e + 4*c**3*d**3))/b**3 + (b*e - c*d)**2*(b*e + 2*c*d)*log(x + (-3*b**2*c*d**2*e + 2*b*c**2*d**3 + b*(b*e - c*d)**2*(b*e + 2*c*d)/c)/(b**3*e**3 - 6*b*c**2*d**2*e + 4*c**3*d**3))/(b**3*c**2)","B",0
270,1,173,0,0.750152," ","integrate((e*x+d)**2/(c*x**2+b*x)**2,x)","\frac{- b c d^{2} + x \left(- b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{b^{3} c x + b^{2} c^{2} x^{2}} + \frac{2 d \left(b e - c d\right) \log{\left(x + \frac{2 b^{2} d e - 2 b c d^{2} - 2 b d \left(b e - c d\right)}{4 b c d e - 4 c^{2} d^{2}} \right)}}{b^{3}} - \frac{2 d \left(b e - c d\right) \log{\left(x + \frac{2 b^{2} d e - 2 b c d^{2} + 2 b d \left(b e - c d\right)}{4 b c d e - 4 c^{2} d^{2}} \right)}}{b^{3}}"," ",0,"(-b*c*d**2 + x*(-b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2))/(b**3*c*x + b**2*c**2*x**2) + 2*d*(b*e - c*d)*log(x + (2*b**2*d*e - 2*b*c*d**2 - 2*b*d*(b*e - c*d))/(4*b*c*d*e - 4*c**2*d**2))/b**3 - 2*d*(b*e - c*d)*log(x + (2*b**2*d*e - 2*b*c*d**2 + 2*b*d*(b*e - c*d))/(4*b*c*d*e - 4*c**2*d**2))/b**3","B",0
271,1,128,0,0.513757," ","integrate((e*x+d)/(c*x**2+b*x)**2,x)","\frac{- b d + x \left(b e - 2 c d\right)}{b^{3} x + b^{2} c x^{2}} + \frac{\left(b e - 2 c d\right) \log{\left(x + \frac{b^{2} e - 2 b c d - b \left(b e - 2 c d\right)}{2 b c e - 4 c^{2} d} \right)}}{b^{3}} - \frac{\left(b e - 2 c d\right) \log{\left(x + \frac{b^{2} e - 2 b c d + b \left(b e - 2 c d\right)}{2 b c e - 4 c^{2} d} \right)}}{b^{3}}"," ",0,"(-b*d + x*(b*e - 2*c*d))/(b**3*x + b**2*c*x**2) + (b*e - 2*c*d)*log(x + (b**2*e - 2*b*c*d - b*(b*e - 2*c*d))/(2*b*c*e - 4*c**2*d))/b**3 - (b*e - 2*c*d)*log(x + (b**2*e - 2*b*c*d + b*(b*e - 2*c*d))/(2*b*c*e - 4*c**2*d))/b**3","B",0
272,1,37,0,0.269499," ","integrate(1/(c*x**2+b*x)**2,x)","\frac{- b - 2 c x}{b^{3} x + b^{2} c x^{2}} + \frac{2 c \left(- \log{\left(x \right)} + \log{\left(\frac{b}{c} + x \right)}\right)}{b^{3}}"," ",0,"(-b - 2*c*x)/(b**3*x + b**2*c*x**2) + 2*c*(-log(x) + log(b/c + x))/b**3","A",0
273,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,1,687,0,33.366753," ","integrate((e*x+d)**7/(c*x**2+b*x)**3,x)","x \left(- \frac{3 b e^{7}}{c^{4}} + \frac{7 d e^{6}}{c^{3}}\right) + \frac{- b^{3} c^{5} d^{7} + x^{3} \left(8 b^{7} c e^{7} - 42 b^{6} c^{2} d e^{6} + 84 b^{5} c^{3} d^{2} e^{5} - 70 b^{4} c^{4} d^{3} e^{4} + 42 b^{2} c^{6} d^{5} e^{2} - 42 b c^{7} d^{6} e + 12 c^{8} d^{7}\right) + x^{2} \left(7 b^{8} e^{7} - 35 b^{7} c d e^{6} + 63 b^{6} c^{2} d^{2} e^{5} - 35 b^{5} c^{3} d^{3} e^{4} - 35 b^{4} c^{4} d^{4} e^{3} + 63 b^{3} c^{5} d^{5} e^{2} - 63 b^{2} c^{6} d^{6} e + 18 b c^{7} d^{7}\right) + x \left(- 14 b^{3} c^{5} d^{6} e + 4 b^{2} c^{6} d^{7}\right)}{2 b^{6} c^{5} x^{2} + 4 b^{5} c^{6} x^{3} + 2 b^{4} c^{7} x^{4}} + \frac{e^{7} x^{2}}{2 c^{3}} + \frac{3 d^{5} \left(7 b^{2} e^{2} - 7 b c d e + 2 c^{2} d^{2}\right) \log{\left(x + \frac{- 21 b^{3} c^{4} d^{5} e^{2} + 21 b^{2} c^{5} d^{6} e - 6 b c^{6} d^{7} + 3 b c^{4} d^{5} \left(7 b^{2} e^{2} - 7 b c d e + 2 c^{2} d^{2}\right)}{6 b^{7} e^{7} - 21 b^{6} c d e^{6} + 21 b^{5} c^{2} d^{2} e^{5} - 42 b^{2} c^{5} d^{5} e^{2} + 42 b c^{6} d^{6} e - 12 c^{7} d^{7}} \right)}}{b^{5}} + \frac{3 \left(b e - c d\right)^{5} \left(2 b^{2} e^{2} + 3 b c d e + 2 c^{2} d^{2}\right) \log{\left(x + \frac{- 21 b^{3} c^{4} d^{5} e^{2} + 21 b^{2} c^{5} d^{6} e - 6 b c^{6} d^{7} + \frac{3 b \left(b e - c d\right)^{5} \left(2 b^{2} e^{2} + 3 b c d e + 2 c^{2} d^{2}\right)}{c}}{6 b^{7} e^{7} - 21 b^{6} c d e^{6} + 21 b^{5} c^{2} d^{2} e^{5} - 42 b^{2} c^{5} d^{5} e^{2} + 42 b c^{6} d^{6} e - 12 c^{7} d^{7}} \right)}}{b^{5} c^{5}}"," ",0,"x*(-3*b*e**7/c**4 + 7*d*e**6/c**3) + (-b**3*c**5*d**7 + x**3*(8*b**7*c*e**7 - 42*b**6*c**2*d*e**6 + 84*b**5*c**3*d**2*e**5 - 70*b**4*c**4*d**3*e**4 + 42*b**2*c**6*d**5*e**2 - 42*b*c**7*d**6*e + 12*c**8*d**7) + x**2*(7*b**8*e**7 - 35*b**7*c*d*e**6 + 63*b**6*c**2*d**2*e**5 - 35*b**5*c**3*d**3*e**4 - 35*b**4*c**4*d**4*e**3 + 63*b**3*c**5*d**5*e**2 - 63*b**2*c**6*d**6*e + 18*b*c**7*d**7) + x*(-14*b**3*c**5*d**6*e + 4*b**2*c**6*d**7))/(2*b**6*c**5*x**2 + 4*b**5*c**6*x**3 + 2*b**4*c**7*x**4) + e**7*x**2/(2*c**3) + 3*d**5*(7*b**2*e**2 - 7*b*c*d*e + 2*c**2*d**2)*log(x + (-21*b**3*c**4*d**5*e**2 + 21*b**2*c**5*d**6*e - 6*b*c**6*d**7 + 3*b*c**4*d**5*(7*b**2*e**2 - 7*b*c*d*e + 2*c**2*d**2))/(6*b**7*e**7 - 21*b**6*c*d*e**6 + 21*b**5*c**2*d**2*e**5 - 42*b**2*c**5*d**5*e**2 + 42*b*c**6*d**6*e - 12*c**7*d**7))/b**5 + 3*(b*e - c*d)**5*(2*b**2*e**2 + 3*b*c*d*e + 2*c**2*d**2)*log(x + (-21*b**3*c**4*d**5*e**2 + 21*b**2*c**5*d**6*e - 6*b*c**6*d**7 + 3*b*(b*e - c*d)**5*(2*b**2*e**2 + 3*b*c*d*e + 2*c**2*d**2)/c)/(6*b**7*e**7 - 21*b**6*c*d*e**6 + 21*b**5*c**2*d**2*e**5 - 42*b**2*c**5*d**5*e**2 + 42*b*c**6*d**6*e - 12*c**7*d**7))/(b**5*c**5)","B",0
276,1,597,0,12.856574," ","integrate((e*x+d)**6/(c*x**2+b*x)**3,x)","\frac{- b^{3} c^{4} d^{6} + x^{3} \left(- 6 b^{6} c e^{6} + 24 b^{5} c^{2} d e^{5} - 30 b^{4} c^{3} d^{2} e^{4} + 30 b^{2} c^{5} d^{4} e^{2} - 36 b c^{6} d^{5} e + 12 c^{7} d^{6}\right) + x^{2} \left(- 5 b^{7} e^{6} + 18 b^{6} c d e^{5} - 15 b^{5} c^{2} d^{2} e^{4} - 20 b^{4} c^{3} d^{3} e^{3} + 45 b^{3} c^{4} d^{4} e^{2} - 54 b^{2} c^{5} d^{5} e + 18 b c^{6} d^{6}\right) + x \left(- 12 b^{3} c^{4} d^{5} e + 4 b^{2} c^{5} d^{6}\right)}{2 b^{6} c^{4} x^{2} + 4 b^{5} c^{5} x^{3} + 2 b^{4} c^{6} x^{4}} + \frac{e^{6} x}{c^{3}} + \frac{3 d^{4} \left(5 b^{2} e^{2} - 6 b c d e + 2 c^{2} d^{2}\right) \log{\left(x + \frac{15 b^{3} c^{3} d^{4} e^{2} - 18 b^{2} c^{4} d^{5} e + 6 b c^{5} d^{6} - 3 b c^{3} d^{4} \left(5 b^{2} e^{2} - 6 b c d e + 2 c^{2} d^{2}\right)}{3 b^{6} e^{6} - 6 b^{5} c d e^{5} + 30 b^{2} c^{4} d^{4} e^{2} - 36 b c^{5} d^{5} e + 12 c^{6} d^{6}} \right)}}{b^{5}} - \frac{3 \left(b e - c d\right)^{4} \left(b^{2} e^{2} + 2 b c d e + 2 c^{2} d^{2}\right) \log{\left(x + \frac{15 b^{3} c^{3} d^{4} e^{2} - 18 b^{2} c^{4} d^{5} e + 6 b c^{5} d^{6} + \frac{3 b \left(b e - c d\right)^{4} \left(b^{2} e^{2} + 2 b c d e + 2 c^{2} d^{2}\right)}{c}}{3 b^{6} e^{6} - 6 b^{5} c d e^{5} + 30 b^{2} c^{4} d^{4} e^{2} - 36 b c^{5} d^{5} e + 12 c^{6} d^{6}} \right)}}{b^{5} c^{4}}"," ",0,"(-b**3*c**4*d**6 + x**3*(-6*b**6*c*e**6 + 24*b**5*c**2*d*e**5 - 30*b**4*c**3*d**2*e**4 + 30*b**2*c**5*d**4*e**2 - 36*b*c**6*d**5*e + 12*c**7*d**6) + x**2*(-5*b**7*e**6 + 18*b**6*c*d*e**5 - 15*b**5*c**2*d**2*e**4 - 20*b**4*c**3*d**3*e**3 + 45*b**3*c**4*d**4*e**2 - 54*b**2*c**5*d**5*e + 18*b*c**6*d**6) + x*(-12*b**3*c**4*d**5*e + 4*b**2*c**5*d**6))/(2*b**6*c**4*x**2 + 4*b**5*c**5*x**3 + 2*b**4*c**6*x**4) + e**6*x/c**3 + 3*d**4*(5*b**2*e**2 - 6*b*c*d*e + 2*c**2*d**2)*log(x + (15*b**3*c**3*d**4*e**2 - 18*b**2*c**4*d**5*e + 6*b*c**5*d**6 - 3*b*c**3*d**4*(5*b**2*e**2 - 6*b*c*d*e + 2*c**2*d**2))/(3*b**6*e**6 - 6*b**5*c*d*e**5 + 30*b**2*c**4*d**4*e**2 - 36*b*c**5*d**5*e + 12*c**6*d**6))/b**5 - 3*(b*e - c*d)**4*(b**2*e**2 + 2*b*c*d*e + 2*c**2*d**2)*log(x + (15*b**3*c**3*d**4*e**2 - 18*b**2*c**4*d**5*e + 6*b*c**5*d**6 + 3*b*(b*e - c*d)**4*(b**2*e**2 + 2*b*c*d*e + 2*c**2*d**2)/c)/(3*b**6*e**6 - 6*b**5*c*d*e**5 + 30*b**2*c**4*d**4*e**2 - 36*b*c**5*d**5*e + 12*c**6*d**6))/(b**5*c**4)","B",0
277,1,524,0,5.806093," ","integrate((e*x+d)**5/(c*x**2+b*x)**3,x)","\frac{- b^{3} c^{3} d^{5} + x^{3} \left(4 b^{5} c e^{5} - 10 b^{4} c^{2} d e^{4} + 20 b^{2} c^{4} d^{3} e^{2} - 30 b c^{5} d^{4} e + 12 c^{6} d^{5}\right) + x^{2} \left(3 b^{6} e^{5} - 5 b^{5} c d e^{4} - 10 b^{4} c^{2} d^{2} e^{3} + 30 b^{3} c^{3} d^{3} e^{2} - 45 b^{2} c^{4} d^{4} e + 18 b c^{5} d^{5}\right) + x \left(- 10 b^{3} c^{3} d^{4} e + 4 b^{2} c^{4} d^{5}\right)}{2 b^{6} c^{3} x^{2} + 4 b^{5} c^{4} x^{3} + 2 b^{4} c^{5} x^{4}} + \frac{d^{3} \left(10 b^{2} e^{2} - 15 b c d e + 6 c^{2} d^{2}\right) \log{\left(x + \frac{- 10 b^{3} c^{2} d^{3} e^{2} + 15 b^{2} c^{3} d^{4} e - 6 b c^{4} d^{5} + b c^{2} d^{3} \left(10 b^{2} e^{2} - 15 b c d e + 6 c^{2} d^{2}\right)}{b^{5} e^{5} - 20 b^{2} c^{3} d^{3} e^{2} + 30 b c^{4} d^{4} e - 12 c^{5} d^{5}} \right)}}{b^{5}} + \frac{\left(b e - c d\right)^{3} \left(b^{2} e^{2} + 3 b c d e + 6 c^{2} d^{2}\right) \log{\left(x + \frac{- 10 b^{3} c^{2} d^{3} e^{2} + 15 b^{2} c^{3} d^{4} e - 6 b c^{4} d^{5} + \frac{b \left(b e - c d\right)^{3} \left(b^{2} e^{2} + 3 b c d e + 6 c^{2} d^{2}\right)}{c}}{b^{5} e^{5} - 20 b^{2} c^{3} d^{3} e^{2} + 30 b c^{4} d^{4} e - 12 c^{5} d^{5}} \right)}}{b^{5} c^{3}}"," ",0,"(-b**3*c**3*d**5 + x**3*(4*b**5*c*e**5 - 10*b**4*c**2*d*e**4 + 20*b**2*c**4*d**3*e**2 - 30*b*c**5*d**4*e + 12*c**6*d**5) + x**2*(3*b**6*e**5 - 5*b**5*c*d*e**4 - 10*b**4*c**2*d**2*e**3 + 30*b**3*c**3*d**3*e**2 - 45*b**2*c**4*d**4*e + 18*b*c**5*d**5) + x*(-10*b**3*c**3*d**4*e + 4*b**2*c**4*d**5))/(2*b**6*c**3*x**2 + 4*b**5*c**4*x**3 + 2*b**4*c**5*x**4) + d**3*(10*b**2*e**2 - 15*b*c*d*e + 6*c**2*d**2)*log(x + (-10*b**3*c**2*d**3*e**2 + 15*b**2*c**3*d**4*e - 6*b*c**4*d**5 + b*c**2*d**3*(10*b**2*e**2 - 15*b*c*d*e + 6*c**2*d**2))/(b**5*e**5 - 20*b**2*c**3*d**3*e**2 + 30*b*c**4*d**4*e - 12*c**5*d**5))/b**5 + (b*e - c*d)**3*(b**2*e**2 + 3*b*c*d*e + 6*c**2*d**2)*log(x + (-10*b**3*c**2*d**3*e**2 + 15*b**2*c**3*d**4*e - 6*b*c**4*d**5 + b*(b*e - c*d)**3*(b**2*e**2 + 3*b*c*d*e + 6*c**2*d**2)/c)/(b**5*e**5 - 20*b**2*c**3*d**3*e**2 + 30*b*c**4*d**4*e - 12*c**5*d**5))/(b**5*c**3)","B",0
278,1,389,0,2.846969," ","integrate((e*x+d)**4/(c*x**2+b*x)**3,x)","\frac{- b^{3} c^{2} d^{4} + x^{3} \left(- 2 b^{4} c e^{4} + 12 b^{2} c^{3} d^{2} e^{2} - 24 b c^{4} d^{3} e + 12 c^{5} d^{4}\right) + x^{2} \left(- b^{5} e^{4} - 4 b^{4} c d e^{3} + 18 b^{3} c^{2} d^{2} e^{2} - 36 b^{2} c^{3} d^{3} e + 18 b c^{4} d^{4}\right) + x \left(- 8 b^{3} c^{2} d^{3} e + 4 b^{2} c^{3} d^{4}\right)}{2 b^{6} c^{2} x^{2} + 4 b^{5} c^{3} x^{3} + 2 b^{4} c^{4} x^{4}} + \frac{6 d^{2} \left(b e - c d\right)^{2} \log{\left(x + \frac{6 b^{3} d^{2} e^{2} - 12 b^{2} c d^{3} e + 6 b c^{2} d^{4} - 6 b d^{2} \left(b e - c d\right)^{2}}{12 b^{2} c d^{2} e^{2} - 24 b c^{2} d^{3} e + 12 c^{3} d^{4}} \right)}}{b^{5}} - \frac{6 d^{2} \left(b e - c d\right)^{2} \log{\left(x + \frac{6 b^{3} d^{2} e^{2} - 12 b^{2} c d^{3} e + 6 b c^{2} d^{4} + 6 b d^{2} \left(b e - c d\right)^{2}}{12 b^{2} c d^{2} e^{2} - 24 b c^{2} d^{3} e + 12 c^{3} d^{4}} \right)}}{b^{5}}"," ",0,"(-b**3*c**2*d**4 + x**3*(-2*b**4*c*e**4 + 12*b**2*c**3*d**2*e**2 - 24*b*c**4*d**3*e + 12*c**5*d**4) + x**2*(-b**5*e**4 - 4*b**4*c*d*e**3 + 18*b**3*c**2*d**2*e**2 - 36*b**2*c**3*d**3*e + 18*b*c**4*d**4) + x*(-8*b**3*c**2*d**3*e + 4*b**2*c**3*d**4))/(2*b**6*c**2*x**2 + 4*b**5*c**3*x**3 + 2*b**4*c**4*x**4) + 6*d**2*(b*e - c*d)**2*log(x + (6*b**3*d**2*e**2 - 12*b**2*c*d**3*e + 6*b*c**2*d**4 - 6*b*d**2*(b*e - c*d)**2)/(12*b**2*c*d**2*e**2 - 24*b*c**2*d**3*e + 12*c**3*d**4))/b**5 - 6*d**2*(b*e - c*d)**2*log(x + (6*b**3*d**2*e**2 - 12*b**2*c*d**3*e + 6*b*c**2*d**4 + 6*b*d**2*(b*e - c*d)**2)/(12*b**2*c*d**2*e**2 - 24*b*c**2*d**3*e + 12*c**3*d**4))/b**5","B",0
279,1,371,0,1.758907," ","integrate((e*x+d)**3/(c*x**2+b*x)**3,x)","\frac{- b^{3} c d^{3} + x^{3} \left(6 b^{2} c^{2} d e^{2} - 18 b c^{3} d^{2} e + 12 c^{4} d^{3}\right) + x^{2} \left(- b^{4} e^{3} + 9 b^{3} c d e^{2} - 27 b^{2} c^{2} d^{2} e + 18 b c^{3} d^{3}\right) + x \left(- 6 b^{3} c d^{2} e + 4 b^{2} c^{2} d^{3}\right)}{2 b^{6} c x^{2} + 4 b^{5} c^{2} x^{3} + 2 b^{4} c^{3} x^{4}} + \frac{3 d \left(b e - 2 c d\right) \left(b e - c d\right) \log{\left(x + \frac{3 b^{3} d e^{2} - 9 b^{2} c d^{2} e + 6 b c^{2} d^{3} - 3 b d \left(b e - 2 c d\right) \left(b e - c d\right)}{6 b^{2} c d e^{2} - 18 b c^{2} d^{2} e + 12 c^{3} d^{3}} \right)}}{b^{5}} - \frac{3 d \left(b e - 2 c d\right) \left(b e - c d\right) \log{\left(x + \frac{3 b^{3} d e^{2} - 9 b^{2} c d^{2} e + 6 b c^{2} d^{3} + 3 b d \left(b e - 2 c d\right) \left(b e - c d\right)}{6 b^{2} c d e^{2} - 18 b c^{2} d^{2} e + 12 c^{3} d^{3}} \right)}}{b^{5}}"," ",0,"(-b**3*c*d**3 + x**3*(6*b**2*c**2*d*e**2 - 18*b*c**3*d**2*e + 12*c**4*d**3) + x**2*(-b**4*e**3 + 9*b**3*c*d*e**2 - 27*b**2*c**2*d**2*e + 18*b*c**3*d**3) + x*(-6*b**3*c*d**2*e + 4*b**2*c**2*d**3))/(2*b**6*c*x**2 + 4*b**5*c**2*x**3 + 2*b**4*c**3*x**4) + 3*d*(b*e - 2*c*d)*(b*e - c*d)*log(x + (3*b**3*d*e**2 - 9*b**2*c*d**2*e + 6*b*c**2*d**3 - 3*b*d*(b*e - 2*c*d)*(b*e - c*d))/(6*b**2*c*d*e**2 - 18*b*c**2*d**2*e + 12*c**3*d**3))/b**5 - 3*d*(b*e - 2*c*d)*(b*e - c*d)*log(x + (3*b**3*d*e**2 - 9*b**2*c*d**2*e + 6*b*c**2*d**3 + 3*b*d*(b*e - 2*c*d)*(b*e - c*d))/(6*b**2*c*d*e**2 - 18*b*c**2*d**2*e + 12*c**3*d**3))/b**5","B",0
280,1,345,0,1.088378," ","integrate((e*x+d)**2/(c*x**2+b*x)**3,x)","\frac{- b^{3} d^{2} + x^{3} \left(2 b^{2} c e^{2} - 12 b c^{2} d e + 12 c^{3} d^{2}\right) + x^{2} \left(3 b^{3} e^{2} - 18 b^{2} c d e + 18 b c^{2} d^{2}\right) + x \left(- 4 b^{3} d e + 4 b^{2} c d^{2}\right)}{2 b^{6} x^{2} + 4 b^{5} c x^{3} + 2 b^{4} c^{2} x^{4}} + \frac{\left(b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) \log{\left(x + \frac{b^{3} e^{2} - 6 b^{2} c d e + 6 b c^{2} d^{2} - b \left(b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right)}{2 b^{2} c e^{2} - 12 b c^{2} d e + 12 c^{3} d^{2}} \right)}}{b^{5}} - \frac{\left(b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) \log{\left(x + \frac{b^{3} e^{2} - 6 b^{2} c d e + 6 b c^{2} d^{2} + b \left(b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right)}{2 b^{2} c e^{2} - 12 b c^{2} d e + 12 c^{3} d^{2}} \right)}}{b^{5}}"," ",0,"(-b**3*d**2 + x**3*(2*b**2*c*e**2 - 12*b*c**2*d*e + 12*c**3*d**2) + x**2*(3*b**3*e**2 - 18*b**2*c*d*e + 18*b*c**2*d**2) + x*(-4*b**3*d*e + 4*b**2*c*d**2))/(2*b**6*x**2 + 4*b**5*c*x**3 + 2*b**4*c**2*x**4) + (b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2)*log(x + (b**3*e**2 - 6*b**2*c*d*e + 6*b*c**2*d**2 - b*(b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2))/(2*b**2*c*e**2 - 12*b*c**2*d*e + 12*c**3*d**2))/b**5 - (b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2)*log(x + (b**3*e**2 - 6*b**2*c*d*e + 6*b*c**2*d**2 + b*(b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2))/(2*b**2*c*e**2 - 12*b*c**2*d*e + 12*c**3*d**2))/b**5","B",0
281,1,219,0,0.727505," ","integrate((e*x+d)/(c*x**2+b*x)**3,x)","\frac{- b^{3} d + x^{3} \left(- 6 b c^{2} e + 12 c^{3} d\right) + x^{2} \left(- 9 b^{2} c e + 18 b c^{2} d\right) + x \left(- 2 b^{3} e + 4 b^{2} c d\right)}{2 b^{6} x^{2} + 4 b^{5} c x^{3} + 2 b^{4} c^{2} x^{4}} - \frac{3 c \left(b e - 2 c d\right) \log{\left(x + \frac{3 b^{2} c e - 6 b c^{2} d - 3 b c \left(b e - 2 c d\right)}{6 b c^{2} e - 12 c^{3} d} \right)}}{b^{5}} + \frac{3 c \left(b e - 2 c d\right) \log{\left(x + \frac{3 b^{2} c e - 6 b c^{2} d + 3 b c \left(b e - 2 c d\right)}{6 b c^{2} e - 12 c^{3} d} \right)}}{b^{5}}"," ",0,"(-b**3*d + x**3*(-6*b*c**2*e + 12*c**3*d) + x**2*(-9*b**2*c*e + 18*b*c**2*d) + x*(-2*b**3*e + 4*b**2*c*d))/(2*b**6*x**2 + 4*b**5*c*x**3 + 2*b**4*c**2*x**4) - 3*c*(b*e - 2*c*d)*log(x + (3*b**2*c*e - 6*b*c**2*d - 3*b*c*(b*e - 2*c*d))/(6*b*c**2*e - 12*c**3*d))/b**5 + 3*c*(b*e - 2*c*d)*log(x + (3*b**2*c*e - 6*b*c**2*d + 3*b*c*(b*e - 2*c*d))/(6*b*c**2*e - 12*c**3*d))/b**5","B",0
282,1,78,0,0.383500," ","integrate(1/(c*x**2+b*x)**3,x)","\frac{- b^{3} + 4 b^{2} c x + 18 b c^{2} x^{2} + 12 c^{3} x^{3}}{2 b^{6} x^{2} + 4 b^{5} c x^{3} + 2 b^{4} c^{2} x^{4}} + \frac{6 c^{2} \left(\log{\left(x \right)} - \log{\left(\frac{b}{c} + x \right)}\right)}{b^{5}}"," ",0,"(-b**3 + 4*b**2*c*x + 18*b*c**2*x**2 + 12*c**3*x**3)/(2*b**6*x**2 + 4*b**5*c*x**3 + 2*b**4*c**2*x**4) + 6*c**2*(log(x) - log(b/c + x))/b**5","A",0
283,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,0,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(d + e x\right)^{3}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(d + e*x)**3, x)","F",0
286,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(d + e x\right)^{2}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(d + e*x)**2, x)","F",0
287,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(d + e x\right)\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(d + e*x), x)","F",0
288,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2),x)","\int \sqrt{b x + c x^{2}}\, dx"," ",0,"Integral(sqrt(b*x + c*x**2), x)","F",0
289,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{d + e x}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/(d + e*x), x)","F",0
290,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/(d + e*x)**2, x)","F",0
291,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/(e*x+d)**3,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/(d + e*x)**3, x)","F",0
292,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/(e*x+d)**4,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/(d + e*x)**4, x)","F",0
293,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/(e*x+d)**5,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/(d + e*x)**5, x)","F",0
294,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/(e*x+d)**6,x)","\int \frac{\sqrt{x \left(b + c x\right)}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/(d + e*x)**6, x)","F",0
295,0,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x)**(3/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{3}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(d + e*x)**3, x)","F",0
296,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x)**(3/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(d + e*x)**2, x)","F",0
297,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x)**(3/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(d + e*x), x)","F",0
298,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2),x)","\int \left(b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*x + c*x**2)**(3/2), x)","F",0
299,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/(e*x+d),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/(d + e*x), x)","F",0
300,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/(d + e*x)**2, x)","F",0
301,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/(e*x+d)**3,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/(d + e*x)**3, x)","F",0
302,0,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x)**(5/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{3}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(d + e*x)**3, x)","F",0
303,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x)**(5/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{2}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(d + e*x)**2, x)","F",0
304,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x)**(5/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(d + e x\right)\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(d + e*x), x)","F",0
305,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2),x)","\int \left(b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((b*x + c*x**2)**(5/2), x)","F",0
306,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2)/(e*x+d),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}{d + e x}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)/(d + e*x), x)","F",0
307,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2)/(e*x+d)**2,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)/(d + e*x)**2, x)","F",0
308,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)/(d + e*x)**3, x)","F",0
309,0,0,0,0.000000," ","integrate((x**2+2*x)**(1/2)/(1+x),x)","\int \frac{\sqrt{x \left(x + 2\right)}}{x + 1}\, dx"," ",0,"Integral(sqrt(x*(x + 2))/(x + 1), x)","F",0
310,0,0,0,0.000000," ","integrate((-x**2+2*x)**(3/2)/(2-2*x),x)","- \frac{\int \frac{2 x \sqrt{- x^{2} + 2 x}}{x - 1}\, dx + \int \left(- \frac{x^{2} \sqrt{- x^{2} + 2 x}}{x - 1}\right)\, dx}{2}"," ",0,"-(Integral(2*x*sqrt(-x**2 + 2*x)/(x - 1), x) + Integral(-x**2*sqrt(-x**2 + 2*x)/(x - 1), x))/2","F",0
311,0,0,0,0.000000," ","integrate((-x**2+2*x)**(1/2)/(2-2*x),x)","- \frac{\int \frac{\sqrt{- x^{2} + 2 x}}{x - 1}\, dx}{2}"," ",0,"-Integral(sqrt(-x**2 + 2*x)/(x - 1), x)/2","F",0
312,0,0,0,0.000000," ","integrate(1/(2-2*x)/(-x**2+2*x)**(1/2),x)","- \frac{\int \frac{1}{x \sqrt{- x^{2} + 2 x} - \sqrt{- x^{2} + 2 x}}\, dx}{2}"," ",0,"-Integral(1/(x*sqrt(-x**2 + 2*x) - sqrt(-x**2 + 2*x)), x)/2","F",0
313,0,0,0,0.000000," ","integrate(1/(2-2*x)/(-x**2+2*x)**(3/2),x)","- \frac{\int \frac{1}{- x^{3} \sqrt{- x^{2} + 2 x} + 3 x^{2} \sqrt{- x^{2} + 2 x} - 2 x \sqrt{- x^{2} + 2 x}}\, dx}{2}"," ",0,"-Integral(1/(-x**3*sqrt(-x**2 + 2*x) + 3*x**2*sqrt(-x**2 + 2*x) - 2*x*sqrt(-x**2 + 2*x)), x)/2","F",0
314,0,0,0,0.000000," ","integrate(1/(2-2*x)/(-x**2+2*x)**(5/2),x)","- \frac{\int \frac{1}{x^{5} \sqrt{- x^{2} + 2 x} - 5 x^{4} \sqrt{- x^{2} + 2 x} + 8 x^{3} \sqrt{- x^{2} + 2 x} - 4 x^{2} \sqrt{- x^{2} + 2 x}}\, dx}{2}"," ",0,"-Integral(1/(x**5*sqrt(-x**2 + 2*x) - 5*x**4*sqrt(-x**2 + 2*x) + 8*x**3*sqrt(-x**2 + 2*x) - 4*x**2*sqrt(-x**2 + 2*x)), x)/2","F",0
315,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(d + e x\right)^{3}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((d + e*x)**3/sqrt(x*(b + c*x)), x)","F",0
316,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(d + e x\right)^{2}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((d + e*x)**2/sqrt(x*(b + c*x)), x)","F",0
317,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x)**(1/2),x)","\int \frac{d + e x}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((d + e*x)/sqrt(x*(b + c*x)), x)","F",0
318,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{\sqrt{b x + c x^{2}}}\, dx"," ",0,"Integral(1/sqrt(b*x + c*x**2), x)","F",0
319,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(sqrt(x*(b + c*x))*(d + e*x)), x)","F",0
320,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(x*(b + c*x))*(d + e*x)**2), x)","F",0
321,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(x*(b + c*x))*(d + e*x)**3), x)","F",0
322,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+b*x)**(3/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(x*(b + c*x))**(3/2), x)","F",0
323,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+b*x)**(3/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(x*(b + c*x))**(3/2), x)","F",0
324,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x)**(3/2),x)","\int \frac{d + e x}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)/(x*(b + c*x))**(3/2), x)","F",0
325,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{\left(b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*x + c*x**2)**(-3/2), x)","F",0
326,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((x*(b + c*x))**(3/2)*(d + e*x)), x)","F",0
327,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((x*(b + c*x))**(3/2)*(d + e*x)**2), x)","F",0
328,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/((x*(b + c*x))**(3/2)*(d + e*x)**3), x)","F",0
329,0,0,0,0.000000," ","integrate((e*x+d)**4/(c*x**2+b*x)**(5/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/(x*(b + c*x))**(5/2), x)","F",0
330,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+b*x)**(5/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(x*(b + c*x))**(5/2), x)","F",0
331,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+b*x)**(5/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(x*(b + c*x))**(5/2), x)","F",0
332,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x)**(5/2),x)","\int \frac{d + e x}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)/(x*(b + c*x))**(5/2), x)","F",0
333,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x)**(5/2),x)","\int \frac{1}{\left(b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b*x + c*x**2)**(-5/2), x)","F",0
334,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x)**(5/2),x)","\int \frac{1}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((x*(b + c*x))**(5/2)*(d + e*x)), x)","F",0
335,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x)**(5/2),x)","\int \frac{1}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((x*(b + c*x))**(5/2)*(d + e*x)**2), x)","F",0
336,0,0,0,0.000000," ","integrate(1/(2+x)/(x**2+2*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(x + 2\right)} \left(x + 2\right)}\, dx"," ",0,"Integral(1/(sqrt(x*(x + 2))*(x + 2)), x)","F",0
337,1,292,0,8.525266," ","integrate((e*x+d)**(7/2)*(c*x**2+b*x),x)","\begin{cases} - \frac{4 b d^{5} \sqrt{d + e x}}{99 e^{2}} + \frac{2 b d^{4} x \sqrt{d + e x}}{99 e} + \frac{16 b d^{3} x^{2} \sqrt{d + e x}}{33} + \frac{92 b d^{2} e x^{3} \sqrt{d + e x}}{99} + \frac{68 b d e^{2} x^{4} \sqrt{d + e x}}{99} + \frac{2 b e^{3} x^{5} \sqrt{d + e x}}{11} + \frac{16 c d^{6} \sqrt{d + e x}}{1287 e^{3}} - \frac{8 c d^{5} x \sqrt{d + e x}}{1287 e^{2}} + \frac{2 c d^{4} x^{2} \sqrt{d + e x}}{429 e} + \frac{424 c d^{3} x^{3} \sqrt{d + e x}}{1287} + \frac{916 c d^{2} e x^{4} \sqrt{d + e x}}{1287} + \frac{80 c d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{2 c e^{3} x^{6} \sqrt{d + e x}}{13} & \text{for}\: e \neq 0 \\d^{\frac{7}{2}} \left(\frac{b x^{2}}{2} + \frac{c x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*b*d**5*sqrt(d + e*x)/(99*e**2) + 2*b*d**4*x*sqrt(d + e*x)/(99*e) + 16*b*d**3*x**2*sqrt(d + e*x)/33 + 92*b*d**2*e*x**3*sqrt(d + e*x)/99 + 68*b*d*e**2*x**4*sqrt(d + e*x)/99 + 2*b*e**3*x**5*sqrt(d + e*x)/11 + 16*c*d**6*sqrt(d + e*x)/(1287*e**3) - 8*c*d**5*x*sqrt(d + e*x)/(1287*e**2) + 2*c*d**4*x**2*sqrt(d + e*x)/(429*e) + 424*c*d**3*x**3*sqrt(d + e*x)/1287 + 916*c*d**2*e*x**4*sqrt(d + e*x)/1287 + 80*c*d*e**2*x**5*sqrt(d + e*x)/143 + 2*c*e**3*x**6*sqrt(d + e*x)/13, Ne(e, 0)), (d**(7/2)*(b*x**2/2 + c*x**3/3), True))","A",0
338,1,245,0,3.665603," ","integrate((e*x+d)**(5/2)*(c*x**2+b*x),x)","\begin{cases} - \frac{4 b d^{4} \sqrt{d + e x}}{63 e^{2}} + \frac{2 b d^{3} x \sqrt{d + e x}}{63 e} + \frac{10 b d^{2} x^{2} \sqrt{d + e x}}{21} + \frac{38 b d e x^{3} \sqrt{d + e x}}{63} + \frac{2 b e^{2} x^{4} \sqrt{d + e x}}{9} + \frac{16 c d^{5} \sqrt{d + e x}}{693 e^{3}} - \frac{8 c d^{4} x \sqrt{d + e x}}{693 e^{2}} + \frac{2 c d^{3} x^{2} \sqrt{d + e x}}{231 e} + \frac{226 c d^{2} x^{3} \sqrt{d + e x}}{693} + \frac{46 c d e x^{4} \sqrt{d + e x}}{99} + \frac{2 c e^{2} x^{5} \sqrt{d + e x}}{11} & \text{for}\: e \neq 0 \\d^{\frac{5}{2}} \left(\frac{b x^{2}}{2} + \frac{c x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*b*d**4*sqrt(d + e*x)/(63*e**2) + 2*b*d**3*x*sqrt(d + e*x)/(63*e) + 10*b*d**2*x**2*sqrt(d + e*x)/21 + 38*b*d*e*x**3*sqrt(d + e*x)/63 + 2*b*e**2*x**4*sqrt(d + e*x)/9 + 16*c*d**5*sqrt(d + e*x)/(693*e**3) - 8*c*d**4*x*sqrt(d + e*x)/(693*e**2) + 2*c*d**3*x**2*sqrt(d + e*x)/(231*e) + 226*c*d**2*x**3*sqrt(d + e*x)/693 + 46*c*d*e*x**4*sqrt(d + e*x)/99 + 2*c*e**2*x**5*sqrt(d + e*x)/11, Ne(e, 0)), (d**(5/2)*(b*x**2/2 + c*x**3/3), True))","A",0
339,1,178,0,8.835786," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x),x)","\frac{2 b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{2 b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}}"," ",0,"2*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 2*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3","B",0
340,1,66,0,2.671023," ","integrate((e*x+d)**(1/2)*(c*x**2+b*x),x)","\frac{2 \left(\frac{c \left(d + e x\right)^{\frac{7}{2}}}{7 e^{2}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(b e - 2 c d\right)}{5 e^{2}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(- b d e + c d^{2}\right)}{3 e^{2}}\right)}{e}"," ",0,"2*(c*(d + e*x)**(7/2)/(7*e**2) + (d + e*x)**(5/2)*(b*e - 2*c*d)/(5*e**2) + (d + e*x)**(3/2)*(-b*d*e + c*d**2)/(3*e**2))/e","A",0
341,1,182,0,10.653424," ","integrate((c*x**2+b*x)/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{2 b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{2 c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}}}{e} & \text{for}\: e \neq 0 \\\frac{\frac{b x^{2}}{2} + \frac{c x^{3}}{3}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 2*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 2*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2)/e, Ne(e, 0)), ((b*x**2/2 + c*x**3/3)/sqrt(d), True))","A",0
342,1,60,0,10.758869," ","integrate((c*x**2+b*x)/(e*x+d)**(3/2),x)","\frac{2 c \left(d + e x\right)^{\frac{3}{2}}}{3 e^{3}} + \frac{2 d \left(b e - c d\right)}{e^{3} \sqrt{d + e x}} + \frac{\sqrt{d + e x} \left(2 b e - 4 c d\right)}{e^{3}}"," ",0,"2*c*(d + e*x)**(3/2)/(3*e**3) + 2*d*(b*e - c*d)/(e**3*sqrt(d + e*x)) + sqrt(d + e*x)*(2*b*e - 4*c*d)/e**3","A",0
343,1,211,0,1.352380," ","integrate((c*x**2+b*x)/(e*x+d)**(5/2),x)","\begin{cases} - \frac{4 b d e}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} - \frac{6 b e^{2} x}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{16 c d^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{24 c d e x}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{6 c e^{2} x^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{\frac{b x^{2}}{2} + \frac{c x^{3}}{3}}{d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*b*d*e/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) - 6*b*e**2*x/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 16*c*d**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 24*c*d*e*x/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 6*c*e**2*x**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)), Ne(e, 0)), ((b*x**2/2 + c*x**3/3)/d**(5/2), True))","A",0
344,1,314,0,2.994040," ","integrate((c*x**2+b*x)/(e*x+d)**(7/2),x)","\begin{cases} - \frac{4 b d e}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{10 b e^{2} x}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{16 c d^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{40 c d e x}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{30 c e^{2} x^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{\frac{b x^{2}}{2} + \frac{c x^{3}}{3}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*b*d*e/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 10*b*e**2*x/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 16*c*d**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 40*c*d*e*x/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 30*c*e**2*x**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)), Ne(e, 0)), ((b*x**2/2 + c*x**3/3)/d**(7/2), True))","A",0
345,1,590,0,13.611388," ","integrate((e*x+d)**(7/2)*(c*x**2+b*x)**2,x)","\begin{cases} \frac{16 b^{2} d^{6} \sqrt{d + e x}}{1287 e^{3}} - \frac{8 b^{2} d^{5} x \sqrt{d + e x}}{1287 e^{2}} + \frac{2 b^{2} d^{4} x^{2} \sqrt{d + e x}}{429 e} + \frac{424 b^{2} d^{3} x^{3} \sqrt{d + e x}}{1287} + \frac{916 b^{2} d^{2} e x^{4} \sqrt{d + e x}}{1287} + \frac{80 b^{2} d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{2 b^{2} e^{3} x^{6} \sqrt{d + e x}}{13} - \frac{64 b c d^{7} \sqrt{d + e x}}{6435 e^{4}} + \frac{32 b c d^{6} x \sqrt{d + e x}}{6435 e^{3}} - \frac{8 b c d^{5} x^{2} \sqrt{d + e x}}{2145 e^{2}} + \frac{4 b c d^{4} x^{3} \sqrt{d + e x}}{1287 e} + \frac{640 b c d^{3} x^{4} \sqrt{d + e x}}{1287} + \frac{824 b c d^{2} e x^{5} \sqrt{d + e x}}{715} + \frac{184 b c d e^{2} x^{6} \sqrt{d + e x}}{195} + \frac{4 b c e^{3} x^{7} \sqrt{d + e x}}{15} + \frac{256 c^{2} d^{8} \sqrt{d + e x}}{109395 e^{5}} - \frac{128 c^{2} d^{7} x \sqrt{d + e x}}{109395 e^{4}} + \frac{32 c^{2} d^{6} x^{2} \sqrt{d + e x}}{36465 e^{3}} - \frac{16 c^{2} d^{5} x^{3} \sqrt{d + e x}}{21879 e^{2}} + \frac{14 c^{2} d^{4} x^{4} \sqrt{d + e x}}{21879 e} + \frac{2424 c^{2} d^{3} x^{5} \sqrt{d + e x}}{12155} + \frac{1604 c^{2} d^{2} e x^{6} \sqrt{d + e x}}{3315} + \frac{104 c^{2} d e^{2} x^{7} \sqrt{d + e x}}{255} + \frac{2 c^{2} e^{3} x^{8} \sqrt{d + e x}}{17} & \text{for}\: e \neq 0 \\d^{\frac{7}{2}} \left(\frac{b^{2} x^{3}}{3} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*b**2*d**6*sqrt(d + e*x)/(1287*e**3) - 8*b**2*d**5*x*sqrt(d + e*x)/(1287*e**2) + 2*b**2*d**4*x**2*sqrt(d + e*x)/(429*e) + 424*b**2*d**3*x**3*sqrt(d + e*x)/1287 + 916*b**2*d**2*e*x**4*sqrt(d + e*x)/1287 + 80*b**2*d*e**2*x**5*sqrt(d + e*x)/143 + 2*b**2*e**3*x**6*sqrt(d + e*x)/13 - 64*b*c*d**7*sqrt(d + e*x)/(6435*e**4) + 32*b*c*d**6*x*sqrt(d + e*x)/(6435*e**3) - 8*b*c*d**5*x**2*sqrt(d + e*x)/(2145*e**2) + 4*b*c*d**4*x**3*sqrt(d + e*x)/(1287*e) + 640*b*c*d**3*x**4*sqrt(d + e*x)/1287 + 824*b*c*d**2*e*x**5*sqrt(d + e*x)/715 + 184*b*c*d*e**2*x**6*sqrt(d + e*x)/195 + 4*b*c*e**3*x**7*sqrt(d + e*x)/15 + 256*c**2*d**8*sqrt(d + e*x)/(109395*e**5) - 128*c**2*d**7*x*sqrt(d + e*x)/(109395*e**4) + 32*c**2*d**6*x**2*sqrt(d + e*x)/(36465*e**3) - 16*c**2*d**5*x**3*sqrt(d + e*x)/(21879*e**2) + 14*c**2*d**4*x**4*sqrt(d + e*x)/(21879*e) + 2424*c**2*d**3*x**5*sqrt(d + e*x)/12155 + 1604*c**2*d**2*e*x**6*sqrt(d + e*x)/3315 + 104*c**2*d*e**2*x**7*sqrt(d + e*x)/255 + 2*c**2*e**3*x**8*sqrt(d + e*x)/17, Ne(e, 0)), (d**(7/2)*(b**2*x**3/3 + b*c*x**4/2 + c**2*x**5/5), True))","A",0
346,1,695,0,27.199328," ","integrate((e*x+d)**(5/2)*(c*x**2+b*x)**2,x)","\frac{2 b^{2} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{4 b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{4 b c d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{8 b c d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{4 b c \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{2 c^{2} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{4 c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}}"," ",0,"2*b**2*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 4*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 4*b*c*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 8*b*c*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 4*b*c*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 2*c**2*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 4*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5","B",0
347,1,413,0,17.226686," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x)**2,x)","\frac{2 b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{4 b c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{4 b c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 c^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{2 c^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}}"," ",0,"2*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 4*b*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 4*b*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*c**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 2*c**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5","B",0
348,1,173,0,4.072343," ","integrate((e*x+d)**(1/2)*(c*x**2+b*x)**2,x)","\frac{2 \left(\frac{c^{2} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{4}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(2 b c e - 4 c^{2} d\right)}{9 e^{4}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right)}{7 e^{4}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(- 2 b^{2} d e^{2} + 6 b c d^{2} e - 4 c^{2} d^{3}\right)}{5 e^{4}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(b^{2} d^{2} e^{2} - 2 b c d^{3} e + c^{2} d^{4}\right)}{3 e^{4}}\right)}{e}"," ",0,"2*(c**2*(d + e*x)**(11/2)/(11*e**4) + (d + e*x)**(9/2)*(2*b*c*e - 4*c**2*d)/(9*e**4) + (d + e*x)**(7/2)*(b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2)/(7*e**4) + (d + e*x)**(5/2)*(-2*b**2*d*e**2 + 6*b*c*d**2*e - 4*c**2*d**3)/(5*e**4) + (d + e*x)**(3/2)*(b**2*d**2*e**2 - 2*b*c*d**3*e + c**2*d**4)/(3*e**4))/e","A",0
349,1,418,0,51.400522," ","integrate((c*x**2+b*x)**2/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{4 b c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{4 b c \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{2 c^{2} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{2 c^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}}}{e} & \text{for}\: e \neq 0 \\\frac{\frac{b^{2} x^{3}}{3} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 4*b*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 4*b*c*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 2*c**2*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 2*c**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4)/e, Ne(e, 0)), ((b**2*x**3/3 + b*c*x**4/2 + c**2*x**5/5)/sqrt(d), True))","A",0
350,1,150,0,23.936826," ","integrate((c*x**2+b*x)**2/(e*x+d)**(3/2),x)","\frac{2 c^{2} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{5}} - \frac{2 d^{2} \left(b e - c d\right)^{2}}{e^{5} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(4 b c e - 8 c^{2} d\right)}{5 e^{5}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(2 b^{2} e^{2} - 12 b c d e + 12 c^{2} d^{2}\right)}{3 e^{5}} + \frac{\sqrt{d + e x} \left(- 4 b^{2} d e^{2} + 12 b c d^{2} e - 8 c^{2} d^{3}\right)}{e^{5}}"," ",0,"2*c**2*(d + e*x)**(7/2)/(7*e**5) - 2*d**2*(b*e - c*d)**2/(e**5*sqrt(d + e*x)) + (d + e*x)**(5/2)*(4*b*c*e - 8*c**2*d)/(5*e**5) + (d + e*x)**(3/2)*(2*b**2*e**2 - 12*b*c*d*e + 12*c**2*d**2)/(3*e**5) + sqrt(d + e*x)*(-4*b**2*d*e**2 + 12*b*c*d**2*e - 8*c**2*d**3)/e**5","A",0
351,1,139,0,34.661584," ","integrate((c*x**2+b*x)**2/(e*x+d)**(5/2),x)","\frac{2 c^{2} \left(d + e x\right)^{\frac{5}{2}}}{5 e^{5}} - \frac{2 d^{2} \left(b e - c d\right)^{2}}{3 e^{5} \left(d + e x\right)^{\frac{3}{2}}} + \frac{4 d \left(b e - 2 c d\right) \left(b e - c d\right)}{e^{5} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(4 b c e - 8 c^{2} d\right)}{3 e^{5}} + \frac{\sqrt{d + e x} \left(2 b^{2} e^{2} - 12 b c d e + 12 c^{2} d^{2}\right)}{e^{5}}"," ",0,"2*c**2*(d + e*x)**(5/2)/(5*e**5) - 2*d**2*(b*e - c*d)**2/(3*e**5*(d + e*x)**(3/2)) + 4*d*(b*e - 2*c*d)*(b*e - c*d)/(e**5*sqrt(d + e*x)) + (d + e*x)**(3/2)*(4*b*c*e - 8*c**2*d)/(3*e**5) + sqrt(d + e*x)*(2*b**2*e**2 - 12*b*c*d*e + 12*c**2*d**2)/e**5","A",0
352,1,787,0,3.733032," ","integrate((c*x**2+b*x)**2/(e*x+d)**(7/2),x)","\begin{cases} - \frac{16 b^{2} d^{2} e^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{40 b^{2} d e^{3} x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{30 b^{2} e^{4} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{192 b c d^{3} e}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{480 b c d^{2} e^{2} x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{360 b c d e^{3} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{60 b c e^{4} x^{3}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{256 c^{2} d^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{640 c^{2} d^{3} e x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{480 c^{2} d^{2} e^{2} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{80 c^{2} d e^{3} x^{3}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{10 c^{2} e^{4} x^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{\frac{b^{2} x^{3}}{3} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*b**2*d**2*e**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 40*b**2*d*e**3*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 30*b**2*e**4*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 192*b*c*d**3*e/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 480*b*c*d**2*e**2*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 360*b*c*d*e**3*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 60*b*c*e**4*x**3/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 256*c**2*d**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 640*c**2*d**3*e*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 480*c**2*d**2*e**2*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 80*c**2*d*e**3*x**3/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 10*c**2*e**4*x**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)), Ne(e, 0)), ((b**2*x**3/3 + b*c*x**4/2 + c**2*x**5/5)/d**(7/2), True))","A",0
353,1,1741,0,61.790858," ","integrate((e*x+d)**(7/2)*(c*x**2+b*x)**3,x)","\frac{2 b^{3} d^{3} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{6 b^{3} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{6 b^{3} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{2 b^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{4}} + \frac{6 b^{2} c d^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{18 b^{2} c d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{18 b^{2} c d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{6 b^{2} c \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{5}} + \frac{6 b c^{2} d^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{18 b c^{2} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{18 b c^{2} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{6 b c^{2} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{6}} + \frac{2 c^{3} d^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{6 c^{3} d^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{6 c^{3} d \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}} + \frac{2 c^{3} \left(- \frac{d^{9} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{9 d^{8} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{36 d^{7} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{28 d^{6} \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{126 d^{5} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{126 d^{4} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{28 d^{3} \left(d + e x\right)^{\frac{15}{2}}}{5} + \frac{36 d^{2} \left(d + e x\right)^{\frac{17}{2}}}{17} - \frac{9 d \left(d + e x\right)^{\frac{19}{2}}}{19} + \frac{\left(d + e x\right)^{\frac{21}{2}}}{21}\right)}{e^{7}}"," ",0,"2*b**3*d**3*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 6*b**3*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 6*b**3*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 2*b**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**4 + 6*b**2*c*d**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 18*b**2*c*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 18*b**2*c*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 6*b**2*c*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**5 + 6*b*c**2*d**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 18*b*c**2*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 18*b*c**2*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 6*b*c**2*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**6 + 2*c**3*d**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 6*c**3*d**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 6*c**3*d*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 2*c**3*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**7","B",0
354,1,1207,0,43.845283," ","integrate((e*x+d)**(5/2)*(c*x**2+b*x)**3,x)","\frac{2 b^{3} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{4 b^{3} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 b^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{6 b^{2} c d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{12 b^{2} c d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{6 b^{2} c \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{6 b c^{2} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{12 b c^{2} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{6 b c^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{2 c^{3} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{4 c^{3} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{2 c^{3} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}}"," ",0,"2*b**3*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 4*b**3*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*b**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 6*b**2*c*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 12*b**2*c*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 6*b**2*c*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 6*b*c**2*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 12*b*c**2*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 6*b*c**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 2*c**3*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 4*c**3*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 2*c**3*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7","B",0
355,1,738,0,27.323314," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x)**3,x)","\frac{2 b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{2 b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{6 b^{2} c d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{6 b^{2} c \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{6 b c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{6 b c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{2 c^{3} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{2 c^{3} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}}"," ",0,"2*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 2*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 6*b**2*c*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 6*b**2*c*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 6*b*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 6*b*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 2*c**3*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 2*c**3*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7","B",0
356,1,326,0,5.885000," ","integrate((e*x+d)**(1/2)*(c*x**2+b*x)**3,x)","\frac{2 \left(\frac{c^{3} \left(d + e x\right)^{\frac{15}{2}}}{15 e^{6}} + \frac{\left(d + e x\right)^{\frac{13}{2}} \left(3 b c^{2} e - 6 c^{3} d\right)}{13 e^{6}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(3 b^{2} c e^{2} - 15 b c^{2} d e + 15 c^{3} d^{2}\right)}{11 e^{6}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(b^{3} e^{3} - 12 b^{2} c d e^{2} + 30 b c^{2} d^{2} e - 20 c^{3} d^{3}\right)}{9 e^{6}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(- 3 b^{3} d e^{3} + 18 b^{2} c d^{2} e^{2} - 30 b c^{2} d^{3} e + 15 c^{3} d^{4}\right)}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(3 b^{3} d^{2} e^{3} - 12 b^{2} c d^{3} e^{2} + 15 b c^{2} d^{4} e - 6 c^{3} d^{5}\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(- b^{3} d^{3} e^{3} + 3 b^{2} c d^{4} e^{2} - 3 b c^{2} d^{5} e + c^{3} d^{6}\right)}{3 e^{6}}\right)}{e}"," ",0,"2*(c**3*(d + e*x)**(15/2)/(15*e**6) + (d + e*x)**(13/2)*(3*b*c**2*e - 6*c**3*d)/(13*e**6) + (d + e*x)**(11/2)*(3*b**2*c*e**2 - 15*b*c**2*d*e + 15*c**3*d**2)/(11*e**6) + (d + e*x)**(9/2)*(b**3*e**3 - 12*b**2*c*d*e**2 + 30*b*c**2*d**2*e - 20*c**3*d**3)/(9*e**6) + (d + e*x)**(7/2)*(-3*b**3*d*e**3 + 18*b**2*c*d**2*e**2 - 30*b*c**2*d**3*e + 15*c**3*d**4)/(7*e**6) + (d + e*x)**(5/2)*(3*b**3*d**2*e**3 - 12*b**2*c*d**3*e**2 + 15*b*c**2*d**4*e - 6*c**3*d**5)/(5*e**6) + (d + e*x)**(3/2)*(-b**3*d**3*e**3 + 3*b**2*c*d**4*e**2 - 3*b*c**2*d**5*e + c**3*d**6)/(3*e**6))/e","A",0
357,1,745,0,90.847400," ","integrate((c*x**2+b*x)**3/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 b^{3} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{2 b^{3} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{6 b^{2} c d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{6 b^{2} c \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{6 b c^{2} d \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{5}} - \frac{6 b c^{2} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} - \frac{2 c^{3} d \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{6}} - \frac{2 c^{3} \left(- \frac{d^{7}}{\sqrt{d + e x}} - 7 d^{6} \sqrt{d + e x} + 7 d^{5} \left(d + e x\right)^{\frac{3}{2}} - 7 d^{4} \left(d + e x\right)^{\frac{5}{2}} + 5 d^{3} \left(d + e x\right)^{\frac{7}{2}} - \frac{7 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{3} + \frac{7 d \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}}}{e} & \text{for}\: e \neq 0 \\\frac{\frac{b^{3} x^{4}}{4} + \frac{3 b^{2} c x^{5}}{5} + \frac{b c^{2} x^{6}}{2} + \frac{c^{3} x^{7}}{7}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*b**3*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 2*b**3*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 6*b**2*c*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 6*b**2*c*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 6*b*c**2*d*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**5 - 6*b*c**2*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**5 - 2*c**3*d*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**6 - 2*c**3*(-d**7/sqrt(d + e*x) - 7*d**6*sqrt(d + e*x) + 7*d**5*(d + e*x)**(3/2) - 7*d**4*(d + e*x)**(5/2) + 5*d**3*(d + e*x)**(7/2) - 7*d**2*(d + e*x)**(9/2)/3 + 7*d*(d + e*x)**(11/2)/11 - (d + e*x)**(13/2)/13)/e**6)/e, Ne(e, 0)), ((b**3*x**4/4 + 3*b**2*c*x**5/5 + b*c**2*x**6/2 + c**3*x**7/7)/sqrt(d), True))","A",0
358,1,284,0,46.534990," ","integrate((c*x**2+b*x)**3/(e*x+d)**(3/2),x)","\frac{2 c^{3} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{7}} + \frac{2 d^{3} \left(b e - c d\right)^{3}}{e^{7} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(6 b c^{2} e - 12 c^{3} d\right)}{9 e^{7}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(6 b^{2} c e^{2} - 30 b c^{2} d e + 30 c^{3} d^{2}\right)}{7 e^{7}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(2 b^{3} e^{3} - 24 b^{2} c d e^{2} + 60 b c^{2} d^{2} e - 40 c^{3} d^{3}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(- 6 b^{3} d e^{3} + 36 b^{2} c d^{2} e^{2} - 60 b c^{2} d^{3} e + 30 c^{3} d^{4}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(6 b^{3} d^{2} e^{3} - 24 b^{2} c d^{3} e^{2} + 30 b c^{2} d^{4} e - 12 c^{3} d^{5}\right)}{e^{7}}"," ",0,"2*c**3*(d + e*x)**(11/2)/(11*e**7) + 2*d**3*(b*e - c*d)**3/(e**7*sqrt(d + e*x)) + (d + e*x)**(9/2)*(6*b*c**2*e - 12*c**3*d)/(9*e**7) + (d + e*x)**(7/2)*(6*b**2*c*e**2 - 30*b*c**2*d*e + 30*c**3*d**2)/(7*e**7) + (d + e*x)**(5/2)*(2*b**3*e**3 - 24*b**2*c*d*e**2 + 60*b*c**2*d**2*e - 40*c**3*d**3)/(5*e**7) + (d + e*x)**(3/2)*(-6*b**3*d*e**3 + 36*b**2*c*d**2*e**2 - 60*b*c**2*d**3*e + 30*c**3*d**4)/(3*e**7) + sqrt(d + e*x)*(6*b**3*d**2*e**3 - 24*b**2*c*d**3*e**2 + 30*b*c**2*d**4*e - 12*c**3*d**5)/e**7","A",0
359,1,260,0,49.378987," ","integrate((c*x**2+b*x)**3/(e*x+d)**(5/2),x)","\frac{2 c^{3} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{7}} + \frac{2 d^{3} \left(b e - c d\right)^{3}}{3 e^{7} \left(d + e x\right)^{\frac{3}{2}}} - \frac{6 d^{2} \left(b e - 2 c d\right) \left(b e - c d\right)^{2}}{e^{7} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(6 b c^{2} e - 12 c^{3} d\right)}{7 e^{7}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(6 b^{2} c e^{2} - 30 b c^{2} d e + 30 c^{3} d^{2}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(2 b^{3} e^{3} - 24 b^{2} c d e^{2} + 60 b c^{2} d^{2} e - 40 c^{3} d^{3}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(- 6 b^{3} d e^{3} + 36 b^{2} c d^{2} e^{2} - 60 b c^{2} d^{3} e + 30 c^{3} d^{4}\right)}{e^{7}}"," ",0,"2*c**3*(d + e*x)**(9/2)/(9*e**7) + 2*d**3*(b*e - c*d)**3/(3*e**7*(d + e*x)**(3/2)) - 6*d**2*(b*e - 2*c*d)*(b*e - c*d)**2/(e**7*sqrt(d + e*x)) + (d + e*x)**(7/2)*(6*b*c**2*e - 12*c**3*d)/(7*e**7) + (d + e*x)**(5/2)*(6*b**2*c*e**2 - 30*b*c**2*d*e + 30*c**3*d**2)/(5*e**7) + (d + e*x)**(3/2)*(2*b**3*e**3 - 24*b**2*c*d*e**2 + 60*b*c**2*d**2*e - 40*c**3*d**3)/(3*e**7) + sqrt(d + e*x)*(-6*b**3*d*e**3 + 36*b**2*c*d**2*e**2 - 60*b*c**2*d**3*e + 30*c**3*d**4)/e**7","A",0
360,1,248,0,82.245019," ","integrate((c*x**2+b*x)**3/(e*x+d)**(7/2),x)","\frac{2 c^{3} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{7}} + \frac{2 d^{3} \left(b e - c d\right)^{3}}{5 e^{7} \left(d + e x\right)^{\frac{5}{2}}} - \frac{2 d^{2} \left(b e - 2 c d\right) \left(b e - c d\right)^{2}}{e^{7} \left(d + e x\right)^{\frac{3}{2}}} + \frac{6 d \left(b e - c d\right) \left(b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right)}{e^{7} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(6 b c^{2} e - 12 c^{3} d\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(6 b^{2} c e^{2} - 30 b c^{2} d e + 30 c^{3} d^{2}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(2 b^{3} e^{3} - 24 b^{2} c d e^{2} + 60 b c^{2} d^{2} e - 40 c^{3} d^{3}\right)}{e^{7}}"," ",0,"2*c**3*(d + e*x)**(7/2)/(7*e**7) + 2*d**3*(b*e - c*d)**3/(5*e**7*(d + e*x)**(5/2)) - 2*d**2*(b*e - 2*c*d)*(b*e - c*d)**2/(e**7*(d + e*x)**(3/2)) + 6*d*(b*e - c*d)*(b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)/(e**7*sqrt(d + e*x)) + (d + e*x)**(5/2)*(6*b*c**2*e - 12*c**3*d)/(5*e**7) + (d + e*x)**(3/2)*(6*b**2*c*e**2 - 30*b*c**2*d*e + 30*c**3*d**2)/(3*e**7) + sqrt(d + e*x)*(2*b**3*e**3 - 24*b**2*c*d*e**2 + 60*b*c**2*d**2*e - 40*c**3*d**3)/e**7","A",0
361,1,162,0,93.745670," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x),x)","\frac{2 e \left(d + e x\right)^{\frac{5}{2}}}{5 c} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(- 2 b e^{2} + 4 c d e\right)}{3 c^{2}} + \frac{\sqrt{d + e x} \left(2 b^{2} e^{3} - 6 b c d e^{2} + 6 c^{2} d^{2} e\right)}{c^{3}} + \frac{2 d^{4} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b \sqrt{- d}} - \frac{2 \left(b e - c d\right)^{4} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b c^{4} \sqrt{\frac{b e - c d}{c}}}"," ",0,"2*e*(d + e*x)**(5/2)/(5*c) + (d + e*x)**(3/2)*(-2*b*e**2 + 4*c*d*e)/(3*c**2) + sqrt(d + e*x)*(2*b**2*e**3 - 6*b*c*d*e**2 + 6*c**2*d**2*e)/c**3 + 2*d**4*atan(sqrt(d + e*x)/sqrt(-d))/(b*sqrt(-d)) - 2*(b*e - c*d)**4*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*c**4*sqrt((b*e - c*d)/c))","A",0
362,1,119,0,58.856446," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x),x)","\frac{2 e \left(d + e x\right)^{\frac{3}{2}}}{3 c} + \frac{\sqrt{d + e x} \left(- 2 b e^{2} + 4 c d e\right)}{c^{2}} + \frac{2 d^{3} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b \sqrt{- d}} + \frac{2 \left(b e - c d\right)^{3} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b c^{3} \sqrt{\frac{b e - c d}{c}}}"," ",0,"2*e*(d + e*x)**(3/2)/(3*c) + sqrt(d + e*x)*(-2*b*e**2 + 4*c*d*e)/c**2 + 2*d**3*atan(sqrt(d + e*x)/sqrt(-d))/(b*sqrt(-d)) + 2*(b*e - c*d)**3*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*c**3*sqrt((b*e - c*d)/c))","A",0
363,1,92,0,33.672053," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x),x)","\frac{2 e \sqrt{d + e x}}{c} + \frac{2 d^{2} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b \sqrt{- d}} - \frac{2 \left(b e - c d\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b c^{2} \sqrt{\frac{b e - c d}{c}}}"," ",0,"2*e*sqrt(d + e*x)/c + 2*d**2*atan(sqrt(d + e*x)/sqrt(-d))/(b*sqrt(-d)) - 2*(b*e - c*d)**2*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*c**2*sqrt((b*e - c*d)/c))","A",0
364,1,78,0,6.778661," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x),x)","\frac{2 \left(\frac{d e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b \sqrt{- d}} + \frac{e \left(b e - c d\right) \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b c \sqrt{\frac{b e - c d}{c}}}\right)}{e}"," ",0,"2*(d*e*atan(sqrt(d + e*x)/sqrt(-d))/(b*sqrt(-d)) + e*(b*e - c*d)*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*c*sqrt((b*e - c*d)/c)))/e","A",0
365,1,80,0,27.301564," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x),x)","\frac{2 c \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{c}{b e - c d}} \sqrt{d + e x}} \right)}}{b \sqrt{\frac{c}{b e - c d}} \left(b e - c d\right)} + \frac{2 \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{d}} \sqrt{d + e x}} \right)}}{b d \sqrt{- \frac{1}{d}}}"," ",0,"2*c*atan(1/(sqrt(c/(b*e - c*d))*sqrt(d + e*x)))/(b*sqrt(c/(b*e - c*d))*(b*e - c*d)) + 2*atan(1/(sqrt(-1/d)*sqrt(d + e*x)))/(b*d*sqrt(-1/d))","A",0
366,1,94,0,20.190603," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x),x)","\frac{2 e}{d \sqrt{d + e x} \left(b e - c d\right)} + \frac{2 c \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b \sqrt{\frac{b e - c d}{c}} \left(b e - c d\right)} + \frac{2 \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b d \sqrt{- d}}"," ",0,"2*e/(d*sqrt(d + e*x)*(b*e - c*d)) + 2*c*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*sqrt((b*e - c*d)/c)*(b*e - c*d)) + 2*atan(sqrt(d + e*x)/sqrt(-d))/(b*d*sqrt(-d))","A",0
367,1,133,0,21.141908," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+b*x),x)","\frac{2 e}{3 d \left(d + e x\right)^{\frac{3}{2}} \left(b e - c d\right)} + \frac{2 e \left(b e - 2 c d\right)}{d^{2} \sqrt{d + e x} \left(b e - c d\right)^{2}} - \frac{2 c^{2} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b \sqrt{\frac{b e - c d}{c}} \left(b e - c d\right)^{2}} + \frac{2 \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b d^{2} \sqrt{- d}}"," ",0,"2*e/(3*d*(d + e*x)**(3/2)*(b*e - c*d)) + 2*e*(b*e - 2*c*d)/(d**2*sqrt(d + e*x)*(b*e - c*d)**2) - 2*c**2*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*sqrt((b*e - c*d)/c)*(b*e - c*d)**2) + 2*atan(sqrt(d + e*x)/sqrt(-d))/(b*d**2*sqrt(-d))","A",0
368,1,182,0,25.165652," ","integrate(1/(e*x+d)**(7/2)/(c*x**2+b*x),x)","\frac{2 e}{5 d \left(d + e x\right)^{\frac{5}{2}} \left(b e - c d\right)} + \frac{2 e \left(b e - 2 c d\right)}{3 d^{2} \left(d + e x\right)^{\frac{3}{2}} \left(b e - c d\right)^{2}} + \frac{2 e \left(b^{2} e^{2} - 3 b c d e + 3 c^{2} d^{2}\right)}{d^{3} \sqrt{d + e x} \left(b e - c d\right)^{3}} + \frac{2 c^{3} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b \sqrt{\frac{b e - c d}{c}} \left(b e - c d\right)^{3}} + \frac{2 \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b d^{3} \sqrt{- d}}"," ",0,"2*e/(5*d*(d + e*x)**(5/2)*(b*e - c*d)) + 2*e*(b*e - 2*c*d)/(3*d**2*(d + e*x)**(3/2)*(b*e - c*d)**2) + 2*e*(b**2*e**2 - 3*b*c*d*e + 3*c**2*d**2)/(d**3*sqrt(d + e*x)*(b*e - c*d)**3) + 2*c**3*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*sqrt((b*e - c*d)/c)*(b*e - c*d)**3) + 2*atan(sqrt(d + e*x)/sqrt(-d))/(b*d**3*sqrt(-d))","A",0
369,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,1,790,0,55.423901," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x)**2,x)","\frac{2 c^{2} d e \sqrt{d + e x}}{2 b^{4} e^{2} - 2 b^{3} c d e + 2 b^{3} c e^{2} x - 2 b^{2} c^{2} d e x} - \frac{2 c e^{2} \sqrt{d + e x}}{2 b^{3} e^{2} - 2 b^{2} c d e + 2 b^{2} c e^{2} x - 2 b c^{2} d e x} + \frac{c e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(- b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{c e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{c^{2} d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(- b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b^{2}} + \frac{c^{2} d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b^{2}} - \frac{d e \sqrt{\frac{1}{d^{3}}} \log{\left(- d^{2} \sqrt{\frac{1}{d^{3}}} + \sqrt{d + e x} \right)}}{2 b^{2}} + \frac{d e \sqrt{\frac{1}{d^{3}}} \log{\left(d^{2} \sqrt{\frac{1}{d^{3}}} + \sqrt{d + e x} \right)}}{2 b^{2}} - \frac{2 e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e}{c} - d}} \right)}}{b^{2} \sqrt{\frac{b e}{c} - d}} + \frac{2 e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b^{2} \sqrt{- d}} - \frac{\sqrt{d + e x}}{b^{2} x} + \frac{4 c d \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e}{c} - d}} \right)}}{b^{3} \sqrt{\frac{b e}{c} - d}} - \frac{4 c d \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b^{3} \sqrt{- d}}"," ",0,"2*c**2*d*e*sqrt(d + e*x)/(2*b**4*e**2 - 2*b**3*c*d*e + 2*b**3*c*e**2*x - 2*b**2*c**2*d*e*x) - 2*c*e**2*sqrt(d + e*x)/(2*b**3*e**2 - 2*b**2*c*d*e + 2*b**2*c*e**2*x - 2*b*c**2*d*e*x) + c*e**2*sqrt(-1/(c*(b*e - c*d)**3))*log(-b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) + 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) - c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b) - c*e**2*sqrt(-1/(c*(b*e - c*d)**3))*log(b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) - 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) + c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b) - c**2*d*e*sqrt(-1/(c*(b*e - c*d)**3))*log(-b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) + 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) - c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b**2) + c**2*d*e*sqrt(-1/(c*(b*e - c*d)**3))*log(b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) - 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) + c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b**2) - d*e*sqrt(d**(-3))*log(-d**2*sqrt(d**(-3)) + sqrt(d + e*x))/(2*b**2) + d*e*sqrt(d**(-3))*log(d**2*sqrt(d**(-3)) + sqrt(d + e*x))/(2*b**2) - 2*e*atan(sqrt(d + e*x)/sqrt(b*e/c - d))/(b**2*sqrt(b*e/c - d)) + 2*e*atan(sqrt(d + e*x)/sqrt(-d))/(b**2*sqrt(-d)) - sqrt(d + e*x)/(b**2*x) + 4*c*d*atan(sqrt(d + e*x)/sqrt(b*e/c - d))/(b**3*sqrt(b*e/c - d)) - 4*c*d*atan(sqrt(d + e*x)/sqrt(-d))/(b**3*sqrt(-d))","B",0
374,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x)**2,x)","\int \frac{1}{x^{2} \left(b + c x\right)^{2} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(b + c*x)**2*(d + e*x)**(3/2)), x)","F",0
376,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+b*x)**2,x)","\int \frac{1}{x^{2} \left(b + c x\right)^{2} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*(b + c*x)**2*(d + e*x)**(5/2)), x)","F",0
377,0,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(c*x**2+b*x)**2,x)","\int \frac{1}{x^{2} \left(b + c x\right)^{2} \left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(1/(x**2*(b + c*x)**2*(d + e*x)**(7/2)), x)","F",0
378,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,1,2584,0,177.266499," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x)**3,x)","\frac{10 c^{4} d^{2} e^{2} \sqrt{d + e x}}{8 b^{7} e^{4} - 16 b^{6} c d e^{3} + 16 b^{6} c e^{4} x - 48 b^{5} c^{2} d e^{3} x + 8 b^{5} c^{2} e^{2} \left(d + e x\right)^{2} + 16 b^{4} c^{3} d^{3} e + 48 b^{4} c^{3} d^{2} e^{2} x - 16 b^{4} c^{3} d e \left(d + e x\right)^{2} - 8 b^{3} c^{4} d^{4} - 16 b^{3} c^{4} d^{3} e x + 8 b^{3} c^{4} d^{2} \left(d + e x\right)^{2}} - \frac{6 c^{4} d e^{2} \left(d + e x\right)^{\frac{3}{2}}}{8 b^{7} e^{4} - 16 b^{6} c d e^{3} + 16 b^{6} c e^{4} x - 48 b^{5} c^{2} d e^{3} x + 8 b^{5} c^{2} e^{2} \left(d + e x\right)^{2} + 16 b^{4} c^{3} d^{3} e + 48 b^{4} c^{3} d^{2} e^{2} x - 16 b^{4} c^{3} d e \left(d + e x\right)^{2} - 8 b^{3} c^{4} d^{4} - 16 b^{3} c^{4} d^{3} e x + 8 b^{3} c^{4} d^{2} \left(d + e x\right)^{2}} - \frac{20 c^{3} d e^{3} \sqrt{d + e x}}{8 b^{6} e^{4} - 16 b^{5} c d e^{3} + 16 b^{5} c e^{4} x - 48 b^{4} c^{2} d e^{3} x + 8 b^{4} c^{2} e^{2} \left(d + e x\right)^{2} + 16 b^{3} c^{3} d^{3} e + 48 b^{3} c^{3} d^{2} e^{2} x - 16 b^{3} c^{3} d e \left(d + e x\right)^{2} - 8 b^{2} c^{4} d^{4} - 16 b^{2} c^{4} d^{3} e x + 8 b^{2} c^{4} d^{2} \left(d + e x\right)^{2}} - \frac{6 c^{3} d e \sqrt{d + e x}}{2 b^{6} e^{2} - 2 b^{5} c d e + 2 b^{5} c e^{2} x - 2 b^{4} c^{2} d e x} + \frac{6 c^{3} e^{3} \left(d + e x\right)^{\frac{3}{2}}}{8 b^{6} e^{4} - 16 b^{5} c d e^{3} + 16 b^{5} c e^{4} x - 48 b^{4} c^{2} d e^{3} x + 8 b^{4} c^{2} e^{2} \left(d + e x\right)^{2} + 16 b^{3} c^{3} d^{3} e + 48 b^{3} c^{3} d^{2} e^{2} x - 16 b^{3} c^{3} d e \left(d + e x\right)^{2} - 8 b^{2} c^{4} d^{4} - 16 b^{2} c^{4} d^{3} e x + 8 b^{2} c^{4} d^{2} \left(d + e x\right)^{2}} + \frac{10 c^{2} e^{4} \sqrt{d + e x}}{8 b^{5} e^{4} - 16 b^{4} c d e^{3} + 16 b^{4} c e^{4} x - 48 b^{3} c^{2} d e^{3} x + 8 b^{3} c^{2} e^{2} \left(d + e x\right)^{2} + 16 b^{2} c^{3} d^{3} e + 48 b^{2} c^{3} d^{2} e^{2} x - 16 b^{2} c^{3} d e \left(d + e x\right)^{2} - 8 b c^{4} d^{4} - 16 b c^{4} d^{3} e x + 8 b c^{4} d^{2} \left(d + e x\right)^{2}} + \frac{4 c^{2} e^{2} \sqrt{d + e x}}{2 b^{5} e^{2} - 2 b^{4} c d e + 2 b^{4} c e^{2} x - 2 b^{3} c^{2} d e x} - \frac{10 d^{2} e^{2} \sqrt{d + e x}}{- 8 b^{3} d^{4} - 16 b^{3} d^{3} e x + 8 b^{3} d^{2} \left(d + e x\right)^{2}} + \frac{6 d e^{2} \left(d + e x\right)^{\frac{3}{2}}}{- 8 b^{3} d^{4} - 16 b^{3} d^{3} e x + 8 b^{3} d^{2} \left(d + e x\right)^{2}} - \frac{3 c^{2} e^{3} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} \log{\left(- b^{3} e^{3} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} + 3 b^{2} c d e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} - 3 b c^{2} d^{2} e \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} + c^{3} d^{3} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} + \sqrt{d + e x} \right)}}{8 b^{2}} + \frac{3 c^{2} e^{3} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} \log{\left(b^{3} e^{3} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} - 3 b^{2} c d e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} + 3 b c^{2} d^{2} e \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} - c^{3} d^{3} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} + \sqrt{d + e x} \right)}}{8 b^{2}} + \frac{3 c^{3} d e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} \log{\left(- b^{3} e^{3} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} + 3 b^{2} c d e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} - 3 b c^{2} d^{2} e \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} + c^{3} d^{3} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} + \sqrt{d + e x} \right)}}{8 b^{3}} - \frac{3 c^{3} d e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} \log{\left(b^{3} e^{3} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} - 3 b^{2} c d e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} + 3 b c^{2} d^{2} e \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} - c^{3} d^{3} \sqrt{- \frac{1}{c \left(b e - c d\right)^{5}}} + \sqrt{d + e x} \right)}}{8 b^{3}} - \frac{c^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(- b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{b^{3}} + \frac{c^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{b^{3}} + \frac{3 d e^{2} \sqrt{\frac{1}{d^{5}}} \log{\left(- d^{3} \sqrt{\frac{1}{d^{5}}} + \sqrt{d + e x} \right)}}{8 b^{3}} - \frac{3 d e^{2} \sqrt{\frac{1}{d^{5}}} \log{\left(d^{3} \sqrt{\frac{1}{d^{5}}} + \sqrt{d + e x} \right)}}{8 b^{3}} - \frac{e^{2} \sqrt{\frac{1}{d^{3}}} \log{\left(- d^{2} \sqrt{\frac{1}{d^{3}}} + \sqrt{d + e x} \right)}}{2 b^{3}} + \frac{e^{2} \sqrt{\frac{1}{d^{3}}} \log{\left(d^{2} \sqrt{\frac{1}{d^{3}}} + \sqrt{d + e x} \right)}}{2 b^{3}} - \frac{e \sqrt{d + e x}}{b^{3} d x} + \frac{3 c^{3} d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(- b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b^{4}} - \frac{3 c^{3} d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b^{4}} + \frac{3 c d e \sqrt{\frac{1}{d^{3}}} \log{\left(- d^{2} \sqrt{\frac{1}{d^{3}}} + \sqrt{d + e x} \right)}}{2 b^{4}} - \frac{3 c d e \sqrt{\frac{1}{d^{3}}} \log{\left(d^{2} \sqrt{\frac{1}{d^{3}}} + \sqrt{d + e x} \right)}}{2 b^{4}} + \frac{6 c e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e}{c} - d}} \right)}}{b^{4} \sqrt{\frac{b e}{c} - d}} - \frac{6 c e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b^{4} \sqrt{- d}} + \frac{3 c \sqrt{d + e x}}{b^{4} x} - \frac{12 c^{2} d \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e}{c} - d}} \right)}}{b^{5} \sqrt{\frac{b e}{c} - d}} + \frac{12 c^{2} d \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b^{5} \sqrt{- d}}"," ",0,"10*c**4*d**2*e**2*sqrt(d + e*x)/(8*b**7*e**4 - 16*b**6*c*d*e**3 + 16*b**6*c*e**4*x - 48*b**5*c**2*d*e**3*x + 8*b**5*c**2*e**2*(d + e*x)**2 + 16*b**4*c**3*d**3*e + 48*b**4*c**3*d**2*e**2*x - 16*b**4*c**3*d*e*(d + e*x)**2 - 8*b**3*c**4*d**4 - 16*b**3*c**4*d**3*e*x + 8*b**3*c**4*d**2*(d + e*x)**2) - 6*c**4*d*e**2*(d + e*x)**(3/2)/(8*b**7*e**4 - 16*b**6*c*d*e**3 + 16*b**6*c*e**4*x - 48*b**5*c**2*d*e**3*x + 8*b**5*c**2*e**2*(d + e*x)**2 + 16*b**4*c**3*d**3*e + 48*b**4*c**3*d**2*e**2*x - 16*b**4*c**3*d*e*(d + e*x)**2 - 8*b**3*c**4*d**4 - 16*b**3*c**4*d**3*e*x + 8*b**3*c**4*d**2*(d + e*x)**2) - 20*c**3*d*e**3*sqrt(d + e*x)/(8*b**6*e**4 - 16*b**5*c*d*e**3 + 16*b**5*c*e**4*x - 48*b**4*c**2*d*e**3*x + 8*b**4*c**2*e**2*(d + e*x)**2 + 16*b**3*c**3*d**3*e + 48*b**3*c**3*d**2*e**2*x - 16*b**3*c**3*d*e*(d + e*x)**2 - 8*b**2*c**4*d**4 - 16*b**2*c**4*d**3*e*x + 8*b**2*c**4*d**2*(d + e*x)**2) - 6*c**3*d*e*sqrt(d + e*x)/(2*b**6*e**2 - 2*b**5*c*d*e + 2*b**5*c*e**2*x - 2*b**4*c**2*d*e*x) + 6*c**3*e**3*(d + e*x)**(3/2)/(8*b**6*e**4 - 16*b**5*c*d*e**3 + 16*b**5*c*e**4*x - 48*b**4*c**2*d*e**3*x + 8*b**4*c**2*e**2*(d + e*x)**2 + 16*b**3*c**3*d**3*e + 48*b**3*c**3*d**2*e**2*x - 16*b**3*c**3*d*e*(d + e*x)**2 - 8*b**2*c**4*d**4 - 16*b**2*c**4*d**3*e*x + 8*b**2*c**4*d**2*(d + e*x)**2) + 10*c**2*e**4*sqrt(d + e*x)/(8*b**5*e**4 - 16*b**4*c*d*e**3 + 16*b**4*c*e**4*x - 48*b**3*c**2*d*e**3*x + 8*b**3*c**2*e**2*(d + e*x)**2 + 16*b**2*c**3*d**3*e + 48*b**2*c**3*d**2*e**2*x - 16*b**2*c**3*d*e*(d + e*x)**2 - 8*b*c**4*d**4 - 16*b*c**4*d**3*e*x + 8*b*c**4*d**2*(d + e*x)**2) + 4*c**2*e**2*sqrt(d + e*x)/(2*b**5*e**2 - 2*b**4*c*d*e + 2*b**4*c*e**2*x - 2*b**3*c**2*d*e*x) - 10*d**2*e**2*sqrt(d + e*x)/(-8*b**3*d**4 - 16*b**3*d**3*e*x + 8*b**3*d**2*(d + e*x)**2) + 6*d*e**2*(d + e*x)**(3/2)/(-8*b**3*d**4 - 16*b**3*d**3*e*x + 8*b**3*d**2*(d + e*x)**2) - 3*c**2*e**3*sqrt(-1/(c*(b*e - c*d)**5))*log(-b**3*e**3*sqrt(-1/(c*(b*e - c*d)**5)) + 3*b**2*c*d*e**2*sqrt(-1/(c*(b*e - c*d)**5)) - 3*b*c**2*d**2*e*sqrt(-1/(c*(b*e - c*d)**5)) + c**3*d**3*sqrt(-1/(c*(b*e - c*d)**5)) + sqrt(d + e*x))/(8*b**2) + 3*c**2*e**3*sqrt(-1/(c*(b*e - c*d)**5))*log(b**3*e**3*sqrt(-1/(c*(b*e - c*d)**5)) - 3*b**2*c*d*e**2*sqrt(-1/(c*(b*e - c*d)**5)) + 3*b*c**2*d**2*e*sqrt(-1/(c*(b*e - c*d)**5)) - c**3*d**3*sqrt(-1/(c*(b*e - c*d)**5)) + sqrt(d + e*x))/(8*b**2) + 3*c**3*d*e**2*sqrt(-1/(c*(b*e - c*d)**5))*log(-b**3*e**3*sqrt(-1/(c*(b*e - c*d)**5)) + 3*b**2*c*d*e**2*sqrt(-1/(c*(b*e - c*d)**5)) - 3*b*c**2*d**2*e*sqrt(-1/(c*(b*e - c*d)**5)) + c**3*d**3*sqrt(-1/(c*(b*e - c*d)**5)) + sqrt(d + e*x))/(8*b**3) - 3*c**3*d*e**2*sqrt(-1/(c*(b*e - c*d)**5))*log(b**3*e**3*sqrt(-1/(c*(b*e - c*d)**5)) - 3*b**2*c*d*e**2*sqrt(-1/(c*(b*e - c*d)**5)) + 3*b*c**2*d**2*e*sqrt(-1/(c*(b*e - c*d)**5)) - c**3*d**3*sqrt(-1/(c*(b*e - c*d)**5)) + sqrt(d + e*x))/(8*b**3) - c**2*e**2*sqrt(-1/(c*(b*e - c*d)**3))*log(-b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) + 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) - c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/b**3 + c**2*e**2*sqrt(-1/(c*(b*e - c*d)**3))*log(b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) - 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) + c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/b**3 + 3*d*e**2*sqrt(d**(-5))*log(-d**3*sqrt(d**(-5)) + sqrt(d + e*x))/(8*b**3) - 3*d*e**2*sqrt(d**(-5))*log(d**3*sqrt(d**(-5)) + sqrt(d + e*x))/(8*b**3) - e**2*sqrt(d**(-3))*log(-d**2*sqrt(d**(-3)) + sqrt(d + e*x))/(2*b**3) + e**2*sqrt(d**(-3))*log(d**2*sqrt(d**(-3)) + sqrt(d + e*x))/(2*b**3) - e*sqrt(d + e*x)/(b**3*d*x) + 3*c**3*d*e*sqrt(-1/(c*(b*e - c*d)**3))*log(-b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) + 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) - c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b**4) - 3*c**3*d*e*sqrt(-1/(c*(b*e - c*d)**3))*log(b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) - 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) + c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b**4) + 3*c*d*e*sqrt(d**(-3))*log(-d**2*sqrt(d**(-3)) + sqrt(d + e*x))/(2*b**4) - 3*c*d*e*sqrt(d**(-3))*log(d**2*sqrt(d**(-3)) + sqrt(d + e*x))/(2*b**4) + 6*c*e*atan(sqrt(d + e*x)/sqrt(b*e/c - d))/(b**4*sqrt(b*e/c - d)) - 6*c*e*atan(sqrt(d + e*x)/sqrt(-d))/(b**4*sqrt(-d)) + 3*c*sqrt(d + e*x)/(b**4*x) - 12*c**2*d*atan(sqrt(d + e*x)/sqrt(b*e/c - d))/(b**5*sqrt(b*e/c - d)) + 12*c**2*d*atan(sqrt(d + e*x)/sqrt(-d))/(b**5*sqrt(-d))","B",0
383,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(d + e x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(d + e*x)**(3/2), x)","F",0
387,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \sqrt{d + e x}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*sqrt(d + e*x), x)","F",0
388,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/sqrt(d + e*x), x)","F",0
389,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/(d + e*x)**(3/2), x)","F",0
390,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/(d + e*x)**(5/2), x)","F",0
391,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(1/2)/(e*x+d)**(7/2),x)","\int \frac{\sqrt{x \left(b + c x\right)}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))/(d + e*x)**(7/2), x)","F",0
392,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x)**(3/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(d + e*x)**(3/2), x)","F",0
393,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)*(e*x+d)**(1/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \sqrt{d + e x}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*sqrt(d + e*x), x)","F",0
394,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/sqrt(d + e*x), x)","F",0
395,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/(d + e*x)**(3/2), x)","F",0
396,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/(d + e*x)**(5/2), x)","F",0
397,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/(e*x+d)**(7/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/(d + e*x)**(7/2), x)","F",0
398,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(3/2)/(e*x+d)**(9/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)/(d + e*x)**(9/2), x)","F",0
399,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2)*(e*x+d)**(1/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \sqrt{d + e x}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*sqrt(d + e*x), x)","F",0
400,-1,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2)/(e*x+d)**(3/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)/(d + e*x)**(3/2), x)","F",0
402,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2)/(e*x+d)**(5/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)/(d + e*x)**(5/2), x)","F",0
403,0,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2)/(e*x+d)**(7/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)/(d + e*x)**(7/2), x)","F",0
404,-1,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2)/(e*x+d)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
405,-1,0,0,0.000000," ","integrate((c*x**2+b*x)**(5/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
406,0,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{7}{2}}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((d + e*x)**(7/2)/sqrt(x*(b + c*x)), x)","F",0
407,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{5}{2}}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((d + e*x)**(5/2)/sqrt(x*(b + c*x)), x)","F",0
408,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/sqrt(x*(b + c*x)), x)","F",0
409,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)/sqrt(x*(b + c*x)), x)","F",0
410,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(b + c x\right)} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/(sqrt(x*(b + c*x))*sqrt(d + e*x)), x)","F",0
411,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(x*(b + c*x))*(d + e*x)**(3/2)), x)","F",0
412,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(x*(b + c*x))*(d + e*x)**(5/2)), x)","F",0
413,0,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(1/(sqrt(x*(b + c*x))*(d + e*x)**(7/2)), x)","F",0
414,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{5}{2}}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(5/2)/(x*(b + c*x))**(3/2), x)","F",0
416,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/(x*(b + c*x))**(3/2), x)","F",0
417,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{\sqrt{d + e x}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/(x*(b + c*x))**(3/2), x)","F",0
418,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{1}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/((x*(b + c*x))**(3/2)*sqrt(d + e*x)), x)","F",0
419,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((x*(b + c*x))**(3/2)*(d + e*x)**(3/2)), x)","F",0
420,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{1}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((x*(b + c*x))**(3/2)*(d + e*x)**(5/2)), x)","F",0
421,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x)**(5/2)/(e*x+d)**(1/2),x)","\int \frac{1}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/((x*(b + c*x))**(5/2)*sqrt(d + e*x)), x)","F",0
427,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x)**(5/2),x)","\int \frac{1}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((x*(b + c*x))**(5/2)*(d + e*x)**(3/2)), x)","F",0
428,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(-3*x**2+2*x)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{- x \left(3 x - 2\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)/sqrt(-x*(3*x - 2)), x)","F",0
429,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(-3*x**2+2*x)**(1/2),x)","\int \frac{1}{\sqrt{- x \left(3 x - 2\right)} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/(sqrt(-x*(3*x - 2))*sqrt(d + e*x)), x)","F",0
430,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(-3*x**2-2*x)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{- x \left(3 x + 2\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)/sqrt(-x*(3*x + 2)), x)","F",0
431,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(-3*x**2-2*x)**(1/2),x)","\int \frac{1}{\sqrt{- x \left(3 x + 2\right)} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/(sqrt(-x*(3*x + 2))*sqrt(d + e*x)), x)","F",0
432,0,0,0,0.000000," ","integrate((1-x)**(1/2)/(-x)**(1/2)/(1+x)**(1/2),x)","\int \frac{\sqrt{1 - x}}{\sqrt{- x} \sqrt{x + 1}}\, dx"," ",0,"Integral(sqrt(1 - x)/(sqrt(-x)*sqrt(x + 1)), x)","F",0
433,0,0,0,0.000000," ","integrate((1-x)**(1/2)/(-x**2-x)**(1/2),x)","\int \frac{\sqrt{1 - x}}{\sqrt{- x \left(x + 1\right)}}\, dx"," ",0,"Integral(sqrt(1 - x)/sqrt(-x*(x + 1)), x)","F",0
434,1,2218,0,6.477930," ","integrate((e*x+d)**m*(c*e*x**2+c*d*x)**3,x)","\begin{cases} \frac{c^{3} d^{3} d^{m} x^{4}}{4} & \text{for}\: e = 0 \\\frac{6 c^{3} d^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{11 c^{3} d^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c^{3} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{27 c^{3} d^{2} e x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c^{3} d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c^{3} d e^{2} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 c^{3} e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} & \text{for}\: m = -7 \\- \frac{6 c^{3} d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{15 c^{3} d^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 c^{3} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{24 c^{3} d^{2} e x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 c^{3} d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 c^{3} d e^{2} x^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 c^{3} e^{3} x^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} & \text{for}\: m = -6 \\\frac{6 c^{3} d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{12 c^{3} d^{3}}{2 d e^{4} + 2 e^{5} x} + \frac{6 c^{3} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 c^{3} d^{2} e x}{2 d e^{4} + 2 e^{5} x} - \frac{3 c^{3} d e^{2} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{c^{3} e^{3} x^{3}}{2 d e^{4} + 2 e^{5} x} & \text{for}\: m = -5 \\- \frac{c^{3} d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{c^{3} d^{2} x}{e^{3}} - \frac{c^{3} d x^{2}}{2 e^{2}} + \frac{c^{3} x^{3}}{3 e} & \text{for}\: m = -4 \\- \frac{6 c^{3} d^{7} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{6 c^{3} d^{6} e m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} - \frac{3 c^{3} d^{5} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} - \frac{3 c^{3} d^{5} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{c^{3} d^{4} e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{3 c^{3} d^{4} e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{2 c^{3} d^{4} e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{4 c^{3} d^{3} e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{42 c^{3} d^{3} e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{158 c^{3} d^{3} e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{210 c^{3} d^{3} e^{4} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{6 c^{3} d^{2} e^{5} m^{3} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{78 c^{3} d^{2} e^{5} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{342 c^{3} d^{2} e^{5} m x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{504 c^{3} d^{2} e^{5} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{4 c^{3} d e^{6} m^{3} x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{57 c^{3} d e^{6} m^{2} x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{269 c^{3} d e^{6} m x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{420 c^{3} d e^{6} x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{c^{3} e^{7} m^{3} x^{7} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{15 c^{3} e^{7} m^{2} x^{7} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{74 c^{3} e^{7} m x^{7} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{120 c^{3} e^{7} x^{7} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*d**3*d**m*x**4/4, Eq(e, 0)), (6*c**3*d**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 11*c**3*d**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c**3*d**2*e*x*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 27*c**3*d**2*e*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c**3*d*e**2*x**2*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c**3*d*e**2*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*c**3*e**3*x**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3), Eq(m, -7)), (-6*c**3*d**3*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 15*c**3*d**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*c**3*d**2*e*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 24*c**3*d**2*e*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*c**3*d*e**2*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*c**3*d*e**2*x**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*c**3*e**3*x**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2), Eq(m, -6)), (6*c**3*d**3*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 12*c**3*d**3/(2*d*e**4 + 2*e**5*x) + 6*c**3*d**2*e*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*c**3*d**2*e*x/(2*d*e**4 + 2*e**5*x) - 3*c**3*d*e**2*x**2/(2*d*e**4 + 2*e**5*x) + c**3*e**3*x**3/(2*d*e**4 + 2*e**5*x), Eq(m, -5)), (-c**3*d**3*log(d/e + x)/e**4 + c**3*d**2*x/e**3 - c**3*d*x**2/(2*e**2) + c**3*x**3/(3*e), Eq(m, -4)), (-6*c**3*d**7*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 6*c**3*d**6*e*m*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) - 3*c**3*d**5*e**2*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) - 3*c**3*d**5*e**2*m*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + c**3*d**4*e**3*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 3*c**3*d**4*e**3*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 2*c**3*d**4*e**3*m*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 4*c**3*d**3*e**4*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 42*c**3*d**3*e**4*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 158*c**3*d**3*e**4*m*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 210*c**3*d**3*e**4*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 6*c**3*d**2*e**5*m**3*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 78*c**3*d**2*e**5*m**2*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 342*c**3*d**2*e**5*m*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 504*c**3*d**2*e**5*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 4*c**3*d*e**6*m**3*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 57*c**3*d*e**6*m**2*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 269*c**3*d*e**6*m*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 420*c**3*d*e**6*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + c**3*e**7*m**3*x**7*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 15*c**3*e**7*m**2*x**7*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 74*c**3*e**7*m*x**7*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 120*c**3*e**7*x**7*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4), True))","A",0
435,1,993,0,2.989198," ","integrate((e*x+d)**m*(c*e*x**2+c*d*x)**2,x)","\begin{cases} \frac{c^{2} d^{2} d^{m} x^{3}}{3} & \text{for}\: e = 0 \\\frac{2 c^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{3 c^{2} d^{2}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 c^{2} d e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 c^{2} d e x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 c^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} & \text{for}\: m = -5 \\- \frac{2 c^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{4 c^{2} d^{2}}{d e^{3} + e^{4} x} - \frac{2 c^{2} d e x \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{2 c^{2} d e x}{d e^{3} + e^{4} x} + \frac{c^{2} e^{2} x^{2}}{d e^{3} + e^{4} x} & \text{for}\: m = -4 \\\frac{c^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{c^{2} d x}{e^{2}} + \frac{c^{2} x^{2}}{2 e} & \text{for}\: m = -3 \\\frac{2 c^{2} d^{5} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} - \frac{2 c^{2} d^{4} e m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{c^{2} d^{3} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{c^{2} d^{3} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{3 c^{2} d^{2} e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{15 c^{2} d^{2} e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{20 c^{2} d^{2} e^{3} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{3 c^{2} d e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{19 c^{2} d e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{30 c^{2} d e^{4} x^{4} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{c^{2} e^{5} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{7 c^{2} e^{5} m x^{5} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{12 c^{2} e^{5} x^{5} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*d**2*d**m*x**3/3, Eq(e, 0)), (2*c**2*d**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 3*c**2*d**2/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*c**2*d*e*x*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*c**2*d*e*x/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*c**2*e**2*x**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2), Eq(m, -5)), (-2*c**2*d**2*log(d/e + x)/(d*e**3 + e**4*x) - 4*c**2*d**2/(d*e**3 + e**4*x) - 2*c**2*d*e*x*log(d/e + x)/(d*e**3 + e**4*x) - 2*c**2*d*e*x/(d*e**3 + e**4*x) + c**2*e**2*x**2/(d*e**3 + e**4*x), Eq(m, -4)), (c**2*d**2*log(d/e + x)/e**3 - c**2*d*x/e**2 + c**2*x**2/(2*e), Eq(m, -3)), (2*c**2*d**5*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) - 2*c**2*d**4*e*m*x*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + c**2*d**3*e**2*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + c**2*d**3*e**2*m*x**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 3*c**2*d**2*e**3*m**2*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 15*c**2*d**2*e**3*m*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 20*c**2*d**2*e**3*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 3*c**2*d*e**4*m**2*x**4*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 19*c**2*d*e**4*m*x**4*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 30*c**2*d*e**4*x**4*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + c**2*e**5*m**2*x**5*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 7*c**2*e**5*m*x**5*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 12*c**2*e**5*x**5*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3), True))","A",0
436,1,299,0,1.172837," ","integrate((e*x+d)**m*(c*e*x**2+c*d*x),x)","\begin{cases} \frac{c d d^{m} x^{2}}{2} & \text{for}\: e = 0 \\\frac{c d \log{\left(\frac{d}{e} + x \right)}}{d e^{2} + e^{3} x} + \frac{c d}{d e^{2} + e^{3} x} + \frac{c e x \log{\left(\frac{d}{e} + x \right)}}{d e^{2} + e^{3} x} & \text{for}\: m = -3 \\- \frac{c d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{c x}{e} & \text{for}\: m = -2 \\- \frac{c d^{3} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{c d^{2} e m x \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{2 c d e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{3 c d e^{2} x^{2} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{c e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{2 c e^{3} x^{3} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*d*d**m*x**2/2, Eq(e, 0)), (c*d*log(d/e + x)/(d*e**2 + e**3*x) + c*d/(d*e**2 + e**3*x) + c*e*x*log(d/e + x)/(d*e**2 + e**3*x), Eq(m, -3)), (-c*d*log(d/e + x)/e**2 + c*x/e, Eq(m, -2)), (-c*d**3*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + c*d**2*e*m*x*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + 2*c*d*e**2*m*x**2*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + 3*c*d*e**2*x**2*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + c*e**3*m*x**3*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + 2*c*e**3*x**3*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2), True))","A",0
437,1,20,0,0.064397," ","integrate((e*x+d)**m,x)","\frac{\begin{cases} \frac{\left(d + e x\right)^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(d + e x \right)} & \text{otherwise} \end{cases}}{e}"," ",0,"Piecewise(((d + e*x)**(m + 1)/(m + 1), Ne(m, -1)), (log(d + e*x), True))/e","A",0
438,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*e*x**2+c*d*x),x)","\frac{\int \frac{\left(d + e x\right)^{m}}{d x + e x^{2}}\, dx}{c}"," ",0,"Integral((d + e*x)**m/(d*x + e*x**2), x)/c","F",0
439,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*e*x**2+c*d*x)**2,x)","\frac{\int \frac{\left(d + e x\right)^{m}}{d^{2} x^{2} + 2 d e x^{3} + e^{2} x^{4}}\, dx}{c^{2}}"," ",0,"Integral((d + e*x)**m/(d**2*x**2 + 2*d*e*x**3 + e**2*x**4), x)/c**2","F",0
440,-1,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,1,6418,0,6.674560," ","integrate((e*x+d)**m*(c*x**2+b*x)**2,x)","\begin{cases} d^{m} \left(\frac{b^{2} x^{3}}{3} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5}\right) & \text{for}\: e = 0 \\- \frac{b^{2} d^{2} e^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{4 b^{2} d e^{3} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{6 b^{2} e^{4} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{6 b c d^{3} e}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{24 b c d^{2} e^{2} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{36 b c d e^{3} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{24 b c e^{4} x^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{25 c^{2} d^{4}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{88 c^{2} d^{3} e x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{72 c^{2} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{108 c^{2} d^{2} e^{2} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c^{2} d e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c^{2} d e^{3} x^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{12 c^{2} e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} & \text{for}\: m = -5 \\- \frac{b^{2} d^{2} e^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{3 b^{2} d e^{3} x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{3 b^{2} e^{4} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{6 b c d^{3} e \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{11 b c d^{3} e}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{18 b c d^{2} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{27 b c d^{2} e^{2} x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{18 b c d e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{18 b c d e^{3} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{6 b c e^{4} x^{3} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{22 c^{2} d^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{54 c^{2} d^{3} e x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 c^{2} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 c^{2} d^{2} e^{2} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{12 c^{2} d e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{3 c^{2} e^{4} x^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} & \text{for}\: m = -4 \\\frac{2 b^{2} d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{3 b^{2} d^{2} e^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 b^{2} d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 b^{2} d e^{3} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 b^{2} e^{4} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{12 b c d^{3} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{18 b c d^{3} e}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{24 b c d^{2} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{24 b c d^{2} e^{2} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{12 b c d e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 b c e^{4} x^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{18 c^{2} d^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 c^{2} d^{3} e x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 c^{2} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{4 c^{2} d e^{3} x^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{c^{2} e^{4} x^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} & \text{for}\: m = -3 \\- \frac{6 b^{2} d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{6 b^{2} d^{2} e^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{6 b^{2} d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{3 b^{2} e^{4} x^{2}}{3 d e^{5} + 3 e^{6} x} + \frac{18 b c d^{3} e \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{18 b c d^{3} e}{3 d e^{5} + 3 e^{6} x} + \frac{18 b c d^{2} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{9 b c d e^{3} x^{2}}{3 d e^{5} + 3 e^{6} x} + \frac{3 b c e^{4} x^{3}}{3 d e^{5} + 3 e^{6} x} - \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{12 c^{2} d^{4}}{3 d e^{5} + 3 e^{6} x} - \frac{12 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{6 c^{2} d^{2} e^{2} x^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{2 c^{2} d e^{3} x^{3}}{3 d e^{5} + 3 e^{6} x} + \frac{c^{2} e^{4} x^{4}}{3 d e^{5} + 3 e^{6} x} & \text{for}\: m = -2 \\\frac{b^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{b^{2} d x}{e^{2}} + \frac{b^{2} x^{2}}{2 e} - \frac{2 b c d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{2 b c d^{2} x}{e^{3}} - \frac{b c d x^{2}}{e^{2}} + \frac{2 b c x^{3}}{3 e} + \frac{c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{e^{5}} - \frac{c^{2} d^{3} x}{e^{4}} + \frac{c^{2} d^{2} x^{2}}{2 e^{3}} - \frac{c^{2} d x^{3}}{3 e^{2}} + \frac{c^{2} x^{4}}{4 e} & \text{for}\: m = -1 \\\frac{2 b^{2} d^{3} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{18 b^{2} d^{3} e^{2} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 b^{2} d^{3} e^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{2 b^{2} d^{2} e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{18 b^{2} d^{2} e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{40 b^{2} d^{2} e^{3} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{b^{2} d e^{4} m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{10 b^{2} d e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{29 b^{2} d e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{20 b^{2} d e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{b^{2} e^{5} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 b^{2} e^{5} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{49 b^{2} e^{5} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{78 b^{2} e^{5} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 b^{2} e^{5} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 b c d^{4} e m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{60 b c d^{4} e \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 b c d^{3} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{60 b c d^{3} e^{2} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{6 b c d^{2} e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{36 b c d^{2} e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{30 b c d^{2} e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 b c d e^{4} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{16 b c d e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{34 b c d e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{20 b c d e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 b c e^{5} m^{4} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{22 b c e^{5} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{82 b c e^{5} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{122 b c e^{5} m x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{60 b c e^{5} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 c^{2} d^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{24 c^{2} d^{4} e m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 c^{2} d^{3} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 c^{2} d^{3} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{4 c^{2} d^{2} e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 c^{2} d^{2} e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{8 c^{2} d^{2} e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{c^{2} d e^{4} m^{4} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 c^{2} d e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{11 c^{2} d e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 c^{2} d e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{c^{2} e^{5} m^{4} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{10 c^{2} e^{5} m^{3} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{35 c^{2} e^{5} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{50 c^{2} e^{5} m x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 c^{2} e^{5} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(b**2*x**3/3 + b*c*x**4/2 + c**2*x**5/5), Eq(e, 0)), (-b**2*d**2*e**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 4*b**2*d*e**3*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 6*b**2*e**4*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 6*b*c*d**3*e/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 24*b*c*d**2*e**2*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 36*b*c*d*e**3*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 24*b*c*e**4*x**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 12*c**2*d**4*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 25*c**2*d**4/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c**2*d**3*e*x*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 88*c**2*d**3*e*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 72*c**2*d**2*e**2*x**2*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 108*c**2*d**2*e**2*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c**2*d*e**3*x**3*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c**2*d*e**3*x**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 12*c**2*e**4*x**4*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4), Eq(m, -5)), (-b**2*d**2*e**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 3*b**2*d*e**3*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 3*b**2*e**4*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 6*b*c*d**3*e*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 11*b*c*d**3*e/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 18*b*c*d**2*e**2*x*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 27*b*c*d**2*e**2*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 18*b*c*d*e**3*x**2*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 18*b*c*d*e**3*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 6*b*c*e**4*x**3*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 12*c**2*d**4*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 22*c**2*d**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*c**2*d**3*e*x*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 54*c**2*d**3*e*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*c**2*d**2*e**2*x**2*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*c**2*d**2*e**2*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 12*c**2*d*e**3*x**3*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 3*c**2*e**4*x**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3), Eq(m, -4)), (2*b**2*d**2*e**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 3*b**2*d**2*e**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*b**2*d*e**3*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*b**2*d*e**3*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*b**2*e**4*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 12*b*c*d**3*e*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 18*b*c*d**3*e/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 24*b*c*d**2*e**2*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 24*b*c*d**2*e**2*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 12*b*c*d*e**3*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*b*c*e**4*x**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*c**2*d**4*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 18*c**2*d**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*c**2*d**3*e*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*c**2*d**3*e*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*c**2*d**2*e**2*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 4*c**2*d*e**3*x**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + c**2*e**4*x**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2), Eq(m, -3)), (-6*b**2*d**2*e**2*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 6*b**2*d**2*e**2/(3*d*e**5 + 3*e**6*x) - 6*b**2*d*e**3*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 3*b**2*e**4*x**2/(3*d*e**5 + 3*e**6*x) + 18*b*c*d**3*e*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 18*b*c*d**3*e/(3*d*e**5 + 3*e**6*x) + 18*b*c*d**2*e**2*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 9*b*c*d*e**3*x**2/(3*d*e**5 + 3*e**6*x) + 3*b*c*e**4*x**3/(3*d*e**5 + 3*e**6*x) - 12*c**2*d**4*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 12*c**2*d**4/(3*d*e**5 + 3*e**6*x) - 12*c**2*d**3*e*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 6*c**2*d**2*e**2*x**2/(3*d*e**5 + 3*e**6*x) - 2*c**2*d*e**3*x**3/(3*d*e**5 + 3*e**6*x) + c**2*e**4*x**4/(3*d*e**5 + 3*e**6*x), Eq(m, -2)), (b**2*d**2*log(d/e + x)/e**3 - b**2*d*x/e**2 + b**2*x**2/(2*e) - 2*b*c*d**3*log(d/e + x)/e**4 + 2*b*c*d**2*x/e**3 - b*c*d*x**2/e**2 + 2*b*c*x**3/(3*e) + c**2*d**4*log(d/e + x)/e**5 - c**2*d**3*x/e**4 + c**2*d**2*x**2/(2*e**3) - c**2*d*x**3/(3*e**2) + c**2*x**4/(4*e), Eq(m, -1)), (2*b**2*d**3*e**2*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 18*b**2*d**3*e**2*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*b**2*d**3*e**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 2*b**2*d**2*e**3*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 18*b**2*d**2*e**3*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 40*b**2*d**2*e**3*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + b**2*d*e**4*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 10*b**2*d*e**4*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 29*b**2*d*e**4*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 20*b**2*d*e**4*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + b**2*e**5*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*b**2*e**5*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 49*b**2*e**5*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 78*b**2*e**5*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*b**2*e**5*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*b*c*d**4*e*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 60*b*c*d**4*e*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*b*c*d**3*e**2*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 60*b*c*d**3*e**2*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 6*b*c*d**2*e**3*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 36*b*c*d**2*e**3*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 30*b*c*d**2*e**3*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*b*c*d*e**4*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 16*b*c*d*e**4*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 34*b*c*d*e**4*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 20*b*c*d*e**4*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*b*c*e**5*m**4*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 22*b*c*e**5*m**3*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 82*b*c*e**5*m**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 122*b*c*e**5*m*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 60*b*c*e**5*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*c**2*d**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 24*c**2*d**4*e*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*c**2*d**3*e**2*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*c**2*d**3*e**2*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 4*c**2*d**2*e**3*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*c**2*d**2*e**3*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 8*c**2*d**2*e**3*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + c**2*d*e**4*m**4*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*c**2*d*e**4*m**3*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 11*c**2*d*e**4*m**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*c**2*d*e**4*m*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + c**2*e**5*m**4*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 10*c**2*e**5*m**3*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 35*c**2*e**5*m**2*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 50*c**2*e**5*m*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*c**2*e**5*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5), True))","A",0
442,1,1095,0,1.724210," ","integrate((e*x+d)**m*(c*x**2+b*x),x)","\begin{cases} d^{m} \left(\frac{b x^{2}}{2} + \frac{c x^{3}}{3}\right) & \text{for}\: e = 0 \\- \frac{b d e}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} - \frac{2 b e^{2} x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 c d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{3 c d^{2}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 c d e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 c d e x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 c e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} & \text{for}\: m = -3 \\\frac{b d e \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} + \frac{b d e}{d e^{3} + e^{4} x} + \frac{b e^{2} x \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{2 c d^{2} \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{2 c d^{2}}{d e^{3} + e^{4} x} - \frac{2 c d e x \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} + \frac{c e^{2} x^{2}}{d e^{3} + e^{4} x} & \text{for}\: m = -2 \\- \frac{b d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{b x}{e} + \frac{c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{c d x}{e^{2}} + \frac{c x^{2}}{2 e} & \text{for}\: m = -1 \\- \frac{b d^{2} e m \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} - \frac{3 b d^{2} e \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{b d e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{3 b d e^{2} m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{b e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{4 b e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{3 b e^{3} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{2 c d^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} - \frac{2 c d^{2} e m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{c d e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{c d e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{c e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{3 c e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{2 c e^{3} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(b*x**2/2 + c*x**3/3), Eq(e, 0)), (-b*d*e/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) - 2*b*e**2*x/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*c*d**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 3*c*d**2/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*c*d*e*x*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*c*d*e*x/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*c*e**2*x**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2), Eq(m, -3)), (b*d*e*log(d/e + x)/(d*e**3 + e**4*x) + b*d*e/(d*e**3 + e**4*x) + b*e**2*x*log(d/e + x)/(d*e**3 + e**4*x) - 2*c*d**2*log(d/e + x)/(d*e**3 + e**4*x) - 2*c*d**2/(d*e**3 + e**4*x) - 2*c*d*e*x*log(d/e + x)/(d*e**3 + e**4*x) + c*e**2*x**2/(d*e**3 + e**4*x), Eq(m, -2)), (-b*d*log(d/e + x)/e**2 + b*x/e + c*d**2*log(d/e + x)/e**3 - c*d*x/e**2 + c*x**2/(2*e), Eq(m, -1)), (-b*d**2*e*m*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) - 3*b*d**2*e*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + b*d*e**2*m**2*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 3*b*d*e**2*m*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + b*e**3*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 4*b*e**3*m*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 3*b*e**3*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 2*c*d**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) - 2*c*d**2*e*m*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + c*d*e**2*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + c*d*e**2*m*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + c*e**3*m**2*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 3*c*e**3*m*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 2*c*e**3*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3), True))","A",0
443,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x),x)","\int \frac{\left(d + e x\right)^{m}}{x \left(b + c x\right)}\, dx"," ",0,"Integral((d + e*x)**m/(x*(b + c*x)), x)","F",0
444,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x)**2,x)","\int \frac{\left(d + e x\right)^{m}}{x^{2} \left(b + c x\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**m/(x**2*(b + c*x)**2), x)","F",0
445,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x)**3,x)","\int \frac{\left(d + e x\right)^{m}}{x^{3} \left(b + c x\right)^{3}}\, dx"," ",0,"Integral((d + e*x)**m/(x**3*(b + c*x)**3), x)","F",0
446,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x)**(3/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{m}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(d + e*x)**m, x)","F",0
447,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(d + e x\right)^{m}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(d + e*x)**m, x)","F",0
448,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(d + e x\right)^{m}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((d + e*x)**m/sqrt(x*(b + c*x)), x)","F",0
449,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x)**(3/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**m/(x*(b + c*x))**(3/2), x)","F",0
450,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x)**p,x)","\int \left(x \left(b + c x\right)\right)^{p} \left(d + e x\right)^{m}\, dx"," ",0,"Integral((x*(b + c*x))**p*(d + e*x)**m, x)","F",0
451,1,100,0,0.085620," ","integrate((e*x+d)**4*(c*x**2+a),x)","a d^{4} x + 2 a d^{3} e x^{2} + \frac{2 c d e^{3} x^{6}}{3} + \frac{c e^{4} x^{7}}{7} + x^{5} \left(\frac{a e^{4}}{5} + \frac{6 c d^{2} e^{2}}{5}\right) + x^{4} \left(a d e^{3} + c d^{3} e\right) + x^{3} \left(2 a d^{2} e^{2} + \frac{c d^{4}}{3}\right)"," ",0,"a*d**4*x + 2*a*d**3*e*x**2 + 2*c*d*e**3*x**6/3 + c*e**4*x**7/7 + x**5*(a*e**4/5 + 6*c*d**2*e**2/5) + x**4*(a*d*e**3 + c*d**3*e) + x**3*(2*a*d**2*e**2 + c*d**4/3)","A",0
452,1,80,0,0.080400," ","integrate((e*x+d)**3*(c*x**2+a),x)","a d^{3} x + \frac{3 a d^{2} e x^{2}}{2} + \frac{3 c d e^{2} x^{5}}{5} + \frac{c e^{3} x^{6}}{6} + x^{4} \left(\frac{a e^{3}}{4} + \frac{3 c d^{2} e}{4}\right) + x^{3} \left(a d e^{2} + \frac{c d^{3}}{3}\right)"," ",0,"a*d**3*x + 3*a*d**2*e*x**2/2 + 3*c*d*e**2*x**5/5 + c*e**3*x**6/6 + x**4*(a*e**3/4 + 3*c*d**2*e/4) + x**3*(a*d*e**2 + c*d**3/3)","A",0
453,1,51,0,0.074187," ","integrate((e*x+d)**2*(c*x**2+a),x)","a d^{2} x + a d e x^{2} + \frac{c d e x^{4}}{2} + \frac{c e^{2} x^{5}}{5} + x^{3} \left(\frac{a e^{2}}{3} + \frac{c d^{2}}{3}\right)"," ",0,"a*d**2*x + a*d*e*x**2 + c*d*e*x**4/2 + c*e**2*x**5/5 + x**3*(a*e**2/3 + c*d**2/3)","A",0
454,1,29,0,0.064385," ","integrate((e*x+d)*(c*x**2+a),x)","a d x + \frac{a e x^{2}}{2} + \frac{c d x^{3}}{3} + \frac{c e x^{4}}{4}"," ",0,"a*d*x + a*e*x**2/2 + c*d*x**3/3 + c*e*x**4/4","A",0
455,1,36,0,0.169326," ","integrate((c*x**2+a)/(e*x+d),x)","- \frac{c d x}{e^{2}} + \frac{c x^{2}}{2 e} + \frac{\left(a e^{2} + c d^{2}\right) \log{\left(d + e x \right)}}{e^{3}}"," ",0,"-c*d*x/e**2 + c*x**2/(2*e) + (a*e**2 + c*d**2)*log(d + e*x)/e**3","A",0
456,1,42,0,0.235909," ","integrate((c*x**2+a)/(e*x+d)**2,x)","- \frac{2 c d \log{\left(d + e x \right)}}{e^{3}} + \frac{c x}{e^{2}} + \frac{- a e^{2} - c d^{2}}{d e^{3} + e^{4} x}"," ",0,"-2*c*d*log(d + e*x)/e**3 + c*x/e**2 + (-a*e**2 - c*d**2)/(d*e**3 + e**4*x)","A",0
457,1,56,0,0.331177," ","integrate((c*x**2+a)/(e*x+d)**3,x)","\frac{c \log{\left(d + e x \right)}}{e^{3}} + \frac{- a e^{2} + 3 c d^{2} + 4 c d e x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}}"," ",0,"c*log(d + e*x)/e**3 + (-a*e**2 + 3*c*d**2 + 4*c*d*e*x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2)","A",0
458,1,66,0,0.443159," ","integrate((c*x**2+a)/(e*x+d)**4,x)","\frac{- a e^{2} - c d^{2} - 3 c d e x - 3 c e^{2} x^{2}}{3 d^{3} e^{3} + 9 d^{2} e^{4} x + 9 d e^{5} x^{2} + 3 e^{6} x^{3}}"," ",0,"(-a*e**2 - c*d**2 - 3*c*d*e*x - 3*c*e**2*x**2)/(3*d**3*e**3 + 9*d**2*e**4*x + 9*d*e**5*x**2 + 3*e**6*x**3)","A",0
459,1,80,0,0.553578," ","integrate((c*x**2+a)/(e*x+d)**5,x)","\frac{- 3 a e^{2} - c d^{2} - 4 c d e x - 6 c e^{2} x^{2}}{12 d^{4} e^{3} + 48 d^{3} e^{4} x + 72 d^{2} e^{5} x^{2} + 48 d e^{6} x^{3} + 12 e^{7} x^{4}}"," ",0,"(-3*a*e**2 - c*d**2 - 4*c*d*e*x - 6*c*e**2*x**2)/(12*d**4*e**3 + 48*d**3*e**4*x + 72*d**2*e**5*x**2 + 48*d*e**6*x**3 + 12*e**7*x**4)","A",0
460,1,182,0,0.099326," ","integrate((e*x+d)**4*(c*x**2+a)**2,x)","a^{2} d^{4} x + 2 a^{2} d^{3} e x^{2} + \frac{c^{2} d e^{3} x^{8}}{2} + \frac{c^{2} e^{4} x^{9}}{9} + x^{7} \left(\frac{2 a c e^{4}}{7} + \frac{6 c^{2} d^{2} e^{2}}{7}\right) + x^{6} \left(\frac{4 a c d e^{3}}{3} + \frac{2 c^{2} d^{3} e}{3}\right) + x^{5} \left(\frac{a^{2} e^{4}}{5} + \frac{12 a c d^{2} e^{2}}{5} + \frac{c^{2} d^{4}}{5}\right) + x^{4} \left(a^{2} d e^{3} + 2 a c d^{3} e\right) + x^{3} \left(2 a^{2} d^{2} e^{2} + \frac{2 a c d^{4}}{3}\right)"," ",0,"a**2*d**4*x + 2*a**2*d**3*e*x**2 + c**2*d*e**3*x**8/2 + c**2*e**4*x**9/9 + x**7*(2*a*c*e**4/7 + 6*c**2*d**2*e**2/7) + x**6*(4*a*c*d*e**3/3 + 2*c**2*d**3*e/3) + x**5*(a**2*e**4/5 + 12*a*c*d**2*e**2/5 + c**2*d**4/5) + x**4*(a**2*d*e**3 + 2*a*c*d**3*e) + x**3*(2*a**2*d**2*e**2 + 2*a*c*d**4/3)","A",0
461,1,141,0,0.092325," ","integrate((e*x+d)**3*(c*x**2+a)**2,x)","a^{2} d^{3} x + \frac{3 a^{2} d^{2} e x^{2}}{2} + \frac{3 c^{2} d e^{2} x^{7}}{7} + \frac{c^{2} e^{3} x^{8}}{8} + x^{6} \left(\frac{a c e^{3}}{3} + \frac{c^{2} d^{2} e}{2}\right) + x^{5} \left(\frac{6 a c d e^{2}}{5} + \frac{c^{2} d^{3}}{5}\right) + x^{4} \left(\frac{a^{2} e^{3}}{4} + \frac{3 a c d^{2} e}{2}\right) + x^{3} \left(a^{2} d e^{2} + \frac{2 a c d^{3}}{3}\right)"," ",0,"a**2*d**3*x + 3*a**2*d**2*e*x**2/2 + 3*c**2*d*e**2*x**7/7 + c**2*e**3*x**8/8 + x**6*(a*c*e**3/3 + c**2*d**2*e/2) + x**5*(6*a*c*d*e**2/5 + c**2*d**3/5) + x**4*(a**2*e**3/4 + 3*a*c*d**2*e/2) + x**3*(a**2*d*e**2 + 2*a*c*d**3/3)","A",0
462,1,95,0,0.084741," ","integrate((e*x+d)**2*(c*x**2+a)**2,x)","a^{2} d^{2} x + a^{2} d e x^{2} + a c d e x^{4} + \frac{c^{2} d e x^{6}}{3} + \frac{c^{2} e^{2} x^{7}}{7} + x^{5} \left(\frac{2 a c e^{2}}{5} + \frac{c^{2} d^{2}}{5}\right) + x^{3} \left(\frac{a^{2} e^{2}}{3} + \frac{2 a c d^{2}}{3}\right)"," ",0,"a**2*d**2*x + a**2*d*e*x**2 + a*c*d*e*x**4 + c**2*d*e*x**6/3 + c**2*e**2*x**7/7 + x**5*(2*a*c*e**2/5 + c**2*d**2/5) + x**3*(a**2*e**2/3 + 2*a*c*d**2/3)","A",0
463,1,58,0,0.073104," ","integrate((e*x+d)*(c*x**2+a)**2,x)","a^{2} d x + \frac{a^{2} e x^{2}}{2} + \frac{2 a c d x^{3}}{3} + \frac{a c e x^{4}}{2} + \frac{c^{2} d x^{5}}{5} + \frac{c^{2} e x^{6}}{6}"," ",0,"a**2*d*x + a**2*e*x**2/2 + 2*a*c*d*x**3/3 + a*c*e*x**4/2 + c**2*d*x**5/5 + c**2*e*x**6/6","A",0
464,1,88,0,0.276974," ","integrate((c*x**2+a)**2/(e*x+d),x)","- \frac{c^{2} d x^{3}}{3 e^{2}} + \frac{c^{2} x^{4}}{4 e} + x^{2} \left(\frac{a c}{e} + \frac{c^{2} d^{2}}{2 e^{3}}\right) + x \left(- \frac{2 a c d}{e^{2}} - \frac{c^{2} d^{3}}{e^{4}}\right) + \frac{\left(a e^{2} + c d^{2}\right)^{2} \log{\left(d + e x \right)}}{e^{5}}"," ",0,"-c**2*d*x**3/(3*e**2) + c**2*x**4/(4*e) + x**2*(a*c/e + c**2*d**2/(2*e**3)) + x*(-2*a*c*d/e**2 - c**2*d**3/e**4) + (a*e**2 + c*d**2)**2*log(d + e*x)/e**5","A",0
465,1,107,0,0.455638," ","integrate((c*x**2+a)**2/(e*x+d)**2,x)","- \frac{c^{2} d x^{2}}{e^{3}} + \frac{c^{2} x^{3}}{3 e^{2}} - \frac{4 c d \left(a e^{2} + c d^{2}\right) \log{\left(d + e x \right)}}{e^{5}} + x \left(\frac{2 a c}{e^{2}} + \frac{3 c^{2} d^{2}}{e^{4}}\right) + \frac{- a^{2} e^{4} - 2 a c d^{2} e^{2} - c^{2} d^{4}}{d e^{5} + e^{6} x}"," ",0,"-c**2*d*x**2/e**3 + c**2*x**3/(3*e**2) - 4*c*d*(a*e**2 + c*d**2)*log(d + e*x)/e**5 + x*(2*a*c/e**2 + 3*c**2*d**2/e**4) + (-a**2*e**4 - 2*a*c*d**2*e**2 - c**2*d**4)/(d*e**5 + e**6*x)","A",0
466,1,122,0,0.751531," ","integrate((c*x**2+a)**2/(e*x+d)**3,x)","- \frac{3 c^{2} d x}{e^{4}} + \frac{c^{2} x^{2}}{2 e^{3}} + \frac{2 c \left(a e^{2} + 3 c d^{2}\right) \log{\left(d + e x \right)}}{e^{5}} + \frac{- a^{2} e^{4} + 6 a c d^{2} e^{2} + 7 c^{2} d^{4} + x \left(8 a c d e^{3} + 8 c^{2} d^{3} e\right)}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}}"," ",0,"-3*c**2*d*x/e**4 + c**2*x**2/(2*e**3) + 2*c*(a*e**2 + 3*c*d**2)*log(d + e*x)/e**5 + (-a**2*e**4 + 6*a*c*d**2*e**2 + 7*c**2*d**4 + x*(8*a*c*d*e**3 + 8*c**2*d**3*e))/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2)","A",0
467,1,138,0,1.079569," ","integrate((c*x**2+a)**2/(e*x+d)**4,x)","- \frac{4 c^{2} d \log{\left(d + e x \right)}}{e^{5}} + \frac{c^{2} x}{e^{4}} + \frac{- a^{2} e^{4} - 2 a c d^{2} e^{2} - 13 c^{2} d^{4} + x^{2} \left(- 6 a c e^{4} - 18 c^{2} d^{2} e^{2}\right) + x \left(- 6 a c d e^{3} - 30 c^{2} d^{3} e\right)}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}}"," ",0,"-4*c**2*d*log(d + e*x)/e**5 + c**2*x/e**4 + (-a**2*e**4 - 2*a*c*d**2*e**2 - 13*c**2*d**4 + x**2*(-6*a*c*e**4 - 18*c**2*d**2*e**2) + x*(-6*a*c*d*e**3 - 30*c**2*d**3*e))/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3)","A",0
468,1,150,0,1.452252," ","integrate((c*x**2+a)**2/(e*x+d)**5,x)","\frac{c^{2} \log{\left(d + e x \right)}}{e^{5}} + \frac{- 3 a^{2} e^{4} - 2 a c d^{2} e^{2} + 25 c^{2} d^{4} + 48 c^{2} d e^{3} x^{3} + x^{2} \left(- 12 a c e^{4} + 108 c^{2} d^{2} e^{2}\right) + x \left(- 8 a c d e^{3} + 88 c^{2} d^{3} e\right)}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}}"," ",0,"c**2*log(d + e*x)/e**5 + (-3*a**2*e**4 - 2*a*c*d**2*e**2 + 25*c**2*d**4 + 48*c**2*d*e**3*x**3 + x**2*(-12*a*c*e**4 + 108*c**2*d**2*e**2) + x*(-8*a*c*d*e**3 + 88*c**2*d**3*e))/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4)","A",0
469,1,162,0,1.871742," ","integrate((c*x**2+a)**2/(e*x+d)**6,x)","\frac{- 3 a^{2} e^{4} - a c d^{2} e^{2} - 3 c^{2} d^{4} - 30 c^{2} d e^{3} x^{3} - 15 c^{2} e^{4} x^{4} + x^{2} \left(- 10 a c e^{4} - 30 c^{2} d^{2} e^{2}\right) + x \left(- 5 a c d e^{3} - 15 c^{2} d^{3} e\right)}{15 d^{5} e^{5} + 75 d^{4} e^{6} x + 150 d^{3} e^{7} x^{2} + 150 d^{2} e^{8} x^{3} + 75 d e^{9} x^{4} + 15 e^{10} x^{5}}"," ",0,"(-3*a**2*e**4 - a*c*d**2*e**2 - 3*c**2*d**4 - 30*c**2*d*e**3*x**3 - 15*c**2*e**4*x**4 + x**2*(-10*a*c*e**4 - 30*c**2*d**2*e**2) + x*(-5*a*c*d*e**3 - 15*c**2*d**3*e))/(15*d**5*e**5 + 75*d**4*e**6*x + 150*d**3*e**7*x**2 + 150*d**2*e**8*x**3 + 75*d*e**9*x**4 + 15*e**10*x**5)","A",0
470,1,172,0,2.323112," ","integrate((c*x**2+a)**2/(e*x+d)**7,x)","\frac{- 5 a^{2} e^{4} - a c d^{2} e^{2} - c^{2} d^{4} - 20 c^{2} d e^{3} x^{3} - 15 c^{2} e^{4} x^{4} + x^{2} \left(- 15 a c e^{4} - 15 c^{2} d^{2} e^{2}\right) + x \left(- 6 a c d e^{3} - 6 c^{2} d^{3} e\right)}{30 d^{6} e^{5} + 180 d^{5} e^{6} x + 450 d^{4} e^{7} x^{2} + 600 d^{3} e^{8} x^{3} + 450 d^{2} e^{9} x^{4} + 180 d e^{10} x^{5} + 30 e^{11} x^{6}}"," ",0,"(-5*a**2*e**4 - a*c*d**2*e**2 - c**2*d**4 - 20*c**2*d*e**3*x**3 - 15*c**2*e**4*x**4 + x**2*(-15*a*c*e**4 - 15*c**2*d**2*e**2) + x*(-6*a*c*d*e**3 - 6*c**2*d**3*e))/(30*d**6*e**5 + 180*d**5*e**6*x + 450*d**4*e**7*x**2 + 600*d**3*e**8*x**3 + 450*d**2*e**9*x**4 + 180*d*e**10*x**5 + 30*e**11*x**6)","A",0
471,1,185,0,2.857614," ","integrate((c*x**2+a)**2/(e*x+d)**8,x)","\frac{- 15 a^{2} e^{4} - 2 a c d^{2} e^{2} - c^{2} d^{4} - 35 c^{2} d e^{3} x^{3} - 35 c^{2} e^{4} x^{4} + x^{2} \left(- 42 a c e^{4} - 21 c^{2} d^{2} e^{2}\right) + x \left(- 14 a c d e^{3} - 7 c^{2} d^{3} e\right)}{105 d^{7} e^{5} + 735 d^{6} e^{6} x + 2205 d^{5} e^{7} x^{2} + 3675 d^{4} e^{8} x^{3} + 3675 d^{3} e^{9} x^{4} + 2205 d^{2} e^{10} x^{5} + 735 d e^{11} x^{6} + 105 e^{12} x^{7}}"," ",0,"(-15*a**2*e**4 - 2*a*c*d**2*e**2 - c**2*d**4 - 35*c**2*d*e**3*x**3 - 35*c**2*e**4*x**4 + x**2*(-42*a*c*e**4 - 21*c**2*d**2*e**2) + x*(-14*a*c*d*e**3 - 7*c**2*d**3*e))/(105*d**7*e**5 + 735*d**6*e**6*x + 2205*d**5*e**7*x**2 + 3675*d**4*e**8*x**3 + 3675*d**3*e**9*x**4 + 2205*d**2*e**10*x**5 + 735*d*e**11*x**6 + 105*e**12*x**7)","A",0
472,1,371,0,0.128343," ","integrate((e*x+d)**6*(c*x**2+a)**3,x)","a^{3} d^{6} x + 3 a^{3} d^{5} e x^{2} + \frac{c^{3} d e^{5} x^{12}}{2} + \frac{c^{3} e^{6} x^{13}}{13} + x^{11} \left(\frac{3 a c^{2} e^{6}}{11} + \frac{15 c^{3} d^{2} e^{4}}{11}\right) + x^{10} \left(\frac{9 a c^{2} d e^{5}}{5} + 2 c^{3} d^{3} e^{3}\right) + x^{9} \left(\frac{a^{2} c e^{6}}{3} + 5 a c^{2} d^{2} e^{4} + \frac{5 c^{3} d^{4} e^{2}}{3}\right) + x^{8} \left(\frac{9 a^{2} c d e^{5}}{4} + \frac{15 a c^{2} d^{3} e^{3}}{2} + \frac{3 c^{3} d^{5} e}{4}\right) + x^{7} \left(\frac{a^{3} e^{6}}{7} + \frac{45 a^{2} c d^{2} e^{4}}{7} + \frac{45 a c^{2} d^{4} e^{2}}{7} + \frac{c^{3} d^{6}}{7}\right) + x^{6} \left(a^{3} d e^{5} + 10 a^{2} c d^{3} e^{3} + 3 a c^{2} d^{5} e\right) + x^{5} \left(3 a^{3} d^{2} e^{4} + 9 a^{2} c d^{4} e^{2} + \frac{3 a c^{2} d^{6}}{5}\right) + x^{4} \left(5 a^{3} d^{3} e^{3} + \frac{9 a^{2} c d^{5} e}{2}\right) + x^{3} \left(5 a^{3} d^{4} e^{2} + a^{2} c d^{6}\right)"," ",0,"a**3*d**6*x + 3*a**3*d**5*e*x**2 + c**3*d*e**5*x**12/2 + c**3*e**6*x**13/13 + x**11*(3*a*c**2*e**6/11 + 15*c**3*d**2*e**4/11) + x**10*(9*a*c**2*d*e**5/5 + 2*c**3*d**3*e**3) + x**9*(a**2*c*e**6/3 + 5*a*c**2*d**2*e**4 + 5*c**3*d**4*e**2/3) + x**8*(9*a**2*c*d*e**5/4 + 15*a*c**2*d**3*e**3/2 + 3*c**3*d**5*e/4) + x**7*(a**3*e**6/7 + 45*a**2*c*d**2*e**4/7 + 45*a*c**2*d**4*e**2/7 + c**3*d**6/7) + x**6*(a**3*d*e**5 + 10*a**2*c*d**3*e**3 + 3*a*c**2*d**5*e) + x**5*(3*a**3*d**2*e**4 + 9*a**2*c*d**4*e**2 + 3*a*c**2*d**6/5) + x**4*(5*a**3*d**3*e**3 + 9*a**2*c*d**5*e/2) + x**3*(5*a**3*d**4*e**2 + a**2*c*d**6)","B",0
473,1,321,0,0.117793," ","integrate((e*x+d)**5*(c*x**2+a)**3,x)","a^{3} d^{5} x + \frac{5 a^{3} d^{4} e x^{2}}{2} + \frac{5 c^{3} d e^{4} x^{11}}{11} + \frac{c^{3} e^{5} x^{12}}{12} + x^{10} \left(\frac{3 a c^{2} e^{5}}{10} + c^{3} d^{2} e^{3}\right) + x^{9} \left(\frac{5 a c^{2} d e^{4}}{3} + \frac{10 c^{3} d^{3} e^{2}}{9}\right) + x^{8} \left(\frac{3 a^{2} c e^{5}}{8} + \frac{15 a c^{2} d^{2} e^{3}}{4} + \frac{5 c^{3} d^{4} e}{8}\right) + x^{7} \left(\frac{15 a^{2} c d e^{4}}{7} + \frac{30 a c^{2} d^{3} e^{2}}{7} + \frac{c^{3} d^{5}}{7}\right) + x^{6} \left(\frac{a^{3} e^{5}}{6} + 5 a^{2} c d^{2} e^{3} + \frac{5 a c^{2} d^{4} e}{2}\right) + x^{5} \left(a^{3} d e^{4} + 6 a^{2} c d^{3} e^{2} + \frac{3 a c^{2} d^{5}}{5}\right) + x^{4} \left(\frac{5 a^{3} d^{2} e^{3}}{2} + \frac{15 a^{2} c d^{4} e}{4}\right) + x^{3} \left(\frac{10 a^{3} d^{3} e^{2}}{3} + a^{2} c d^{5}\right)"," ",0,"a**3*d**5*x + 5*a**3*d**4*e*x**2/2 + 5*c**3*d*e**4*x**11/11 + c**3*e**5*x**12/12 + x**10*(3*a*c**2*e**5/10 + c**3*d**2*e**3) + x**9*(5*a*c**2*d*e**4/3 + 10*c**3*d**3*e**2/9) + x**8*(3*a**2*c*e**5/8 + 15*a*c**2*d**2*e**3/4 + 5*c**3*d**4*e/8) + x**7*(15*a**2*c*d*e**4/7 + 30*a*c**2*d**3*e**2/7 + c**3*d**5/7) + x**6*(a**3*e**5/6 + 5*a**2*c*d**2*e**3 + 5*a*c**2*d**4*e/2) + x**5*(a**3*d*e**4 + 6*a**2*c*d**3*e**2 + 3*a*c**2*d**5/5) + x**4*(5*a**3*d**2*e**3/2 + 15*a**2*c*d**4*e/4) + x**3*(10*a**3*d**3*e**2/3 + a**2*c*d**5)","A",0
474,1,255,0,0.110209," ","integrate((e*x+d)**4*(c*x**2+a)**3,x)","a^{3} d^{4} x + 2 a^{3} d^{3} e x^{2} + \frac{2 c^{3} d e^{3} x^{10}}{5} + \frac{c^{3} e^{4} x^{11}}{11} + x^{9} \left(\frac{a c^{2} e^{4}}{3} + \frac{2 c^{3} d^{2} e^{2}}{3}\right) + x^{8} \left(\frac{3 a c^{2} d e^{3}}{2} + \frac{c^{3} d^{3} e}{2}\right) + x^{7} \left(\frac{3 a^{2} c e^{4}}{7} + \frac{18 a c^{2} d^{2} e^{2}}{7} + \frac{c^{3} d^{4}}{7}\right) + x^{6} \left(2 a^{2} c d e^{3} + 2 a c^{2} d^{3} e\right) + x^{5} \left(\frac{a^{3} e^{4}}{5} + \frac{18 a^{2} c d^{2} e^{2}}{5} + \frac{3 a c^{2} d^{4}}{5}\right) + x^{4} \left(a^{3} d e^{3} + 3 a^{2} c d^{3} e\right) + x^{3} \left(2 a^{3} d^{2} e^{2} + a^{2} c d^{4}\right)"," ",0,"a**3*d**4*x + 2*a**3*d**3*e*x**2 + 2*c**3*d*e**3*x**10/5 + c**3*e**4*x**11/11 + x**9*(a*c**2*e**4/3 + 2*c**3*d**2*e**2/3) + x**8*(3*a*c**2*d*e**3/2 + c**3*d**3*e/2) + x**7*(3*a**2*c*e**4/7 + 18*a*c**2*d**2*e**2/7 + c**3*d**4/7) + x**6*(2*a**2*c*d*e**3 + 2*a*c**2*d**3*e) + x**5*(a**3*e**4/5 + 18*a**2*c*d**2*e**2/5 + 3*a*c**2*d**4/5) + x**4*(a**3*d*e**3 + 3*a**2*c*d**3*e) + x**3*(2*a**3*d**2*e**2 + a**2*c*d**4)","A",0
475,1,202,0,0.099884," ","integrate((e*x+d)**3*(c*x**2+a)**3,x)","a^{3} d^{3} x + \frac{3 a^{3} d^{2} e x^{2}}{2} + \frac{c^{3} d e^{2} x^{9}}{3} + \frac{c^{3} e^{3} x^{10}}{10} + x^{8} \left(\frac{3 a c^{2} e^{3}}{8} + \frac{3 c^{3} d^{2} e}{8}\right) + x^{7} \left(\frac{9 a c^{2} d e^{2}}{7} + \frac{c^{3} d^{3}}{7}\right) + x^{6} \left(\frac{a^{2} c e^{3}}{2} + \frac{3 a c^{2} d^{2} e}{2}\right) + x^{5} \left(\frac{9 a^{2} c d e^{2}}{5} + \frac{3 a c^{2} d^{3}}{5}\right) + x^{4} \left(\frac{a^{3} e^{3}}{4} + \frac{9 a^{2} c d^{2} e}{4}\right) + x^{3} \left(a^{3} d e^{2} + a^{2} c d^{3}\right)"," ",0,"a**3*d**3*x + 3*a**3*d**2*e*x**2/2 + c**3*d*e**2*x**9/3 + c**3*e**3*x**10/10 + x**8*(3*a*c**2*e**3/8 + 3*c**3*d**2*e/8) + x**7*(9*a*c**2*d*e**2/7 + c**3*d**3/7) + x**6*(a**2*c*e**3/2 + 3*a*c**2*d**2*e/2) + x**5*(9*a**2*c*d*e**2/5 + 3*a*c**2*d**3/5) + x**4*(a**3*e**3/4 + 9*a**2*c*d**2*e/4) + x**3*(a**3*d*e**2 + a**2*c*d**3)","A",0
476,1,139,0,0.092303," ","integrate((e*x+d)**2*(c*x**2+a)**3,x)","a^{3} d^{2} x + a^{3} d e x^{2} + \frac{3 a^{2} c d e x^{4}}{2} + a c^{2} d e x^{6} + \frac{c^{3} d e x^{8}}{4} + \frac{c^{3} e^{2} x^{9}}{9} + x^{7} \left(\frac{3 a c^{2} e^{2}}{7} + \frac{c^{3} d^{2}}{7}\right) + x^{5} \left(\frac{3 a^{2} c e^{2}}{5} + \frac{3 a c^{2} d^{2}}{5}\right) + x^{3} \left(\frac{a^{3} e^{2}}{3} + a^{2} c d^{2}\right)"," ",0,"a**3*d**2*x + a**3*d*e*x**2 + 3*a**2*c*d*e*x**4/2 + a*c**2*d*e*x**6 + c**3*d*e*x**8/4 + c**3*e**2*x**9/9 + x**7*(3*a*c**2*e**2/7 + c**3*d**2/7) + x**5*(3*a**2*c*e**2/5 + 3*a*c**2*d**2/5) + x**3*(a**3*e**2/3 + a**2*c*d**2)","A",0
477,1,85,0,0.077799," ","integrate((e*x+d)*(c*x**2+a)**3,x)","a^{3} d x + \frac{a^{3} e x^{2}}{2} + a^{2} c d x^{3} + \frac{3 a^{2} c e x^{4}}{4} + \frac{3 a c^{2} d x^{5}}{5} + \frac{a c^{2} e x^{6}}{2} + \frac{c^{3} d x^{7}}{7} + \frac{c^{3} e x^{8}}{8}"," ",0,"a**3*d*x + a**3*e*x**2/2 + a**2*c*d*x**3 + 3*a**2*c*e*x**4/4 + 3*a*c**2*d*x**5/5 + a*c**2*e*x**6/2 + c**3*d*x**7/7 + c**3*e*x**8/8","A",0
478,1,177,0,0.388152," ","integrate((c*x**2+a)**3/(e*x+d),x)","- \frac{c^{3} d x^{5}}{5 e^{2}} + \frac{c^{3} x^{6}}{6 e} + x^{4} \left(\frac{3 a c^{2}}{4 e} + \frac{c^{3} d^{2}}{4 e^{3}}\right) + x^{3} \left(- \frac{a c^{2} d}{e^{2}} - \frac{c^{3} d^{3}}{3 e^{4}}\right) + x^{2} \left(\frac{3 a^{2} c}{2 e} + \frac{3 a c^{2} d^{2}}{2 e^{3}} + \frac{c^{3} d^{4}}{2 e^{5}}\right) + x \left(- \frac{3 a^{2} c d}{e^{2}} - \frac{3 a c^{2} d^{3}}{e^{4}} - \frac{c^{3} d^{5}}{e^{6}}\right) + \frac{\left(a e^{2} + c d^{2}\right)^{3} \log{\left(d + e x \right)}}{e^{7}}"," ",0,"-c**3*d*x**5/(5*e**2) + c**3*x**6/(6*e) + x**4*(3*a*c**2/(4*e) + c**3*d**2/(4*e**3)) + x**3*(-a*c**2*d/e**2 - c**3*d**3/(3*e**4)) + x**2*(3*a**2*c/(2*e) + 3*a*c**2*d**2/(2*e**3) + c**3*d**4/(2*e**5)) + x*(-3*a**2*c*d/e**2 - 3*a*c**2*d**3/e**4 - c**3*d**5/e**6) + (a*e**2 + c*d**2)**3*log(d + e*x)/e**7","A",0
479,1,192,0,0.692096," ","integrate((c*x**2+a)**3/(e*x+d)**2,x)","- \frac{c^{3} d x^{4}}{2 e^{3}} + \frac{c^{3} x^{5}}{5 e^{2}} - \frac{6 c d \left(a e^{2} + c d^{2}\right)^{2} \log{\left(d + e x \right)}}{e^{7}} + x^{3} \left(\frac{a c^{2}}{e^{2}} + \frac{c^{3} d^{2}}{e^{4}}\right) + x^{2} \left(- \frac{3 a c^{2} d}{e^{3}} - \frac{2 c^{3} d^{3}}{e^{5}}\right) + x \left(\frac{3 a^{2} c}{e^{2}} + \frac{9 a c^{2} d^{2}}{e^{4}} + \frac{5 c^{3} d^{4}}{e^{6}}\right) + \frac{- a^{3} e^{6} - 3 a^{2} c d^{2} e^{4} - 3 a c^{2} d^{4} e^{2} - c^{3} d^{6}}{d e^{7} + e^{8} x}"," ",0,"-c**3*d*x**4/(2*e**3) + c**3*x**5/(5*e**2) - 6*c*d*(a*e**2 + c*d**2)**2*log(d + e*x)/e**7 + x**3*(a*c**2/e**2 + c**3*d**2/e**4) + x**2*(-3*a*c**2*d/e**3 - 2*c**3*d**3/e**5) + x*(3*a**2*c/e**2 + 9*a*c**2*d**2/e**4 + 5*c**3*d**4/e**6) + (-a**3*e**6 - 3*a**2*c*d**2*e**4 - 3*a*c**2*d**4*e**2 - c**3*d**6)/(d*e**7 + e**8*x)","A",0
480,1,218,0,1.181766," ","integrate((c*x**2+a)**3/(e*x+d)**3,x)","- \frac{c^{3} d x^{3}}{e^{4}} + \frac{c^{3} x^{4}}{4 e^{3}} + \frac{3 c \left(a e^{2} + c d^{2}\right) \left(a e^{2} + 5 c d^{2}\right) \log{\left(d + e x \right)}}{e^{7}} + x^{2} \left(\frac{3 a c^{2}}{2 e^{3}} + \frac{3 c^{3} d^{2}}{e^{5}}\right) + x \left(- \frac{9 a c^{2} d}{e^{4}} - \frac{10 c^{3} d^{3}}{e^{6}}\right) + \frac{- a^{3} e^{6} + 9 a^{2} c d^{2} e^{4} + 21 a c^{2} d^{4} e^{2} + 11 c^{3} d^{6} + x \left(12 a^{2} c d e^{5} + 24 a c^{2} d^{3} e^{3} + 12 c^{3} d^{5} e\right)}{2 d^{2} e^{7} + 4 d e^{8} x + 2 e^{9} x^{2}}"," ",0,"-c**3*d*x**3/e**4 + c**3*x**4/(4*e**3) + 3*c*(a*e**2 + c*d**2)*(a*e**2 + 5*c*d**2)*log(d + e*x)/e**7 + x**2*(3*a*c**2/(2*e**3) + 3*c**3*d**2/e**5) + x*(-9*a*c**2*d/e**4 - 10*c**3*d**3/e**6) + (-a**3*e**6 + 9*a**2*c*d**2*e**4 + 21*a*c**2*d**4*e**2 + 11*c**3*d**6 + x*(12*a**2*c*d*e**5 + 24*a*c**2*d**3*e**3 + 12*c**3*d**5*e))/(2*d**2*e**7 + 4*d*e**8*x + 2*e**9*x**2)","A",0
481,1,238,0,1.977852," ","integrate((c*x**2+a)**3/(e*x+d)**4,x)","- \frac{2 c^{3} d x^{2}}{e^{5}} + \frac{c^{3} x^{3}}{3 e^{4}} - \frac{4 c^{2} d \left(3 a e^{2} + 5 c d^{2}\right) \log{\left(d + e x \right)}}{e^{7}} + x \left(\frac{3 a c^{2}}{e^{4}} + \frac{10 c^{3} d^{2}}{e^{6}}\right) + \frac{- a^{3} e^{6} - 3 a^{2} c d^{2} e^{4} - 39 a c^{2} d^{4} e^{2} - 37 c^{3} d^{6} + x^{2} \left(- 9 a^{2} c e^{6} - 54 a c^{2} d^{2} e^{4} - 45 c^{3} d^{4} e^{2}\right) + x \left(- 9 a^{2} c d e^{5} - 90 a c^{2} d^{3} e^{3} - 81 c^{3} d^{5} e\right)}{3 d^{3} e^{7} + 9 d^{2} e^{8} x + 9 d e^{9} x^{2} + 3 e^{10} x^{3}}"," ",0,"-2*c**3*d*x**2/e**5 + c**3*x**3/(3*e**4) - 4*c**2*d*(3*a*e**2 + 5*c*d**2)*log(d + e*x)/e**7 + x*(3*a*c**2/e**4 + 10*c**3*d**2/e**6) + (-a**3*e**6 - 3*a**2*c*d**2*e**4 - 39*a*c**2*d**4*e**2 - 37*c**3*d**6 + x**2*(-9*a**2*c*e**6 - 54*a*c**2*d**2*e**4 - 45*c**3*d**4*e**2) + x*(-9*a**2*c*d*e**5 - 90*a*c**2*d**3*e**3 - 81*c**3*d**5*e))/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3)","A",0
482,1,243,0,3.089976," ","integrate((c*x**2+a)**3/(e*x+d)**5,x)","- \frac{5 c^{3} d x}{e^{6}} + \frac{c^{3} x^{2}}{2 e^{5}} + \frac{3 c^{2} \left(a e^{2} + 5 c d^{2}\right) \log{\left(d + e x \right)}}{e^{7}} + \frac{- a^{3} e^{6} - a^{2} c d^{2} e^{4} + 25 a c^{2} d^{4} e^{2} + 57 c^{3} d^{6} + x^{3} \left(48 a c^{2} d e^{5} + 80 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 6 a^{2} c e^{6} + 108 a c^{2} d^{2} e^{4} + 210 c^{3} d^{4} e^{2}\right) + x \left(- 4 a^{2} c d e^{5} + 88 a c^{2} d^{3} e^{3} + 188 c^{3} d^{5} e\right)}{4 d^{4} e^{7} + 16 d^{3} e^{8} x + 24 d^{2} e^{9} x^{2} + 16 d e^{10} x^{3} + 4 e^{11} x^{4}}"," ",0,"-5*c**3*d*x/e**6 + c**3*x**2/(2*e**5) + 3*c**2*(a*e**2 + 5*c*d**2)*log(d + e*x)/e**7 + (-a**3*e**6 - a**2*c*d**2*e**4 + 25*a*c**2*d**4*e**2 + 57*c**3*d**6 + x**3*(48*a*c**2*d*e**5 + 80*c**3*d**3*e**3) + x**2*(-6*a**2*c*e**6 + 108*a*c**2*d**2*e**4 + 210*c**3*d**4*e**2) + x*(-4*a**2*c*d*e**5 + 88*a*c**2*d**3*e**3 + 188*c**3*d**5*e))/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4)","A",0
483,1,264,0,4.512594," ","integrate((c*x**2+a)**3/(e*x+d)**6,x)","- \frac{6 c^{3} d \log{\left(d + e x \right)}}{e^{7}} + \frac{c^{3} x}{e^{6}} + \frac{- 2 a^{3} e^{6} - a^{2} c d^{2} e^{4} - 6 a c^{2} d^{4} e^{2} - 87 c^{3} d^{6} + x^{4} \left(- 30 a c^{2} e^{6} - 150 c^{3} d^{2} e^{4}\right) + x^{3} \left(- 60 a c^{2} d e^{5} - 500 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 10 a^{2} c e^{6} - 60 a c^{2} d^{2} e^{4} - 650 c^{3} d^{4} e^{2}\right) + x \left(- 5 a^{2} c d e^{5} - 30 a c^{2} d^{3} e^{3} - 385 c^{3} d^{5} e\right)}{10 d^{5} e^{7} + 50 d^{4} e^{8} x + 100 d^{3} e^{9} x^{2} + 100 d^{2} e^{10} x^{3} + 50 d e^{11} x^{4} + 10 e^{12} x^{5}}"," ",0,"-6*c**3*d*log(d + e*x)/e**7 + c**3*x/e**6 + (-2*a**3*e**6 - a**2*c*d**2*e**4 - 6*a*c**2*d**4*e**2 - 87*c**3*d**6 + x**4*(-30*a*c**2*e**6 - 150*c**3*d**2*e**4) + x**3*(-60*a*c**2*d*e**5 - 500*c**3*d**3*e**3) + x**2*(-10*a**2*c*e**6 - 60*a*c**2*d**2*e**4 - 650*c**3*d**4*e**2) + x*(-5*a**2*c*d*e**5 - 30*a*c**2*d**3*e**3 - 385*c**3*d**5*e))/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5)","A",0
484,1,272,0,6.933436," ","integrate((c*x**2+a)**3/(e*x+d)**7,x)","\frac{c^{3} \log{\left(d + e x \right)}}{e^{7}} + \frac{- 10 a^{3} e^{6} - 3 a^{2} c d^{2} e^{4} - 6 a c^{2} d^{4} e^{2} + 147 c^{3} d^{6} + 360 c^{3} d e^{5} x^{5} + x^{4} \left(- 90 a c^{2} e^{6} + 1350 c^{3} d^{2} e^{4}\right) + x^{3} \left(- 120 a c^{2} d e^{5} + 2200 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 45 a^{2} c e^{6} - 90 a c^{2} d^{2} e^{4} + 1875 c^{3} d^{4} e^{2}\right) + x \left(- 18 a^{2} c d e^{5} - 36 a c^{2} d^{3} e^{3} + 822 c^{3} d^{5} e\right)}{60 d^{6} e^{7} + 360 d^{5} e^{8} x + 900 d^{4} e^{9} x^{2} + 1200 d^{3} e^{10} x^{3} + 900 d^{2} e^{11} x^{4} + 360 d e^{12} x^{5} + 60 e^{13} x^{6}}"," ",0,"c**3*log(d + e*x)/e**7 + (-10*a**3*e**6 - 3*a**2*c*d**2*e**4 - 6*a*c**2*d**4*e**2 + 147*c**3*d**6 + 360*c**3*d*e**5*x**5 + x**4*(-90*a*c**2*e**6 + 1350*c**3*d**2*e**4) + x**3*(-120*a*c**2*d*e**5 + 2200*c**3*d**3*e**3) + x**2*(-45*a**2*c*e**6 - 90*a*c**2*d**2*e**4 + 1875*c**3*d**4*e**2) + x*(-18*a**2*c*d*e**5 - 36*a*c**2*d**3*e**3 + 822*c**3*d**5*e))/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6)","A",0
485,1,286,0,11.350122," ","integrate((c*x**2+a)**3/(e*x+d)**8,x)","\frac{- 5 a^{3} e^{6} - a^{2} c d^{2} e^{4} - a c^{2} d^{4} e^{2} - 5 c^{3} d^{6} - 105 c^{3} d e^{5} x^{5} - 35 c^{3} e^{6} x^{6} + x^{4} \left(- 35 a c^{2} e^{6} - 175 c^{3} d^{2} e^{4}\right) + x^{3} \left(- 35 a c^{2} d e^{5} - 175 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 21 a^{2} c e^{6} - 21 a c^{2} d^{2} e^{4} - 105 c^{3} d^{4} e^{2}\right) + x \left(- 7 a^{2} c d e^{5} - 7 a c^{2} d^{3} e^{3} - 35 c^{3} d^{5} e\right)}{35 d^{7} e^{7} + 245 d^{6} e^{8} x + 735 d^{5} e^{9} x^{2} + 1225 d^{4} e^{10} x^{3} + 1225 d^{3} e^{11} x^{4} + 735 d^{2} e^{12} x^{5} + 245 d e^{13} x^{6} + 35 e^{14} x^{7}}"," ",0,"(-5*a**3*e**6 - a**2*c*d**2*e**4 - a*c**2*d**4*e**2 - 5*c**3*d**6 - 105*c**3*d*e**5*x**5 - 35*c**3*e**6*x**6 + x**4*(-35*a*c**2*e**6 - 175*c**3*d**2*e**4) + x**3*(-35*a*c**2*d*e**5 - 175*c**3*d**3*e**3) + x**2*(-21*a**2*c*e**6 - 21*a*c**2*d**2*e**4 - 105*c**3*d**4*e**2) + x*(-7*a**2*c*d*e**5 - 7*a*c**2*d**3*e**3 - 35*c**3*d**5*e))/(35*d**7*e**7 + 245*d**6*e**8*x + 735*d**5*e**9*x**2 + 1225*d**4*e**10*x**3 + 1225*d**3*e**11*x**4 + 735*d**2*e**12*x**5 + 245*d*e**13*x**6 + 35*e**14*x**7)","A",0
486,1,301,0,19.809500," ","integrate((c*x**2+a)**3/(e*x+d)**9,x)","\frac{- 35 a^{3} e^{6} - 5 a^{2} c d^{2} e^{4} - 3 a c^{2} d^{4} e^{2} - 5 c^{3} d^{6} - 280 c^{3} d e^{5} x^{5} - 140 c^{3} e^{6} x^{6} + x^{4} \left(- 210 a c^{2} e^{6} - 350 c^{3} d^{2} e^{4}\right) + x^{3} \left(- 168 a c^{2} d e^{5} - 280 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 140 a^{2} c e^{6} - 84 a c^{2} d^{2} e^{4} - 140 c^{3} d^{4} e^{2}\right) + x \left(- 40 a^{2} c d e^{5} - 24 a c^{2} d^{3} e^{3} - 40 c^{3} d^{5} e\right)}{280 d^{8} e^{7} + 2240 d^{7} e^{8} x + 7840 d^{6} e^{9} x^{2} + 15680 d^{5} e^{10} x^{3} + 19600 d^{4} e^{11} x^{4} + 15680 d^{3} e^{12} x^{5} + 7840 d^{2} e^{13} x^{6} + 2240 d e^{14} x^{7} + 280 e^{15} x^{8}}"," ",0,"(-35*a**3*e**6 - 5*a**2*c*d**2*e**4 - 3*a*c**2*d**4*e**2 - 5*c**3*d**6 - 280*c**3*d*e**5*x**5 - 140*c**3*e**6*x**6 + x**4*(-210*a*c**2*e**6 - 350*c**3*d**2*e**4) + x**3*(-168*a*c**2*d*e**5 - 280*c**3*d**3*e**3) + x**2*(-140*a**2*c*e**6 - 84*a*c**2*d**2*e**4 - 140*c**3*d**4*e**2) + x*(-40*a**2*c*d*e**5 - 24*a*c**2*d**3*e**3 - 40*c**3*d**5*e))/(280*d**8*e**7 + 2240*d**7*e**8*x + 7840*d**6*e**9*x**2 + 15680*d**5*e**10*x**3 + 19600*d**4*e**11*x**4 + 15680*d**3*e**12*x**5 + 7840*d**2*e**13*x**6 + 2240*d*e**14*x**7 + 280*e**15*x**8)","A",0
487,1,313,0,37.182982," ","integrate((c*x**2+a)**3/(e*x+d)**10,x)","\frac{- 140 a^{3} e^{6} - 15 a^{2} c d^{2} e^{4} - 6 a c^{2} d^{4} e^{2} - 5 c^{3} d^{6} - 630 c^{3} d e^{5} x^{5} - 420 c^{3} e^{6} x^{6} + x^{4} \left(- 756 a c^{2} e^{6} - 630 c^{3} d^{2} e^{4}\right) + x^{3} \left(- 504 a c^{2} d e^{5} - 420 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 540 a^{2} c e^{6} - 216 a c^{2} d^{2} e^{4} - 180 c^{3} d^{4} e^{2}\right) + x \left(- 135 a^{2} c d e^{5} - 54 a c^{2} d^{3} e^{3} - 45 c^{3} d^{5} e\right)}{1260 d^{9} e^{7} + 11340 d^{8} e^{8} x + 45360 d^{7} e^{9} x^{2} + 105840 d^{6} e^{10} x^{3} + 158760 d^{5} e^{11} x^{4} + 158760 d^{4} e^{12} x^{5} + 105840 d^{3} e^{13} x^{6} + 45360 d^{2} e^{14} x^{7} + 11340 d e^{15} x^{8} + 1260 e^{16} x^{9}}"," ",0,"(-140*a**3*e**6 - 15*a**2*c*d**2*e**4 - 6*a*c**2*d**4*e**2 - 5*c**3*d**6 - 630*c**3*d*e**5*x**5 - 420*c**3*e**6*x**6 + x**4*(-756*a*c**2*e**6 - 630*c**3*d**2*e**4) + x**3*(-504*a*c**2*d*e**5 - 420*c**3*d**3*e**3) + x**2*(-540*a**2*c*e**6 - 216*a*c**2*d**2*e**4 - 180*c**3*d**4*e**2) + x*(-135*a**2*c*d*e**5 - 54*a*c**2*d**3*e**3 - 45*c**3*d**5*e))/(1260*d**9*e**7 + 11340*d**8*e**8*x + 45360*d**7*e**9*x**2 + 105840*d**6*e**10*x**3 + 158760*d**5*e**11*x**4 + 158760*d**4*e**12*x**5 + 105840*d**3*e**13*x**6 + 45360*d**2*e**14*x**7 + 11340*d*e**15*x**8 + 1260*e**16*x**9)","A",0
488,1,571,0,0.155459," ","integrate((e*x+d)**7*(c*x**2+a)**4,x)","a^{4} d^{7} x + \frac{7 a^{4} d^{6} e x^{2}}{2} + \frac{7 c^{4} d e^{6} x^{15}}{15} + \frac{c^{4} e^{7} x^{16}}{16} + x^{14} \left(\frac{2 a c^{3} e^{7}}{7} + \frac{3 c^{4} d^{2} e^{5}}{2}\right) + x^{13} \left(\frac{28 a c^{3} d e^{6}}{13} + \frac{35 c^{4} d^{3} e^{4}}{13}\right) + x^{12} \left(\frac{a^{2} c^{2} e^{7}}{2} + 7 a c^{3} d^{2} e^{5} + \frac{35 c^{4} d^{4} e^{3}}{12}\right) + x^{11} \left(\frac{42 a^{2} c^{2} d e^{6}}{11} + \frac{140 a c^{3} d^{3} e^{4}}{11} + \frac{21 c^{4} d^{5} e^{2}}{11}\right) + x^{10} \left(\frac{2 a^{3} c e^{7}}{5} + \frac{63 a^{2} c^{2} d^{2} e^{5}}{5} + 14 a c^{3} d^{4} e^{3} + \frac{7 c^{4} d^{6} e}{10}\right) + x^{9} \left(\frac{28 a^{3} c d e^{6}}{9} + \frac{70 a^{2} c^{2} d^{3} e^{4}}{3} + \frac{28 a c^{3} d^{5} e^{2}}{3} + \frac{c^{4} d^{7}}{9}\right) + x^{8} \left(\frac{a^{4} e^{7}}{8} + \frac{21 a^{3} c d^{2} e^{5}}{2} + \frac{105 a^{2} c^{2} d^{4} e^{3}}{4} + \frac{7 a c^{3} d^{6} e}{2}\right) + x^{7} \left(a^{4} d e^{6} + 20 a^{3} c d^{3} e^{4} + 18 a^{2} c^{2} d^{5} e^{2} + \frac{4 a c^{3} d^{7}}{7}\right) + x^{6} \left(\frac{7 a^{4} d^{2} e^{5}}{2} + \frac{70 a^{3} c d^{4} e^{3}}{3} + 7 a^{2} c^{2} d^{6} e\right) + x^{5} \left(7 a^{4} d^{3} e^{4} + \frac{84 a^{3} c d^{5} e^{2}}{5} + \frac{6 a^{2} c^{2} d^{7}}{5}\right) + x^{4} \left(\frac{35 a^{4} d^{4} e^{3}}{4} + 7 a^{3} c d^{6} e\right) + x^{3} \left(7 a^{4} d^{5} e^{2} + \frac{4 a^{3} c d^{7}}{3}\right)"," ",0,"a**4*d**7*x + 7*a**4*d**6*e*x**2/2 + 7*c**4*d*e**6*x**15/15 + c**4*e**7*x**16/16 + x**14*(2*a*c**3*e**7/7 + 3*c**4*d**2*e**5/2) + x**13*(28*a*c**3*d*e**6/13 + 35*c**4*d**3*e**4/13) + x**12*(a**2*c**2*e**7/2 + 7*a*c**3*d**2*e**5 + 35*c**4*d**4*e**3/12) + x**11*(42*a**2*c**2*d*e**6/11 + 140*a*c**3*d**3*e**4/11 + 21*c**4*d**5*e**2/11) + x**10*(2*a**3*c*e**7/5 + 63*a**2*c**2*d**2*e**5/5 + 14*a*c**3*d**4*e**3 + 7*c**4*d**6*e/10) + x**9*(28*a**3*c*d*e**6/9 + 70*a**2*c**2*d**3*e**4/3 + 28*a*c**3*d**5*e**2/3 + c**4*d**7/9) + x**8*(a**4*e**7/8 + 21*a**3*c*d**2*e**5/2 + 105*a**2*c**2*d**4*e**3/4 + 7*a*c**3*d**6*e/2) + x**7*(a**4*d*e**6 + 20*a**3*c*d**3*e**4 + 18*a**2*c**2*d**5*e**2 + 4*a*c**3*d**7/7) + x**6*(7*a**4*d**2*e**5/2 + 70*a**3*c*d**4*e**3/3 + 7*a**2*c**2*d**6*e) + x**5*(7*a**4*d**3*e**4 + 84*a**3*c*d**5*e**2/5 + 6*a**2*c**2*d**7/5) + x**4*(35*a**4*d**4*e**3/4 + 7*a**3*c*d**6*e) + x**3*(7*a**4*d**5*e**2 + 4*a**3*c*d**7/3)","B",0
489,1,486,0,0.144378," ","integrate((e*x+d)**6*(c*x**2+a)**4,x)","a^{4} d^{6} x + 3 a^{4} d^{5} e x^{2} + \frac{3 c^{4} d e^{5} x^{14}}{7} + \frac{c^{4} e^{6} x^{15}}{15} + x^{13} \left(\frac{4 a c^{3} e^{6}}{13} + \frac{15 c^{4} d^{2} e^{4}}{13}\right) + x^{12} \left(2 a c^{3} d e^{5} + \frac{5 c^{4} d^{3} e^{3}}{3}\right) + x^{11} \left(\frac{6 a^{2} c^{2} e^{6}}{11} + \frac{60 a c^{3} d^{2} e^{4}}{11} + \frac{15 c^{4} d^{4} e^{2}}{11}\right) + x^{10} \left(\frac{18 a^{2} c^{2} d e^{5}}{5} + 8 a c^{3} d^{3} e^{3} + \frac{3 c^{4} d^{5} e}{5}\right) + x^{9} \left(\frac{4 a^{3} c e^{6}}{9} + 10 a^{2} c^{2} d^{2} e^{4} + \frac{20 a c^{3} d^{4} e^{2}}{3} + \frac{c^{4} d^{6}}{9}\right) + x^{8} \left(3 a^{3} c d e^{5} + 15 a^{2} c^{2} d^{3} e^{3} + 3 a c^{3} d^{5} e\right) + x^{7} \left(\frac{a^{4} e^{6}}{7} + \frac{60 a^{3} c d^{2} e^{4}}{7} + \frac{90 a^{2} c^{2} d^{4} e^{2}}{7} + \frac{4 a c^{3} d^{6}}{7}\right) + x^{6} \left(a^{4} d e^{5} + \frac{40 a^{3} c d^{3} e^{3}}{3} + 6 a^{2} c^{2} d^{5} e\right) + x^{5} \left(3 a^{4} d^{2} e^{4} + 12 a^{3} c d^{4} e^{2} + \frac{6 a^{2} c^{2} d^{6}}{5}\right) + x^{4} \left(5 a^{4} d^{3} e^{3} + 6 a^{3} c d^{5} e\right) + x^{3} \left(5 a^{4} d^{4} e^{2} + \frac{4 a^{3} c d^{6}}{3}\right)"," ",0,"a**4*d**6*x + 3*a**4*d**5*e*x**2 + 3*c**4*d*e**5*x**14/7 + c**4*e**6*x**15/15 + x**13*(4*a*c**3*e**6/13 + 15*c**4*d**2*e**4/13) + x**12*(2*a*c**3*d*e**5 + 5*c**4*d**3*e**3/3) + x**11*(6*a**2*c**2*e**6/11 + 60*a*c**3*d**2*e**4/11 + 15*c**4*d**4*e**2/11) + x**10*(18*a**2*c**2*d*e**5/5 + 8*a*c**3*d**3*e**3 + 3*c**4*d**5*e/5) + x**9*(4*a**3*c*e**6/9 + 10*a**2*c**2*d**2*e**4 + 20*a*c**3*d**4*e**2/3 + c**4*d**6/9) + x**8*(3*a**3*c*d*e**5 + 15*a**2*c**2*d**3*e**3 + 3*a*c**3*d**5*e) + x**7*(a**4*e**6/7 + 60*a**3*c*d**2*e**4/7 + 90*a**2*c**2*d**4*e**2/7 + 4*a*c**3*d**6/7) + x**6*(a**4*d*e**5 + 40*a**3*c*d**3*e**3/3 + 6*a**2*c**2*d**5*e) + x**5*(3*a**4*d**2*e**4 + 12*a**3*c*d**4*e**2 + 6*a**2*c**2*d**6/5) + x**4*(5*a**4*d**3*e**3 + 6*a**3*c*d**5*e) + x**3*(5*a**4*d**4*e**2 + 4*a**3*c*d**6/3)","A",0
490,1,418,0,0.136690," ","integrate((e*x+d)**5*(c*x**2+a)**4,x)","a^{4} d^{5} x + \frac{5 a^{4} d^{4} e x^{2}}{2} + \frac{5 c^{4} d e^{4} x^{13}}{13} + \frac{c^{4} e^{5} x^{14}}{14} + x^{12} \left(\frac{a c^{3} e^{5}}{3} + \frac{5 c^{4} d^{2} e^{3}}{6}\right) + x^{11} \left(\frac{20 a c^{3} d e^{4}}{11} + \frac{10 c^{4} d^{3} e^{2}}{11}\right) + x^{10} \left(\frac{3 a^{2} c^{2} e^{5}}{5} + 4 a c^{3} d^{2} e^{3} + \frac{c^{4} d^{4} e}{2}\right) + x^{9} \left(\frac{10 a^{2} c^{2} d e^{4}}{3} + \frac{40 a c^{3} d^{3} e^{2}}{9} + \frac{c^{4} d^{5}}{9}\right) + x^{8} \left(\frac{a^{3} c e^{5}}{2} + \frac{15 a^{2} c^{2} d^{2} e^{3}}{2} + \frac{5 a c^{3} d^{4} e}{2}\right) + x^{7} \left(\frac{20 a^{3} c d e^{4}}{7} + \frac{60 a^{2} c^{2} d^{3} e^{2}}{7} + \frac{4 a c^{3} d^{5}}{7}\right) + x^{6} \left(\frac{a^{4} e^{5}}{6} + \frac{20 a^{3} c d^{2} e^{3}}{3} + 5 a^{2} c^{2} d^{4} e\right) + x^{5} \left(a^{4} d e^{4} + 8 a^{3} c d^{3} e^{2} + \frac{6 a^{2} c^{2} d^{5}}{5}\right) + x^{4} \left(\frac{5 a^{4} d^{2} e^{3}}{2} + 5 a^{3} c d^{4} e\right) + x^{3} \left(\frac{10 a^{4} d^{3} e^{2}}{3} + \frac{4 a^{3} c d^{5}}{3}\right)"," ",0,"a**4*d**5*x + 5*a**4*d**4*e*x**2/2 + 5*c**4*d*e**4*x**13/13 + c**4*e**5*x**14/14 + x**12*(a*c**3*e**5/3 + 5*c**4*d**2*e**3/6) + x**11*(20*a*c**3*d*e**4/11 + 10*c**4*d**3*e**2/11) + x**10*(3*a**2*c**2*e**5/5 + 4*a*c**3*d**2*e**3 + c**4*d**4*e/2) + x**9*(10*a**2*c**2*d*e**4/3 + 40*a*c**3*d**3*e**2/9 + c**4*d**5/9) + x**8*(a**3*c*e**5/2 + 15*a**2*c**2*d**2*e**3/2 + 5*a*c**3*d**4*e/2) + x**7*(20*a**3*c*d*e**4/7 + 60*a**2*c**2*d**3*e**2/7 + 4*a*c**3*d**5/7) + x**6*(a**4*e**5/6 + 20*a**3*c*d**2*e**3/3 + 5*a**2*c**2*d**4*e) + x**5*(a**4*d*e**4 + 8*a**3*c*d**3*e**2 + 6*a**2*c**2*d**5/5) + x**4*(5*a**4*d**2*e**3/2 + 5*a**3*c*d**4*e) + x**3*(10*a**4*d**3*e**2/3 + 4*a**3*c*d**5/3)","A",0
491,1,340,0,0.125423," ","integrate((e*x+d)**4*(c*x**2+a)**4,x)","a^{4} d^{4} x + 2 a^{4} d^{3} e x^{2} + \frac{c^{4} d e^{3} x^{12}}{3} + \frac{c^{4} e^{4} x^{13}}{13} + x^{11} \left(\frac{4 a c^{3} e^{4}}{11} + \frac{6 c^{4} d^{2} e^{2}}{11}\right) + x^{10} \left(\frac{8 a c^{3} d e^{3}}{5} + \frac{2 c^{4} d^{3} e}{5}\right) + x^{9} \left(\frac{2 a^{2} c^{2} e^{4}}{3} + \frac{8 a c^{3} d^{2} e^{2}}{3} + \frac{c^{4} d^{4}}{9}\right) + x^{8} \left(3 a^{2} c^{2} d e^{3} + 2 a c^{3} d^{3} e\right) + x^{7} \left(\frac{4 a^{3} c e^{4}}{7} + \frac{36 a^{2} c^{2} d^{2} e^{2}}{7} + \frac{4 a c^{3} d^{4}}{7}\right) + x^{6} \left(\frac{8 a^{3} c d e^{3}}{3} + 4 a^{2} c^{2} d^{3} e\right) + x^{5} \left(\frac{a^{4} e^{4}}{5} + \frac{24 a^{3} c d^{2} e^{2}}{5} + \frac{6 a^{2} c^{2} d^{4}}{5}\right) + x^{4} \left(a^{4} d e^{3} + 4 a^{3} c d^{3} e\right) + x^{3} \left(2 a^{4} d^{2} e^{2} + \frac{4 a^{3} c d^{4}}{3}\right)"," ",0,"a**4*d**4*x + 2*a**4*d**3*e*x**2 + c**4*d*e**3*x**12/3 + c**4*e**4*x**13/13 + x**11*(4*a*c**3*e**4/11 + 6*c**4*d**2*e**2/11) + x**10*(8*a*c**3*d*e**3/5 + 2*c**4*d**3*e/5) + x**9*(2*a**2*c**2*e**4/3 + 8*a*c**3*d**2*e**2/3 + c**4*d**4/9) + x**8*(3*a**2*c**2*d*e**3 + 2*a*c**3*d**3*e) + x**7*(4*a**3*c*e**4/7 + 36*a**2*c**2*d**2*e**2/7 + 4*a*c**3*d**4/7) + x**6*(8*a**3*c*d*e**3/3 + 4*a**2*c**2*d**3*e) + x**5*(a**4*e**4/5 + 24*a**3*c*d**2*e**2/5 + 6*a**2*c**2*d**4/5) + x**4*(a**4*d*e**3 + 4*a**3*c*d**3*e) + x**3*(2*a**4*d**2*e**2 + 4*a**3*c*d**4/3)","A",0
492,1,270,0,0.115875," ","integrate((e*x+d)**3*(c*x**2+a)**4,x)","a^{4} d^{3} x + \frac{3 a^{4} d^{2} e x^{2}}{2} + \frac{3 c^{4} d e^{2} x^{11}}{11} + \frac{c^{4} e^{3} x^{12}}{12} + x^{10} \left(\frac{2 a c^{3} e^{3}}{5} + \frac{3 c^{4} d^{2} e}{10}\right) + x^{9} \left(\frac{4 a c^{3} d e^{2}}{3} + \frac{c^{4} d^{3}}{9}\right) + x^{8} \left(\frac{3 a^{2} c^{2} e^{3}}{4} + \frac{3 a c^{3} d^{2} e}{2}\right) + x^{7} \left(\frac{18 a^{2} c^{2} d e^{2}}{7} + \frac{4 a c^{3} d^{3}}{7}\right) + x^{6} \left(\frac{2 a^{3} c e^{3}}{3} + 3 a^{2} c^{2} d^{2} e\right) + x^{5} \left(\frac{12 a^{3} c d e^{2}}{5} + \frac{6 a^{2} c^{2} d^{3}}{5}\right) + x^{4} \left(\frac{a^{4} e^{3}}{4} + 3 a^{3} c d^{2} e\right) + x^{3} \left(a^{4} d e^{2} + \frac{4 a^{3} c d^{3}}{3}\right)"," ",0,"a**4*d**3*x + 3*a**4*d**2*e*x**2/2 + 3*c**4*d*e**2*x**11/11 + c**4*e**3*x**12/12 + x**10*(2*a*c**3*e**3/5 + 3*c**4*d**2*e/10) + x**9*(4*a*c**3*d*e**2/3 + c**4*d**3/9) + x**8*(3*a**2*c**2*e**3/4 + 3*a*c**3*d**2*e/2) + x**7*(18*a**2*c**2*d*e**2/7 + 4*a*c**3*d**3/7) + x**6*(2*a**3*c*e**3/3 + 3*a**2*c**2*d**2*e) + x**5*(12*a**3*c*d*e**2/5 + 6*a**2*c**2*d**3/5) + x**4*(a**4*e**3/4 + 3*a**3*c*d**2*e) + x**3*(a**4*d*e**2 + 4*a**3*c*d**3/3)","A",0
493,1,187,0,0.101083," ","integrate((e*x+d)**2*(c*x**2+a)**4,x)","a^{4} d^{2} x + a^{4} d e x^{2} + 2 a^{3} c d e x^{4} + 2 a^{2} c^{2} d e x^{6} + a c^{3} d e x^{8} + \frac{c^{4} d e x^{10}}{5} + \frac{c^{4} e^{2} x^{11}}{11} + x^{9} \left(\frac{4 a c^{3} e^{2}}{9} + \frac{c^{4} d^{2}}{9}\right) + x^{7} \left(\frac{6 a^{2} c^{2} e^{2}}{7} + \frac{4 a c^{3} d^{2}}{7}\right) + x^{5} \left(\frac{4 a^{3} c e^{2}}{5} + \frac{6 a^{2} c^{2} d^{2}}{5}\right) + x^{3} \left(\frac{a^{4} e^{2}}{3} + \frac{4 a^{3} c d^{2}}{3}\right)"," ",0,"a**4*d**2*x + a**4*d*e*x**2 + 2*a**3*c*d*e*x**4 + 2*a**2*c**2*d*e*x**6 + a*c**3*d*e*x**8 + c**4*d*e*x**10/5 + c**4*e**2*x**11/11 + x**9*(4*a*c**3*e**2/9 + c**4*d**2/9) + x**7*(6*a**2*c**2*e**2/7 + 4*a*c**3*d**2/7) + x**5*(4*a**3*c*e**2/5 + 6*a**2*c**2*d**2/5) + x**3*(a**4*e**2/3 + 4*a**3*c*d**2/3)","A",0
494,1,112,0,0.088116," ","integrate((e*x+d)*(c*x**2+a)**4,x)","a^{4} d x + \frac{a^{4} e x^{2}}{2} + \frac{4 a^{3} c d x^{3}}{3} + a^{3} c e x^{4} + \frac{6 a^{2} c^{2} d x^{5}}{5} + a^{2} c^{2} e x^{6} + \frac{4 a c^{3} d x^{7}}{7} + \frac{a c^{3} e x^{8}}{2} + \frac{c^{4} d x^{9}}{9} + \frac{c^{4} e x^{10}}{10}"," ",0,"a**4*d*x + a**4*e*x**2/2 + 4*a**3*c*d*x**3/3 + a**3*c*e*x**4 + 6*a**2*c**2*d*x**5/5 + a**2*c**2*e*x**6 + 4*a*c**3*d*x**7/7 + a*c**3*e*x**8/2 + c**4*d*x**9/9 + c**4*e*x**10/10","A",0
495,1,292,0,0.572087," ","integrate((c*x**2+a)**4/(e*x+d),x)","- \frac{c^{4} d x^{7}}{7 e^{2}} + \frac{c^{4} x^{8}}{8 e} + x^{6} \left(\frac{2 a c^{3}}{3 e} + \frac{c^{4} d^{2}}{6 e^{3}}\right) + x^{5} \left(- \frac{4 a c^{3} d}{5 e^{2}} - \frac{c^{4} d^{3}}{5 e^{4}}\right) + x^{4} \left(\frac{3 a^{2} c^{2}}{2 e} + \frac{a c^{3} d^{2}}{e^{3}} + \frac{c^{4} d^{4}}{4 e^{5}}\right) + x^{3} \left(- \frac{2 a^{2} c^{2} d}{e^{2}} - \frac{4 a c^{3} d^{3}}{3 e^{4}} - \frac{c^{4} d^{5}}{3 e^{6}}\right) + x^{2} \left(\frac{2 a^{3} c}{e} + \frac{3 a^{2} c^{2} d^{2}}{e^{3}} + \frac{2 a c^{3} d^{4}}{e^{5}} + \frac{c^{4} d^{6}}{2 e^{7}}\right) + x \left(- \frac{4 a^{3} c d}{e^{2}} - \frac{6 a^{2} c^{2} d^{3}}{e^{4}} - \frac{4 a c^{3} d^{5}}{e^{6}} - \frac{c^{4} d^{7}}{e^{8}}\right) + \frac{\left(a e^{2} + c d^{2}\right)^{4} \log{\left(d + e x \right)}}{e^{9}}"," ",0,"-c**4*d*x**7/(7*e**2) + c**4*x**8/(8*e) + x**6*(2*a*c**3/(3*e) + c**4*d**2/(6*e**3)) + x**5*(-4*a*c**3*d/(5*e**2) - c**4*d**3/(5*e**4)) + x**4*(3*a**2*c**2/(2*e) + a*c**3*d**2/e**3 + c**4*d**4/(4*e**5)) + x**3*(-2*a**2*c**2*d/e**2 - 4*a*c**3*d**3/(3*e**4) - c**4*d**5/(3*e**6)) + x**2*(2*a**3*c/e + 3*a**2*c**2*d**2/e**3 + 2*a*c**3*d**4/e**5 + c**4*d**6/(2*e**7)) + x*(-4*a**3*c*d/e**2 - 6*a**2*c**2*d**3/e**4 - 4*a*c**3*d**5/e**6 - c**4*d**7/e**8) + (a*e**2 + c*d**2)**4*log(d + e*x)/e**9","A",0
496,1,314,0,1.015515," ","integrate((c*x**2+a)**4/(e*x+d)**2,x)","- \frac{c^{4} d x^{6}}{3 e^{3}} + \frac{c^{4} x^{7}}{7 e^{2}} - \frac{8 c d \left(a e^{2} + c d^{2}\right)^{3} \log{\left(d + e x \right)}}{e^{9}} + x^{5} \left(\frac{4 a c^{3}}{5 e^{2}} + \frac{3 c^{4} d^{2}}{5 e^{4}}\right) + x^{4} \left(- \frac{2 a c^{3} d}{e^{3}} - \frac{c^{4} d^{3}}{e^{5}}\right) + x^{3} \left(\frac{2 a^{2} c^{2}}{e^{2}} + \frac{4 a c^{3} d^{2}}{e^{4}} + \frac{5 c^{4} d^{4}}{3 e^{6}}\right) + x^{2} \left(- \frac{6 a^{2} c^{2} d}{e^{3}} - \frac{8 a c^{3} d^{3}}{e^{5}} - \frac{3 c^{4} d^{5}}{e^{7}}\right) + x \left(\frac{4 a^{3} c}{e^{2}} + \frac{18 a^{2} c^{2} d^{2}}{e^{4}} + \frac{20 a c^{3} d^{4}}{e^{6}} + \frac{7 c^{4} d^{6}}{e^{8}}\right) + \frac{- a^{4} e^{8} - 4 a^{3} c d^{2} e^{6} - 6 a^{2} c^{2} d^{4} e^{4} - 4 a c^{3} d^{6} e^{2} - c^{4} d^{8}}{d e^{9} + e^{10} x}"," ",0,"-c**4*d*x**6/(3*e**3) + c**4*x**7/(7*e**2) - 8*c*d*(a*e**2 + c*d**2)**3*log(d + e*x)/e**9 + x**5*(4*a*c**3/(5*e**2) + 3*c**4*d**2/(5*e**4)) + x**4*(-2*a*c**3*d/e**3 - c**4*d**3/e**5) + x**3*(2*a**2*c**2/e**2 + 4*a*c**3*d**2/e**4 + 5*c**4*d**4/(3*e**6)) + x**2*(-6*a**2*c**2*d/e**3 - 8*a*c**3*d**3/e**5 - 3*c**4*d**5/e**7) + x*(4*a**3*c/e**2 + 18*a**2*c**2*d**2/e**4 + 20*a*c**3*d**4/e**6 + 7*c**4*d**6/e**8) + (-a**4*e**8 - 4*a**3*c*d**2*e**6 - 6*a**2*c**2*d**4*e**4 - 4*a*c**3*d**6*e**2 - c**4*d**8)/(d*e**9 + e**10*x)","A",0
497,1,112,0,0.085155," ","integrate((d*x+c)*(b*x**2+a)**4,x)","a^{4} c x + \frac{a^{4} d x^{2}}{2} + \frac{4 a^{3} b c x^{3}}{3} + a^{3} b d x^{4} + \frac{6 a^{2} b^{2} c x^{5}}{5} + a^{2} b^{2} d x^{6} + \frac{4 a b^{3} c x^{7}}{7} + \frac{a b^{3} d x^{8}}{2} + \frac{b^{4} c x^{9}}{9} + \frac{b^{4} d x^{10}}{10}"," ",0,"a**4*c*x + a**4*d*x**2/2 + 4*a**3*b*c*x**3/3 + a**3*b*d*x**4 + 6*a**2*b**2*c*x**5/5 + a**2*b**2*d*x**6 + 4*a*b**3*c*x**7/7 + a*b**3*d*x**8/2 + b**4*c*x**9/9 + b**4*d*x**10/10","A",0
498,1,401,0,1.009589," ","integrate((e*x+d)**4/(c*x**2+a),x)","x \left(- \frac{a e^{4}}{c^{2}} + \frac{6 d^{2} e^{2}}{c}\right) + \left(- \frac{2 d e \left(a e^{2} - c d^{2}\right)}{c^{2}} - \frac{\sqrt{- a c^{5}} \left(a^{2} e^{4} - 6 a c d^{2} e^{2} + c^{2} d^{4}\right)}{2 a c^{5}}\right) \log{\left(x + \frac{4 a^{2} d e^{3} + 2 a c^{2} \left(- \frac{2 d e \left(a e^{2} - c d^{2}\right)}{c^{2}} - \frac{\sqrt{- a c^{5}} \left(a^{2} e^{4} - 6 a c d^{2} e^{2} + c^{2} d^{4}\right)}{2 a c^{5}}\right) - 4 a c d^{3} e}{a^{2} e^{4} - 6 a c d^{2} e^{2} + c^{2} d^{4}} \right)} + \left(- \frac{2 d e \left(a e^{2} - c d^{2}\right)}{c^{2}} + \frac{\sqrt{- a c^{5}} \left(a^{2} e^{4} - 6 a c d^{2} e^{2} + c^{2} d^{4}\right)}{2 a c^{5}}\right) \log{\left(x + \frac{4 a^{2} d e^{3} + 2 a c^{2} \left(- \frac{2 d e \left(a e^{2} - c d^{2}\right)}{c^{2}} + \frac{\sqrt{- a c^{5}} \left(a^{2} e^{4} - 6 a c d^{2} e^{2} + c^{2} d^{4}\right)}{2 a c^{5}}\right) - 4 a c d^{3} e}{a^{2} e^{4} - 6 a c d^{2} e^{2} + c^{2} d^{4}} \right)} + \frac{2 d e^{3} x^{2}}{c} + \frac{e^{4} x^{3}}{3 c}"," ",0,"x*(-a*e**4/c**2 + 6*d**2*e**2/c) + (-2*d*e*(a*e**2 - c*d**2)/c**2 - sqrt(-a*c**5)*(a**2*e**4 - 6*a*c*d**2*e**2 + c**2*d**4)/(2*a*c**5))*log(x + (4*a**2*d*e**3 + 2*a*c**2*(-2*d*e*(a*e**2 - c*d**2)/c**2 - sqrt(-a*c**5)*(a**2*e**4 - 6*a*c*d**2*e**2 + c**2*d**4)/(2*a*c**5)) - 4*a*c*d**3*e)/(a**2*e**4 - 6*a*c*d**2*e**2 + c**2*d**4)) + (-2*d*e*(a*e**2 - c*d**2)/c**2 + sqrt(-a*c**5)*(a**2*e**4 - 6*a*c*d**2*e**2 + c**2*d**4)/(2*a*c**5))*log(x + (4*a**2*d*e**3 + 2*a*c**2*(-2*d*e*(a*e**2 - c*d**2)/c**2 + sqrt(-a*c**5)*(a**2*e**4 - 6*a*c*d**2*e**2 + c**2*d**4)/(2*a*c**5)) - 4*a*c*d**3*e)/(a**2*e**4 - 6*a*c*d**2*e**2 + c**2*d**4)) + 2*d*e**3*x**2/c + e**4*x**3/(3*c)","B",0
499,1,308,0,0.802393," ","integrate((e*x+d)**3/(c*x**2+a),x)","\left(- \frac{e \left(a e^{2} - 3 c d^{2}\right)}{2 c^{2}} - \frac{d \sqrt{- a c^{5}} \left(3 a e^{2} - c d^{2}\right)}{2 a c^{4}}\right) \log{\left(x + \frac{- a^{2} e^{3} - 2 a c^{2} \left(- \frac{e \left(a e^{2} - 3 c d^{2}\right)}{2 c^{2}} - \frac{d \sqrt{- a c^{5}} \left(3 a e^{2} - c d^{2}\right)}{2 a c^{4}}\right) + 3 a c d^{2} e}{3 a c d e^{2} - c^{2} d^{3}} \right)} + \left(- \frac{e \left(a e^{2} - 3 c d^{2}\right)}{2 c^{2}} + \frac{d \sqrt{- a c^{5}} \left(3 a e^{2} - c d^{2}\right)}{2 a c^{4}}\right) \log{\left(x + \frac{- a^{2} e^{3} - 2 a c^{2} \left(- \frac{e \left(a e^{2} - 3 c d^{2}\right)}{2 c^{2}} + \frac{d \sqrt{- a c^{5}} \left(3 a e^{2} - c d^{2}\right)}{2 a c^{4}}\right) + 3 a c d^{2} e}{3 a c d e^{2} - c^{2} d^{3}} \right)} + \frac{3 d e^{2} x}{c} + \frac{e^{3} x^{2}}{2 c}"," ",0,"(-e*(a*e**2 - 3*c*d**2)/(2*c**2) - d*sqrt(-a*c**5)*(3*a*e**2 - c*d**2)/(2*a*c**4))*log(x + (-a**2*e**3 - 2*a*c**2*(-e*(a*e**2 - 3*c*d**2)/(2*c**2) - d*sqrt(-a*c**5)*(3*a*e**2 - c*d**2)/(2*a*c**4)) + 3*a*c*d**2*e)/(3*a*c*d*e**2 - c**2*d**3)) + (-e*(a*e**2 - 3*c*d**2)/(2*c**2) + d*sqrt(-a*c**5)*(3*a*e**2 - c*d**2)/(2*a*c**4))*log(x + (-a**2*e**3 - 2*a*c**2*(-e*(a*e**2 - 3*c*d**2)/(2*c**2) + d*sqrt(-a*c**5)*(3*a*e**2 - c*d**2)/(2*a*c**4)) + 3*a*c*d**2*e)/(3*a*c*d*e**2 - c**2*d**3)) + 3*d*e**2*x/c + e**3*x**2/(2*c)","B",0
500,1,185,0,0.479380," ","integrate((e*x+d)**2/(c*x**2+a),x)","\left(\frac{d e}{c} - \frac{\sqrt{- a c^{3}} \left(a e^{2} - c d^{2}\right)}{2 a c^{3}}\right) \log{\left(x + \frac{- 2 a c \left(\frac{d e}{c} - \frac{\sqrt{- a c^{3}} \left(a e^{2} - c d^{2}\right)}{2 a c^{3}}\right) + 2 a d e}{a e^{2} - c d^{2}} \right)} + \left(\frac{d e}{c} + \frac{\sqrt{- a c^{3}} \left(a e^{2} - c d^{2}\right)}{2 a c^{3}}\right) \log{\left(x + \frac{- 2 a c \left(\frac{d e}{c} + \frac{\sqrt{- a c^{3}} \left(a e^{2} - c d^{2}\right)}{2 a c^{3}}\right) + 2 a d e}{a e^{2} - c d^{2}} \right)} + \frac{e^{2} x}{c}"," ",0,"(d*e/c - sqrt(-a*c**3)*(a*e**2 - c*d**2)/(2*a*c**3))*log(x + (-2*a*c*(d*e/c - sqrt(-a*c**3)*(a*e**2 - c*d**2)/(2*a*c**3)) + 2*a*d*e)/(a*e**2 - c*d**2)) + (d*e/c + sqrt(-a*c**3)*(a*e**2 - c*d**2)/(2*a*c**3))*log(x + (-2*a*c*(d*e/c + sqrt(-a*c**3)*(a*e**2 - c*d**2)/(2*a*c**3)) + 2*a*d*e)/(a*e**2 - c*d**2)) + e**2*x/c","B",0
501,1,124,0,0.267043," ","integrate((e*x+d)/(c*x**2+a),x)","\left(\frac{e}{2 c} - \frac{d \sqrt{- a c^{3}}}{2 a c^{2}}\right) \log{\left(x + \frac{2 a c \left(\frac{e}{2 c} - \frac{d \sqrt{- a c^{3}}}{2 a c^{2}}\right) - a e}{c d} \right)} + \left(\frac{e}{2 c} + \frac{d \sqrt{- a c^{3}}}{2 a c^{2}}\right) \log{\left(x + \frac{2 a c \left(\frac{e}{2 c} + \frac{d \sqrt{- a c^{3}}}{2 a c^{2}}\right) - a e}{c d} \right)}"," ",0,"(e/(2*c) - d*sqrt(-a*c**3)/(2*a*c**2))*log(x + (2*a*c*(e/(2*c) - d*sqrt(-a*c**3)/(2*a*c**2)) - a*e)/(c*d)) + (e/(2*c) + d*sqrt(-a*c**3)/(2*a*c**2))*log(x + (2*a*c*(e/(2*c) + d*sqrt(-a*c**3)/(2*a*c**2)) - a*e)/(c*d))","B",0
502,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,1,515,0,2.158192," ","integrate((e*x+d)**5/(c*x**2+a)**2,x)","\left(- \frac{e^{3} \left(a e^{2} - 5 c d^{2}\right)}{c^{3}} - \frac{d \sqrt{- a^{3} c^{7}} \left(15 a^{2} e^{4} - 10 a c d^{2} e^{2} - c^{2} d^{4}\right)}{4 a^{3} c^{6}}\right) \log{\left(x + \frac{- 4 a^{3} e^{5} - 4 a^{2} c^{3} \left(- \frac{e^{3} \left(a e^{2} - 5 c d^{2}\right)}{c^{3}} - \frac{d \sqrt{- a^{3} c^{7}} \left(15 a^{2} e^{4} - 10 a c d^{2} e^{2} - c^{2} d^{4}\right)}{4 a^{3} c^{6}}\right) + 20 a^{2} c d^{2} e^{3}}{15 a^{2} c d e^{4} - 10 a c^{2} d^{3} e^{2} - c^{3} d^{5}} \right)} + \left(- \frac{e^{3} \left(a e^{2} - 5 c d^{2}\right)}{c^{3}} + \frac{d \sqrt{- a^{3} c^{7}} \left(15 a^{2} e^{4} - 10 a c d^{2} e^{2} - c^{2} d^{4}\right)}{4 a^{3} c^{6}}\right) \log{\left(x + \frac{- 4 a^{3} e^{5} - 4 a^{2} c^{3} \left(- \frac{e^{3} \left(a e^{2} - 5 c d^{2}\right)}{c^{3}} + \frac{d \sqrt{- a^{3} c^{7}} \left(15 a^{2} e^{4} - 10 a c d^{2} e^{2} - c^{2} d^{4}\right)}{4 a^{3} c^{6}}\right) + 20 a^{2} c d^{2} e^{3}}{15 a^{2} c d e^{4} - 10 a c^{2} d^{3} e^{2} - c^{3} d^{5}} \right)} + \frac{- a^{3} e^{5} + 10 a^{2} c d^{2} e^{3} - 5 a c^{2} d^{4} e + x \left(5 a^{2} c d e^{4} - 10 a c^{2} d^{3} e^{2} + c^{3} d^{5}\right)}{2 a^{2} c^{3} + 2 a c^{4} x^{2}} + \frac{5 d e^{4} x}{c^{2}} + \frac{e^{5} x^{2}}{2 c^{2}}"," ",0,"(-e**3*(a*e**2 - 5*c*d**2)/c**3 - d*sqrt(-a**3*c**7)*(15*a**2*e**4 - 10*a*c*d**2*e**2 - c**2*d**4)/(4*a**3*c**6))*log(x + (-4*a**3*e**5 - 4*a**2*c**3*(-e**3*(a*e**2 - 5*c*d**2)/c**3 - d*sqrt(-a**3*c**7)*(15*a**2*e**4 - 10*a*c*d**2*e**2 - c**2*d**4)/(4*a**3*c**6)) + 20*a**2*c*d**2*e**3)/(15*a**2*c*d*e**4 - 10*a*c**2*d**3*e**2 - c**3*d**5)) + (-e**3*(a*e**2 - 5*c*d**2)/c**3 + d*sqrt(-a**3*c**7)*(15*a**2*e**4 - 10*a*c*d**2*e**2 - c**2*d**4)/(4*a**3*c**6))*log(x + (-4*a**3*e**5 - 4*a**2*c**3*(-e**3*(a*e**2 - 5*c*d**2)/c**3 + d*sqrt(-a**3*c**7)*(15*a**2*e**4 - 10*a*c*d**2*e**2 - c**2*d**4)/(4*a**3*c**6)) + 20*a**2*c*d**2*e**3)/(15*a**2*c*d*e**4 - 10*a*c**2*d**3*e**2 - c**3*d**5)) + (-a**3*e**5 + 10*a**2*c*d**2*e**3 - 5*a*c**2*d**4*e + x*(5*a**2*c*d*e**4 - 10*a*c**2*d**3*e**2 + c**3*d**5))/(2*a**2*c**3 + 2*a*c**4*x**2) + 5*d*e**4*x/c**2 + e**5*x**2/(2*c**2)","B",0
506,1,403,0,1.401561," ","integrate((e*x+d)**4/(c*x**2+a)**2,x)","\left(\frac{2 d e^{3}}{c^{2}} - \frac{\sqrt{- a^{3} c^{5}} \left(3 a^{2} e^{4} - 6 a c d^{2} e^{2} - c^{2} d^{4}\right)}{4 a^{3} c^{5}}\right) \log{\left(x + \frac{- 4 a^{2} c^{2} \left(\frac{2 d e^{3}}{c^{2}} - \frac{\sqrt{- a^{3} c^{5}} \left(3 a^{2} e^{4} - 6 a c d^{2} e^{2} - c^{2} d^{4}\right)}{4 a^{3} c^{5}}\right) + 8 a^{2} d e^{3}}{3 a^{2} e^{4} - 6 a c d^{2} e^{2} - c^{2} d^{4}} \right)} + \left(\frac{2 d e^{3}}{c^{2}} + \frac{\sqrt{- a^{3} c^{5}} \left(3 a^{2} e^{4} - 6 a c d^{2} e^{2} - c^{2} d^{4}\right)}{4 a^{3} c^{5}}\right) \log{\left(x + \frac{- 4 a^{2} c^{2} \left(\frac{2 d e^{3}}{c^{2}} + \frac{\sqrt{- a^{3} c^{5}} \left(3 a^{2} e^{4} - 6 a c d^{2} e^{2} - c^{2} d^{4}\right)}{4 a^{3} c^{5}}\right) + 8 a^{2} d e^{3}}{3 a^{2} e^{4} - 6 a c d^{2} e^{2} - c^{2} d^{4}} \right)} + \frac{4 a^{2} d e^{3} - 4 a c d^{3} e + x \left(a^{2} e^{4} - 6 a c d^{2} e^{2} + c^{2} d^{4}\right)}{2 a^{2} c^{2} + 2 a c^{3} x^{2}} + \frac{e^{4} x}{c^{2}}"," ",0,"(2*d*e**3/c**2 - sqrt(-a**3*c**5)*(3*a**2*e**4 - 6*a*c*d**2*e**2 - c**2*d**4)/(4*a**3*c**5))*log(x + (-4*a**2*c**2*(2*d*e**3/c**2 - sqrt(-a**3*c**5)*(3*a**2*e**4 - 6*a*c*d**2*e**2 - c**2*d**4)/(4*a**3*c**5)) + 8*a**2*d*e**3)/(3*a**2*e**4 - 6*a*c*d**2*e**2 - c**2*d**4)) + (2*d*e**3/c**2 + sqrt(-a**3*c**5)*(3*a**2*e**4 - 6*a*c*d**2*e**2 - c**2*d**4)/(4*a**3*c**5))*log(x + (-4*a**2*c**2*(2*d*e**3/c**2 + sqrt(-a**3*c**5)*(3*a**2*e**4 - 6*a*c*d**2*e**2 - c**2*d**4)/(4*a**3*c**5)) + 8*a**2*d*e**3)/(3*a**2*e**4 - 6*a*c*d**2*e**2 - c**2*d**4)) + (4*a**2*d*e**3 - 4*a*c*d**3*e + x*(a**2*e**4 - 6*a*c*d**2*e**2 + c**2*d**4))/(2*a**2*c**2 + 2*a*c**3*x**2) + e**4*x/c**2","B",0
507,1,298,0,1.012609," ","integrate((e*x+d)**3/(c*x**2+a)**2,x)","\left(\frac{e^{3}}{2 c^{2}} - \frac{d \sqrt{- a^{3} c^{5}} \left(3 a e^{2} + c d^{2}\right)}{4 a^{3} c^{4}}\right) \log{\left(x + \frac{4 a^{2} c^{2} \left(\frac{e^{3}}{2 c^{2}} - \frac{d \sqrt{- a^{3} c^{5}} \left(3 a e^{2} + c d^{2}\right)}{4 a^{3} c^{4}}\right) - 2 a^{2} e^{3}}{3 a c d e^{2} + c^{2} d^{3}} \right)} + \left(\frac{e^{3}}{2 c^{2}} + \frac{d \sqrt{- a^{3} c^{5}} \left(3 a e^{2} + c d^{2}\right)}{4 a^{3} c^{4}}\right) \log{\left(x + \frac{4 a^{2} c^{2} \left(\frac{e^{3}}{2 c^{2}} + \frac{d \sqrt{- a^{3} c^{5}} \left(3 a e^{2} + c d^{2}\right)}{4 a^{3} c^{4}}\right) - 2 a^{2} e^{3}}{3 a c d e^{2} + c^{2} d^{3}} \right)} + \frac{a^{2} e^{3} - 3 a c d^{2} e + x \left(- 3 a c d e^{2} + c^{2} d^{3}\right)}{2 a^{2} c^{2} + 2 a c^{3} x^{2}}"," ",0,"(e**3/(2*c**2) - d*sqrt(-a**3*c**5)*(3*a*e**2 + c*d**2)/(4*a**3*c**4))*log(x + (4*a**2*c**2*(e**3/(2*c**2) - d*sqrt(-a**3*c**5)*(3*a*e**2 + c*d**2)/(4*a**3*c**4)) - 2*a**2*e**3)/(3*a*c*d*e**2 + c**2*d**3)) + (e**3/(2*c**2) + d*sqrt(-a**3*c**5)*(3*a*e**2 + c*d**2)/(4*a**3*c**4))*log(x + (4*a**2*c**2*(e**3/(2*c**2) + d*sqrt(-a**3*c**5)*(3*a*e**2 + c*d**2)/(4*a**3*c**4)) - 2*a**2*e**3)/(3*a*c*d*e**2 + c**2*d**3)) + (a**2*e**3 - 3*a*c*d**2*e + x*(-3*a*c*d*e**2 + c**2*d**3))/(2*a**2*c**2 + 2*a*c**3*x**2)","B",0
508,1,129,0,0.557188," ","integrate((e*x+d)**2/(c*x**2+a)**2,x)","- \frac{\sqrt{- \frac{1}{a^{3} c^{3}}} \left(a e^{2} + c d^{2}\right) \log{\left(- a^{2} c \sqrt{- \frac{1}{a^{3} c^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} c^{3}}} \left(a e^{2} + c d^{2}\right) \log{\left(a^{2} c \sqrt{- \frac{1}{a^{3} c^{3}}} + x \right)}}{4} + \frac{- 2 a d e + x \left(- a e^{2} + c d^{2}\right)}{2 a^{2} c + 2 a c^{2} x^{2}}"," ",0,"-sqrt(-1/(a**3*c**3))*(a*e**2 + c*d**2)*log(-a**2*c*sqrt(-1/(a**3*c**3)) + x)/4 + sqrt(-1/(a**3*c**3))*(a*e**2 + c*d**2)*log(a**2*c*sqrt(-1/(a**3*c**3)) + x)/4 + (-2*a*d*e + x*(-a*e**2 + c*d**2))/(2*a**2*c + 2*a*c**2*x**2)","B",0
509,1,90,0,0.303846," ","integrate((e*x+d)/(c*x**2+a)**2,x)","d \left(- \frac{\sqrt{- \frac{1}{a^{3} c}} \log{\left(- a^{2} \sqrt{- \frac{1}{a^{3} c}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} c}} \log{\left(a^{2} \sqrt{- \frac{1}{a^{3} c}} + x \right)}}{4}\right) + \frac{- a e + c d x}{2 a^{2} c + 2 a c^{2} x^{2}}"," ",0,"d*(-sqrt(-1/(a**3*c))*log(-a**2*sqrt(-1/(a**3*c)) + x)/4 + sqrt(-1/(a**3*c))*log(a**2*sqrt(-1/(a**3*c)) + x)/4) + (-a*e + c*d*x)/(2*a**2*c + 2*a*c**2*x**2)","A",0
510,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
512,1,520,0,3.536175," ","integrate((e*x+d)**5/(c*x**2+a)**3,x)","\left(\frac{e^{5}}{2 c^{3}} - \frac{d \sqrt{- a^{5} c^{7}} \left(15 a^{2} e^{4} + 10 a c d^{2} e^{2} + 3 c^{2} d^{4}\right)}{16 a^{5} c^{6}}\right) \log{\left(x + \frac{16 a^{3} c^{3} \left(\frac{e^{5}}{2 c^{3}} - \frac{d \sqrt{- a^{5} c^{7}} \left(15 a^{2} e^{4} + 10 a c d^{2} e^{2} + 3 c^{2} d^{4}\right)}{16 a^{5} c^{6}}\right) - 8 a^{3} e^{5}}{15 a^{2} c d e^{4} + 10 a c^{2} d^{3} e^{2} + 3 c^{3} d^{5}} \right)} + \left(\frac{e^{5}}{2 c^{3}} + \frac{d \sqrt{- a^{5} c^{7}} \left(15 a^{2} e^{4} + 10 a c d^{2} e^{2} + 3 c^{2} d^{4}\right)}{16 a^{5} c^{6}}\right) \log{\left(x + \frac{16 a^{3} c^{3} \left(\frac{e^{5}}{2 c^{3}} + \frac{d \sqrt{- a^{5} c^{7}} \left(15 a^{2} e^{4} + 10 a c d^{2} e^{2} + 3 c^{2} d^{4}\right)}{16 a^{5} c^{6}}\right) - 8 a^{3} e^{5}}{15 a^{2} c d e^{4} + 10 a c^{2} d^{3} e^{2} + 3 c^{3} d^{5}} \right)} + \frac{6 a^{4} e^{5} - 20 a^{3} c d^{2} e^{3} - 10 a^{2} c^{2} d^{4} e + x^{3} \left(- 25 a^{2} c^{2} d e^{4} + 10 a c^{3} d^{3} e^{2} + 3 c^{4} d^{5}\right) + x^{2} \left(8 a^{3} c e^{5} - 40 a^{2} c^{2} d^{2} e^{3}\right) + x \left(- 15 a^{3} c d e^{4} - 10 a^{2} c^{2} d^{3} e^{2} + 5 a c^{3} d^{5}\right)}{8 a^{4} c^{3} + 16 a^{3} c^{4} x^{2} + 8 a^{2} c^{5} x^{4}}"," ",0,"(e**5/(2*c**3) - d*sqrt(-a**5*c**7)*(15*a**2*e**4 + 10*a*c*d**2*e**2 + 3*c**2*d**4)/(16*a**5*c**6))*log(x + (16*a**3*c**3*(e**5/(2*c**3) - d*sqrt(-a**5*c**7)*(15*a**2*e**4 + 10*a*c*d**2*e**2 + 3*c**2*d**4)/(16*a**5*c**6)) - 8*a**3*e**5)/(15*a**2*c*d*e**4 + 10*a*c**2*d**3*e**2 + 3*c**3*d**5)) + (e**5/(2*c**3) + d*sqrt(-a**5*c**7)*(15*a**2*e**4 + 10*a*c*d**2*e**2 + 3*c**2*d**4)/(16*a**5*c**6))*log(x + (16*a**3*c**3*(e**5/(2*c**3) + d*sqrt(-a**5*c**7)*(15*a**2*e**4 + 10*a*c*d**2*e**2 + 3*c**2*d**4)/(16*a**5*c**6)) - 8*a**3*e**5)/(15*a**2*c*d*e**4 + 10*a*c**2*d**3*e**2 + 3*c**3*d**5)) + (6*a**4*e**5 - 20*a**3*c*d**2*e**3 - 10*a**2*c**2*d**4*e + x**3*(-25*a**2*c**2*d*e**4 + 10*a*c**3*d**3*e**2 + 3*c**4*d**5) + x**2*(8*a**3*c*e**5 - 40*a**2*c**2*d**2*e**3) + x*(-15*a**3*c*d*e**4 - 10*a**2*c**2*d**3*e**2 + 5*a*c**3*d**5))/(8*a**4*c**3 + 16*a**3*c**4*x**2 + 8*a**2*c**5*x**4)","B",0
513,1,328,0,2.148307," ","integrate((e*x+d)**4/(c*x**2+a)**3,x)","- \frac{3 \sqrt{- \frac{1}{a^{5} c^{5}}} \left(a e^{2} + c d^{2}\right)^{2} \log{\left(- \frac{3 a^{3} c^{2} \sqrt{- \frac{1}{a^{5} c^{5}}} \left(a e^{2} + c d^{2}\right)^{2}}{3 a^{2} e^{4} + 6 a c d^{2} e^{2} + 3 c^{2} d^{4}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{a^{5} c^{5}}} \left(a e^{2} + c d^{2}\right)^{2} \log{\left(\frac{3 a^{3} c^{2} \sqrt{- \frac{1}{a^{5} c^{5}}} \left(a e^{2} + c d^{2}\right)^{2}}{3 a^{2} e^{4} + 6 a c d^{2} e^{2} + 3 c^{2} d^{4}} + x \right)}}{16} + \frac{- 8 a^{3} d e^{3} - 8 a^{2} c d^{3} e - 16 a^{2} c d e^{3} x^{2} + x^{3} \left(- 5 a^{2} c e^{4} + 6 a c^{2} d^{2} e^{2} + 3 c^{3} d^{4}\right) + x \left(- 3 a^{3} e^{4} - 6 a^{2} c d^{2} e^{2} + 5 a c^{2} d^{4}\right)}{8 a^{4} c^{2} + 16 a^{3} c^{3} x^{2} + 8 a^{2} c^{4} x^{4}}"," ",0,"-3*sqrt(-1/(a**5*c**5))*(a*e**2 + c*d**2)**2*log(-3*a**3*c**2*sqrt(-1/(a**5*c**5))*(a*e**2 + c*d**2)**2/(3*a**2*e**4 + 6*a*c*d**2*e**2 + 3*c**2*d**4) + x)/16 + 3*sqrt(-1/(a**5*c**5))*(a*e**2 + c*d**2)**2*log(3*a**3*c**2*sqrt(-1/(a**5*c**5))*(a*e**2 + c*d**2)**2/(3*a**2*e**4 + 6*a*c*d**2*e**2 + 3*c**2*d**4) + x)/16 + (-8*a**3*d*e**3 - 8*a**2*c*d**3*e - 16*a**2*c*d*e**3*x**2 + x**3*(-5*a**2*c*e**4 + 6*a*c**2*d**2*e**2 + 3*c**3*d**4) + x*(-3*a**3*e**4 - 6*a**2*c*d**2*e**2 + 5*a*c**2*d**4))/(8*a**4*c**2 + 16*a**3*c**3*x**2 + 8*a**2*c**4*x**4)","B",0
514,1,272,0,1.271801," ","integrate((e*x+d)**3/(c*x**2+a)**3,x)","- \frac{3 d \sqrt{- \frac{1}{a^{5} c^{3}}} \left(a e^{2} + c d^{2}\right) \log{\left(- \frac{3 a^{3} c d \sqrt{- \frac{1}{a^{5} c^{3}}} \left(a e^{2} + c d^{2}\right)}{3 a d e^{2} + 3 c d^{3}} + x \right)}}{16} + \frac{3 d \sqrt{- \frac{1}{a^{5} c^{3}}} \left(a e^{2} + c d^{2}\right) \log{\left(\frac{3 a^{3} c d \sqrt{- \frac{1}{a^{5} c^{3}}} \left(a e^{2} + c d^{2}\right)}{3 a d e^{2} + 3 c d^{3}} + x \right)}}{16} + \frac{- 2 a^{3} e^{3} - 6 a^{2} c d^{2} e - 4 a^{2} c e^{3} x^{2} + x^{3} \left(3 a c^{2} d e^{2} + 3 c^{3} d^{3}\right) + x \left(- 3 a^{2} c d e^{2} + 5 a c^{2} d^{3}\right)}{8 a^{4} c^{2} + 16 a^{3} c^{3} x^{2} + 8 a^{2} c^{4} x^{4}}"," ",0,"-3*d*sqrt(-1/(a**5*c**3))*(a*e**2 + c*d**2)*log(-3*a**3*c*d*sqrt(-1/(a**5*c**3))*(a*e**2 + c*d**2)/(3*a*d*e**2 + 3*c*d**3) + x)/16 + 3*d*sqrt(-1/(a**5*c**3))*(a*e**2 + c*d**2)*log(3*a**3*c*d*sqrt(-1/(a**5*c**3))*(a*e**2 + c*d**2)/(3*a*d*e**2 + 3*c*d**3) + x)/16 + (-2*a**3*e**3 - 6*a**2*c*d**2*e - 4*a**2*c*e**3*x**2 + x**3*(3*a*c**2*d*e**2 + 3*c**3*d**3) + x*(-3*a**2*c*d*e**2 + 5*a*c**2*d**3))/(8*a**4*c**2 + 16*a**3*c**3*x**2 + 8*a**2*c**4*x**4)","B",0
515,1,172,0,0.800635," ","integrate((e*x+d)**2/(c*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{5} c^{3}}} \left(a e^{2} + 3 c d^{2}\right) \log{\left(- a^{3} c \sqrt{- \frac{1}{a^{5} c^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{5} c^{3}}} \left(a e^{2} + 3 c d^{2}\right) \log{\left(a^{3} c \sqrt{- \frac{1}{a^{5} c^{3}}} + x \right)}}{16} + \frac{- 4 a^{2} d e + x^{3} \left(a c e^{2} + 3 c^{2} d^{2}\right) + x \left(- a^{2} e^{2} + 5 a c d^{2}\right)}{8 a^{4} c + 16 a^{3} c^{2} x^{2} + 8 a^{2} c^{3} x^{4}}"," ",0,"-sqrt(-1/(a**5*c**3))*(a*e**2 + 3*c*d**2)*log(-a**3*c*sqrt(-1/(a**5*c**3)) + x)/16 + sqrt(-1/(a**5*c**3))*(a*e**2 + 3*c*d**2)*log(a**3*c*sqrt(-1/(a**5*c**3)) + x)/16 + (-4*a**2*d*e + x**3*(a*c*e**2 + 3*c**2*d**2) + x*(-a**2*e**2 + 5*a*c*d**2))/(8*a**4*c + 16*a**3*c**2*x**2 + 8*a**2*c**3*x**4)","A",0
516,1,124,0,0.457476," ","integrate((e*x+d)/(c*x**2+a)**3,x)","d \left(- \frac{3 \sqrt{- \frac{1}{a^{5} c}} \log{\left(- a^{3} \sqrt{- \frac{1}{a^{5} c}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{a^{5} c}} \log{\left(a^{3} \sqrt{- \frac{1}{a^{5} c}} + x \right)}}{16}\right) + \frac{- 2 a^{2} e + 5 a c d x + 3 c^{2} d x^{3}}{8 a^{4} c + 16 a^{3} c^{2} x^{2} + 8 a^{2} c^{3} x^{4}}"," ",0,"d*(-3*sqrt(-1/(a**5*c))*log(-a**3*sqrt(-1/(a**5*c)) + x)/16 + 3*sqrt(-1/(a**5*c))*log(a**3*sqrt(-1/(a**5*c)) + x)/16) + (-2*a**2*e + 5*a*c*d*x + 3*c**2*d*x**3)/(8*a**4*c + 16*a**3*c**2*x**2 + 8*a**2*c**3*x**4)","A",0
517,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,1,413,0,3.146942," ","integrate((e*x+d)**4/(c*x**2+a)**4,x)","- \frac{\sqrt{- \frac{1}{a^{7} c^{5}}} \left(a e^{2} + c d^{2}\right) \left(a e^{2} + 5 c d^{2}\right) \log{\left(- \frac{a^{4} c^{2} \sqrt{- \frac{1}{a^{7} c^{5}}} \left(a e^{2} + c d^{2}\right) \left(a e^{2} + 5 c d^{2}\right)}{a^{2} e^{4} + 6 a c d^{2} e^{2} + 5 c^{2} d^{4}} + x \right)}}{32} + \frac{\sqrt{- \frac{1}{a^{7} c^{5}}} \left(a e^{2} + c d^{2}\right) \left(a e^{2} + 5 c d^{2}\right) \log{\left(\frac{a^{4} c^{2} \sqrt{- \frac{1}{a^{7} c^{5}}} \left(a e^{2} + c d^{2}\right) \left(a e^{2} + 5 c d^{2}\right)}{a^{2} e^{4} + 6 a c d^{2} e^{2} + 5 c^{2} d^{4}} + x \right)}}{32} + \frac{- 16 a^{4} d e^{3} - 32 a^{3} c d^{3} e - 48 a^{3} c d e^{3} x^{2} + x^{5} \left(3 a^{2} c^{2} e^{4} + 18 a c^{3} d^{2} e^{2} + 15 c^{4} d^{4}\right) + x^{3} \left(- 8 a^{3} c e^{4} + 48 a^{2} c^{2} d^{2} e^{2} + 40 a c^{3} d^{4}\right) + x \left(- 3 a^{4} e^{4} - 18 a^{3} c d^{2} e^{2} + 33 a^{2} c^{2} d^{4}\right)}{48 a^{6} c^{2} + 144 a^{5} c^{3} x^{2} + 144 a^{4} c^{4} x^{4} + 48 a^{3} c^{5} x^{6}}"," ",0,"-sqrt(-1/(a**7*c**5))*(a*e**2 + c*d**2)*(a*e**2 + 5*c*d**2)*log(-a**4*c**2*sqrt(-1/(a**7*c**5))*(a*e**2 + c*d**2)*(a*e**2 + 5*c*d**2)/(a**2*e**4 + 6*a*c*d**2*e**2 + 5*c**2*d**4) + x)/32 + sqrt(-1/(a**7*c**5))*(a*e**2 + c*d**2)*(a*e**2 + 5*c*d**2)*log(a**4*c**2*sqrt(-1/(a**7*c**5))*(a*e**2 + c*d**2)*(a*e**2 + 5*c*d**2)/(a**2*e**4 + 6*a*c*d**2*e**2 + 5*c**2*d**4) + x)/32 + (-16*a**4*d*e**3 - 32*a**3*c*d**3*e - 48*a**3*c*d*e**3*x**2 + x**5*(3*a**2*c**2*e**4 + 18*a*c**3*d**2*e**2 + 15*c**4*d**4) + x**3*(-8*a**3*c*e**4 + 48*a**2*c**2*d**2*e**2 + 40*a*c**3*d**4) + x*(-3*a**4*e**4 - 18*a**3*c*d**2*e**2 + 33*a**2*c**2*d**4))/(48*a**6*c**2 + 144*a**5*c**3*x**2 + 144*a**4*c**4*x**4 + 48*a**3*c**5*x**6)","B",0
520,1,320,0,1.747901," ","integrate((e*x+d)**3/(c*x**2+a)**4,x)","- \frac{d \sqrt{- \frac{1}{a^{7} c^{3}}} \left(3 a e^{2} + 5 c d^{2}\right) \log{\left(- \frac{a^{4} c d \sqrt{- \frac{1}{a^{7} c^{3}}} \left(3 a e^{2} + 5 c d^{2}\right)}{3 a d e^{2} + 5 c d^{3}} + x \right)}}{32} + \frac{d \sqrt{- \frac{1}{a^{7} c^{3}}} \left(3 a e^{2} + 5 c d^{2}\right) \log{\left(\frac{a^{4} c d \sqrt{- \frac{1}{a^{7} c^{3}}} \left(3 a e^{2} + 5 c d^{2}\right)}{3 a d e^{2} + 5 c d^{3}} + x \right)}}{32} + \frac{- 4 a^{4} e^{3} - 24 a^{3} c d^{2} e - 12 a^{3} c e^{3} x^{2} + x^{5} \left(9 a c^{3} d e^{2} + 15 c^{4} d^{3}\right) + x^{3} \left(24 a^{2} c^{2} d e^{2} + 40 a c^{3} d^{3}\right) + x \left(- 9 a^{3} c d e^{2} + 33 a^{2} c^{2} d^{3}\right)}{48 a^{6} c^{2} + 144 a^{5} c^{3} x^{2} + 144 a^{4} c^{4} x^{4} + 48 a^{3} c^{5} x^{6}}"," ",0,"-d*sqrt(-1/(a**7*c**3))*(3*a*e**2 + 5*c*d**2)*log(-a**4*c*d*sqrt(-1/(a**7*c**3))*(3*a*e**2 + 5*c*d**2)/(3*a*d*e**2 + 5*c*d**3) + x)/32 + d*sqrt(-1/(a**7*c**3))*(3*a*e**2 + 5*c*d**2)*log(a**4*c*d*sqrt(-1/(a**7*c**3))*(3*a*e**2 + 5*c*d**2)/(3*a*d*e**2 + 5*c*d**3) + x)/32 + (-4*a**4*e**3 - 24*a**3*c*d**2*e - 12*a**3*c*e**3*x**2 + x**5*(9*a*c**3*d*e**2 + 15*c**4*d**3) + x**3*(24*a**2*c**2*d*e**2 + 40*a*c**3*d**3) + x*(-9*a**3*c*d*e**2 + 33*a**2*c**2*d**3))/(48*a**6*c**2 + 144*a**5*c**3*x**2 + 144*a**4*c**4*x**4 + 48*a**3*c**5*x**6)","B",0
521,1,214,0,1.039592," ","integrate((e*x+d)**2/(c*x**2+a)**4,x)","- \frac{\sqrt{- \frac{1}{a^{7} c^{3}}} \left(a e^{2} + 5 c d^{2}\right) \log{\left(- a^{4} c \sqrt{- \frac{1}{a^{7} c^{3}}} + x \right)}}{32} + \frac{\sqrt{- \frac{1}{a^{7} c^{3}}} \left(a e^{2} + 5 c d^{2}\right) \log{\left(a^{4} c \sqrt{- \frac{1}{a^{7} c^{3}}} + x \right)}}{32} + \frac{- 16 a^{3} d e + x^{5} \left(3 a c^{2} e^{2} + 15 c^{3} d^{2}\right) + x^{3} \left(8 a^{2} c e^{2} + 40 a c^{2} d^{2}\right) + x \left(- 3 a^{3} e^{2} + 33 a^{2} c d^{2}\right)}{48 a^{6} c + 144 a^{5} c^{2} x^{2} + 144 a^{4} c^{3} x^{4} + 48 a^{3} c^{4} x^{6}}"," ",0,"-sqrt(-1/(a**7*c**3))*(a*e**2 + 5*c*d**2)*log(-a**4*c*sqrt(-1/(a**7*c**3)) + x)/32 + sqrt(-1/(a**7*c**3))*(a*e**2 + 5*c*d**2)*log(a**4*c*sqrt(-1/(a**7*c**3)) + x)/32 + (-16*a**3*d*e + x**5*(3*a*c**2*e**2 + 15*c**3*d**2) + x**3*(8*a**2*c*e**2 + 40*a*c**2*d**2) + x*(-3*a**3*e**2 + 33*a**2*c*d**2))/(48*a**6*c + 144*a**5*c**2*x**2 + 144*a**4*c**3*x**4 + 48*a**3*c**4*x**6)","A",0
522,1,150,0,0.615262," ","integrate((e*x+d)/(c*x**2+a)**4,x)","d \left(- \frac{5 \sqrt{- \frac{1}{a^{7} c}} \log{\left(- a^{4} \sqrt{- \frac{1}{a^{7} c}} + x \right)}}{32} + \frac{5 \sqrt{- \frac{1}{a^{7} c}} \log{\left(a^{4} \sqrt{- \frac{1}{a^{7} c}} + x \right)}}{32}\right) + \frac{- 8 a^{3} e + 33 a^{2} c d x + 40 a c^{2} d x^{3} + 15 c^{3} d x^{5}}{48 a^{6} c + 144 a^{5} c^{2} x^{2} + 144 a^{4} c^{3} x^{4} + 48 a^{3} c^{4} x^{6}}"," ",0,"d*(-5*sqrt(-1/(a**7*c))*log(-a**4*sqrt(-1/(a**7*c)) + x)/32 + 5*sqrt(-1/(a**7*c))*log(a**4*sqrt(-1/(a**7*c)) + x)/32) + (-8*a**3*e + 33*a**2*c*d*x + 40*a*c**2*d*x**3 + 15*c**3*d*x**5)/(48*a**6*c + 144*a**5*c**2*x**2 + 144*a**4*c**3*x**4 + 48*a**3*c**4*x**6)","A",0
523,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
525,1,411,0,12.684869," ","integrate((e*x+d)**4*(c*x**2+a)**(1/2),x)","- \frac{a^{\frac{5}{2}} e^{4} x}{16 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{\frac{3}{2}} d^{2} e^{2} x}{4 c \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{\frac{3}{2}} e^{4} x^{3}}{48 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{\sqrt{a} d^{4} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{9 \sqrt{a} d^{2} e^{2} x^{3}}{4 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 \sqrt{a} e^{4} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{3} e^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{5}{2}}} - \frac{3 a^{2} d^{2} e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{4 c^{\frac{3}{2}}} + \frac{a d^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 \sqrt{c}} + 4 d^{3} e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 4 d e^{3} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + \frac{3 c d^{2} e^{2} x^{5}}{2 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c e^{4} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-a**(5/2)*e**4*x/(16*c**2*sqrt(1 + c*x**2/a)) + 3*a**(3/2)*d**2*e**2*x/(4*c*sqrt(1 + c*x**2/a)) - a**(3/2)*e**4*x**3/(48*c*sqrt(1 + c*x**2/a)) + sqrt(a)*d**4*x*sqrt(1 + c*x**2/a)/2 + 9*sqrt(a)*d**2*e**2*x**3/(4*sqrt(1 + c*x**2/a)) + 5*sqrt(a)*e**4*x**5/(24*sqrt(1 + c*x**2/a)) + a**3*e**4*asinh(sqrt(c)*x/sqrt(a))/(16*c**(5/2)) - 3*a**2*d**2*e**2*asinh(sqrt(c)*x/sqrt(a))/(4*c**(3/2)) + a*d**4*asinh(sqrt(c)*x/sqrt(a))/(2*sqrt(c)) + 4*d**3*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 4*d*e**3*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 3*c*d**2*e**2*x**5/(2*sqrt(a)*sqrt(1 + c*x**2/a)) + c*e**4*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
526,1,265,0,7.079874," ","integrate((e*x+d)**3*(c*x**2+a)**(1/2),x)","\frac{3 a^{\frac{3}{2}} d e^{2} x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{\sqrt{a} d^{3} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{9 \sqrt{a} d e^{2} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{3 a^{2} d e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} + \frac{a d^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 \sqrt{c}} + 3 d^{2} e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + \frac{3 c d e^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"3*a**(3/2)*d*e**2*x/(8*c*sqrt(1 + c*x**2/a)) + sqrt(a)*d**3*x*sqrt(1 + c*x**2/a)/2 + 9*sqrt(a)*d*e**2*x**3/(8*sqrt(1 + c*x**2/a)) - 3*a**2*d*e**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) + a*d**3*asinh(sqrt(c)*x/sqrt(a))/(2*sqrt(c)) + 3*d**2*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + e**3*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 3*c*d*e**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
527,1,184,0,6.592987," ","integrate((e*x+d)**2*(c*x**2+a)**(1/2),x)","\frac{a^{\frac{3}{2}} e^{2} x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{\sqrt{a} d^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 \sqrt{a} e^{2} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{2} e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} + \frac{a d^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 \sqrt{c}} + 2 d e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + \frac{c e^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"a**(3/2)*e**2*x/(8*c*sqrt(1 + c*x**2/a)) + sqrt(a)*d**2*x*sqrt(1 + c*x**2/a)/2 + 3*sqrt(a)*e**2*x**3/(8*sqrt(1 + c*x**2/a)) - a**2*e**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) + a*d**2*asinh(sqrt(c)*x/sqrt(a))/(2*sqrt(c)) + 2*d*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + c*e**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
528,1,70,0,3.340315," ","integrate((e*x+d)*(c*x**2+a)**(1/2),x)","\frac{\sqrt{a} d x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{a d \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 \sqrt{c}} + e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*d*x*sqrt(1 + c*x**2/a)/2 + a*d*asinh(sqrt(c)*x/sqrt(a))/(2*sqrt(c)) + e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True))","A",0
529,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{a + c x^{2}}}{d + e x}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(d + e*x), x)","F",0
530,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{a + c x^{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(d + e*x)**2, x)","F",0
531,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)**3,x)","\int \frac{\sqrt{a + c x^{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(d + e*x)**3, x)","F",0
532,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)**4,x)","\int \frac{\sqrt{a + c x^{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(d + e*x)**4, x)","F",0
533,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)**5,x)","\int \frac{\sqrt{a + c x^{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(d + e*x)**5, x)","F",0
534,1,734,0,32.489269," ","integrate((e*x+d)**4*(c*x**2+a)**(3/2),x)","- \frac{3 a^{\frac{7}{2}} e^{4} x}{128 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{\frac{5}{2}} d^{2} e^{2} x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{\frac{5}{2}} e^{4} x^{3}}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} d^{4} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} d^{4} x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} d^{2} e^{2} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{13 a^{\frac{3}{2}} e^{4} x^{5}}{64 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} c d^{4} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c d^{2} e^{2} x^{5}}{4 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 \sqrt{a} c e^{4} x^{7}}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{4} e^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{5}{2}}} - \frac{3 a^{3} d^{2} e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} + \frac{3 a^{2} d^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 \sqrt{c}} + 4 a d^{3} e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 4 a d e^{3} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 4 c d^{3} e \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 4 c d e^{3} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + \frac{c^{2} d^{4} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} d^{2} e^{2} x^{7}}{\sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} e^{4} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-3*a**(7/2)*e**4*x/(128*c**2*sqrt(1 + c*x**2/a)) + 3*a**(5/2)*d**2*e**2*x/(8*c*sqrt(1 + c*x**2/a)) - a**(5/2)*e**4*x**3/(128*c*sqrt(1 + c*x**2/a)) + a**(3/2)*d**4*x*sqrt(1 + c*x**2/a)/2 + a**(3/2)*d**4*x/(8*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*d**2*e**2*x**3/(8*sqrt(1 + c*x**2/a)) + 13*a**(3/2)*e**4*x**5/(64*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*c*d**4*x**3/(8*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*d**2*e**2*x**5/(4*sqrt(1 + c*x**2/a)) + 5*sqrt(a)*c*e**4*x**7/(16*sqrt(1 + c*x**2/a)) + 3*a**4*e**4*asinh(sqrt(c)*x/sqrt(a))/(128*c**(5/2)) - 3*a**3*d**2*e**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) + 3*a**2*d**4*asinh(sqrt(c)*x/sqrt(a))/(8*sqrt(c)) + 4*a*d**3*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 4*a*d*e**3*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 4*c*d**3*e*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 4*c*d*e**3*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + c**2*d**4*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*d**2*e**2*x**7/(sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*e**4*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
535,1,551,0,17.452352," ","integrate((e*x+d)**3*(c*x**2+a)**(3/2),x)","\frac{3 a^{\frac{5}{2}} d e^{2} x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} d^{3} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} d^{3} x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} d e^{2} x^{3}}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} c d^{3} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c d e^{2} x^{5}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{3 a^{3} d e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} + \frac{3 a^{2} d^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 \sqrt{c}} + 3 a d^{2} e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + a e^{3} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 3 c d^{2} e \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + c e^{3} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + \frac{c^{2} d^{3} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} d e^{2} x^{7}}{2 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"3*a**(5/2)*d*e**2*x/(16*c*sqrt(1 + c*x**2/a)) + a**(3/2)*d**3*x*sqrt(1 + c*x**2/a)/2 + a**(3/2)*d**3*x/(8*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*d*e**2*x**3/(16*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*c*d**3*x**3/(8*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*d*e**2*x**5/(8*sqrt(1 + c*x**2/a)) - 3*a**3*d*e**2*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) + 3*a**2*d**3*asinh(sqrt(c)*x/sqrt(a))/(8*sqrt(c)) + 3*a*d**2*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + a*e**3*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 3*c*d**2*e*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c*e**3*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + c**2*d**3*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*d*e**2*x**7/(2*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
536,1,372,0,15.776386," ","integrate((e*x+d)**2*(c*x**2+a)**(3/2),x)","\frac{a^{\frac{5}{2}} e^{2} x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} d^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} d^{2} x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} e^{2} x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} c d^{2} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c e^{2} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{3} e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} + \frac{3 a^{2} d^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 \sqrt{c}} + 2 a d e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 2 c d e \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + \frac{c^{2} d^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} e^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"a**(5/2)*e**2*x/(16*c*sqrt(1 + c*x**2/a)) + a**(3/2)*d**2*x*sqrt(1 + c*x**2/a)/2 + a**(3/2)*d**2*x/(8*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*e**2*x**3/(48*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*c*d**2*x**3/(8*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*e**2*x**5/(24*sqrt(1 + c*x**2/a)) - a**3*e**2*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) + 3*a**2*d**2*asinh(sqrt(c)*x/sqrt(a))/(8*sqrt(c)) + 2*a*d*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 2*c*d*e*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c**2*d**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*e**2*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
537,1,219,0,7.032796," ","integrate((e*x+d)*(c*x**2+a)**(3/2),x)","\frac{a^{\frac{3}{2}} d x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} d x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} c d x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{2} d \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 \sqrt{c}} + a e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + c e \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + \frac{c^{2} d x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"a**(3/2)*d*x*sqrt(1 + c*x**2/a)/2 + a**(3/2)*d*x/(8*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*c*d*x**3/(8*sqrt(1 + c*x**2/a)) + 3*a**2*d*asinh(sqrt(c)*x/sqrt(a))/(8*sqrt(c)) + a*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + c*e*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c**2*d*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
538,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x), x)","F",0
539,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x)**2, x)","F",0
540,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**3,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x)**3, x)","F",0
541,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**4,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x)**4, x)","F",0
542,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**5,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x)**5, x)","F",0
543,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**6,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x)**6, x)","F",0
544,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**7,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x)**7, x)","F",0
545,1,1062,0,63.412983," ","integrate((e*x+d)**4*(c*x**2+a)**(5/2),x)","- \frac{3 a^{\frac{9}{2}} e^{4} x}{256 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{15 a^{\frac{7}{2}} d^{2} e^{2} x}{64 c \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{\frac{7}{2}} e^{4} x^{3}}{256 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{5}{2}} d^{4} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 a^{\frac{5}{2}} d^{4} x}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{133 a^{\frac{5}{2}} d^{2} e^{2} x^{3}}{64 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{129 a^{\frac{5}{2}} e^{4} x^{5}}{640 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{35 a^{\frac{3}{2}} c d^{4} x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{127 a^{\frac{3}{2}} c d^{2} e^{2} x^{5}}{32 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{73 a^{\frac{3}{2}} c e^{4} x^{7}}{160 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 \sqrt{a} c^{2} d^{4} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{23 \sqrt{a} c^{2} d^{2} e^{2} x^{7}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{29 \sqrt{a} c^{2} e^{4} x^{9}}{80 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{5} e^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{256 c^{\frac{5}{2}}} - \frac{15 a^{4} d^{2} e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{64 c^{\frac{3}{2}}} + \frac{5 a^{3} d^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 \sqrt{c}} + 4 a^{2} d^{3} e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 4 a^{2} d e^{3} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 8 a c d^{3} e \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 8 a c d e^{3} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + 4 c^{2} d^{3} e \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + 4 c^{2} d e^{3} \left(\begin{cases} - \frac{16 a^{4} \sqrt{a + c x^{2}}}{315 c^{4}} + \frac{8 a^{3} x^{2} \sqrt{a + c x^{2}}}{315 c^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{6} \sqrt{a + c x^{2}}}{63 c} + \frac{x^{8} \sqrt{a + c x^{2}}}{9} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) + \frac{c^{3} d^{4} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 c^{3} d^{2} e^{2} x^{9}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{3} e^{4} x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-3*a**(9/2)*e**4*x/(256*c**2*sqrt(1 + c*x**2/a)) + 15*a**(7/2)*d**2*e**2*x/(64*c*sqrt(1 + c*x**2/a)) - a**(7/2)*e**4*x**3/(256*c*sqrt(1 + c*x**2/a)) + a**(5/2)*d**4*x*sqrt(1 + c*x**2/a)/2 + 3*a**(5/2)*d**4*x/(16*sqrt(1 + c*x**2/a)) + 133*a**(5/2)*d**2*e**2*x**3/(64*sqrt(1 + c*x**2/a)) + 129*a**(5/2)*e**4*x**5/(640*sqrt(1 + c*x**2/a)) + 35*a**(3/2)*c*d**4*x**3/(48*sqrt(1 + c*x**2/a)) + 127*a**(3/2)*c*d**2*e**2*x**5/(32*sqrt(1 + c*x**2/a)) + 73*a**(3/2)*c*e**4*x**7/(160*sqrt(1 + c*x**2/a)) + 17*sqrt(a)*c**2*d**4*x**5/(24*sqrt(1 + c*x**2/a)) + 23*sqrt(a)*c**2*d**2*e**2*x**7/(8*sqrt(1 + c*x**2/a)) + 29*sqrt(a)*c**2*e**4*x**9/(80*sqrt(1 + c*x**2/a)) + 3*a**5*e**4*asinh(sqrt(c)*x/sqrt(a))/(256*c**(5/2)) - 15*a**4*d**2*e**2*asinh(sqrt(c)*x/sqrt(a))/(64*c**(3/2)) + 5*a**3*d**4*asinh(sqrt(c)*x/sqrt(a))/(16*sqrt(c)) + 4*a**2*d**3*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 4*a**2*d*e**3*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 8*a*c*d**3*e*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 8*a*c*d*e**3*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + 4*c**2*d**3*e*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + 4*c**2*d*e**3*Piecewise((-16*a**4*sqrt(a + c*x**2)/(315*c**4) + 8*a**3*x**2*sqrt(a + c*x**2)/(315*c**3) - 2*a**2*x**4*sqrt(a + c*x**2)/(105*c**2) + a*x**6*sqrt(a + c*x**2)/(63*c) + x**8*sqrt(a + c*x**2)/9, Ne(c, 0)), (sqrt(a)*x**8/8, True)) + c**3*d**4*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + 3*c**3*d**2*e**2*x**9/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c**3*e**4*x**11/(10*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
546,1,843,0,35.037672," ","integrate((e*x+d)**3*(c*x**2+a)**(5/2),x)","\frac{15 a^{\frac{7}{2}} d e^{2} x}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{5}{2}} d^{3} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 a^{\frac{5}{2}} d^{3} x}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{133 a^{\frac{5}{2}} d e^{2} x^{3}}{128 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{35 a^{\frac{3}{2}} c d^{3} x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{127 a^{\frac{3}{2}} c d e^{2} x^{5}}{64 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 \sqrt{a} c^{2} d^{3} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{23 \sqrt{a} c^{2} d e^{2} x^{7}}{16 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{15 a^{4} d e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{3}{2}}} + \frac{5 a^{3} d^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 \sqrt{c}} + 3 a^{2} d^{2} e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + a^{2} e^{3} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 6 a c d^{2} e \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 2 a c e^{3} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + 3 c^{2} d^{2} e \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + c^{2} e^{3} \left(\begin{cases} - \frac{16 a^{4} \sqrt{a + c x^{2}}}{315 c^{4}} + \frac{8 a^{3} x^{2} \sqrt{a + c x^{2}}}{315 c^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{6} \sqrt{a + c x^{2}}}{63 c} + \frac{x^{8} \sqrt{a + c x^{2}}}{9} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) + \frac{c^{3} d^{3} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 c^{3} d e^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"15*a**(7/2)*d*e**2*x/(128*c*sqrt(1 + c*x**2/a)) + a**(5/2)*d**3*x*sqrt(1 + c*x**2/a)/2 + 3*a**(5/2)*d**3*x/(16*sqrt(1 + c*x**2/a)) + 133*a**(5/2)*d*e**2*x**3/(128*sqrt(1 + c*x**2/a)) + 35*a**(3/2)*c*d**3*x**3/(48*sqrt(1 + c*x**2/a)) + 127*a**(3/2)*c*d*e**2*x**5/(64*sqrt(1 + c*x**2/a)) + 17*sqrt(a)*c**2*d**3*x**5/(24*sqrt(1 + c*x**2/a)) + 23*sqrt(a)*c**2*d*e**2*x**7/(16*sqrt(1 + c*x**2/a)) - 15*a**4*d*e**2*asinh(sqrt(c)*x/sqrt(a))/(128*c**(3/2)) + 5*a**3*d**3*asinh(sqrt(c)*x/sqrt(a))/(16*sqrt(c)) + 3*a**2*d**2*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + a**2*e**3*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 6*a*c*d**2*e*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 2*a*c*e**3*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + 3*c**2*d**2*e*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + c**2*e**3*Piecewise((-16*a**4*sqrt(a + c*x**2)/(315*c**4) + 8*a**3*x**2*sqrt(a + c*x**2)/(315*c**3) - 2*a**2*x**4*sqrt(a + c*x**2)/(105*c**2) + a*x**6*sqrt(a + c*x**2)/(63*c) + x**8*sqrt(a + c*x**2)/9, Ne(c, 0)), (sqrt(a)*x**8/8, True)) + c**3*d**3*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + 3*c**3*d*e**2*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
547,1,539,0,31.734911," ","integrate((e*x+d)**2*(c*x**2+a)**(5/2),x)","\frac{5 a^{\frac{7}{2}} e^{2} x}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{5}{2}} d^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 a^{\frac{5}{2}} d^{2} x}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{133 a^{\frac{5}{2}} e^{2} x^{3}}{384 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{35 a^{\frac{3}{2}} c d^{2} x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{127 a^{\frac{3}{2}} c e^{2} x^{5}}{192 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 \sqrt{a} c^{2} d^{2} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{23 \sqrt{a} c^{2} e^{2} x^{7}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{5 a^{4} e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{3}{2}}} + \frac{5 a^{3} d^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 \sqrt{c}} + 2 a^{2} d e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 4 a c d e \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 2 c^{2} d e \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + \frac{c^{3} d^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{3} e^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"5*a**(7/2)*e**2*x/(128*c*sqrt(1 + c*x**2/a)) + a**(5/2)*d**2*x*sqrt(1 + c*x**2/a)/2 + 3*a**(5/2)*d**2*x/(16*sqrt(1 + c*x**2/a)) + 133*a**(5/2)*e**2*x**3/(384*sqrt(1 + c*x**2/a)) + 35*a**(3/2)*c*d**2*x**3/(48*sqrt(1 + c*x**2/a)) + 127*a**(3/2)*c*e**2*x**5/(192*sqrt(1 + c*x**2/a)) + 17*sqrt(a)*c**2*d**2*x**5/(24*sqrt(1 + c*x**2/a)) + 23*sqrt(a)*c**2*e**2*x**7/(48*sqrt(1 + c*x**2/a)) - 5*a**4*e**2*asinh(sqrt(c)*x/sqrt(a))/(128*c**(3/2)) + 5*a**3*d**2*asinh(sqrt(c)*x/sqrt(a))/(16*sqrt(c)) + 2*a**2*d*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 4*a*c*d*e*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 2*c**2*d*e*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + c**3*d**2*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + c**3*e**2*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
548,1,348,0,14.056402," ","integrate((e*x+d)*(c*x**2+a)**(5/2),x)","\frac{a^{\frac{5}{2}} d x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 a^{\frac{5}{2}} d x}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{35 a^{\frac{3}{2}} c d x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 \sqrt{a} c^{2} d x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 a^{3} d \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 \sqrt{c}} + a^{2} e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 2 a c e \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + c^{2} e \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + \frac{c^{3} d x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"a**(5/2)*d*x*sqrt(1 + c*x**2/a)/2 + 3*a**(5/2)*d*x/(16*sqrt(1 + c*x**2/a)) + 35*a**(3/2)*c*d*x**3/(48*sqrt(1 + c*x**2/a)) + 17*sqrt(a)*c**2*d*x**5/(24*sqrt(1 + c*x**2/a)) + 5*a**3*d*asinh(sqrt(c)*x/sqrt(a))/(16*sqrt(c)) + a**2*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 2*a*c*e*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c**2*e*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + c**3*d*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
549,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{d + e x}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x), x)","F",0
550,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**2,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**2, x)","F",0
551,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**3, x)","F",0
552,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**4, x)","F",0
553,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**5,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**5, x)","F",0
554,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**6,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**6, x)","F",0
555,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**7,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**7, x)","F",0
556,-1,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,0,0,0,0.000000," ","integrate((x**2+2)**(1/2)/(1+4*x),x)","\int \frac{\sqrt{x^{2} + 2}}{4 x + 1}\, dx"," ",0,"Integral(sqrt(x**2 + 2)/(4*x + 1), x)","F",0
559,0,0,0,0.000000," ","integrate((4*x**2+2)**(1/2)/(5+4*x),x)","\sqrt{2} \int \frac{\sqrt{2 x^{2} + 1}}{4 x + 5}\, dx"," ",0,"sqrt(2)*Integral(sqrt(2*x**2 + 1)/(4*x + 5), x)","F",0
560,1,56,0,0.255100," ","integrate((2+3*x)*(7*x**2-5)**(1/2),x)","x^{2} \sqrt{7 x^{2} - 5} + x \sqrt{7 x^{2} - 5} - \frac{5 \sqrt{7 x^{2} - 5}}{7} - \frac{5 \sqrt{7} \operatorname{acosh}{\left(\frac{\sqrt{35} x}{5} \right)}}{7}"," ",0,"x**2*sqrt(7*x**2 - 5) + x*sqrt(7*x**2 - 5) - 5*sqrt(7*x**2 - 5)/7 - 5*sqrt(7)*acosh(sqrt(35)*x/5)/7","A",0
561,1,330,0,8.671492," ","integrate((e*x+d)**4/(c*x**2+a)**(1/2),x)","- \frac{3 a^{\frac{3}{2}} e^{4} x}{8 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} d^{2} e^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{c} - \frac{\sqrt{a} e^{4} x^{3}}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{2} e^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{5}{2}}} - \frac{3 a d^{2} e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{c^{\frac{3}{2}}} + d^{4} \left(\begin{cases} \frac{\sqrt{- \frac{a}{c}} \operatorname{asin}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c < 0 \\\frac{\sqrt{\frac{a}{c}} \operatorname{asinh}{\left(x \sqrt{\frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c > 0 \\\frac{\sqrt{- \frac{a}{c}} \operatorname{acosh}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{- a}} & \text{for}\: c > 0 \wedge a < 0 \end{cases}\right) + 4 d^{3} e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right) + 4 d e^{3} \left(\begin{cases} - \frac{2 a \sqrt{a + c x^{2}}}{3 c^{2}} + \frac{x^{2} \sqrt{a + c x^{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right) + \frac{e^{4} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-3*a**(3/2)*e**4*x/(8*c**2*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*d**2*e**2*x*sqrt(1 + c*x**2/a)/c - sqrt(a)*e**4*x**3/(8*c*sqrt(1 + c*x**2/a)) + 3*a**2*e**4*asinh(sqrt(c)*x/sqrt(a))/(8*c**(5/2)) - 3*a*d**2*e**2*asinh(sqrt(c)*x/sqrt(a))/c**(3/2) + d**4*Piecewise((sqrt(-a/c)*asin(x*sqrt(-c/a))/sqrt(a), (a > 0) & (c < 0)), (sqrt(a/c)*asinh(x*sqrt(c/a))/sqrt(a), (a > 0) & (c > 0)), (sqrt(-a/c)*acosh(x*sqrt(-c/a))/sqrt(-a), (c > 0) & (a < 0))) + 4*d**3*e*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True)) + 4*d*e**3*Piecewise((-2*a*sqrt(a + c*x**2)/(3*c**2) + x**2*sqrt(a + c*x**2)/(3*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True)) + e**4*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
562,1,216,0,4.860636," ","integrate((e*x+d)**3/(c*x**2+a)**(1/2),x)","\frac{3 \sqrt{a} d e^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} - \frac{3 a d e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} + d^{3} \left(\begin{cases} \frac{\sqrt{- \frac{a}{c}} \operatorname{asin}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c < 0 \\\frac{\sqrt{\frac{a}{c}} \operatorname{asinh}{\left(x \sqrt{\frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c > 0 \\\frac{\sqrt{- \frac{a}{c}} \operatorname{acosh}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{- a}} & \text{for}\: c > 0 \wedge a < 0 \end{cases}\right) + 3 d^{2} e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{2 a \sqrt{a + c x^{2}}}{3 c^{2}} + \frac{x^{2} \sqrt{a + c x^{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right)"," ",0,"3*sqrt(a)*d*e**2*x*sqrt(1 + c*x**2/a)/(2*c) - 3*a*d*e**2*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) + d**3*Piecewise((sqrt(-a/c)*asin(x*sqrt(-c/a))/sqrt(a), (a > 0) & (c < 0)), (sqrt(a/c)*asinh(x*sqrt(c/a))/sqrt(a), (a > 0) & (c > 0)), (sqrt(-a/c)*acosh(x*sqrt(-c/a))/sqrt(-a), (c > 0) & (a < 0))) + 3*d**2*e*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True)) + e**3*Piecewise((-2*a*sqrt(a + c*x**2)/(3*c**2) + x**2*sqrt(a + c*x**2)/(3*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True))","A",0
563,1,158,0,4.152076," ","integrate((e*x+d)**2/(c*x**2+a)**(1/2),x)","\frac{\sqrt{a} e^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} - \frac{a e^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} + d^{2} \left(\begin{cases} \frac{\sqrt{- \frac{a}{c}} \operatorname{asin}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c < 0 \\\frac{\sqrt{\frac{a}{c}} \operatorname{asinh}{\left(x \sqrt{\frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c > 0 \\\frac{\sqrt{- \frac{a}{c}} \operatorname{acosh}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{- a}} & \text{for}\: c > 0 \wedge a < 0 \end{cases}\right) + 2 d e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*e**2*x*sqrt(1 + c*x**2/a)/(2*c) - a*e**2*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) + d**2*Piecewise((sqrt(-a/c)*asin(x*sqrt(-c/a))/sqrt(a), (a > 0) & (c < 0)), (sqrt(a/c)*asinh(x*sqrt(c/a))/sqrt(a), (a > 0) & (c > 0)), (sqrt(-a/c)*acosh(x*sqrt(-c/a))/sqrt(-a), (c > 0) & (a < 0))) + 2*d*e*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True))","A",0
564,1,102,0,1.425764," ","integrate((e*x+d)/(c*x**2+a)**(1/2),x)","d \left(\begin{cases} \frac{\sqrt{- \frac{a}{c}} \operatorname{asin}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c < 0 \\\frac{\sqrt{\frac{a}{c}} \operatorname{asinh}{\left(x \sqrt{\frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c > 0 \\\frac{\sqrt{- \frac{a}{c}} \operatorname{acosh}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{- a}} & \text{for}\: c > 0 \wedge a < 0 \end{cases}\right) + e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((sqrt(-a/c)*asin(x*sqrt(-c/a))/sqrt(a), (a > 0) & (c < 0)), (sqrt(a/c)*asinh(x*sqrt(c/a))/sqrt(a), (a > 0) & (c > 0)), (sqrt(-a/c)*acosh(x*sqrt(-c/a))/sqrt(-a), (c > 0) & (a < 0))) + e*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True))","B",0
565,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)), x)","F",0
566,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
567,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)**3), x)","F",0
568,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)**4), x)","F",0
569,0,0,0,0.000000," ","integrate((e*x+d)**4/(c*x**2+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(a + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/(a + c*x**2)**(3/2), x)","F",0
570,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(a + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(a + c*x**2)**(3/2), x)","F",0
571,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(a + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(a + c*x**2)**(3/2), x)","F",0
572,1,46,0,6.661420," ","integrate((e*x+d)/(c*x**2+a)**(3/2),x)","e \left(\begin{cases} - \frac{1}{c \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{d x}{a^{\frac{3}{2}} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"e*Piecewise((-1/(c*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(3/2)), True)) + d*x/(a**(3/2)*sqrt(1 + c*x**2/a))","A",0
573,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + c*x**2)**(3/2)*(d + e*x)), x)","F",0
574,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+a)**(3/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(3/2)*(d + e*x)**2), x)","F",0
575,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+a)**(3/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(3/2)*(d + e*x)**3), x)","F",0
576,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(c*x**2+a)**(3/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(3/2)*(d + e*x)**4), x)","F",0
577,0,0,0,0.000000," ","integrate((e*x+d)**5/(c*x**2+a)**(5/2),x)","\int \frac{\left(d + e x\right)^{5}}{\left(a + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**5/(a + c*x**2)**(5/2), x)","F",0
578,0,0,0,0.000000," ","integrate((e*x+d)**4/(c*x**2+a)**(5/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(a + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/(a + c*x**2)**(5/2), x)","F",0
579,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+a)**(5/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(a + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(a + c*x**2)**(5/2), x)","F",0
580,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+a)**(5/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(a + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(a + c*x**2)**(5/2), x)","F",0
581,1,146,0,12.174507," ","integrate((e*x+d)/(c*x**2+a)**(5/2),x)","d \left(\frac{3 a x}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{5}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{2 c x^{3}}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{5}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}\right) + e \left(\begin{cases} - \frac{1}{3 a c \sqrt{a + c x^{2}} + 3 c^{2} x^{2} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*(3*a*x/(3*a**(7/2)*sqrt(1 + c*x**2/a) + 3*a**(5/2)*c*x**2*sqrt(1 + c*x**2/a)) + 2*c*x**3/(3*a**(7/2)*sqrt(1 + c*x**2/a) + 3*a**(5/2)*c*x**2*sqrt(1 + c*x**2/a))) + e*Piecewise((-1/(3*a*c*sqrt(a + c*x**2) + 3*c**2*x**2*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(5/2)), True))","B",0
582,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+a)**(5/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + c*x**2)**(5/2)*(d + e*x)), x)","F",0
583,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+a)**(5/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{5}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(5/2)*(d + e*x)**2), x)","F",0
584,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+a)**(5/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{5}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(5/2)*(d + e*x)**3), x)","F",0
585,1,12,0,0.150771," ","integrate((3+x)/(-x**2+1)**(1/2),x)","- \sqrt{1 - x^{2}} + 3 \operatorname{asin}{\left(x \right)}"," ",0,"-sqrt(1 - x**2) + 3*asin(x)","A",0
586,1,12,0,0.153181," ","integrate((1+x)/(-x**2+4)**(1/2),x)","- \sqrt{4 - x^{2}} + \operatorname{asin}{\left(\frac{x}{2} \right)}"," ",0,"-sqrt(4 - x**2) + asin(x/2)","A",0
587,1,14,0,0.152297," ","integrate((2+x)/(x**2+9)**(1/2),x)","\sqrt{x^{2} + 9} + 2 \operatorname{asinh}{\left(\frac{x}{3} \right)}"," ",0,"sqrt(x**2 + 9) + 2*asinh(x/3)","A",0
588,1,42,0,0.254351," ","integrate((b*x+a)**2/(-x**2+1)**(1/2),x)","a^{2} \operatorname{asin}{\left(x \right)} - 2 a b \sqrt{1 - x^{2}} - \frac{b^{2} x \sqrt{1 - x^{2}}}{2} + \frac{b^{2} \operatorname{asin}{\left(x \right)}}{2}"," ",0,"a**2*asin(x) - 2*a*b*sqrt(1 - x**2) - b**2*x*sqrt(1 - x**2)/2 + b**2*asin(x)/2","A",0
589,1,42,0,0.251674," ","integrate((b*x+a)**2/(x**2+1)**(1/2),x)","a^{2} \operatorname{asinh}{\left(x \right)} + 2 a b \sqrt{x^{2} + 1} + \frac{b^{2} x \sqrt{x^{2} + 1}}{2} - \frac{b^{2} \operatorname{asinh}{\left(x \right)}}{2}"," ",0,"a**2*asinh(x) + 2*a*b*sqrt(x**2 + 1) + b**2*x*sqrt(x**2 + 1)/2 - b**2*asinh(x)/2","A",0
590,1,20,0,4.199798," ","integrate((2+3*x)/(x**2+4)**(3/2),x)","\frac{x}{2 \sqrt{x^{2} + 4}} - \frac{3}{\sqrt{x^{2} + 4}}"," ",0,"x/(2*sqrt(x**2 + 4)) - 3/sqrt(x**2 + 4)","A",0
591,1,218,0,3.335459," ","integrate((e*x+d)**(5/2)*(c*x**2+a),x)","\begin{cases} \frac{2 a d^{3} \sqrt{d + e x}}{7 e} + \frac{6 a d^{2} x \sqrt{d + e x}}{7} + \frac{6 a d e x^{2} \sqrt{d + e x}}{7} + \frac{2 a e^{2} x^{3} \sqrt{d + e x}}{7} + \frac{16 c d^{5} \sqrt{d + e x}}{693 e^{3}} - \frac{8 c d^{4} x \sqrt{d + e x}}{693 e^{2}} + \frac{2 c d^{3} x^{2} \sqrt{d + e x}}{231 e} + \frac{226 c d^{2} x^{3} \sqrt{d + e x}}{693} + \frac{46 c d e x^{4} \sqrt{d + e x}}{99} + \frac{2 c e^{2} x^{5} \sqrt{d + e x}}{11} & \text{for}\: e \neq 0 \\d^{\frac{5}{2}} \left(a x + \frac{c x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*d**3*sqrt(d + e*x)/(7*e) + 6*a*d**2*x*sqrt(d + e*x)/7 + 6*a*d*e*x**2*sqrt(d + e*x)/7 + 2*a*e**2*x**3*sqrt(d + e*x)/7 + 16*c*d**5*sqrt(d + e*x)/(693*e**3) - 8*c*d**4*x*sqrt(d + e*x)/(693*e**2) + 2*c*d**3*x**2*sqrt(d + e*x)/(231*e) + 226*c*d**2*x**3*sqrt(d + e*x)/693 + 46*c*d*e*x**4*sqrt(d + e*x)/99 + 2*c*e**2*x**5*sqrt(d + e*x)/11, Ne(e, 0)), (d**(5/2)*(a*x + c*x**3/3), True))","A",0
592,1,155,0,6.825417," ","integrate((e*x+d)**(3/2)*(c*x**2+a),x)","a d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}}"," ",0,"a*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3","A",0
593,1,61,0,2.182822," ","integrate((c*x**2+a)*(e*x+d)**(1/2),x)","\frac{2 \left(- \frac{2 c d \left(d + e x\right)^{\frac{5}{2}}}{5 e^{2}} + \frac{c \left(d + e x\right)^{\frac{7}{2}}}{7 e^{2}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a e^{2} + c d^{2}\right)}{3 e^{2}}\right)}{e}"," ",0,"2*(-2*c*d*(d + e*x)**(5/2)/(5*e**2) + c*(d + e*x)**(7/2)/(7*e**2) + (d + e*x)**(3/2)*(a*e**2 + c*d**2)/(3*e**2))/e","A",0
594,1,150,0,7.463578," ","integrate((c*x**2+a)/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a d}{\sqrt{d + e x}} - 2 a \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{2 c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}}}{e} & \text{for}\: e \neq 0 \\\frac{a x + \frac{c x^{3}}{3}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*d/sqrt(d + e*x) - 2*a*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 2*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2)/e, Ne(e, 0)), ((a*x + c*x**3/3)/sqrt(d), True))","A",0
595,1,58,0,8.432781," ","integrate((c*x**2+a)/(e*x+d)**(3/2),x)","- \frac{4 c d \sqrt{d + e x}}{e^{3}} + \frac{2 c \left(d + e x\right)^{\frac{3}{2}}}{3 e^{3}} - \frac{2 \left(a e^{2} + c d^{2}\right)}{e^{3} \sqrt{d + e x}}"," ",0,"-4*c*d*sqrt(d + e*x)/e**3 + 2*c*(d + e*x)**(3/2)/(3*e**3) - 2*(a*e**2 + c*d**2)/(e**3*sqrt(d + e*x))","A",0
596,1,168,0,1.202873," ","integrate((c*x**2+a)/(e*x+d)**(5/2),x)","\begin{cases} - \frac{2 a e^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{16 c d^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{24 c d e x}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{6 c e^{2} x^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a x + \frac{c x^{3}}{3}}{d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*e**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 16*c*d**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 24*c*d*e*x/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 6*c*e**2*x**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)), Ne(e, 0)), ((a*x + c*x**3/3)/d**(5/2), True))","A",0
597,1,252,0,2.796299," ","integrate((c*x**2+a)/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 a e^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{16 c d^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{40 c d e x}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{30 c e^{2} x^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a x + \frac{c x^{3}}{3}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a*e**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 16*c*d**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 40*c*d*e*x/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 30*c*e**2*x**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)), Ne(e, 0)), ((a*x + c*x**3/3)/d**(7/2), True))","A",0
598,1,566,0,20.817615," ","integrate((e*x+d)**(5/2)*(c*x**2+a)**2,x)","a^{2} d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 a^{2} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 a^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{4 a c d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{8 a c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{4 a c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{2 c^{2} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{4 c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}}"," ",0,"a**2*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a**2*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*a**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 4*a*c*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 8*a*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 4*a*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 2*c**2*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 4*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5","A",0
599,1,328,0,12.680382," ","integrate((e*x+d)**(3/2)*(c*x**2+a)**2,x)","a^{2} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{4 a c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{4 a c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 c^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{2 c^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}}"," ",0,"a**2*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 4*a*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 4*a*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*c**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 2*c**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5","A",0
600,1,148,0,3.206335," ","integrate((c*x**2+a)**2*(e*x+d)**(1/2),x)","\frac{2 \left(- \frac{4 c^{2} d \left(d + e x\right)^{\frac{9}{2}}}{9 e^{4}} + \frac{c^{2} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{4}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(2 a c e^{2} + 6 c^{2} d^{2}\right)}{7 e^{4}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(- 4 a c d e^{2} - 4 c^{2} d^{3}\right)}{5 e^{4}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{2} e^{4} + 2 a c d^{2} e^{2} + c^{2} d^{4}\right)}{3 e^{4}}\right)}{e}"," ",0,"2*(-4*c**2*d*(d + e*x)**(9/2)/(9*e**4) + c**2*(d + e*x)**(11/2)/(11*e**4) + (d + e*x)**(7/2)*(2*a*c*e**2 + 6*c**2*d**2)/(7*e**4) + (d + e*x)**(5/2)*(-4*a*c*d*e**2 - 4*c**2*d**3)/(5*e**4) + (d + e*x)**(3/2)*(a**2*e**4 + 2*a*c*d**2*e**2 + c**2*d**4)/(3*e**4))/e","A",0
601,1,330,0,33.904509," ","integrate((c*x**2+a)**2/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{2} d}{\sqrt{d + e x}} - 2 a^{2} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{4 a c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{4 a c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{2 c^{2} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{2 c^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}}}{e} & \text{for}\: e \neq 0 \\\frac{a^{2} x + \frac{2 a c x^{3}}{3} + \frac{c^{2} x^{5}}{5}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**2*d/sqrt(d + e*x) - 2*a**2*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 4*a*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 4*a*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 2*c**2*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 2*c**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4)/e, Ne(e, 0)), ((a**2*x + 2*a*c*x**3/3 + c**2*x**5/5)/sqrt(d), True))","A",0
602,1,126,0,17.783926," ","integrate((c*x**2+a)**2/(e*x+d)**(3/2),x)","- \frac{8 c^{2} d \left(d + e x\right)^{\frac{5}{2}}}{5 e^{5}} + \frac{2 c^{2} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{5}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(4 a c e^{2} + 12 c^{2} d^{2}\right)}{3 e^{5}} + \frac{\sqrt{d + e x} \left(- 8 a c d e^{2} - 8 c^{2} d^{3}\right)}{e^{5}} - \frac{2 \left(a e^{2} + c d^{2}\right)^{2}}{e^{5} \sqrt{d + e x}}"," ",0,"-8*c**2*d*(d + e*x)**(5/2)/(5*e**5) + 2*c**2*(d + e*x)**(7/2)/(7*e**5) + (d + e*x)**(3/2)*(4*a*c*e**2 + 12*c**2*d**2)/(3*e**5) + sqrt(d + e*x)*(-8*a*c*d*e**2 - 8*c**2*d**3)/e**5 - 2*(a*e**2 + c*d**2)**2/(e**5*sqrt(d + e*x))","A",0
603,1,121,0,28.389043," ","integrate((c*x**2+a)**2/(e*x+d)**(5/2),x)","- \frac{8 c^{2} d \left(d + e x\right)^{\frac{3}{2}}}{3 e^{5}} + \frac{2 c^{2} \left(d + e x\right)^{\frac{5}{2}}}{5 e^{5}} + \frac{8 c d \left(a e^{2} + c d^{2}\right)}{e^{5} \sqrt{d + e x}} + \frac{\sqrt{d + e x} \left(4 a c e^{2} + 12 c^{2} d^{2}\right)}{e^{5}} - \frac{2 \left(a e^{2} + c d^{2}\right)^{2}}{3 e^{5} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"-8*c**2*d*(d + e*x)**(3/2)/(3*e**5) + 2*c**2*(d + e*x)**(5/2)/(5*e**5) + 8*c*d*(a*e**2 + c*d**2)/(e**5*sqrt(d + e*x)) + sqrt(d + e*x)*(4*a*c*e**2 + 12*c**2*d**2)/e**5 - 2*(a*e**2 + c*d**2)**2/(3*e**5*(d + e*x)**(3/2))","A",0
604,1,592,0,3.176255," ","integrate((c*x**2+a)**2/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 a^{2} e^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{32 a c d^{2} e^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{80 a c d e^{3} x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{60 a c e^{4} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{256 c^{2} d^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{640 c^{2} d^{3} e x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{480 c^{2} d^{2} e^{2} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{80 c^{2} d e^{3} x^{3}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{10 c^{2} e^{4} x^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a^{2} x + \frac{2 a c x^{3}}{3} + \frac{c^{2} x^{5}}{5}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a**2*e**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 32*a*c*d**2*e**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 80*a*c*d*e**3*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 60*a*c*e**4*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 256*c**2*d**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 640*c**2*d**3*e*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 480*c**2*d**2*e**2*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 80*c**2*d*e**3*x**3/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 10*c**2*e**4*x**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)), Ne(e, 0)), ((a**2*x + 2*a*c*x**3/3 + c**2*x**5/5)/d**(7/2), True))","A",0
605,1,945,0,32.812953," ","integrate((e*x+d)**(5/2)*(c*x**2+a)**3,x)","a^{3} d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 a^{3} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 a^{3} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{6 a^{2} c d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{12 a^{2} c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{6 a^{2} c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{6 a c^{2} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{12 a c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{6 a c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{2 c^{3} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{4 c^{3} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{2 c^{3} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}}"," ",0,"a**3*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a**3*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*a**3*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 6*a**2*c*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 12*a**2*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 6*a**2*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 6*a*c**2*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 12*a*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 6*a*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 2*c**3*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 4*c**3*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 2*c**3*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7","A",0
606,1,564,0,20.202164," ","integrate((e*x+d)**(3/2)*(c*x**2+a)**3,x)","a^{3} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{3} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{6 a^{2} c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{6 a^{2} c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{6 a c^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{6 a c^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 c^{3} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{2 c^{3} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}}"," ",0,"a**3*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**3*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 6*a**2*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 6*a**2*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 6*a*c**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 6*a*c**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*c**3*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 2*c**3*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7","A",0
607,1,265,0,4.496905," ","integrate((c*x**2+a)**3*(e*x+d)**(1/2),x)","\frac{2 \left(- \frac{6 c^{3} d \left(d + e x\right)^{\frac{13}{2}}}{13 e^{6}} + \frac{c^{3} \left(d + e x\right)^{\frac{15}{2}}}{15 e^{6}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(3 a c^{2} e^{2} + 15 c^{3} d^{2}\right)}{11 e^{6}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(- 12 a c^{2} d e^{2} - 20 c^{3} d^{3}\right)}{9 e^{6}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(3 a^{2} c e^{4} + 18 a c^{2} d^{2} e^{2} + 15 c^{3} d^{4}\right)}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(- 6 a^{2} c d e^{4} - 12 a c^{2} d^{3} e^{2} - 6 c^{3} d^{5}\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{3} e^{6} + 3 a^{2} c d^{2} e^{4} + 3 a c^{2} d^{4} e^{2} + c^{3} d^{6}\right)}{3 e^{6}}\right)}{e}"," ",0,"2*(-6*c**3*d*(d + e*x)**(13/2)/(13*e**6) + c**3*(d + e*x)**(15/2)/(15*e**6) + (d + e*x)**(11/2)*(3*a*c**2*e**2 + 15*c**3*d**2)/(11*e**6) + (d + e*x)**(9/2)*(-12*a*c**2*d*e**2 - 20*c**3*d**3)/(9*e**6) + (d + e*x)**(7/2)*(3*a**2*c*e**4 + 18*a*c**2*d**2*e**2 + 15*c**3*d**4)/(7*e**6) + (d + e*x)**(5/2)*(-6*a**2*c*d*e**4 - 12*a*c**2*d**3*e**2 - 6*c**3*d**5)/(5*e**6) + (d + e*x)**(3/2)*(a**3*e**6 + 3*a**2*c*d**2*e**4 + 3*a*c**2*d**4*e**2 + c**3*d**6)/(3*e**6))/e","A",0
608,1,563,0,60.375676," ","integrate((c*x**2+a)**3/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{3} d}{\sqrt{d + e x}} - 2 a^{3} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{6 a^{2} c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{6 a^{2} c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{6 a c^{2} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{6 a c^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{2 c^{3} d \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{6}} - \frac{2 c^{3} \left(- \frac{d^{7}}{\sqrt{d + e x}} - 7 d^{6} \sqrt{d + e x} + 7 d^{5} \left(d + e x\right)^{\frac{3}{2}} - 7 d^{4} \left(d + e x\right)^{\frac{5}{2}} + 5 d^{3} \left(d + e x\right)^{\frac{7}{2}} - \frac{7 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{3} + \frac{7 d \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}}}{e} & \text{for}\: e \neq 0 \\\frac{a^{3} x + a^{2} c x^{3} + \frac{3 a c^{2} x^{5}}{5} + \frac{c^{3} x^{7}}{7}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**3*d/sqrt(d + e*x) - 2*a**3*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 6*a**2*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 6*a**2*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 6*a*c**2*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 6*a*c**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 2*c**3*d*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**6 - 2*c**3*(-d**7/sqrt(d + e*x) - 7*d**6*sqrt(d + e*x) + 7*d**5*(d + e*x)**(3/2) - 7*d**4*(d + e*x)**(5/2) + 5*d**3*(d + e*x)**(7/2) - 7*d**2*(d + e*x)**(9/2)/3 + 7*d*(d + e*x)**(11/2)/11 - (d + e*x)**(13/2)/13)/e**6)/e, Ne(e, 0)), ((a**3*x + a**2*c*x**3 + 3*a*c**2*x**5/5 + c**3*x**7/7)/sqrt(d), True))","A",0
609,1,224,0,31.808097," ","integrate((c*x**2+a)**3/(e*x+d)**(3/2),x)","- \frac{4 c^{3} d \left(d + e x\right)^{\frac{9}{2}}}{3 e^{7}} + \frac{2 c^{3} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{7}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(6 a c^{2} e^{2} + 30 c^{3} d^{2}\right)}{7 e^{7}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(- 24 a c^{2} d e^{2} - 40 c^{3} d^{3}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(6 a^{2} c e^{4} + 36 a c^{2} d^{2} e^{2} + 30 c^{3} d^{4}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(- 12 a^{2} c d e^{4} - 24 a c^{2} d^{3} e^{2} - 12 c^{3} d^{5}\right)}{e^{7}} - \frac{2 \left(a e^{2} + c d^{2}\right)^{3}}{e^{7} \sqrt{d + e x}}"," ",0,"-4*c**3*d*(d + e*x)**(9/2)/(3*e**7) + 2*c**3*(d + e*x)**(11/2)/(11*e**7) + (d + e*x)**(7/2)*(6*a*c**2*e**2 + 30*c**3*d**2)/(7*e**7) + (d + e*x)**(5/2)*(-24*a*c**2*d*e**2 - 40*c**3*d**3)/(5*e**7) + (d + e*x)**(3/2)*(6*a**2*c*e**4 + 36*a*c**2*d**2*e**2 + 30*c**3*d**4)/(3*e**7) + sqrt(d + e*x)*(-12*a**2*c*d*e**4 - 24*a*c**2*d**3*e**2 - 12*c**3*d**5)/e**7 - 2*(a*e**2 + c*d**2)**3/(e**7*sqrt(d + e*x))","A",0
610,1,206,0,43.139298," ","integrate((c*x**2+a)**3/(e*x+d)**(5/2),x)","- \frac{12 c^{3} d \left(d + e x\right)^{\frac{7}{2}}}{7 e^{7}} + \frac{2 c^{3} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{7}} + \frac{12 c d \left(a e^{2} + c d^{2}\right)^{2}}{e^{7} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(6 a c^{2} e^{2} + 30 c^{3} d^{2}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(- 24 a c^{2} d e^{2} - 40 c^{3} d^{3}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(6 a^{2} c e^{4} + 36 a c^{2} d^{2} e^{2} + 30 c^{3} d^{4}\right)}{e^{7}} - \frac{2 \left(a e^{2} + c d^{2}\right)^{3}}{3 e^{7} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"-12*c**3*d*(d + e*x)**(7/2)/(7*e**7) + 2*c**3*(d + e*x)**(9/2)/(9*e**7) + 12*c*d*(a*e**2 + c*d**2)**2/(e**7*sqrt(d + e*x)) + (d + e*x)**(5/2)*(6*a*c**2*e**2 + 30*c**3*d**2)/(5*e**7) + (d + e*x)**(3/2)*(-24*a*c**2*d*e**2 - 40*c**3*d**3)/(3*e**7) + sqrt(d + e*x)*(6*a**2*c*e**4 + 36*a*c**2*d**2*e**2 + 30*c**3*d**4)/e**7 - 2*(a*e**2 + c*d**2)**3/(3*e**7*(d + e*x)**(3/2))","A",0
611,1,197,0,78.228777," ","integrate((c*x**2+a)**3/(e*x+d)**(7/2),x)","- \frac{12 c^{3} d \left(d + e x\right)^{\frac{5}{2}}}{5 e^{7}} + \frac{2 c^{3} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{7}} + \frac{4 c d \left(a e^{2} + c d^{2}\right)^{2}}{e^{7} \left(d + e x\right)^{\frac{3}{2}}} - \frac{6 c \left(a e^{2} + c d^{2}\right) \left(a e^{2} + 5 c d^{2}\right)}{e^{7} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(6 a c^{2} e^{2} + 30 c^{3} d^{2}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(- 24 a c^{2} d e^{2} - 40 c^{3} d^{3}\right)}{e^{7}} - \frac{2 \left(a e^{2} + c d^{2}\right)^{3}}{5 e^{7} \left(d + e x\right)^{\frac{5}{2}}}"," ",0,"-12*c**3*d*(d + e*x)**(5/2)/(5*e**7) + 2*c**3*(d + e*x)**(7/2)/(7*e**7) + 4*c*d*(a*e**2 + c*d**2)**2/(e**7*(d + e*x)**(3/2)) - 6*c*(a*e**2 + c*d**2)*(a*e**2 + 5*c*d**2)/(e**7*sqrt(d + e*x)) + (d + e*x)**(3/2)*(6*a*c**2*e**2 + 30*c**3*d**2)/(3*e**7) + sqrt(d + e*x)*(-24*a*c**2*d*e**2 - 40*c**3*d**3)/e**7 - 2*(a*e**2 + c*d**2)**3/(5*e**7*(d + e*x)**(5/2))","A",0
612,1,498,0,124.492603," ","integrate((e*x+d)**(5/2)/(-c*x**2+a),x)","- \frac{4 a d e^{3} \operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c e^{6} - 256 a^{2} c^{2} d^{2} e^{4}\right) + 32 t^{2} a c d e^{2} - 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} c d e^{4} + 64 t^{3} a c^{2} d^{3} e^{2} - 4 t a e^{2} - 4 t c d^{2} + \sqrt{d + e x} \right)} \right)\right)}}{c} - \frac{2 a e^{3} \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} - 32 t^{2} a c^{2} d e^{2} - a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(- 64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)}}{c} + 4 d^{3} e \operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c e^{6} - 256 a^{2} c^{2} d^{2} e^{4}\right) + 32 t^{2} a c d e^{2} - 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} c d e^{4} + 64 t^{3} a c^{2} d^{3} e^{2} - 4 t a e^{2} - 4 t c d^{2} + \sqrt{d + e x} \right)} \right)\right)} - 4 d^{2} e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} - 32 t^{2} a c^{2} d e^{2} - a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(- 64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)} - 2 d^{2} e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} - 32 t^{2} a c^{2} d e^{2} - a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(- 64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)} - \frac{4 d e \sqrt{d + e x}}{c} - \frac{2 e \left(d + e x\right)^{\frac{3}{2}}}{3 c}"," ",0,"-4*a*d*e**3*RootSum(_t**4*(256*a**3*c*e**6 - 256*a**2*c**2*d**2*e**4) + 32*_t**2*a*c*d*e**2 - 1, Lambda(_t, _t*log(-64*_t**3*a**2*c*d*e**4 + 64*_t**3*a*c**2*d**3*e**2 - 4*_t*a*e**2 - 4*_t*c*d**2 + sqrt(d + e*x))))/c - 2*a*e**3*RootSum(256*_t**4*a**2*c**3*e**4 - 32*_t**2*a*c**2*d*e**2 - a*e**2 + c*d**2, Lambda(_t, _t*log(-64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x))))/c + 4*d**3*e*RootSum(_t**4*(256*a**3*c*e**6 - 256*a**2*c**2*d**2*e**4) + 32*_t**2*a*c*d*e**2 - 1, Lambda(_t, _t*log(-64*_t**3*a**2*c*d*e**4 + 64*_t**3*a*c**2*d**3*e**2 - 4*_t*a*e**2 - 4*_t*c*d**2 + sqrt(d + e*x)))) - 4*d**2*e*RootSum(256*_t**4*a**2*c**3*e**4 - 32*_t**2*a*c**2*d*e**2 - a*e**2 + c*d**2, Lambda(_t, _t*log(-64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x)))) - 2*d**2*e*RootSum(256*_t**4*a**2*c**3*e**4 - 32*_t**2*a*c**2*d*e**2 - a*e**2 + c*d**2, Lambda(_t, _t*log(-64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x)))) - 4*d*e*sqrt(d + e*x)/c - 2*e*(d + e*x)**(3/2)/(3*c)","B",0
613,1,394,0,65.630899," ","integrate((e*x+d)**(3/2)/(-c*x**2+a),x)","- \frac{2 a e^{3} \operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c e^{6} - 256 a^{2} c^{2} d^{2} e^{4}\right) + 32 t^{2} a c d e^{2} - 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} c d e^{4} + 64 t^{3} a c^{2} d^{3} e^{2} - 4 t a e^{2} - 4 t c d^{2} + \sqrt{d + e x} \right)} \right)\right)}}{c} + 2 d^{2} e \operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c e^{6} - 256 a^{2} c^{2} d^{2} e^{4}\right) + 32 t^{2} a c d e^{2} - 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} c d e^{4} + 64 t^{3} a c^{2} d^{3} e^{2} - 4 t a e^{2} - 4 t c d^{2} + \sqrt{d + e x} \right)} \right)\right)} - 2 d e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} - 32 t^{2} a c^{2} d e^{2} - a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(- 64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)} - 2 d e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} - 32 t^{2} a c^{2} d e^{2} - a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(- 64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)} - \frac{2 e \sqrt{d + e x}}{c}"," ",0,"-2*a*e**3*RootSum(_t**4*(256*a**3*c*e**6 - 256*a**2*c**2*d**2*e**4) + 32*_t**2*a*c*d*e**2 - 1, Lambda(_t, _t*log(-64*_t**3*a**2*c*d*e**4 + 64*_t**3*a*c**2*d**3*e**2 - 4*_t*a*e**2 - 4*_t*c*d**2 + sqrt(d + e*x))))/c + 2*d**2*e*RootSum(_t**4*(256*a**3*c*e**6 - 256*a**2*c**2*d**2*e**4) + 32*_t**2*a*c*d*e**2 - 1, Lambda(_t, _t*log(-64*_t**3*a**2*c*d*e**4 + 64*_t**3*a*c**2*d**3*e**2 - 4*_t*a*e**2 - 4*_t*c*d**2 + sqrt(d + e*x)))) - 2*d*e*RootSum(256*_t**4*a**2*c**3*e**4 - 32*_t**2*a*c**2*d*e**2 - a*e**2 + c*d**2, Lambda(_t, _t*log(-64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x)))) - 2*d*e*RootSum(256*_t**4*a**2*c**3*e**4 - 32*_t**2*a*c**2*d*e**2 - a*e**2 + c*d**2, Lambda(_t, _t*log(-64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x)))) - 2*e*sqrt(d + e*x)/c","B",0
614,1,76,0,7.378061," ","integrate((e*x+d)**(1/2)/(-c*x**2+a),x)","- 2 e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} - 32 t^{2} a c^{2} d e^{2} - a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(- 64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)}"," ",0,"-2*e*RootSum(256*_t**4*a**2*c**3*e**4 - 32*_t**2*a*c**2*d*e**2 - a*e**2 + c*d**2, Lambda(_t, _t*log(-64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x))))","A",0
615,0,0,0,0.000000," ","integrate(1/(-c*x**2+a)/(e*x+d)**(1/2),x)","- \int \frac{1}{- a \sqrt{d + e x} + c x^{2} \sqrt{d + e x}}\, dx"," ",0,"-Integral(1/(-a*sqrt(d + e*x) + c*x**2*sqrt(d + e*x)), x)","F",0
616,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(-c*x**2+a),x)","- \int \frac{1}{- a d \sqrt{d + e x} - a e x \sqrt{d + e x} + c d x^{2} \sqrt{d + e x} + c e x^{3} \sqrt{d + e x}}\, dx"," ",0,"-Integral(1/(-a*d*sqrt(d + e*x) - a*e*x*sqrt(d + e*x) + c*d*x**2*sqrt(d + e*x) + c*e*x**3*sqrt(d + e*x)), x)","F",0
617,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(-c*x**2+a),x)","- \int \frac{1}{- a d^{2} \sqrt{d + e x} - 2 a d e x \sqrt{d + e x} - a e^{2} x^{2} \sqrt{d + e x} + c d^{2} x^{2} \sqrt{d + e x} + 2 c d e x^{3} \sqrt{d + e x} + c e^{2} x^{4} \sqrt{d + e x}}\, dx"," ",0,"-Integral(1/(-a*d**2*sqrt(d + e*x) - 2*a*d*e*x*sqrt(d + e*x) - a*e**2*x**2*sqrt(d + e*x) + c*d**2*x**2*sqrt(d + e*x) + 2*c*d*e*x**3*sqrt(d + e*x) + c*e**2*x**4*sqrt(d + e*x)), x)","F",0
618,1,498,0,118.389590," ","integrate((e*x+d)**(5/2)/(c*x**2+a),x)","- \frac{4 a d e^{3} \operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c e^{6} + 256 a^{2} c^{2} d^{2} e^{4}\right) + 32 t^{2} a c d e^{2} + 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} c d e^{4} - 64 t^{3} a c^{2} d^{3} e^{2} + 4 t a e^{2} - 4 t c d^{2} + \sqrt{d + e x} \right)} \right)\right)}}{c} - \frac{2 a e^{3} \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} + 32 t^{2} a c^{2} d e^{2} + a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)}}{c} - 4 d^{3} e \operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c e^{6} + 256 a^{2} c^{2} d^{2} e^{4}\right) + 32 t^{2} a c d e^{2} + 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} c d e^{4} - 64 t^{3} a c^{2} d^{3} e^{2} + 4 t a e^{2} - 4 t c d^{2} + \sqrt{d + e x} \right)} \right)\right)} + 2 d^{2} e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} + 32 t^{2} a c^{2} d e^{2} + a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)} + 4 d^{2} e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} + 32 t^{2} a c^{2} d e^{2} + a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)} + \frac{4 d e \sqrt{d + e x}}{c} + \frac{2 e \left(d + e x\right)^{\frac{3}{2}}}{3 c}"," ",0,"-4*a*d*e**3*RootSum(_t**4*(256*a**3*c*e**6 + 256*a**2*c**2*d**2*e**4) + 32*_t**2*a*c*d*e**2 + 1, Lambda(_t, _t*log(-64*_t**3*a**2*c*d*e**4 - 64*_t**3*a*c**2*d**3*e**2 + 4*_t*a*e**2 - 4*_t*c*d**2 + sqrt(d + e*x))))/c - 2*a*e**3*RootSum(256*_t**4*a**2*c**3*e**4 + 32*_t**2*a*c**2*d*e**2 + a*e**2 + c*d**2, Lambda(_t, _t*log(64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x))))/c - 4*d**3*e*RootSum(_t**4*(256*a**3*c*e**6 + 256*a**2*c**2*d**2*e**4) + 32*_t**2*a*c*d*e**2 + 1, Lambda(_t, _t*log(-64*_t**3*a**2*c*d*e**4 - 64*_t**3*a*c**2*d**3*e**2 + 4*_t*a*e**2 - 4*_t*c*d**2 + sqrt(d + e*x)))) + 2*d**2*e*RootSum(256*_t**4*a**2*c**3*e**4 + 32*_t**2*a*c**2*d*e**2 + a*e**2 + c*d**2, Lambda(_t, _t*log(64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x)))) + 4*d**2*e*RootSum(256*_t**4*a**2*c**3*e**4 + 32*_t**2*a*c**2*d*e**2 + a*e**2 + c*d**2, Lambda(_t, _t*log(64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x)))) + 4*d*e*sqrt(d + e*x)/c + 2*e*(d + e*x)**(3/2)/(3*c)","A",0
619,1,394,0,61.730365," ","integrate((e*x+d)**(3/2)/(c*x**2+a),x)","- \frac{2 a e^{3} \operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c e^{6} + 256 a^{2} c^{2} d^{2} e^{4}\right) + 32 t^{2} a c d e^{2} + 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} c d e^{4} - 64 t^{3} a c^{2} d^{3} e^{2} + 4 t a e^{2} - 4 t c d^{2} + \sqrt{d + e x} \right)} \right)\right)}}{c} - 2 d^{2} e \operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c e^{6} + 256 a^{2} c^{2} d^{2} e^{4}\right) + 32 t^{2} a c d e^{2} + 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} c d e^{4} - 64 t^{3} a c^{2} d^{3} e^{2} + 4 t a e^{2} - 4 t c d^{2} + \sqrt{d + e x} \right)} \right)\right)} + 2 d e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} + 32 t^{2} a c^{2} d e^{2} + a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)} + 2 d e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} + 32 t^{2} a c^{2} d e^{2} + a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)} + \frac{2 e \sqrt{d + e x}}{c}"," ",0,"-2*a*e**3*RootSum(_t**4*(256*a**3*c*e**6 + 256*a**2*c**2*d**2*e**4) + 32*_t**2*a*c*d*e**2 + 1, Lambda(_t, _t*log(-64*_t**3*a**2*c*d*e**4 - 64*_t**3*a*c**2*d**3*e**2 + 4*_t*a*e**2 - 4*_t*c*d**2 + sqrt(d + e*x))))/c - 2*d**2*e*RootSum(_t**4*(256*a**3*c*e**6 + 256*a**2*c**2*d**2*e**4) + 32*_t**2*a*c*d*e**2 + 1, Lambda(_t, _t*log(-64*_t**3*a**2*c*d*e**4 - 64*_t**3*a*c**2*d**3*e**2 + 4*_t*a*e**2 - 4*_t*c*d**2 + sqrt(d + e*x)))) + 2*d*e*RootSum(256*_t**4*a**2*c**3*e**4 + 32*_t**2*a*c**2*d*e**2 + a*e**2 + c*d**2, Lambda(_t, _t*log(64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x)))) + 2*d*e*RootSum(256*_t**4*a**2*c**3*e**4 + 32*_t**2*a*c**2*d*e**2 + a*e**2 + c*d**2, Lambda(_t, _t*log(64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x)))) + 2*e*sqrt(d + e*x)/c","A",0
620,1,75,0,6.903456," ","integrate((e*x+d)**(1/2)/(c*x**2+a),x)","2 e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} + 32 t^{2} a c^{2} d e^{2} + a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)}"," ",0,"2*e*RootSum(256*_t**4*a**2*c**3*e**4 + 32*_t**2*a*c**2*d*e**2 + a*e**2 + c*d**2, Lambda(_t, _t*log(64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x))))","A",0
621,0,0,0,0.000000," ","integrate(1/(c*x**2+a)/(e*x+d)**(1/2),x)","\int \frac{1}{\left(a + c x^{2}\right) \sqrt{d + e x}}\, dx"," ",0,"Integral(1/((a + c*x**2)*sqrt(d + e*x)), x)","F",0
622,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+a),x)","\int \frac{1}{\left(a + c x^{2}\right) \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + c*x**2)*(d + e*x)**(3/2)), x)","F",0
623,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+a),x)","\int \frac{1}{\left(a + c x^{2}\right) \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + c*x**2)*(d + e*x)**(5/2)), x)","F",0
624,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate(1/(-c*x**2+a)**2/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate(1/(c*x**2+a)**2/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(-c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
639,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(-c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
640,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(-c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(-c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
642,-1,0,0,0.000000," ","integrate(1/(-c*x**2+a)**3/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
645,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
646,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
647,-1,0,0,0.000000," ","integrate(1/(c*x**2+a)**3/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
648,1,32,0,4.355524," ","integrate((2+3*x)**(1/2)/(x**2+1),x)","6 \operatorname{RootSum} {\left(20736 t^{4} + 576 t^{2} + 13, \left( t \mapsto t \log{\left(576 t^{3} + 8 t + \sqrt{3 x + 2} \right)} \right)\right)}"," ",0,"6*RootSum(20736*_t**4 + 576*_t**2 + 13, Lambda(_t, _t*log(576*_t**3 + 8*_t + sqrt(3*x + 2))))","A",0
649,1,53,0,5.290192," ","integrate((d*x+c)**(1/2)/(x**2+1),x)","2 d \operatorname{RootSum} {\left(256 t^{4} d^{4} + 32 t^{2} c d^{2} + c^{2} + d^{2}, \left( t \mapsto t \log{\left(64 t^{3} d^{2} + 4 t c + \sqrt{c + d x} \right)} \right)\right)}"," ",0,"2*d*RootSum(256*_t**4*d**4 + 32*_t**2*c*d**2 + c**2 + d**2, Lambda(_t, _t*log(64*_t**3*d**2 + 4*_t*c + sqrt(c + d*x))))","A",0
650,1,70,0,4.599852," ","integrate((2+3*x)**(1/2)/(-x**2+1),x)","- 5 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} \sqrt{3 x + 2}}{5} \right)}}{5} & \text{for}\: 3 x + 2 > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} \sqrt{3 x + 2}}{5} \right)}}{5} & \text{for}\: 3 x + 2 < 5 \end{cases}\right) - \operatorname{atan}{\left(\sqrt{3 x + 2} \right)}"," ",0,"-5*Piecewise((-sqrt(5)*acoth(sqrt(5)*sqrt(3*x + 2)/5)/5, 3*x + 2 > 5), (-sqrt(5)*atanh(sqrt(5)*sqrt(3*x + 2)/5)/5, 3*x + 2 < 5)) - atan(sqrt(3*x + 2))","A",0
651,1,61,0,5.247418," ","integrate((d*x+c)**(1/2)/(-x**2+1),x)","\frac{2 \left(\frac{d \left(c - d\right) \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{- c + d}} \right)}}{2 \sqrt{- c + d}} - \frac{d \left(c + d\right) \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{- c - d}} \right)}}{2 \sqrt{- c - d}}\right)}{d}"," ",0,"2*(d*(c - d)*atan(sqrt(c + d*x)/sqrt(-c + d))/(2*sqrt(-c + d)) - d*(c + d)*atan(sqrt(c + d*x)/sqrt(-c - d))/(2*sqrt(-c - d)))/d","A",0
652,1,56,0,6.015915," ","integrate((2+3*x)**(1/2)/(b*x**2+a),x)","6 \operatorname{RootSum} {\left(20736 t^{4} a^{2} b^{3} + 576 t^{2} a b^{2} + 9 a + 4 b, \left( t \mapsto t \log{\left(576 t^{3} a b^{2} + 8 t b + \sqrt{3 x + 2} \right)} \right)\right)}"," ",0,"6*RootSum(20736*_t**4*a**2*b**3 + 576*_t**2*a*b**2 + 9*a + 4*b, Lambda(_t, _t*log(576*_t**3*a*b**2 + 8*_t*b + sqrt(3*x + 2))))","A",0
653,1,58,0,6.801736," ","integrate((2+3*x)**(1/2)/(-b*x**2+a),x)","- 6 \operatorname{RootSum} {\left(20736 t^{4} a^{2} b^{3} - 576 t^{2} a b^{2} - 9 a + 4 b, \left( t \mapsto t \log{\left(- 576 t^{3} a b^{2} + 8 t b + \sqrt{3 x + 2} \right)} \right)\right)}"," ",0,"-6*RootSum(20736*_t**4*a**2*b**3 - 576*_t**2*a*b**2 - 9*a + 4*b, Lambda(_t, _t*log(-576*_t**3*a*b**2 + 8*_t*b + sqrt(3*x + 2))))","A",0
654,1,31,0,3.921070," ","integrate((1+x)**(1/2)/(x**2+1),x)","2 \operatorname{RootSum} {\left(128 t^{4} + 16 t^{2} + 1, \left( t \mapsto t \log{\left(64 t^{3} + 4 t + \sqrt{x + 1} \right)} \right)\right)}"," ",0,"2*RootSum(128*_t**4 + 16*_t**2 + 1, Lambda(_t, _t*log(64*_t**3 + 4*_t + sqrt(x + 1))))","A",0
655,0,0,0,0.000000," ","integrate(1/(x**2+1)/(1+x)**(1/2),x)","\int \frac{1}{\sqrt{x + 1} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(x + 1)*(x**2 + 1)), x)","F",0
656,-1,0,0,0.000000," ","integrate((-1+x)**(1/2)/(x**2+1)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
657,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(c*x**2+a)**(1/2),x)","\int \sqrt{a + c x^{2}} \left(d + e x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x)**(3/2), x)","F",0
658,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(c*x**2+a)**(1/2),x)","\int \sqrt{a + c x^{2}} \sqrt{d + e x}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*sqrt(d + e*x), x)","F",0
659,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{a + c x^{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/sqrt(d + e*x), x)","F",0
660,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\sqrt{a + c x^{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(d + e*x)**(3/2), x)","F",0
661,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\sqrt{a + c x^{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(d + e*x)**(5/2), x)","F",0
662,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)**(7/2),x)","\int \frac{\sqrt{a + c x^{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(d + e*x)**(7/2), x)","F",0
663,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(c*x**2+a)**(3/2),x)","\int \left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)*(d + e*x)**(3/2), x)","F",0
664,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)*(e*x+d)**(1/2),x)","\int \left(a + c x^{2}\right)^{\frac{3}{2}} \sqrt{d + e x}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)*sqrt(d + e*x), x)","F",0
665,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/sqrt(d + e*x), x)","F",0
666,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x)**(3/2), x)","F",0
667,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x)**(5/2), x)","F",0
668,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**(7/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x)**(7/2), x)","F",0
669,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)/(e*x+d)**(9/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)/(d + e*x)**(9/2), x)","F",0
670,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)*(e*x+d)**(1/2),x)","\int \left(a + c x^{2}\right)^{\frac{5}{2}} \sqrt{d + e x}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)*sqrt(d + e*x), x)","F",0
671,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**(1/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/sqrt(d + e*x), x)","F",0
672,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**(3/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**(3/2), x)","F",0
673,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**(5/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**(5/2), x)","F",0
674,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**(7/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**(7/2), x)","F",0
675,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**(9/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**(9/2), x)","F",0
676,0,0,0,0.000000," ","integrate((c*x**2+a)**(5/2)/(e*x+d)**(11/2),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{\frac{11}{2}}}\, dx"," ",0,"Integral((a + c*x**2)**(5/2)/(d + e*x)**(11/2), x)","F",0
677,0,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{7}{2}}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**(7/2)/sqrt(a + c*x**2), x)","F",0
678,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{5}{2}}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**(5/2)/sqrt(a + c*x**2), x)","F",0
679,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/sqrt(a + c*x**2), x)","F",0
680,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/sqrt(a + c*x**2), x)","F",0
681,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*sqrt(d + e*x)), x)","F",0
682,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)**(3/2)), x)","F",0
683,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)**(5/2)), x)","F",0
684,0,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)**(7/2)), x)","F",0
685,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
686,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{5}{2}}}{\left(a + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(5/2)/(a + c*x**2)**(3/2), x)","F",0
687,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\left(a + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/(a + c*x**2)**(3/2), x)","F",0
688,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+a)**(3/2),x)","\int \frac{\sqrt{d + e x}}{\left(a + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/(a + c*x**2)**(3/2), x)","F",0
689,0,0,0,0.000000," ","integrate(1/(c*x**2+a)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{3}{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(3/2)*sqrt(d + e*x)), x)","F",0
690,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+a)**(3/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(3/2)*(d + e*x)**(3/2)), x)","F",0
691,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+a)**(3/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(3/2)*(d + e*x)**(5/2)), x)","F",0
692,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
693,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
694,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
695,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
696,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
697,0,0,0,0.000000," ","integrate(1/(c*x**2+a)**(5/2)/(e*x+d)**(1/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{5}{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(5/2)*sqrt(d + e*x)), x)","F",0
698,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+a)**(5/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{5}{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(5/2)*(d + e*x)**(3/2)), x)","F",0
699,0,0,0,0.000000," ","integrate(1/(e*x+d)/(3*e**2*x**2+d**2)**(1/3),x)","\int \frac{1}{\left(d + e x\right) \sqrt[3]{d^{2} + 3 e^{2} x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(d**2 + 3*e**2*x**2)**(1/3)), x)","F",0
700,1,85,0,5.943524," ","integrate((2+3*x)**3/(27*x**2+4)**(1/3),x)","9 \sqrt[3]{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{27 x^{2} e^{i \pi}}{4}} \right)} + \frac{3 x^{2} \left(27 x^{2} + 4\right)^{\frac{2}{3}}}{10} + 4 \sqrt[3]{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{27 x^{2} e^{i \pi}}{4}} \right)} + \frac{14 \left(27 x^{2} + 4\right)^{\frac{2}{3}}}{15}"," ",0,"9*2**(1/3)*x**3*hyper((1/3, 3/2), (5/2,), 27*x**2*exp_polar(I*pi)/4) + 3*x**2*(27*x**2 + 4)**(2/3)/10 + 4*2**(1/3)*x*hyper((1/3, 1/2), (3/2,), 27*x**2*exp_polar(I*pi)/4) + 14*(27*x**2 + 4)**(2/3)/15","A",0
701,1,68,0,4.261498," ","integrate((2+3*x)**2/(27*x**2+4)**(1/3),x)","\frac{3 \sqrt[3]{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{27 x^{2} e^{i \pi}}{4}} \right)}}{2} + 2 \sqrt[3]{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{27 x^{2} e^{i \pi}}{4}} \right)} + \frac{\left(27 x^{2} + 4\right)^{\frac{2}{3}}}{3}"," ",0,"3*2**(1/3)*x**3*hyper((1/3, 3/2), (5/2,), 27*x**2*exp_polar(I*pi)/4)/2 + 2*2**(1/3)*x*hyper((1/3, 1/2), (3/2,), 27*x**2*exp_polar(I*pi)/4) + (27*x**2 + 4)**(2/3)/3","A",0
702,1,36,0,2.842761," ","integrate((2+3*x)/(27*x**2+4)**(1/3),x)","\sqrt[3]{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{27 x^{2} e^{i \pi}}{4}} \right)} + \frac{\left(27 x^{2} + 4\right)^{\frac{2}{3}}}{12}"," ",0,"2**(1/3)*x*hyper((1/3, 1/2), (3/2,), 27*x**2*exp_polar(I*pi)/4) + (27*x**2 + 4)**(2/3)/12","A",0
703,0,0,0,0.000000," ","integrate(1/(2+3*x)/(27*x**2+4)**(1/3),x)","\int \frac{1}{\left(3 x + 2\right) \sqrt[3]{27 x^{2} + 4}}\, dx"," ",0,"Integral(1/((3*x + 2)*(27*x**2 + 4)**(1/3)), x)","F",0
704,0,0,0,0.000000," ","integrate(1/(2+3*x)**2/(27*x**2+4)**(1/3),x)","\int \frac{1}{\left(3 x + 2\right)^{2} \sqrt[3]{27 x^{2} + 4}}\, dx"," ",0,"Integral(1/((3*x + 2)**2*(27*x**2 + 4)**(1/3)), x)","F",0
705,0,0,0,0.000000," ","integrate(1/(2+3*x)**3/(27*x**2+4)**(1/3),x)","\int \frac{1}{\left(3 x + 2\right)^{3} \sqrt[3]{27 x^{2} + 4}}\, dx"," ",0,"Integral(1/((3*x + 2)**3*(27*x**2 + 4)**(1/3)), x)","F",0
706,1,150,0,6.692834," ","integrate((2+3*I*x)**3/(-27*x**2+4)**(1/3),x)","- 9 \sqrt[3]{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{27 x^{2} e^{2 i \pi}}{4}} \right)} + 4 \sqrt[3]{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{27 x^{2} e^{2 i \pi}}{4}} \right)} - i \left(4 - 27 x^{2}\right)^{\frac{2}{3}} - 27 i \left(\begin{cases} \frac{x^{2} \left(27 x^{2} - 4\right)^{\frac{2}{3}} e^{- \frac{i \pi}{3}}}{90} + \frac{\left(27 x^{2} - 4\right)^{\frac{2}{3}} e^{- \frac{i \pi}{3}}}{405} & \text{for}\: \frac{27 \left|{x^{2}}\right|}{4} > 1 \\- \frac{x^{2} \left(4 - 27 x^{2}\right)^{\frac{2}{3}}}{90} - \frac{\left(4 - 27 x^{2}\right)^{\frac{2}{3}}}{405} & \text{otherwise} \end{cases}\right)"," ",0,"-9*2**(1/3)*x**3*hyper((1/3, 3/2), (5/2,), 27*x**2*exp_polar(2*I*pi)/4) + 4*2**(1/3)*x*hyper((1/3, 1/2), (3/2,), 27*x**2*exp_polar(2*I*pi)/4) - I*(4 - 27*x**2)**(2/3) - 27*I*Piecewise((x**2*(27*x**2 - 4)**(2/3)*exp(-I*pi/3)/90 + (27*x**2 - 4)**(2/3)*exp(-I*pi/3)/405, 27*Abs(x**2)/4 > 1), (-x**2*(4 - 27*x**2)**(2/3)/90 - (4 - 27*x**2)**(2/3)/405, True))","A",0
707,1,73,0,4.718987," ","integrate((2+3*I*x)**2/(-27*x**2+4)**(1/3),x)","- \frac{3 \sqrt[3]{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{27 x^{2} e^{2 i \pi}}{4}} \right)}}{2} + 2 \sqrt[3]{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{27 x^{2} e^{2 i \pi}}{4}} \right)} - \frac{i \left(4 - 27 x^{2}\right)^{\frac{2}{3}}}{3}"," ",0,"-3*2**(1/3)*x**3*hyper((1/3, 3/2), (5/2,), 27*x**2*exp_polar(2*I*pi)/4)/2 + 2*2**(1/3)*x*hyper((1/3, 1/2), (3/2,), 27*x**2*exp_polar(2*I*pi)/4) - I*(4 - 27*x**2)**(2/3)/3","A",0
708,1,39,0,2.558977," ","integrate((2+3*I*x)/(-27*x**2+4)**(1/3),x)","\sqrt[3]{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{27 x^{2} e^{2 i \pi}}{4}} \right)} - \frac{i \left(4 - 27 x^{2}\right)^{\frac{2}{3}}}{12}"," ",0,"2**(1/3)*x*hyper((1/3, 1/2), (3/2,), 27*x**2*exp_polar(2*I*pi)/4) - I*(4 - 27*x**2)**(2/3)/12","A",0
709,0,0,0,0.000000," ","integrate(1/(2+3*I*x)/(-27*x**2+4)**(1/3),x)","- i \int \frac{1}{3 x \sqrt[3]{4 - 27 x^{2}} - 2 i \sqrt[3]{4 - 27 x^{2}}}\, dx"," ",0,"-I*Integral(1/(3*x*(4 - 27*x**2)**(1/3) - 2*I*(4 - 27*x**2)**(1/3)), x)","F",0
710,0,0,0,0.000000," ","integrate(1/(2+3*I*x)**2/(-27*x**2+4)**(1/3),x)","- \int \frac{1}{9 x^{2} \sqrt[3]{4 - 27 x^{2}} - 12 i x \sqrt[3]{4 - 27 x^{2}} - 4 \sqrt[3]{4 - 27 x^{2}}}\, dx"," ",0,"-Integral(1/(9*x**2*(4 - 27*x**2)**(1/3) - 12*I*x*(4 - 27*x**2)**(1/3) - 4*(4 - 27*x**2)**(1/3)), x)","F",0
711,0,0,0,0.000000," ","integrate(1/(2+3*I*x)**3/(-27*x**2+4)**(1/3),x)","i \int \frac{1}{27 x^{3} \sqrt[3]{4 - 27 x^{2}} - 54 i x^{2} \sqrt[3]{4 - 27 x^{2}} - 36 x \sqrt[3]{4 - 27 x^{2}} + 8 i \sqrt[3]{4 - 27 x^{2}}}\, dx"," ",0,"I*Integral(1/(27*x**3*(4 - 27*x**2)**(1/3) - 54*I*x**2*(4 - 27*x**2)**(1/3) - 36*x*(4 - 27*x**2)**(1/3) + 8*I*(4 - 27*x**2)**(1/3)), x)","F",0
712,0,0,0,0.000000," ","integrate(1/(x**2+1)**(1/3)/(x+3**(1/2)),x)","\int \frac{1}{\left(x + \sqrt{3}\right) \sqrt[3]{x^{2} + 1}}\, dx"," ",0,"Integral(1/((x + sqrt(3))*(x**2 + 1)**(1/3)), x)","F",0
713,0,0,0,0.000000," ","integrate(1/(x**2+1)**(1/3)/(-x+3**(1/2)),x)","- \int \frac{1}{x \sqrt[3]{x^{2} + 1} - \sqrt{3} \sqrt[3]{x^{2} + 1}}\, dx"," ",0,"-Integral(1/(x*(x**2 + 1)**(1/3) - sqrt(3)*(x**2 + 1)**(1/3)), x)","F",0
714,0,0,0,0.000000," ","integrate(1/(3-x)/(-x**2+1)**(1/3),x)","- \int \frac{1}{x \sqrt[3]{1 - x^{2}} - 3 \sqrt[3]{1 - x^{2}}}\, dx"," ",0,"-Integral(1/(x*(1 - x**2)**(1/3) - 3*(1 - x**2)**(1/3)), x)","F",0
715,0,0,0,0.000000," ","integrate(1/(3+x)/(-x**2+1)**(1/3),x)","\int \frac{1}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x + 3\right)}\, dx"," ",0,"Integral(1/((-(x - 1)*(x + 1))**(1/3)*(x + 3)), x)","F",0
716,0,0,0,0.000000," ","integrate(1/(e*x+d)/(-9*e**2*x**2+d**2)**(1/3),x)","\int \frac{1}{\sqrt[3]{- \left(- d + 3 e x\right) \left(d + 3 e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((-(-d + 3*e*x)*(d + 3*e*x))**(1/3)*(d + e*x)), x)","F",0
717,0,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x**2+c)**(1/4),x)","\int \frac{1}{\left(a + b x\right) \sqrt[4]{c + d x^{2}}}\, dx"," ",0,"Integral(1/((a + b*x)*(c + d*x**2)**(1/4)), x)","F",0
718,0,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x**2+c)**(3/4),x)","\int \frac{1}{\left(a + b x\right) \left(c + d x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)*(c + d*x**2)**(3/4)), x)","F",0
719,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+a)**(1/4),x)","\int \frac{1}{\sqrt[4]{a + c x^{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + c*x**2)**(1/4)*(d + e*x)**(3/2)), x)","F",0
720,0,0,0,0.000000," ","integrate(1/(1+x)/(x**2+1)**(1/6),x)","\int \frac{1}{\left(x + 1\right) \sqrt[6]{x^{2} + 1}}\, dx"," ",0,"Integral(1/((x + 1)*(x**2 + 1)**(1/6)), x)","F",0
721,-1,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
722,1,5097,0,6.581274," ","integrate((e*x+d)**m*(c*x**2+a)**2,x)","\begin{cases} d^{m} \left(a^{2} x + \frac{2 a c x^{3}}{3} + \frac{c^{2} x^{5}}{5}\right) & \text{for}\: e = 0 \\- \frac{3 a^{2} e^{4}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{2 a c d^{2} e^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{8 a c d e^{3} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{12 a c e^{4} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{25 c^{2} d^{4}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{88 c^{2} d^{3} e x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{72 c^{2} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{108 c^{2} d^{2} e^{2} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c^{2} d e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c^{2} d e^{3} x^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{12 c^{2} e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} & \text{for}\: m = -5 \\- \frac{a^{2} e^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{2 a c d^{2} e^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{6 a c d e^{3} x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{6 a c e^{4} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{22 c^{2} d^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{54 c^{2} d^{3} e x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 c^{2} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 c^{2} d^{2} e^{2} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{12 c^{2} d e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{3 c^{2} e^{4} x^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} & \text{for}\: m = -4 \\- \frac{a^{2} e^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 a c d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{6 a c d^{2} e^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{8 a c d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{8 a c d e^{3} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 a c e^{4} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{18 c^{2} d^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 c^{2} d^{3} e x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 c^{2} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{4 c^{2} d e^{3} x^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{c^{2} e^{4} x^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} & \text{for}\: m = -3 \\- \frac{3 a^{2} e^{4}}{3 d e^{5} + 3 e^{6} x} - \frac{12 a c d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{12 a c d^{2} e^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{12 a c d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{6 a c e^{4} x^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{12 c^{2} d^{4}}{3 d e^{5} + 3 e^{6} x} - \frac{12 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{6 c^{2} d^{2} e^{2} x^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{2 c^{2} d e^{3} x^{3}}{3 d e^{5} + 3 e^{6} x} + \frac{c^{2} e^{4} x^{4}}{3 d e^{5} + 3 e^{6} x} & \text{for}\: m = -2 \\\frac{a^{2} \log{\left(\frac{d}{e} + x \right)}}{e} + \frac{2 a c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{2 a c d x}{e^{2}} + \frac{a c x^{2}}{e} + \frac{c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{e^{5}} - \frac{c^{2} d^{3} x}{e^{4}} + \frac{c^{2} d^{2} x^{2}}{2 e^{3}} - \frac{c^{2} d x^{3}}{3 e^{2}} + \frac{c^{2} x^{4}}{4 e} & \text{for}\: m = -1 \\\frac{a^{2} d e^{4} m^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{14 a^{2} d e^{4} m^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{71 a^{2} d e^{4} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{154 a^{2} d e^{4} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a^{2} d e^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{a^{2} e^{5} m^{4} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{14 a^{2} e^{5} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{71 a^{2} e^{5} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{154 a^{2} e^{5} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a^{2} e^{5} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{4 a c d^{3} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{36 a c d^{3} e^{2} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{80 a c d^{3} e^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{4 a c d^{2} e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{36 a c d^{2} e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{80 a c d^{2} e^{3} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 a c d e^{4} m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{20 a c d e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{58 a c d e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 a c d e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 a c e^{5} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 a c e^{5} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{98 a c e^{5} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{156 a c e^{5} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{80 a c e^{5} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 c^{2} d^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{24 c^{2} d^{4} e m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 c^{2} d^{3} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 c^{2} d^{3} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{4 c^{2} d^{2} e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 c^{2} d^{2} e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{8 c^{2} d^{2} e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{c^{2} d e^{4} m^{4} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 c^{2} d e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{11 c^{2} d e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 c^{2} d e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{c^{2} e^{5} m^{4} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{10 c^{2} e^{5} m^{3} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{35 c^{2} e^{5} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{50 c^{2} e^{5} m x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 c^{2} e^{5} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a**2*x + 2*a*c*x**3/3 + c**2*x**5/5), Eq(e, 0)), (-3*a**2*e**4/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 2*a*c*d**2*e**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 8*a*c*d*e**3*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 12*a*c*e**4*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 12*c**2*d**4*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 25*c**2*d**4/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c**2*d**3*e*x*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 88*c**2*d**3*e*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 72*c**2*d**2*e**2*x**2*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 108*c**2*d**2*e**2*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c**2*d*e**3*x**3*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c**2*d*e**3*x**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 12*c**2*e**4*x**4*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4), Eq(m, -5)), (-a**2*e**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 2*a*c*d**2*e**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 6*a*c*d*e**3*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 6*a*c*e**4*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 12*c**2*d**4*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 22*c**2*d**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*c**2*d**3*e*x*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 54*c**2*d**3*e*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*c**2*d**2*e**2*x**2*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*c**2*d**2*e**2*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 12*c**2*d*e**3*x**3*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 3*c**2*e**4*x**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3), Eq(m, -4)), (-a**2*e**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*a*c*d**2*e**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 6*a*c*d**2*e**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 8*a*c*d*e**3*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 8*a*c*d*e**3*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*a*c*e**4*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*c**2*d**4*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 18*c**2*d**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*c**2*d**3*e*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*c**2*d**3*e*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*c**2*d**2*e**2*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 4*c**2*d*e**3*x**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + c**2*e**4*x**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2), Eq(m, -3)), (-3*a**2*e**4/(3*d*e**5 + 3*e**6*x) - 12*a*c*d**2*e**2*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 12*a*c*d**2*e**2/(3*d*e**5 + 3*e**6*x) - 12*a*c*d*e**3*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 6*a*c*e**4*x**2/(3*d*e**5 + 3*e**6*x) - 12*c**2*d**4*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 12*c**2*d**4/(3*d*e**5 + 3*e**6*x) - 12*c**2*d**3*e*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 6*c**2*d**2*e**2*x**2/(3*d*e**5 + 3*e**6*x) - 2*c**2*d*e**3*x**3/(3*d*e**5 + 3*e**6*x) + c**2*e**4*x**4/(3*d*e**5 + 3*e**6*x), Eq(m, -2)), (a**2*log(d/e + x)/e + 2*a*c*d**2*log(d/e + x)/e**3 - 2*a*c*d*x/e**2 + a*c*x**2/e + c**2*d**4*log(d/e + x)/e**5 - c**2*d**3*x/e**4 + c**2*d**2*x**2/(2*e**3) - c**2*d*x**3/(3*e**2) + c**2*x**4/(4*e), Eq(m, -1)), (a**2*d*e**4*m**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 14*a**2*d*e**4*m**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 71*a**2*d*e**4*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 154*a**2*d*e**4*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a**2*d*e**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + a**2*e**5*m**4*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 14*a**2*e**5*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 71*a**2*e**5*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 154*a**2*e**5*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a**2*e**5*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 4*a*c*d**3*e**2*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 36*a*c*d**3*e**2*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 80*a*c*d**3*e**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 4*a*c*d**2*e**3*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 36*a*c*d**2*e**3*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 80*a*c*d**2*e**3*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*a*c*d*e**4*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 20*a*c*d*e**4*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 58*a*c*d*e**4*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*a*c*d*e**4*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*a*c*e**5*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*a*c*e**5*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 98*a*c*e**5*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 156*a*c*e**5*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 80*a*c*e**5*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*c**2*d**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 24*c**2*d**4*e*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*c**2*d**3*e**2*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*c**2*d**3*e**2*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 4*c**2*d**2*e**3*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*c**2*d**2*e**3*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 8*c**2*d**2*e**3*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + c**2*d*e**4*m**4*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*c**2*d*e**4*m**3*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 11*c**2*d*e**4*m**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*c**2*d*e**4*m*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + c**2*e**5*m**4*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 10*c**2*e**5*m**3*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 35*c**2*e**5*m**2*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 50*c**2*e**5*m*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*c**2*e**5*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5), True))","A",0
723,1,952,0,1.733076," ","integrate((e*x+d)**m*(c*x**2+a),x)","\begin{cases} d^{m} \left(a x + \frac{c x^{3}}{3}\right) & \text{for}\: e = 0 \\- \frac{a e^{2}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 c d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{3 c d^{2}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 c d e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 c d e x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 c e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} & \text{for}\: m = -3 \\- \frac{a e^{2}}{d e^{3} + e^{4} x} - \frac{2 c d^{2} \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{2 c d^{2}}{d e^{3} + e^{4} x} - \frac{2 c d e x \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} + \frac{c e^{2} x^{2}}{d e^{3} + e^{4} x} & \text{for}\: m = -2 \\\frac{a \log{\left(\frac{d}{e} + x \right)}}{e} + \frac{c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{c d x}{e^{2}} + \frac{c x^{2}}{2 e} & \text{for}\: m = -1 \\\frac{a d e^{2} m^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{5 a d e^{2} m \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{6 a d e^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{a e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{5 a e^{3} m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{6 a e^{3} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{2 c d^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} - \frac{2 c d^{2} e m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{c d e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{c d e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{c e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{3 c e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{2 c e^{3} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a*x + c*x**3/3), Eq(e, 0)), (-a*e**2/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*c*d**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 3*c*d**2/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*c*d*e*x*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*c*d*e*x/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*c*e**2*x**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2), Eq(m, -3)), (-a*e**2/(d*e**3 + e**4*x) - 2*c*d**2*log(d/e + x)/(d*e**3 + e**4*x) - 2*c*d**2/(d*e**3 + e**4*x) - 2*c*d*e*x*log(d/e + x)/(d*e**3 + e**4*x) + c*e**2*x**2/(d*e**3 + e**4*x), Eq(m, -2)), (a*log(d/e + x)/e + c*d**2*log(d/e + x)/e**3 - c*d*x/e**2 + c*x**2/(2*e), Eq(m, -1)), (a*d*e**2*m**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 5*a*d*e**2*m*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 6*a*d*e**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + a*e**3*m**2*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 5*a*e**3*m*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 6*a*e**3*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 2*c*d**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) - 2*c*d**2*e*m*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + c*d*e**2*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + c*d*e**2*m*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + c*e**3*m**2*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 3*c*e**3*m*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 2*c*e**3*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3), True))","A",0
724,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+a),x)","\int \frac{\left(d + e x\right)^{m}}{a + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**m/(a + c*x**2), x)","F",0
725,-1,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,-1,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+a)**(3/2),x)","\int \left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{m}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)*(d + e*x)**m, x)","F",0
728,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+a)**(1/2),x)","\int \sqrt{a + c x^{2}} \left(d + e x\right)^{m}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x)**m, x)","F",0
729,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{m}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**m/sqrt(a + c*x**2), x)","F",0
730,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(a + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**m/(a + c*x**2)**(3/2), x)","F",0
731,-1,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,1,468,0,16.355226," ","integrate((e*x+d)**3*(c*x**2+a)**p,x)","a^{p} d^{3} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)} + a^{p} d e^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)} + 3 d^{2} e \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\begin{cases} \frac{\left(a + c x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + c x^{2} \right)} & \text{otherwise} \end{cases}}{2 c} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: c = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{a}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{c x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{c x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 c^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 c^{2}} + \frac{x^{2}}{2 c} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} + \frac{a c p x^{2} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} + \frac{c^{2} p x^{4} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} + \frac{c^{2} x^{4} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d**3*x*hyper((1/2, -p), (3/2,), c*x**2*exp_polar(I*pi)/a) + a**p*d*e**2*x**3*hyper((3/2, -p), (5/2,), c*x**2*exp_polar(I*pi)/a) + 3*d**2*e*Piecewise((a**p*x**2/2, Eq(c, 0)), (Piecewise(((a + c*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + c*x**2), True))/(2*c), True)) + e**3*Piecewise((a**p*x**4/4, Eq(c, 0)), (a*log(-I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2) + a*log(I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2) + a/(2*a*c**2 + 2*c**3*x**2) + c*x**2*log(-I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2) + c*x**2*log(I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/c) + x)/(2*c**2) - a*log(I*sqrt(a)*sqrt(1/c) + x)/(2*c**2) + x**2/(2*c), Eq(p, -1)), (-a**2*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2) + a*c*p*x**2*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2) + c**2*p*x**4*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2) + c**2*x**4*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2), True))","C",0
733,1,97,0,12.214924," ","integrate((e*x+d)**2*(c*x**2+a)**p,x)","a^{p} d^{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)} + \frac{a^{p} e^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{3} + 2 d e \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\begin{cases} \frac{\left(a + c x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + c x^{2} \right)} & \text{otherwise} \end{cases}}{2 c} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d**2*x*hyper((1/2, -p), (3/2,), c*x**2*exp_polar(I*pi)/a) + a**p*e**2*x**3*hyper((3/2, -p), (5/2,), c*x**2*exp_polar(I*pi)/a)/3 + 2*d*e*Piecewise((a**p*x**2/2, Eq(c, 0)), (Piecewise(((a + c*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + c*x**2), True))/(2*c), True))","A",0
734,1,61,0,6.888088," ","integrate((e*x+d)*(c*x**2+a)**p,x)","a^{p} d x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)} + e \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\begin{cases} \frac{\left(a + c x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + c x^{2} \right)} & \text{otherwise} \end{cases}}{2 c} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d*x*hyper((1/2, -p), (3/2,), c*x**2*exp_polar(I*pi)/a) + e*Piecewise((a**p*x**2/2, Eq(c, 0)), (Piecewise(((a + c*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + c*x**2), True))/(2*c), True))","A",0
735,1,22,0,2.560531," ","integrate((c*x**2+a)**p,x)","a^{p} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**p*x*hyper((1/2, -p), (3/2,), c*x**2*exp_polar(I*pi)/a)","C",0
736,0,0,0,0.000000," ","integrate((c*x**2+a)**p/(e*x+d),x)","\int \frac{\left(a + c x^{2}\right)^{p}}{d + e x}\, dx"," ",0,"Integral((a + c*x**2)**p/(d + e*x), x)","F",0
737,0,0,0,0.000000," ","integrate((c*x**2+a)**p/(e*x+d)**2,x)","\int \frac{\left(a + c x^{2}\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + c*x**2)**p/(d + e*x)**2, x)","F",0
738,-1,0,0,0.000000," ","integrate((c*x**2+a)**p/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
739,-1,0,0,0.000000," ","integrate((c*x**2+a)**p/((e*x+d)**(2*p)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
740,-2,0,0,0.000000," ","integrate((e*x+d)**(-1-2*p)*(c*x**2+a)**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
741,-1,0,0,0.000000," ","integrate((e*x+d)**(-2-2*p)*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
742,-1,0,0,0.000000," ","integrate((e*x+d)**(-3-2*p)*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,-1,0,0,0.000000," ","integrate((e*x+d)**(-4-2*p)*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,-1,0,0,0.000000," ","integrate((e*x+d)**(-5-2*p)*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate((e*x+d)**(-6-2*p)*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,0,0,0,0.000000," ","integrate((3-4*x)**n/(-x**2+1)**(1/2),x)","\int \frac{\left(3 - 4 x\right)^{n}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}\, dx"," ",0,"Integral((3 - 4*x)**n/sqrt(-(x - 1)*(x + 1)), x)","F",0
747,1,65,0,0.224089," ","integrate((b*x+a)**6/(-b**2*x**2+a**2),x)","- \frac{32 a^{5} \log{\left(- a + b x \right)}}{b} - 31 a^{4} x - 13 a^{3} b x^{2} - \frac{16 a^{2} b^{2} x^{3}}{3} - \frac{3 a b^{3} x^{4}}{2} - \frac{b^{4} x^{5}}{5}"," ",0,"-32*a**5*log(-a + b*x)/b - 31*a**4*x - 13*a**3*b*x**2 - 16*a**2*b**2*x**3/3 - 3*a*b**3*x**4/2 - b**4*x**5/5","A",0
748,1,53,0,0.189129," ","integrate((b*x+a)**5/(-b**2*x**2+a**2),x)","- \frac{16 a^{4} \log{\left(- a + b x \right)}}{b} - 15 a^{3} x - \frac{11 a^{2} b x^{2}}{2} - \frac{5 a b^{2} x^{3}}{3} - \frac{b^{3} x^{4}}{4}"," ",0,"-16*a**4*log(-a + b*x)/b - 15*a**3*x - 11*a**2*b*x**2/2 - 5*a*b**2*x**3/3 - b**3*x**4/4","A",0
749,1,37,0,0.174197," ","integrate((b*x+a)**4/(-b**2*x**2+a**2),x)","- \frac{8 a^{3} \log{\left(- a + b x \right)}}{b} - 7 a^{2} x - 2 a b x^{2} - \frac{b^{2} x^{3}}{3}"," ",0,"-8*a**3*log(-a + b*x)/b - 7*a**2*x - 2*a*b*x**2 - b**2*x**3/3","A",0
750,1,26,0,0.153748," ","integrate((b*x+a)**3/(-b**2*x**2+a**2),x)","- \frac{4 a^{2} \log{\left(- a + b x \right)}}{b} - 3 a x - \frac{b x^{2}}{2}"," ",0,"-4*a**2*log(-a + b*x)/b - 3*a*x - b*x**2/2","A",0
751,1,14,0,0.126645," ","integrate((b*x+a)**2/(-b**2*x**2+a**2),x)","- \frac{2 a \log{\left(- a + b x \right)}}{b} - x"," ",0,"-2*a*log(-a + b*x)/b - x","A",0
752,1,8,0,0.076392," ","integrate((b*x+a)/(-b**2*x**2+a**2),x)","- \frac{\log{\left(- a + b x \right)}}{b}"," ",0,"-log(-a + b*x)/b","A",0
753,1,39,0,0.328560," ","integrate(1/(b*x+a)/(-b**2*x**2+a**2),x)","- \frac{1}{2 a^{2} b + 2 a b^{2} x} - \frac{\frac{\log{\left(- \frac{a}{b} + x \right)}}{4} - \frac{\log{\left(\frac{a}{b} + x \right)}}{4}}{a^{2} b}"," ",0,"-1/(2*a**2*b + 2*a*b**2*x) - (log(-a/b + x)/4 - log(a/b + x)/4)/(a**2*b)","A",0
754,1,58,0,0.431037," ","integrate(1/(b*x+a)**2/(-b**2*x**2+a**2),x)","- \frac{2 a + b x}{4 a^{4} b + 8 a^{3} b^{2} x + 4 a^{2} b^{3} x^{2}} - \frac{\frac{\log{\left(- \frac{a}{b} + x \right)}}{8} - \frac{\log{\left(\frac{a}{b} + x \right)}}{8}}{a^{3} b}"," ",0,"-(2*a + b*x)/(4*a**4*b + 8*a**3*b**2*x + 4*a**2*b**3*x**2) - (log(-a/b + x)/8 - log(a/b + x)/8)/(a**3*b)","A",0
755,1,83,0,0.497221," ","integrate(1/(b*x+a)**3/(-b**2*x**2+a**2),x)","- \frac{10 a^{2} + 9 a b x + 3 b^{2} x^{2}}{24 a^{6} b + 72 a^{5} b^{2} x + 72 a^{4} b^{3} x^{2} + 24 a^{3} b^{4} x^{3}} - \frac{\frac{\log{\left(- \frac{a}{b} + x \right)}}{16} - \frac{\log{\left(\frac{a}{b} + x \right)}}{16}}{a^{4} b}"," ",0,"-(10*a**2 + 9*a*b*x + 3*b**2*x**2)/(24*a**6*b + 72*a**5*b**2*x + 72*a**4*b**3*x**2 + 24*a**3*b**4*x**3) - (log(-a/b + x)/16 - log(a/b + x)/16)/(a**4*b)","A",0
756,1,107,0,0.569052," ","integrate(1/(b*x+a)**4/(-b**2*x**2+a**2),x)","- \frac{16 a^{3} + 19 a^{2} b x + 12 a b^{2} x^{2} + 3 b^{3} x^{3}}{48 a^{8} b + 192 a^{7} b^{2} x + 288 a^{6} b^{3} x^{2} + 192 a^{5} b^{4} x^{3} + 48 a^{4} b^{5} x^{4}} - \frac{\frac{\log{\left(- \frac{a}{b} + x \right)}}{32} - \frac{\log{\left(\frac{a}{b} + x \right)}}{32}}{a^{5} b}"," ",0,"-(16*a**3 + 19*a**2*b*x + 12*a*b**2*x**2 + 3*b**3*x**3)/(48*a**8*b + 192*a**7*b**2*x + 288*a**6*b**3*x**2 + 192*a**5*b**4*x**3 + 48*a**4*b**5*x**4) - (log(-a/b + x)/32 - log(a/b + x)/32)/(a**5*b)","A",0
757,1,65,0,0.308818," ","integrate((b*x+a)**7/(-b**2*x**2+a**2)**2,x)","- \frac{32 a^{5}}{- a b + b^{2} x} + \frac{80 a^{4} \log{\left(- a + b x \right)}}{b} + 49 a^{3} x + \frac{23 a^{2} b x^{2}}{2} + \frac{7 a b^{2} x^{3}}{3} + \frac{b^{3} x^{4}}{4}"," ",0,"-32*a**5/(-a*b + b**2*x) + 80*a**4*log(-a + b*x)/b + 49*a**3*x + 23*a**2*b*x**2/2 + 7*a*b**2*x**3/3 + b**3*x**4/4","A",0
758,1,49,0,0.282872," ","integrate((b*x+a)**6/(-b**2*x**2+a**2)**2,x)","- \frac{16 a^{4}}{- a b + b^{2} x} + \frac{32 a^{3} \log{\left(- a + b x \right)}}{b} + 17 a^{2} x + 3 a b x^{2} + \frac{b^{2} x^{3}}{3}"," ",0,"-16*a**4/(-a*b + b**2*x) + 32*a**3*log(-a + b*x)/b + 17*a**2*x + 3*a*b*x**2 + b**2*x**3/3","A",0
759,1,37,0,0.236545," ","integrate((b*x+a)**5/(-b**2*x**2+a**2)**2,x)","- \frac{8 a^{3}}{- a b + b^{2} x} + \frac{12 a^{2} \log{\left(- a + b x \right)}}{b} + 5 a x + \frac{b x^{2}}{2}"," ",0,"-8*a**3/(-a*b + b**2*x) + 12*a**2*log(-a + b*x)/b + 5*a*x + b*x**2/2","A",0
760,1,26,0,0.195829," ","integrate((b*x+a)**4/(-b**2*x**2+a**2)**2,x)","- \frac{4 a^{2}}{- a b + b^{2} x} + \frac{4 a \log{\left(- a + b x \right)}}{b} + x"," ",0,"-4*a**2/(-a*b + b**2*x) + 4*a*log(-a + b*x)/b + x","A",0
761,1,19,0,0.177781," ","integrate((b*x+a)**3/(-b**2*x**2+a**2)**2,x)","- \frac{2 a}{- a b + b^{2} x} + \frac{\log{\left(- a + b x \right)}}{b}"," ",0,"-2*a/(-a*b + b**2*x) + log(-a + b*x)/b","A",0
762,1,10,0,0.186007," ","integrate((b*x+a)**2/(-b**2*x**2+a**2)**2,x)","- \frac{1}{- a b + b^{2} x}"," ",0,"-1/(-a*b + b**2*x)","A",0
763,1,37,0,0.280243," ","integrate((b*x+a)/(-b**2*x**2+a**2)**2,x)","- \frac{1}{- 2 a^{2} b + 2 a b^{2} x} + \frac{- \frac{\log{\left(- \frac{a}{b} + x \right)}}{4} + \frac{\log{\left(\frac{a}{b} + x \right)}}{4}}{a^{2} b}"," ",0,"-1/(-2*a**2*b + 2*a*b**2*x) + (-log(-a/b + x)/4 + log(a/b + x)/4)/(a**2*b)","A",0
764,1,85,0,0.465502," ","integrate(1/(b*x+a)/(-b**2*x**2+a**2)**2,x)","\frac{2 a^{2} - 3 a b x - 3 b^{2} x^{2}}{- 8 a^{6} b - 8 a^{5} b^{2} x + 8 a^{4} b^{3} x^{2} + 8 a^{3} b^{4} x^{3}} + \frac{- \frac{3 \log{\left(- \frac{a}{b} + x \right)}}{16} + \frac{3 \log{\left(\frac{a}{b} + x \right)}}{16}}{a^{4} b}"," ",0,"(2*a**2 - 3*a*b*x - 3*b**2*x**2)/(-8*a**6*b - 8*a**5*b**2*x + 8*a**4*b**3*x**2 + 8*a**3*b**4*x**3) + (-3*log(-a/b + x)/16 + 3*log(a/b + x)/16)/(a**4*b)","A",0
765,1,92,0,0.546052," ","integrate(1/(b*x+a)**2/(-b**2*x**2+a**2)**2,x)","\frac{4 a^{3} - a^{2} b x - 6 a b^{2} x^{2} - 3 b^{3} x^{3}}{- 12 a^{8} b - 24 a^{7} b^{2} x + 24 a^{5} b^{4} x^{3} + 12 a^{4} b^{5} x^{4}} + \frac{- \frac{\log{\left(- \frac{a}{b} + x \right)}}{8} + \frac{\log{\left(\frac{a}{b} + x \right)}}{8}}{a^{5} b}"," ",0,"(4*a**3 - a**2*b*x - 6*a*b**2*x**2 - 3*b**3*x**3)/(-12*a**8*b - 24*a**7*b**2*x + 24*a**5*b**4*x**3 + 12*a**4*b**5*x**4) + (-log(-a/b + x)/8 + log(a/b + x)/8)/(a**5*b)","A",0
766,1,133,0,0.710675," ","integrate(1/(b*x+a)**3/(-b**2*x**2+a**2)**2,x)","\frac{32 a^{4} + 15 a^{3} b x - 35 a^{2} b^{2} x^{2} - 45 a b^{3} x^{3} - 15 b^{4} x^{4}}{- 96 a^{10} b - 288 a^{9} b^{2} x - 192 a^{8} b^{3} x^{2} + 192 a^{7} b^{4} x^{3} + 288 a^{6} b^{5} x^{4} + 96 a^{5} b^{6} x^{5}} + \frac{- \frac{5 \log{\left(- \frac{a}{b} + x \right)}}{64} + \frac{5 \log{\left(\frac{a}{b} + x \right)}}{64}}{a^{6} b}"," ",0,"(32*a**4 + 15*a**3*b*x - 35*a**2*b**2*x**2 - 45*a*b**3*x**3 - 15*b**4*x**4)/(-96*a**10*b - 288*a**9*b**2*x - 192*a**8*b**3*x**2 + 192*a**7*b**4*x**3 + 288*a**6*b**5*x**4 + 96*a**5*b**6*x**5) + (-5*log(-a/b + x)/64 + 5*log(a/b + x)/64)/(a**6*b)","A",0
767,1,71,0,0.410684," ","integrate((b*x+a)**8/(-b**2*x**2+a**2)**3,x)","- \frac{80 a^{3} \log{\left(- a + b x \right)}}{b} - 31 a^{2} x - 4 a b x^{2} - \frac{b^{2} x^{3}}{3} - \frac{64 a^{5} - 80 a^{4} b x}{a^{2} b - 2 a b^{2} x + b^{3} x^{2}}"," ",0,"-80*a**3*log(-a + b*x)/b - 31*a**2*x - 4*a*b*x**2 - b**2*x**3/3 - (64*a**5 - 80*a**4*b*x)/(a**2*b - 2*a*b**2*x + b**3*x**2)","A",0
768,1,60,0,0.378042," ","integrate((b*x+a)**7/(-b**2*x**2+a**2)**3,x)","- \frac{24 a^{2} \log{\left(- a + b x \right)}}{b} - 7 a x - \frac{b x^{2}}{2} - \frac{24 a^{4} - 32 a^{3} b x}{a^{2} b - 2 a b^{2} x + b^{3} x^{2}}"," ",0,"-24*a**2*log(-a + b*x)/b - 7*a*x - b*x**2/2 - (24*a**4 - 32*a**3*b*x)/(a**2*b - 2*a*b**2*x + b**3*x**2)","A",0
769,1,48,0,0.306841," ","integrate((b*x+a)**6/(-b**2*x**2+a**2)**3,x)","- \frac{6 a \log{\left(- a + b x \right)}}{b} - x - \frac{8 a^{3} - 12 a^{2} b x}{a^{2} b - 2 a b^{2} x + b^{3} x^{2}}"," ",0,"-6*a*log(-a + b*x)/b - x - (8*a**3 - 12*a**2*b*x)/(a**2*b - 2*a*b**2*x + b**3*x**2)","A",0
770,1,41,0,0.310038," ","integrate((b*x+a)**5/(-b**2*x**2+a**2)**3,x)","- \frac{2 a^{2} - 4 a b x}{a^{2} b - 2 a b^{2} x + b^{3} x^{2}} - \frac{\log{\left(- a + b x \right)}}{b}"," ",0,"-(2*a**2 - 4*a*b*x)/(a**2*b - 2*a*b**2*x + b**3*x**2) - log(-a + b*x)/b","A",0
771,1,17,0,0.250806," ","integrate((b*x+a)**4/(-b**2*x**2+a**2)**3,x)","\frac{x}{a^{2} - 2 a b x + b^{2} x^{2}}"," ",0,"x/(a**2 - 2*a*b*x + b**2*x**2)","B",0
772,1,24,0,0.230021," ","integrate((b*x+a)**3/(-b**2*x**2+a**2)**3,x)","\frac{1}{2 a^{2} b - 4 a b^{2} x + 2 b^{3} x^{2}}"," ",0,"1/(2*a**2*b - 4*a*b**2*x + 2*b**3*x**2)","B",0
773,1,58,0,0.376402," ","integrate((b*x+a)**2/(-b**2*x**2+a**2)**3,x)","- \frac{- 2 a + b x}{4 a^{4} b - 8 a^{3} b^{2} x + 4 a^{2} b^{3} x^{2}} - \frac{\frac{\log{\left(- \frac{a}{b} + x \right)}}{8} - \frac{\log{\left(\frac{a}{b} + x \right)}}{8}}{a^{3} b}"," ",0,"-(-2*a + b*x)/(4*a**4*b - 8*a**3*b**2*x + 4*a**2*b**3*x**2) - (log(-a/b + x)/8 - log(a/b + x)/8)/(a**3*b)","A",0
774,1,87,0,0.480922," ","integrate((b*x+a)/(-b**2*x**2+a**2)**3,x)","- \frac{- 2 a^{2} - 3 a b x + 3 b^{2} x^{2}}{8 a^{6} b - 8 a^{5} b^{2} x - 8 a^{4} b^{3} x^{2} + 8 a^{3} b^{4} x^{3}} - \frac{\frac{3 \log{\left(- \frac{a}{b} + x \right)}}{16} - \frac{3 \log{\left(\frac{a}{b} + x \right)}}{16}}{a^{4} b}"," ",0,"-(-2*a**2 - 3*a*b*x + 3*b**2*x**2)/(8*a**6*b - 8*a**5*b**2*x - 8*a**4*b**3*x**2 + 8*a**3*b**4*x**3) - (3*log(-a/b + x)/16 - 3*log(a/b + x)/16)/(a**4*b)","A",0
775,1,134,0,0.679935," ","integrate(1/(b*x+a)/(-b**2*x**2+a**2)**3,x)","- \frac{8 a^{4} - 25 a^{3} b x - 25 a^{2} b^{2} x^{2} + 15 a b^{3} x^{3} + 15 b^{4} x^{4}}{48 a^{10} b + 48 a^{9} b^{2} x - 96 a^{8} b^{3} x^{2} - 96 a^{7} b^{4} x^{3} + 48 a^{6} b^{5} x^{4} + 48 a^{5} b^{6} x^{5}} - \frac{\frac{5 \log{\left(- \frac{a}{b} + x \right)}}{32} - \frac{5 \log{\left(\frac{a}{b} + x \right)}}{32}}{a^{6} b}"," ",0,"-(8*a**4 - 25*a**3*b*x - 25*a**2*b**2*x**2 + 15*a*b**3*x**3 + 15*b**4*x**4)/(48*a**10*b + 48*a**9*b**2*x - 96*a**8*b**3*x**2 - 96*a**7*b**4*x**3 + 48*a**6*b**5*x**4 + 48*a**5*b**6*x**5) - (5*log(-a/b + x)/32 - 5*log(a/b + x)/32)/(a**6*b)","A",0
776,1,158,0,0.766917," ","integrate(1/(b*x+a)**2/(-b**2*x**2+a**2)**3,x)","- \frac{16 a^{5} - 17 a^{4} b x - 50 a^{3} b^{2} x^{2} - 10 a^{2} b^{3} x^{3} + 30 a b^{4} x^{4} + 15 b^{5} x^{5}}{64 a^{12} b + 128 a^{11} b^{2} x - 64 a^{10} b^{3} x^{2} - 256 a^{9} b^{4} x^{3} - 64 a^{8} b^{5} x^{4} + 128 a^{7} b^{6} x^{5} + 64 a^{6} b^{7} x^{6}} - \frac{\frac{15 \log{\left(- \frac{a}{b} + x \right)}}{128} - \frac{15 \log{\left(\frac{a}{b} + x \right)}}{128}}{a^{7} b}"," ",0,"-(16*a**5 - 17*a**4*b*x - 50*a**3*b**2*x**2 - 10*a**2*b**3*x**3 + 30*a*b**4*x**4 + 15*b**5*x**5)/(64*a**12*b + 128*a**11*b**2*x - 64*a**10*b**3*x**2 - 256*a**9*b**4*x**3 - 64*a**8*b**5*x**4 + 128*a**7*b**6*x**5 + 64*a**6*b**7*x**6) - (15*log(-a/b + x)/128 - 15*log(a/b + x)/128)/(a**7*b)","A",0
777,1,700,0,14.606255," ","integrate((b*x+a)**4*(-b**2*x**2+a**2)**(1/2),x)","a^{4} \left(\begin{cases} - \frac{i a^{2} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{2 b} - \frac{i a x}{2 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{3}}{2 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{2} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{2 b} + \frac{a x \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}}{2} & \text{otherwise} \end{cases}\right) + 4 a^{3} b \left(\begin{cases} \frac{x^{2} \sqrt{a^{2}}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\left(a^{2} - b^{2} x^{2}\right)^{\frac{3}{2}}}{3 b^{2}} & \text{otherwise} \end{cases}\right) + 6 a^{2} b^{2} \left(\begin{cases} - \frac{i a^{4} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{8 b^{3}} + \frac{i a^{3} x}{8 b^{2} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{3 i a x^{3}}{8 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{5}}{4 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{4} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{8 b^{3}} - \frac{a^{3} x}{8 b^{2} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{3 a x^{3}}{8 \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} - \frac{b^{2} x^{5}}{4 a \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} & \text{otherwise} \end{cases}\right) + 4 a b^{3} \left(\begin{cases} - \frac{2 a^{4} \sqrt{a^{2} - b^{2} x^{2}}}{15 b^{4}} - \frac{a^{2} x^{2} \sqrt{a^{2} - b^{2} x^{2}}}{15 b^{2}} + \frac{x^{4} \sqrt{a^{2} - b^{2} x^{2}}}{5} & \text{for}\: b \neq 0 \\\frac{x^{4} \sqrt{a^{2}}}{4} & \text{otherwise} \end{cases}\right) + b^{4} \left(\begin{cases} - \frac{i a^{6} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{16 b^{5}} + \frac{i a^{5} x}{16 b^{4} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{i a^{3} x^{3}}{48 b^{2} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{5 i a x^{5}}{24 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{7}}{6 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{6} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{16 b^{5}} - \frac{a^{5} x}{16 b^{4} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{a^{3} x^{3}}{48 b^{2} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{5 a x^{5}}{24 \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} - \frac{b^{2} x^{7}}{6 a \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"a**4*Piecewise((-I*a**2*acosh(b*x/a)/(2*b) - I*a*x/(2*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**3/(2*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**2*asin(b*x/a)/(2*b) + a*x*sqrt(1 - b**2*x**2/a**2)/2, True)) + 4*a**3*b*Piecewise((x**2*sqrt(a**2)/2, Eq(b**2, 0)), (-(a**2 - b**2*x**2)**(3/2)/(3*b**2), True)) + 6*a**2*b**2*Piecewise((-I*a**4*acosh(b*x/a)/(8*b**3) + I*a**3*x/(8*b**2*sqrt(-1 + b**2*x**2/a**2)) - 3*I*a*x**3/(8*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**5/(4*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**4*asin(b*x/a)/(8*b**3) - a**3*x/(8*b**2*sqrt(1 - b**2*x**2/a**2)) + 3*a*x**3/(8*sqrt(1 - b**2*x**2/a**2)) - b**2*x**5/(4*a*sqrt(1 - b**2*x**2/a**2)), True)) + 4*a*b**3*Piecewise((-2*a**4*sqrt(a**2 - b**2*x**2)/(15*b**4) - a**2*x**2*sqrt(a**2 - b**2*x**2)/(15*b**2) + x**4*sqrt(a**2 - b**2*x**2)/5, Ne(b, 0)), (x**4*sqrt(a**2)/4, True)) + b**4*Piecewise((-I*a**6*acosh(b*x/a)/(16*b**5) + I*a**5*x/(16*b**4*sqrt(-1 + b**2*x**2/a**2)) - I*a**3*x**3/(48*b**2*sqrt(-1 + b**2*x**2/a**2)) - 5*I*a*x**5/(24*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**7/(6*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**6*asin(b*x/a)/(16*b**5) - a**5*x/(16*b**4*sqrt(1 - b**2*x**2/a**2)) + a**3*x**3/(48*b**2*sqrt(1 - b**2*x**2/a**2)) + 5*a*x**5/(24*sqrt(1 - b**2*x**2/a**2)) - b**2*x**7/(6*a*sqrt(1 - b**2*x**2/a**2)), True))","C",0
778,1,439,0,8.244592," ","integrate((b*x+a)**3*(-b**2*x**2+a**2)**(1/2),x)","a^{3} \left(\begin{cases} - \frac{i a^{2} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{2 b} - \frac{i a x}{2 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{3}}{2 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{2} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{2 b} + \frac{a x \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}}{2} & \text{otherwise} \end{cases}\right) + 3 a^{2} b \left(\begin{cases} \frac{x^{2} \sqrt{a^{2}}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\left(a^{2} - b^{2} x^{2}\right)^{\frac{3}{2}}}{3 b^{2}} & \text{otherwise} \end{cases}\right) + 3 a b^{2} \left(\begin{cases} - \frac{i a^{4} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{8 b^{3}} + \frac{i a^{3} x}{8 b^{2} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{3 i a x^{3}}{8 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{5}}{4 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{4} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{8 b^{3}} - \frac{a^{3} x}{8 b^{2} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{3 a x^{3}}{8 \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} - \frac{b^{2} x^{5}}{4 a \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} & \text{otherwise} \end{cases}\right) + b^{3} \left(\begin{cases} - \frac{2 a^{4} \sqrt{a^{2} - b^{2} x^{2}}}{15 b^{4}} - \frac{a^{2} x^{2} \sqrt{a^{2} - b^{2} x^{2}}}{15 b^{2}} + \frac{x^{4} \sqrt{a^{2} - b^{2} x^{2}}}{5} & \text{for}\: b \neq 0 \\\frac{x^{4} \sqrt{a^{2}}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"a**3*Piecewise((-I*a**2*acosh(b*x/a)/(2*b) - I*a*x/(2*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**3/(2*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**2*asin(b*x/a)/(2*b) + a*x*sqrt(1 - b**2*x**2/a**2)/2, True)) + 3*a**2*b*Piecewise((x**2*sqrt(a**2)/2, Eq(b**2, 0)), (-(a**2 - b**2*x**2)**(3/2)/(3*b**2), True)) + 3*a*b**2*Piecewise((-I*a**4*acosh(b*x/a)/(8*b**3) + I*a**3*x/(8*b**2*sqrt(-1 + b**2*x**2/a**2)) - 3*I*a*x**3/(8*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**5/(4*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**4*asin(b*x/a)/(8*b**3) - a**3*x/(8*b**2*sqrt(1 - b**2*x**2/a**2)) + 3*a*x**3/(8*sqrt(1 - b**2*x**2/a**2)) - b**2*x**5/(4*a*sqrt(1 - b**2*x**2/a**2)), True)) + b**3*Piecewise((-2*a**4*sqrt(a**2 - b**2*x**2)/(15*b**4) - a**2*x**2*sqrt(a**2 - b**2*x**2)/(15*b**2) + x**4*sqrt(a**2 - b**2*x**2)/5, Ne(b, 0)), (x**4*sqrt(a**2)/4, True))","C",0
779,1,350,0,7.733542," ","integrate((b*x+a)**2*(-b**2*x**2+a**2)**(1/2),x)","a^{2} \left(\begin{cases} - \frac{i a^{2} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{2 b} - \frac{i a x}{2 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{3}}{2 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{2} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{2 b} + \frac{a x \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}}{2} & \text{otherwise} \end{cases}\right) + 2 a b \left(\begin{cases} \frac{x^{2} \sqrt{a^{2}}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\left(a^{2} - b^{2} x^{2}\right)^{\frac{3}{2}}}{3 b^{2}} & \text{otherwise} \end{cases}\right) + b^{2} \left(\begin{cases} - \frac{i a^{4} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{8 b^{3}} + \frac{i a^{3} x}{8 b^{2} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{3 i a x^{3}}{8 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{5}}{4 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{4} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{8 b^{3}} - \frac{a^{3} x}{8 b^{2} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{3 a x^{3}}{8 \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} - \frac{b^{2} x^{5}}{4 a \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"a**2*Piecewise((-I*a**2*acosh(b*x/a)/(2*b) - I*a*x/(2*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**3/(2*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**2*asin(b*x/a)/(2*b) + a*x*sqrt(1 - b**2*x**2/a**2)/2, True)) + 2*a*b*Piecewise((x**2*sqrt(a**2)/2, Eq(b**2, 0)), (-(a**2 - b**2*x**2)**(3/2)/(3*b**2), True)) + b**2*Piecewise((-I*a**4*acosh(b*x/a)/(8*b**3) + I*a**3*x/(8*b**2*sqrt(-1 + b**2*x**2/a**2)) - 3*I*a*x**3/(8*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**5/(4*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**4*asin(b*x/a)/(8*b**3) - a**3*x/(8*b**2*sqrt(1 - b**2*x**2/a**2)) + 3*a*x**3/(8*sqrt(1 - b**2*x**2/a**2)) - b**2*x**5/(4*a*sqrt(1 - b**2*x**2/a**2)), True))","C",0
780,1,144,0,4.374927," ","integrate((b*x+a)*(-b**2*x**2+a**2)**(1/2),x)","a \left(\begin{cases} - \frac{i a^{2} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{2 b} - \frac{i a x}{2 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{3}}{2 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{2} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{2 b} + \frac{a x \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}}{2} & \text{otherwise} \end{cases}\right) + b \left(\begin{cases} \frac{x^{2} \sqrt{a^{2}}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\left(a^{2} - b^{2} x^{2}\right)^{\frac{3}{2}}}{3 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a*Piecewise((-I*a**2*acosh(b*x/a)/(2*b) - I*a*x/(2*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**3/(2*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**2*asin(b*x/a)/(2*b) + a*x*sqrt(1 - b**2*x**2/a**2)/2, True)) + b*Piecewise((x**2*sqrt(a**2)/2, Eq(b**2, 0)), (-(a**2 - b**2*x**2)**(3/2)/(3*b**2), True))","C",0
781,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(1/2)/(b*x+a),x)","\int \frac{\sqrt{- \left(- a + b x\right) \left(a + b x\right)}}{a + b x}\, dx"," ",0,"Integral(sqrt(-(-a + b*x)*(a + b*x))/(a + b*x), x)","F",0
782,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(1/2)/(b*x+a)**2,x)","\int \frac{\sqrt{- \left(- a + b x\right) \left(a + b x\right)}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral(sqrt(-(-a + b*x)*(a + b*x))/(a + b*x)**2, x)","F",0
783,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(1/2)/(b*x+a)**3,x)","\int \frac{\sqrt{- \left(- a + b x\right) \left(a + b x\right)}}{\left(a + b x\right)^{3}}\, dx"," ",0,"Integral(sqrt(-(-a + b*x)*(a + b*x))/(a + b*x)**3, x)","F",0
784,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(1/2)/(b*x+a)**4,x)","\int \frac{\sqrt{- \left(- a + b x\right) \left(a + b x\right)}}{\left(a + b x\right)^{4}}\, dx"," ",0,"Integral(sqrt(-(-a + b*x)*(a + b*x))/(a + b*x)**4, x)","F",0
785,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(1/2)/(b*x+a)**5,x)","\int \frac{\sqrt{- \left(- a + b x\right) \left(a + b x\right)}}{\left(a + b x\right)^{5}}\, dx"," ",0,"Integral(sqrt(-(-a + b*x)*(a + b*x))/(a + b*x)**5, x)","F",0
786,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(1/2)/(b*x+a)**6,x)","\int \frac{\sqrt{- \left(- a + b x\right) \left(a + b x\right)}}{\left(a + b x\right)^{6}}\, dx"," ",0,"Integral(sqrt(-(-a + b*x)*(a + b*x))/(a + b*x)**6, x)","F",0
787,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(1/2)/(b*x+a)**7,x)","\int \frac{\sqrt{- \left(- a + b x\right) \left(a + b x\right)}}{\left(a + b x\right)^{7}}\, dx"," ",0,"Integral(sqrt(-(-a + b*x)*(a + b*x))/(a + b*x)**7, x)","F",0
788,1,816,0,16.609580," ","integrate((b*x+a)**3*(-b**2*x**2+a**2)**(3/2),x)","a^{5} \left(\begin{cases} - \frac{i a^{2} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{2 b} - \frac{i a x}{2 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{3}}{2 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{2} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{2 b} + \frac{a x \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}}{2} & \text{otherwise} \end{cases}\right) + 3 a^{4} b \left(\begin{cases} \frac{x^{2} \sqrt{a^{2}}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\left(a^{2} - b^{2} x^{2}\right)^{\frac{3}{2}}}{3 b^{2}} & \text{otherwise} \end{cases}\right) + 2 a^{3} b^{2} \left(\begin{cases} - \frac{i a^{4} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{8 b^{3}} + \frac{i a^{3} x}{8 b^{2} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{3 i a x^{3}}{8 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{5}}{4 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{4} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{8 b^{3}} - \frac{a^{3} x}{8 b^{2} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{3 a x^{3}}{8 \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} - \frac{b^{2} x^{5}}{4 a \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} & \text{otherwise} \end{cases}\right) - 2 a^{2} b^{3} \left(\begin{cases} - \frac{2 a^{4} \sqrt{a^{2} - b^{2} x^{2}}}{15 b^{4}} - \frac{a^{2} x^{2} \sqrt{a^{2} - b^{2} x^{2}}}{15 b^{2}} + \frac{x^{4} \sqrt{a^{2} - b^{2} x^{2}}}{5} & \text{for}\: b \neq 0 \\\frac{x^{4} \sqrt{a^{2}}}{4} & \text{otherwise} \end{cases}\right) - 3 a b^{4} \left(\begin{cases} - \frac{i a^{6} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{16 b^{5}} + \frac{i a^{5} x}{16 b^{4} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{i a^{3} x^{3}}{48 b^{2} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{5 i a x^{5}}{24 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{7}}{6 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{6} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{16 b^{5}} - \frac{a^{5} x}{16 b^{4} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{a^{3} x^{3}}{48 b^{2} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{5 a x^{5}}{24 \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} - \frac{b^{2} x^{7}}{6 a \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} & \text{otherwise} \end{cases}\right) - b^{5} \left(\begin{cases} - \frac{8 a^{6} \sqrt{a^{2} - b^{2} x^{2}}}{105 b^{6}} - \frac{4 a^{4} x^{2} \sqrt{a^{2} - b^{2} x^{2}}}{105 b^{4}} - \frac{a^{2} x^{4} \sqrt{a^{2} - b^{2} x^{2}}}{35 b^{2}} + \frac{x^{6} \sqrt{a^{2} - b^{2} x^{2}}}{7} & \text{for}\: b \neq 0 \\\frac{x^{6} \sqrt{a^{2}}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"a**5*Piecewise((-I*a**2*acosh(b*x/a)/(2*b) - I*a*x/(2*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**3/(2*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**2*asin(b*x/a)/(2*b) + a*x*sqrt(1 - b**2*x**2/a**2)/2, True)) + 3*a**4*b*Piecewise((x**2*sqrt(a**2)/2, Eq(b**2, 0)), (-(a**2 - b**2*x**2)**(3/2)/(3*b**2), True)) + 2*a**3*b**2*Piecewise((-I*a**4*acosh(b*x/a)/(8*b**3) + I*a**3*x/(8*b**2*sqrt(-1 + b**2*x**2/a**2)) - 3*I*a*x**3/(8*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**5/(4*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**4*asin(b*x/a)/(8*b**3) - a**3*x/(8*b**2*sqrt(1 - b**2*x**2/a**2)) + 3*a*x**3/(8*sqrt(1 - b**2*x**2/a**2)) - b**2*x**5/(4*a*sqrt(1 - b**2*x**2/a**2)), True)) - 2*a**2*b**3*Piecewise((-2*a**4*sqrt(a**2 - b**2*x**2)/(15*b**4) - a**2*x**2*sqrt(a**2 - b**2*x**2)/(15*b**2) + x**4*sqrt(a**2 - b**2*x**2)/5, Ne(b, 0)), (x**4*sqrt(a**2)/4, True)) - 3*a*b**4*Piecewise((-I*a**6*acosh(b*x/a)/(16*b**5) + I*a**5*x/(16*b**4*sqrt(-1 + b**2*x**2/a**2)) - I*a**3*x**3/(48*b**2*sqrt(-1 + b**2*x**2/a**2)) - 5*I*a*x**5/(24*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**7/(6*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**6*asin(b*x/a)/(16*b**5) - a**5*x/(16*b**4*sqrt(1 - b**2*x**2/a**2)) + a**3*x**3/(48*b**2*sqrt(1 - b**2*x**2/a**2)) + 5*a*x**5/(24*sqrt(1 - b**2*x**2/a**2)) - b**2*x**7/(6*a*sqrt(1 - b**2*x**2/a**2)), True)) - b**5*Piecewise((-8*a**6*sqrt(a**2 - b**2*x**2)/(105*b**6) - 4*a**4*x**2*sqrt(a**2 - b**2*x**2)/(105*b**4) - a**2*x**4*sqrt(a**2 - b**2*x**2)/(35*b**2) + x**6*sqrt(a**2 - b**2*x**2)/7, Ne(b, 0)), (x**6*sqrt(a**2)/6, True))","C",0
789,1,495,0,11.122011," ","integrate((b*x+a)**2*(-b**2*x**2+a**2)**(3/2),x)","a^{4} \left(\begin{cases} - \frac{i a^{2} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{2 b} - \frac{i a x}{2 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{3}}{2 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{2} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{2 b} + \frac{a x \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}}{2} & \text{otherwise} \end{cases}\right) + 2 a^{3} b \left(\begin{cases} \frac{x^{2} \sqrt{a^{2}}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\left(a^{2} - b^{2} x^{2}\right)^{\frac{3}{2}}}{3 b^{2}} & \text{otherwise} \end{cases}\right) - 2 a b^{3} \left(\begin{cases} - \frac{2 a^{4} \sqrt{a^{2} - b^{2} x^{2}}}{15 b^{4}} - \frac{a^{2} x^{2} \sqrt{a^{2} - b^{2} x^{2}}}{15 b^{2}} + \frac{x^{4} \sqrt{a^{2} - b^{2} x^{2}}}{5} & \text{for}\: b \neq 0 \\\frac{x^{4} \sqrt{a^{2}}}{4} & \text{otherwise} \end{cases}\right) - b^{4} \left(\begin{cases} - \frac{i a^{6} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{16 b^{5}} + \frac{i a^{5} x}{16 b^{4} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{i a^{3} x^{3}}{48 b^{2} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{5 i a x^{5}}{24 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{7}}{6 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{6} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{16 b^{5}} - \frac{a^{5} x}{16 b^{4} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{a^{3} x^{3}}{48 b^{2} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{5 a x^{5}}{24 \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} - \frac{b^{2} x^{7}}{6 a \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"a**4*Piecewise((-I*a**2*acosh(b*x/a)/(2*b) - I*a*x/(2*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**3/(2*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**2*asin(b*x/a)/(2*b) + a*x*sqrt(1 - b**2*x**2/a**2)/2, True)) + 2*a**3*b*Piecewise((x**2*sqrt(a**2)/2, Eq(b**2, 0)), (-(a**2 - b**2*x**2)**(3/2)/(3*b**2), True)) - 2*a*b**3*Piecewise((-2*a**4*sqrt(a**2 - b**2*x**2)/(15*b**4) - a**2*x**2*sqrt(a**2 - b**2*x**2)/(15*b**2) + x**4*sqrt(a**2 - b**2*x**2)/5, Ne(b, 0)), (x**4*sqrt(a**2)/4, True)) - b**4*Piecewise((-I*a**6*acosh(b*x/a)/(16*b**5) + I*a**5*x/(16*b**4*sqrt(-1 + b**2*x**2/a**2)) - I*a**3*x**3/(48*b**2*sqrt(-1 + b**2*x**2/a**2)) - 5*I*a*x**5/(24*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**7/(6*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**6*asin(b*x/a)/(16*b**5) - a**5*x/(16*b**4*sqrt(1 - b**2*x**2/a**2)) + a**3*x**3/(48*b**2*sqrt(1 - b**2*x**2/a**2)) + 5*a*x**5/(24*sqrt(1 - b**2*x**2/a**2)) - b**2*x**7/(6*a*sqrt(1 - b**2*x**2/a**2)), True))","C",0
790,1,435,0,9.169245," ","integrate((b*x+a)*(-b**2*x**2+a**2)**(3/2),x)","a^{3} \left(\begin{cases} - \frac{i a^{2} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{2 b} - \frac{i a x}{2 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{3}}{2 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{2} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{2 b} + \frac{a x \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}}{2} & \text{otherwise} \end{cases}\right) + a^{2} b \left(\begin{cases} \frac{x^{2} \sqrt{a^{2}}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\left(a^{2} - b^{2} x^{2}\right)^{\frac{3}{2}}}{3 b^{2}} & \text{otherwise} \end{cases}\right) - a b^{2} \left(\begin{cases} - \frac{i a^{4} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{8 b^{3}} + \frac{i a^{3} x}{8 b^{2} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{3 i a x^{3}}{8 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{5}}{4 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{4} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{8 b^{3}} - \frac{a^{3} x}{8 b^{2} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{3 a x^{3}}{8 \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} - \frac{b^{2} x^{5}}{4 a \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} & \text{otherwise} \end{cases}\right) - b^{3} \left(\begin{cases} - \frac{2 a^{4} \sqrt{a^{2} - b^{2} x^{2}}}{15 b^{4}} - \frac{a^{2} x^{2} \sqrt{a^{2} - b^{2} x^{2}}}{15 b^{2}} + \frac{x^{4} \sqrt{a^{2} - b^{2} x^{2}}}{5} & \text{for}\: b \neq 0 \\\frac{x^{4} \sqrt{a^{2}}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"a**3*Piecewise((-I*a**2*acosh(b*x/a)/(2*b) - I*a*x/(2*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**3/(2*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**2*asin(b*x/a)/(2*b) + a*x*sqrt(1 - b**2*x**2/a**2)/2, True)) + a**2*b*Piecewise((x**2*sqrt(a**2)/2, Eq(b**2, 0)), (-(a**2 - b**2*x**2)**(3/2)/(3*b**2), True)) - a*b**2*Piecewise((-I*a**4*acosh(b*x/a)/(8*b**3) + I*a**3*x/(8*b**2*sqrt(-1 + b**2*x**2/a**2)) - 3*I*a*x**3/(8*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**5/(4*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**4*asin(b*x/a)/(8*b**3) - a**3*x/(8*b**2*sqrt(1 - b**2*x**2/a**2)) + 3*a*x**3/(8*sqrt(1 - b**2*x**2/a**2)) - b**2*x**5/(4*a*sqrt(1 - b**2*x**2/a**2)), True)) - b**3*Piecewise((-2*a**4*sqrt(a**2 - b**2*x**2)/(15*b**4) - a**2*x**2*sqrt(a**2 - b**2*x**2)/(15*b**2) + x**4*sqrt(a**2 - b**2*x**2)/5, Ne(b, 0)), (x**4*sqrt(a**2)/4, True))","C",0
791,1,144,0,4.412350," ","integrate((-b**2*x**2+a**2)**(3/2)/(b*x+a),x)","a \left(\begin{cases} - \frac{i a^{2} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{2 b} - \frac{i a x}{2 \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{i b^{2} x^{3}}{2 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{a^{2} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{2 b} + \frac{a x \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}}{2} & \text{otherwise} \end{cases}\right) - b \left(\begin{cases} \frac{x^{2} \sqrt{a^{2}}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\left(a^{2} - b^{2} x^{2}\right)^{\frac{3}{2}}}{3 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a*Piecewise((-I*a**2*acosh(b*x/a)/(2*b) - I*a*x/(2*sqrt(-1 + b**2*x**2/a**2)) + I*b**2*x**3/(2*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (a**2*asin(b*x/a)/(2*b) + a*x*sqrt(1 - b**2*x**2/a**2)/2, True)) - b*Piecewise((x**2*sqrt(a**2)/2, Eq(b**2, 0)), (-(a**2 - b**2*x**2)**(3/2)/(3*b**2), True))","C",0
792,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(3/2)/(b*x+a)**2,x)","\int \frac{\left(- \left(- a + b x\right) \left(a + b x\right)\right)^{\frac{3}{2}}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**(3/2)/(a + b*x)**2, x)","F",0
793,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(3/2)/(b*x+a)**3,x)","\int \frac{\left(- \left(- a + b x\right) \left(a + b x\right)\right)^{\frac{3}{2}}}{\left(a + b x\right)^{3}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**(3/2)/(a + b*x)**3, x)","F",0
794,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(3/2)/(b*x+a)**4,x)","\int \frac{\left(- \left(- a + b x\right) \left(a + b x\right)\right)^{\frac{3}{2}}}{\left(a + b x\right)^{4}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**(3/2)/(a + b*x)**4, x)","F",0
795,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(3/2)/(b*x+a)**5,x)","\int \frac{\left(- \left(- a + b x\right) \left(a + b x\right)\right)^{\frac{3}{2}}}{\left(a + b x\right)^{5}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**(3/2)/(a + b*x)**5, x)","F",0
796,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(3/2)/(b*x+a)**6,x)","\int \frac{\left(- \left(- a + b x\right) \left(a + b x\right)\right)^{\frac{3}{2}}}{\left(a + b x\right)^{6}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**(3/2)/(a + b*x)**6, x)","F",0
797,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(3/2)/(b*x+a)**7,x)","\int \frac{\left(- \left(- a + b x\right) \left(a + b x\right)\right)^{\frac{3}{2}}}{\left(a + b x\right)^{7}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**(3/2)/(a + b*x)**7, x)","F",0
798,-1,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(3/2)/(b*x+a)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
799,-1,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(3/2)/(b*x+a)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
800,1,1496,0,41.079183," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(7/2),x)","d^{9} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) + 3 d^{8} e \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) - 8 d^{6} e^{3} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) - 6 d^{5} e^{4} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 6 d^{4} e^{5} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) + 8 d^{3} e^{6} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 3 d e^{8} \left(\begin{cases} - \frac{7 i d^{10} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{256 e^{9}} + \frac{7 i d^{9} x}{256 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{7} x^{3}}{768 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{5} x^{5}}{1920 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{7}}{480 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{9 i d x^{9}}{80 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{11}}{10 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{7 d^{10} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{256 e^{9}} - \frac{7 d^{9} x}{256 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{7} x^{3}}{768 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{5} x^{5}}{1920 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{7}}{480 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{9 d x^{9}}{80 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{11}}{10 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - e^{9} \left(\begin{cases} - \frac{128 d^{10} \sqrt{d^{2} - e^{2} x^{2}}}{3465 e^{10}} - \frac{64 d^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3465 e^{8}} - \frac{16 d^{6} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{1155 e^{6}} - \frac{8 d^{4} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{693 e^{4}} - \frac{d^{2} x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{99 e^{2}} + \frac{x^{10} \sqrt{d^{2} - e^{2} x^{2}}}{11} & \text{for}\: e \neq 0 \\\frac{x^{10} \sqrt{d^{2}}}{10} & \text{otherwise} \end{cases}\right)"," ",0,"d**9*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) + 3*d**8*e*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) - 8*d**6*e**3*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) - 6*d**5*e**4*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) + 6*d**4*e**5*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) + 8*d**3*e**6*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) - 3*d*e**8*Piecewise((-7*I*d**10*acosh(e*x/d)/(256*e**9) + 7*I*d**9*x/(256*e**8*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**7*x**3/(768*e**6*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**5*x**5/(1920*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**7/(480*e**2*sqrt(-1 + e**2*x**2/d**2)) - 9*I*d*x**9/(80*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**11/(10*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (7*d**10*asin(e*x/d)/(256*e**9) - 7*d**9*x/(256*e**8*sqrt(1 - e**2*x**2/d**2)) + 7*d**7*x**3/(768*e**6*sqrt(1 - e**2*x**2/d**2)) + 7*d**5*x**5/(1920*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**7/(480*e**2*sqrt(1 - e**2*x**2/d**2)) + 9*d*x**9/(80*sqrt(1 - e**2*x**2/d**2)) - e**2*x**11/(10*d*sqrt(1 - e**2*x**2/d**2)), True)) - e**9*Piecewise((-128*d**10*sqrt(d**2 - e**2*x**2)/(3465*e**10) - 64*d**8*x**2*sqrt(d**2 - e**2*x**2)/(3465*e**8) - 16*d**6*x**4*sqrt(d**2 - e**2*x**2)/(1155*e**6) - 8*d**4*x**6*sqrt(d**2 - e**2*x**2)/(693*e**4) - d**2*x**8*sqrt(d**2 - e**2*x**2)/(99*e**2) + x**10*sqrt(d**2 - e**2*x**2)/11, Ne(e, 0)), (x**10*sqrt(d**2)/10, True))","C",0
801,1,1413,0,35.735807," ","integrate((e*x+d)**2*(-e**2*x**2+d**2)**(7/2),x)","d^{8} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) + 2 d^{7} e \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) - 2 d^{6} e^{2} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 6 d^{5} e^{3} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + 6 d^{3} e^{5} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) + 2 d^{2} e^{6} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 2 d e^{7} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right) - e^{8} \left(\begin{cases} - \frac{7 i d^{10} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{256 e^{9}} + \frac{7 i d^{9} x}{256 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{7} x^{3}}{768 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{5} x^{5}}{1920 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{7}}{480 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{9 i d x^{9}}{80 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{11}}{10 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{7 d^{10} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{256 e^{9}} - \frac{7 d^{9} x}{256 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{7} x^{3}}{768 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{5} x^{5}}{1920 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{7}}{480 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{9 d x^{9}}{80 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{11}}{10 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**8*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) + 2*d**7*e*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) - 2*d**6*e**2*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - 6*d**5*e**3*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + 6*d**3*e**5*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) + 2*d**2*e**6*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) - 2*d*e**7*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True)) - e**8*Piecewise((-7*I*d**10*acosh(e*x/d)/(256*e**9) + 7*I*d**9*x/(256*e**8*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**7*x**3/(768*e**6*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**5*x**5/(1920*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**7/(480*e**2*sqrt(-1 + e**2*x**2/d**2)) - 9*I*d*x**9/(80*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**11/(10*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (7*d**10*asin(e*x/d)/(256*e**9) - 7*d**9*x/(256*e**8*sqrt(1 - e**2*x**2/d**2)) + 7*d**7*x**3/(768*e**6*sqrt(1 - e**2*x**2/d**2)) + 7*d**5*x**5/(1920*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**7/(480*e**2*sqrt(1 - e**2*x**2/d**2)) + 9*d*x**9/(80*sqrt(1 - e**2*x**2/d**2)) - e**2*x**11/(10*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
802,1,1284,0,27.734547," ","integrate((e*x+d)*(-e**2*x**2+d**2)**(7/2),x)","d^{7} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) + d^{6} e \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) - 3 d^{5} e^{2} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 3 d^{4} e^{3} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + 3 d^{3} e^{4} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 3 d^{2} e^{5} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) - d e^{6} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - e^{7} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) + d**6*e*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) - 3*d**5*e**2*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - 3*d**4*e**3*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + 3*d**3*e**4*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) + 3*d**2*e**5*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) - d*e**6*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) - e**7*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True))","C",0
803,1,813,0,16.131946," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d),x)","d^{5} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) - d^{4} e \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) - 2 d^{3} e^{2} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 2 d^{2} e^{3} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + d e^{4} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - e^{5} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"d**5*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) - d**4*e*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) - 2*d**3*e**2*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + 2*d**2*e**3*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + d*e**4*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) - e**5*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True))","C",0
804,1,495,0,17.753675," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**2,x)","d^{4} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) - 2 d^{3} e \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + 2 d e^{3} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) - e^{4} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**4*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) - 2*d**3*e*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + 2*d*e**3*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) - e**4*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
805,1,439,0,18.056916," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**3,x)","d^{3} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) - 3 d^{2} e \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + 3 d e^{2} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) - 3*d**2*e*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + 3*d*e**2*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - e**3*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True))","C",0
806,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(7/2)/(d + e*x)**4, x)","F",0
807,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**5,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(7/2)/(d + e*x)**5, x)","F",0
808,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**6,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(7/2)/(d + e*x)**6, x)","F",0
809,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**7,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(7/2)/(d + e*x)**7, x)","F",0
810,-1,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
811,-1,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
812,-1,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
813,-1,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
814,-1,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**12,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
815,-1,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**13,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
816,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**(1/2)/(-b*x+a),x)","- \int \frac{\sqrt{a^{2} - b^{2} x^{2}}}{- a + b x}\, dx"," ",0,"-Integral(sqrt(a**2 - b**2*x**2)/(-a + b*x), x)","F",0
817,1,408,0,7.262294," ","integrate((b*x+a)**2*(-a**2*c/b**2+c*x**2)**(1/2),x)","a^{2} \left(\begin{cases} - \frac{a^{2} \sqrt{c} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{2 b^{2}} - \frac{a \sqrt{c} x}{2 b \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{b \sqrt{c} x^{3}}{2 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{i a^{2} \sqrt{c} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{2 b^{2}} + \frac{i a \sqrt{c} x \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}}{2 b} & \text{otherwise} \end{cases}\right) + 2 a b \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{\left(- \frac{a^{2} c}{b^{2}} + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + b^{2} \left(\begin{cases} - \frac{a^{4} \sqrt{c} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{8 b^{4}} + \frac{a^{3} \sqrt{c} x}{8 b^{3} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{3 a \sqrt{c} x^{3}}{8 b \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{b \sqrt{c} x^{5}}{4 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{i a^{4} \sqrt{c} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{8 b^{4}} - \frac{i a^{3} \sqrt{c} x}{8 b^{3} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{3 i a \sqrt{c} x^{3}}{8 b \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} - \frac{i b \sqrt{c} x^{5}}{4 a \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"a**2*Piecewise((-a**2*sqrt(c)*acosh(b*x/a)/(2*b**2) - a*sqrt(c)*x/(2*b*sqrt(-1 + b**2*x**2/a**2)) + b*sqrt(c)*x**3/(2*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (I*a**2*sqrt(c)*asin(b*x/a)/(2*b**2) + I*a*sqrt(c)*x*sqrt(1 - b**2*x**2/a**2)/(2*b), True)) + 2*a*b*Piecewise((0, Eq(c, 0)), ((-a**2*c/b**2 + c*x**2)**(3/2)/(3*c), True)) + b**2*Piecewise((-a**4*sqrt(c)*acosh(b*x/a)/(8*b**4) + a**3*sqrt(c)*x/(8*b**3*sqrt(-1 + b**2*x**2/a**2)) - 3*a*sqrt(c)*x**3/(8*b*sqrt(-1 + b**2*x**2/a**2)) + b*sqrt(c)*x**5/(4*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (I*a**4*sqrt(c)*asin(b*x/a)/(8*b**4) - I*a**3*sqrt(c)*x/(8*b**3*sqrt(1 - b**2*x**2/a**2)) + 3*I*a*sqrt(c)*x**3/(8*b*sqrt(1 - b**2*x**2/a**2)) - I*b*sqrt(c)*x**5/(4*a*sqrt(1 - b**2*x**2/a**2)), True))","C",0
818,1,491,0,7.820681," ","integrate((b*x+a)**3*(-a**2*c/b**2+c*x**2)**(1/2),x)","- \frac{2 a^{4} \sqrt{- \frac{a^{2} c}{b^{2}} + c x^{2}}}{15 b} + a^{3} \left(\begin{cases} - \frac{a^{2} \sqrt{c} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{2 b^{2}} - \frac{a \sqrt{c} x}{2 b \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{b \sqrt{c} x^{3}}{2 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{i a^{2} \sqrt{c} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{2 b^{2}} + \frac{i a \sqrt{c} x \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}}{2 b} & \text{otherwise} \end{cases}\right) - \frac{a^{2} b x^{2} \sqrt{- \frac{a^{2} c}{b^{2}} + c x^{2}}}{15} + 3 a^{2} b \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{\left(- \frac{a^{2} c}{b^{2}} + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 3 a b^{2} \left(\begin{cases} - \frac{a^{4} \sqrt{c} \operatorname{acosh}{\left(\frac{b x}{a} \right)}}{8 b^{4}} + \frac{a^{3} \sqrt{c} x}{8 b^{3} \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} - \frac{3 a \sqrt{c} x^{3}}{8 b \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} + \frac{b \sqrt{c} x^{5}}{4 a \sqrt{-1 + \frac{b^{2} x^{2}}{a^{2}}}} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{i a^{4} \sqrt{c} \operatorname{asin}{\left(\frac{b x}{a} \right)}}{8 b^{4}} - \frac{i a^{3} \sqrt{c} x}{8 b^{3} \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} + \frac{3 i a \sqrt{c} x^{3}}{8 b \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} - \frac{i b \sqrt{c} x^{5}}{4 a \sqrt{1 - \frac{b^{2} x^{2}}{a^{2}}}} & \text{otherwise} \end{cases}\right) + \frac{b^{3} x^{4} \sqrt{- \frac{a^{2} c}{b^{2}} + c x^{2}}}{5}"," ",0,"-2*a**4*sqrt(-a**2*c/b**2 + c*x**2)/(15*b) + a**3*Piecewise((-a**2*sqrt(c)*acosh(b*x/a)/(2*b**2) - a*sqrt(c)*x/(2*b*sqrt(-1 + b**2*x**2/a**2)) + b*sqrt(c)*x**3/(2*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (I*a**2*sqrt(c)*asin(b*x/a)/(2*b**2) + I*a*sqrt(c)*x*sqrt(1 - b**2*x**2/a**2)/(2*b), True)) - a**2*b*x**2*sqrt(-a**2*c/b**2 + c*x**2)/15 + 3*a**2*b*Piecewise((0, Eq(c, 0)), ((-a**2*c/b**2 + c*x**2)**(3/2)/(3*c), True)) + 3*a*b**2*Piecewise((-a**4*sqrt(c)*acosh(b*x/a)/(8*b**4) + a**3*sqrt(c)*x/(8*b**3*sqrt(-1 + b**2*x**2/a**2)) - 3*a*sqrt(c)*x**3/(8*b*sqrt(-1 + b**2*x**2/a**2)) + b*sqrt(c)*x**5/(4*a*sqrt(-1 + b**2*x**2/a**2)), Abs(b**2*x**2/a**2) > 1), (I*a**4*sqrt(c)*asin(b*x/a)/(8*b**4) - I*a**3*sqrt(c)*x/(8*b**3*sqrt(1 - b**2*x**2/a**2)) + 3*I*a*sqrt(c)*x**3/(8*b*sqrt(1 - b**2*x**2/a**2)) - I*b*sqrt(c)*x**5/(4*a*sqrt(1 - b**2*x**2/a**2)), True)) + b**3*x**4*sqrt(-a**2*c/b**2 + c*x**2)/5","C",0
819,1,39,0,0.214610," ","integrate((1+x)*(x**2-1)**(1/2),x)","\frac{x^{2} \sqrt{x^{2} - 1}}{3} + \frac{x \sqrt{x^{2} - 1}}{2} - \frac{\sqrt{x^{2} - 1}}{3} - \frac{\operatorname{acosh}{\left(x \right)}}{2}"," ",0,"x**2*sqrt(x**2 - 1)/3 + x*sqrt(x**2 - 1)/2 - sqrt(x**2 - 1)/3 - acosh(x)/2","A",0
820,1,39,0,0.211467," ","integrate((1+x)*(-x**2+1)**(1/2),x)","\frac{x^{2} \sqrt{1 - x^{2}}}{3} + \frac{x \sqrt{1 - x^{2}}}{2} - \frac{\sqrt{1 - x^{2}}}{3} + \frac{\operatorname{asin}{\left(x \right)}}{2}"," ",0,"x**2*sqrt(1 - x**2)/3 + x*sqrt(1 - x**2)/2 - sqrt(1 - x**2)/3 + asin(x)/2","A",0
821,1,15,0,2.179432," ","integrate((-x**2+1)**(1/2)/(1+x),x)","\begin{cases} \sqrt{1 - x^{2}} + \operatorname{asin}{\left(x \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"Piecewise((sqrt(1 - x**2) + asin(x), (x > -1) & (x < 1)))","A",0
822,1,39,0,0.219928," ","integrate((1-x)*(-x**2+1)**(1/2),x)","- \frac{x^{2} \sqrt{1 - x^{2}}}{3} + \frac{x \sqrt{1 - x^{2}}}{2} + \frac{\sqrt{1 - x^{2}}}{3} + \frac{\operatorname{asin}{\left(x \right)}}{2}"," ",0,"-x**2*sqrt(1 - x**2)/3 + x*sqrt(1 - x**2)/2 + sqrt(1 - x**2)/3 + asin(x)/2","A",0
823,1,17,0,2.403498," ","integrate((-x**2+1)**(1/2)/(1-x),x)","- \begin{cases} \sqrt{1 - x^{2}} - \operatorname{asin}{\left(x \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"-Piecewise((sqrt(1 - x**2) - asin(x), (x > -1) & (x < 1)))","A",0
824,0,0,0,0.000000," ","integrate((-x**2+1)**(1/2)/(1-x)**2,x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}{\left(x - 1\right)^{2}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1))/(x - 1)**2, x)","F",0
825,0,0,0,0.000000," ","integrate((-x**2+1)**(1/2)/(1-x)**3,x)","- \int \frac{\sqrt{1 - x^{2}}}{x^{3} - 3 x^{2} + 3 x - 1}\, dx"," ",0,"-Integral(sqrt(1 - x**2)/(x**3 - 3*x**2 + 3*x - 1), x)","F",0
826,1,641,0,11.019986," ","integrate((e*x+d)**5/(-e**2*x**2+d**2)**(1/2),x)","d^{5} \left(\begin{cases} \frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{asin}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} > 0 \\\frac{\sqrt{- \frac{d^{2}}{e^{2}}} \operatorname{asinh}{\left(x \sqrt{- \frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} < 0 \\\frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{acosh}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{- d^{2}}} & \text{for}\: d^{2} < 0 \wedge e^{2} < 0 \end{cases}\right) + 5 d^{4} e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{d^{2}}} & \text{for}\: e^{2} = 0 \\- \frac{\sqrt{d^{2} - e^{2} x^{2}}}{e^{2}} & \text{otherwise} \end{cases}\right) + 10 d^{3} e^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{i d x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{2 e^{2}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{d x}{2 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{3}}{2 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 10 d^{2} e^{3} \left(\begin{cases} - \frac{2 d^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{4}} - \frac{x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{2}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \sqrt{d^{2}}} & \text{otherwise} \end{cases}\right) + 5 d e^{4} \left(\begin{cases} - \frac{3 i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{5}} + \frac{3 i d^{3} x}{8 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d x^{3}}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{5}} - \frac{3 d^{3} x}{8 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d x^{3}}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{5} \left(\begin{cases} - \frac{8 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{6}} - \frac{4 d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5 e^{2}} & \text{for}\: e \neq 0 \\\frac{x^{6}}{6 \sqrt{d^{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**5*Piecewise((sqrt(d**2/e**2)*asin(x*sqrt(e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 > 0)), (sqrt(-d**2/e**2)*asinh(x*sqrt(-e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 < 0)), (sqrt(d**2/e**2)*acosh(x*sqrt(e**2/d**2))/sqrt(-d**2), (d**2 < 0) & (e**2 < 0))) + 5*d**4*e*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + 10*d**3*e**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e**3) - I*d*x*sqrt(-1 + e**2*x**2/d**2)/(2*e**2), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e**3) - d*x/(2*e**2*sqrt(1 - e**2*x**2/d**2)) + x**3/(2*d*sqrt(1 - e**2*x**2/d**2)), True)) + 10*d**2*e**3*Piecewise((-2*d**2*sqrt(d**2 - e**2*x**2)/(3*e**4) - x**2*sqrt(d**2 - e**2*x**2)/(3*e**2), Ne(e, 0)), (x**4/(4*sqrt(d**2)), True)) + 5*d*e**4*Piecewise((-3*I*d**4*acosh(e*x/d)/(8*e**5) + 3*I*d**3*x/(8*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d*x**3/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - I*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (3*d**4*asin(e*x/d)/(8*e**5) - 3*d**3*x/(8*e**4*sqrt(1 - e**2*x**2/d**2)) + d*x**3/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**5*Piecewise((-8*d**4*sqrt(d**2 - e**2*x**2)/(15*e**6) - 4*d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**4) - x**4*sqrt(d**2 - e**2*x**2)/(5*e**2), Ne(e, 0)), (x**6/(6*sqrt(d**2)), True))","A",0
827,1,546,0,9.623663," ","integrate((e*x+d)**4/(-e**2*x**2+d**2)**(1/2),x)","d^{4} \left(\begin{cases} \frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{asin}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} > 0 \\\frac{\sqrt{- \frac{d^{2}}{e^{2}}} \operatorname{asinh}{\left(x \sqrt{- \frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} < 0 \\\frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{acosh}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{- d^{2}}} & \text{for}\: d^{2} < 0 \wedge e^{2} < 0 \end{cases}\right) + 4 d^{3} e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{d^{2}}} & \text{for}\: e^{2} = 0 \\- \frac{\sqrt{d^{2} - e^{2} x^{2}}}{e^{2}} & \text{otherwise} \end{cases}\right) + 6 d^{2} e^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{i d x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{2 e^{2}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{d x}{2 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{3}}{2 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 4 d e^{3} \left(\begin{cases} - \frac{2 d^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{4}} - \frac{x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{2}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \sqrt{d^{2}}} & \text{otherwise} \end{cases}\right) + e^{4} \left(\begin{cases} - \frac{3 i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{5}} + \frac{3 i d^{3} x}{8 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d x^{3}}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{5}} - \frac{3 d^{3} x}{8 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d x^{3}}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**4*Piecewise((sqrt(d**2/e**2)*asin(x*sqrt(e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 > 0)), (sqrt(-d**2/e**2)*asinh(x*sqrt(-e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 < 0)), (sqrt(d**2/e**2)*acosh(x*sqrt(e**2/d**2))/sqrt(-d**2), (d**2 < 0) & (e**2 < 0))) + 4*d**3*e*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + 6*d**2*e**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e**3) - I*d*x*sqrt(-1 + e**2*x**2/d**2)/(2*e**2), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e**3) - d*x/(2*e**2*sqrt(1 - e**2*x**2/d**2)) + x**3/(2*d*sqrt(1 - e**2*x**2/d**2)), True)) + 4*d*e**3*Piecewise((-2*d**2*sqrt(d**2 - e**2*x**2)/(3*e**4) - x**2*sqrt(d**2 - e**2*x**2)/(3*e**2), Ne(e, 0)), (x**4/(4*sqrt(d**2)), True)) + e**4*Piecewise((-3*I*d**4*acosh(e*x/d)/(8*e**5) + 3*I*d**3*x/(8*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d*x**3/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - I*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (3*d**4*asin(e*x/d)/(8*e**5) - 3*d**3*x/(8*e**4*sqrt(1 - e**2*x**2/d**2)) + d*x**3/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
828,1,337,0,5.583781," ","integrate((e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","d^{3} \left(\begin{cases} \frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{asin}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} > 0 \\\frac{\sqrt{- \frac{d^{2}}{e^{2}}} \operatorname{asinh}{\left(x \sqrt{- \frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} < 0 \\\frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{acosh}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{- d^{2}}} & \text{for}\: d^{2} < 0 \wedge e^{2} < 0 \end{cases}\right) + 3 d^{2} e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{d^{2}}} & \text{for}\: e^{2} = 0 \\- \frac{\sqrt{d^{2} - e^{2} x^{2}}}{e^{2}} & \text{otherwise} \end{cases}\right) + 3 d e^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{i d x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{2 e^{2}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{d x}{2 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{3}}{2 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{2 d^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{4}} - \frac{x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{2}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \sqrt{d^{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((sqrt(d**2/e**2)*asin(x*sqrt(e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 > 0)), (sqrt(-d**2/e**2)*asinh(x*sqrt(-e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 < 0)), (sqrt(d**2/e**2)*acosh(x*sqrt(e**2/d**2))/sqrt(-d**2), (d**2 < 0) & (e**2 < 0))) + 3*d**2*e*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + 3*d*e**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e**3) - I*d*x*sqrt(-1 + e**2*x**2/d**2)/(2*e**2), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e**3) - d*x/(2*e**2*sqrt(1 - e**2*x**2/d**2)) + x**3/(2*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**3*Piecewise((-2*d**2*sqrt(d**2 - e**2*x**2)/(3*e**4) - x**2*sqrt(d**2 - e**2*x**2)/(3*e**2), Ne(e, 0)), (x**4/(4*sqrt(d**2)), True))","A",0
829,1,269,0,4.656376," ","integrate((e*x+d)**2/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} \frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{asin}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} > 0 \\\frac{\sqrt{- \frac{d^{2}}{e^{2}}} \operatorname{asinh}{\left(x \sqrt{- \frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} < 0 \\\frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{acosh}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{- d^{2}}} & \text{for}\: d^{2} < 0 \wedge e^{2} < 0 \end{cases}\right) + 2 d e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{d^{2}}} & \text{for}\: e^{2} = 0 \\- \frac{\sqrt{d^{2} - e^{2} x^{2}}}{e^{2}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{i d x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{2 e^{2}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{d x}{2 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{3}}{2 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((sqrt(d**2/e**2)*asin(x*sqrt(e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 > 0)), (sqrt(-d**2/e**2)*asinh(x*sqrt(-e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 < 0)), (sqrt(d**2/e**2)*acosh(x*sqrt(e**2/d**2))/sqrt(-d**2), (d**2 < 0) & (e**2 < 0))) + 2*d*e*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + e**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e**3) - I*d*x*sqrt(-1 + e**2*x**2/d**2)/(2*e**2), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e**3) - d*x/(2*e**2*sqrt(1 - e**2*x**2/d**2)) + x**3/(2*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
830,1,42,0,2.140086," ","integrate((e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\begin{cases} \frac{d \left(\begin{cases} \operatorname{asin}{\left(e x \sqrt{\frac{1}{d^{2}}} \right)} & \text{for}\: d^{2} > 0 \end{cases}\right) - \sqrt{d^{2} - e^{2} x^{2}}}{e} & \text{for}\: e \neq 0 \\\frac{d x}{\sqrt{d^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((d*Piecewise((asin(e*x*sqrt(d**(-2))), d**2 > 0)) - sqrt(d**2 - e**2*x**2))/e, Ne(e, 0)), (d*x/sqrt(d**2), True))","A",0
831,0,0,0,0.000000," ","integrate(1/(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)), x)","F",0
832,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**2), x)","F",0
833,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
834,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**4), x)","F",0
835,0,0,0,0.000000," ","integrate(1/(e*x+d)**5/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{5}}\, dx"," ",0,"Integral(1/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**5), x)","F",0
836,0,0,0,0.000000," ","integrate((e*x+d)**6/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{6}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**6/(-(-d + e*x)*(d + e*x))**(5/2), x)","F",0
837,0,0,0,0.000000," ","integrate((e*x+d)**5/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{5}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**5/(-(-d + e*x)*(d + e*x))**(5/2), x)","F",0
838,0,0,0,0.000000," ","integrate((e*x+d)**4/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/(-(-d + e*x)*(d + e*x))**(5/2), x)","F",0
839,0,0,0,0.000000," ","integrate((e*x+d)**3/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(-(-d + e*x)*(d + e*x))**(5/2), x)","F",0
840,0,0,0,0.000000," ","integrate((e*x+d)**2/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(-(-d + e*x)*(d + e*x))**(5/2), x)","F",0
841,1,296,0,11.184313," ","integrate((e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","d \left(\begin{cases} \frac{3 i d^{2} x}{- 3 d^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 3 d^{5} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{2 i e^{2} x^{3}}{- 3 d^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 3 d^{5} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{3 d^{2} x}{- 3 d^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 3 d^{5} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{2 e^{2} x^{3}}{- 3 d^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 3 d^{5} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} - \frac{1}{- 3 d^{2} e^{2} \sqrt{d^{2} - e^{2} x^{2}} + 3 e^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{2}}{2 \left(d^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((3*I*d**2*x/(-3*d**7*sqrt(-1 + e**2*x**2/d**2) + 3*d**5*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)) - 2*I*e**2*x**3/(-3*d**7*sqrt(-1 + e**2*x**2/d**2) + 3*d**5*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-3*d**2*x/(-3*d**7*sqrt(1 - e**2*x**2/d**2) + 3*d**5*e**2*x**2*sqrt(1 - e**2*x**2/d**2)) + 2*e**2*x**3/(-3*d**7*sqrt(1 - e**2*x**2/d**2) + 3*d**5*e**2*x**2*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((-1/(-3*d**2*e**2*sqrt(d**2 - e**2*x**2) + 3*e**4*x**2*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**2/(2*(d**2)**(5/2)), True))","C",0
842,0,0,0,0.000000," ","integrate(1/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
843,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)**2), x)","F",0
844,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)**3), x)","F",0
845,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)**4), x)","F",0
846,0,0,0,0.000000," ","integrate((e*x+d)**9/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{9}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**9/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
847,0,0,0,0.000000," ","integrate((e*x+d)**8/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{8}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**8/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
848,0,0,0,0.000000," ","integrate((e*x+d)**7/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{7}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**7/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
849,0,0,0,0.000000," ","integrate((e*x+d)**6/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{6}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**6/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
850,0,0,0,0.000000," ","integrate((e*x+d)**5/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{5}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**5/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
851,0,0,0,0.000000," ","integrate((e*x+d)**4/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
852,0,0,0,0.000000," ","integrate((e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
853,0,0,0,0.000000," ","integrate((e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
854,1,604,0,26.552572," ","integrate((e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} - \frac{15 i d^{4} x}{15 d^{11} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{20 i d^{2} e^{2} x^{3}}{15 d^{11} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{8 i e^{4} x^{5}}{15 d^{11} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{15 d^{4} x}{15 d^{11} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{20 d^{2} e^{2} x^{3}}{15 d^{11} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{8 e^{4} x^{5}}{15 d^{11} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} \frac{1}{5 d^{4} e^{2} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{6} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{2}}{2 \left(d^{2}\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-15*I*d**4*x/(15*d**11*sqrt(-1 + e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)) + 20*I*d**2*e**2*x**3/(15*d**11*sqrt(-1 + e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)) - 8*I*e**4*x**5/(15*d**11*sqrt(-1 + e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (15*d**4*x/(15*d**11*sqrt(1 - e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(1 - e**2*x**2/d**2)) - 20*d**2*e**2*x**3/(15*d**11*sqrt(1 - e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(1 - e**2*x**2/d**2)) + 8*e**4*x**5/(15*d**11*sqrt(1 - e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((1/(5*d**4*e**2*sqrt(d**2 - e**2*x**2) - 10*d**2*e**4*x**2*sqrt(d**2 - e**2*x**2) + 5*e**6*x**4*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**2/(2*(d**2)**(7/2)), True))","C",0
855,0,0,0,0.000000," ","integrate(1/(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)), x)","F",0
856,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)**2), x)","F",0
857,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)**3), x)","F",0
858,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)**4), x)","F",0
859,0,0,0,0.000000," ","integrate(1/(e*x+d)**5/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)^{5}}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)**5), x)","F",0
860,1,10,0,0.152563," ","integrate((1+x)/(-x**2+1)**(1/2),x)","- \sqrt{1 - x^{2}} + \operatorname{asin}{\left(x \right)}"," ",0,"-sqrt(1 - x**2) + asin(x)","A",0
861,1,10,0,0.154040," ","integrate((1-x)/(-x**2+1)**(1/2),x)","\sqrt{1 - x^{2}} + \operatorname{asin}{\left(x \right)}"," ",0,"sqrt(1 - x**2) + asin(x)","A",0
862,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(-c*e**2*x**2+c*d**2)**(1/2),x)","\int \sqrt{- c \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(sqrt(-c*(-d + e*x)*(d + e*x))*(d + e*x)**(5/2), x)","F",0
863,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(-c*e**2*x**2+c*d**2)**(1/2),x)","\int \sqrt{- c \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(-c*(-d + e*x)*(d + e*x))*(d + e*x)**(3/2), x)","F",0
864,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(-c*e**2*x**2+c*d**2)**(1/2),x)","\int \sqrt{- c \left(- d + e x\right) \left(d + e x\right)} \sqrt{d + e x}\, dx"," ",0,"Integral(sqrt(-c*(-d + e*x)*(d + e*x))*sqrt(d + e*x), x)","F",0
865,0,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt(-c*(-d + e*x)*(d + e*x))/sqrt(d + e*x), x)","F",0
866,0,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(-d + e*x)*(d + e*x))/(d + e*x)**(3/2), x)","F",0
867,0,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(-d + e*x)*(d + e*x))/(d + e*x)**(5/2), x)","F",0
868,0,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(1/2)/(e*x+d)**(7/2),x)","\int \frac{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(-d + e*x)*(d + e*x))/(d + e*x)**(7/2), x)","F",0
869,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(-c*e**2*x**2+c*d**2)**(3/2),x)","\int \left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((-c*(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**(5/2), x)","F",0
870,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(-c*e**2*x**2+c*d**2)**(3/2),x)","\int \left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((-c*(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**(3/2), x)","F",0
871,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(-c*e**2*x**2+c*d**2)**(3/2),x)","\int \left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \sqrt{d + e x}\, dx"," ",0,"Integral((-c*(-d + e*x)*(d + e*x))**(3/2)*sqrt(d + e*x), x)","F",0
872,0,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((-c*(-d + e*x)*(d + e*x))**(3/2)/sqrt(d + e*x), x)","F",0
873,0,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-c*(-d + e*x)*(d + e*x))**(3/2)/(d + e*x)**(3/2), x)","F",0
874,0,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-c*(-d + e*x)*(d + e*x))**(3/2)/(d + e*x)**(5/2), x)","F",0
875,0,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(3/2)/(e*x+d)**(7/2),x)","\int \frac{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((-c*(-d + e*x)*(d + e*x))**(3/2)/(d + e*x)**(7/2), x)","F",0
876,0,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(3/2)/(e*x+d)**(9/2),x)","\int \frac{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((-c*(-d + e*x)*(d + e*x))**(3/2)/(d + e*x)**(9/2), x)","F",0
877,0,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(3/2)/(e*x+d)**(11/2),x)","\int \frac{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{11}{2}}}\, dx"," ",0,"Integral((-c*(-d + e*x)*(d + e*x))**(3/2)/(d + e*x)**(11/2), x)","F",0
878,-1,0,0,0.000000," ","integrate((-c*e**2*x**2+c*d**2)**(3/2)/(e*x+d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,0,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(-c*e**2*x**2+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{7}{2}}}{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)}}\, dx"," ",0,"Integral((d + e*x)**(7/2)/sqrt(-c*(-d + e*x)*(d + e*x)), x)","F",0
880,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(-c*e**2*x**2+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{5}{2}}}{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)}}\, dx"," ",0,"Integral((d + e*x)**(5/2)/sqrt(-c*(-d + e*x)*(d + e*x)), x)","F",0
881,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(-c*e**2*x**2+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/sqrt(-c*(-d + e*x)*(d + e*x)), x)","F",0
882,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(-c*e**2*x**2+c*d**2)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)/sqrt(-c*(-d + e*x)*(d + e*x)), x)","F",0
883,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(-c*e**2*x**2+c*d**2)**(1/2),x)","\int \frac{1}{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/(sqrt(-c*(-d + e*x)*(d + e*x))*sqrt(d + e*x)), x)","F",0
884,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(-c*e**2*x**2+c*d**2)**(1/2),x)","\int \frac{1}{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(-c*(-d + e*x)*(d + e*x))*(d + e*x)**(3/2)), x)","F",0
885,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(-c*e**2*x**2+c*d**2)**(1/2),x)","\int \frac{1}{\sqrt{- c \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(-c*(-d + e*x)*(d + e*x))*(d + e*x)**(5/2)), x)","F",0
886,0,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(-c*e**2*x**2+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{9}{2}}}{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(9/2)/(-c*(-d + e*x)*(d + e*x))**(3/2), x)","F",0
887,0,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(-c*e**2*x**2+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{7}{2}}}{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(7/2)/(-c*(-d + e*x)*(d + e*x))**(3/2), x)","F",0
888,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(-c*e**2*x**2+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{5}{2}}}{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(5/2)/(-c*(-d + e*x)*(d + e*x))**(3/2), x)","F",0
889,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(-c*e**2*x**2+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/(-c*(-d + e*x)*(d + e*x))**(3/2), x)","F",0
890,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(-c*e**2*x**2+c*d**2)**(3/2),x)","\int \frac{\sqrt{d + e x}}{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/(-c*(-d + e*x)*(d + e*x))**(3/2), x)","F",0
891,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(-c*e**2*x**2+c*d**2)**(3/2),x)","\int \frac{1}{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/((-c*(-d + e*x)*(d + e*x))**(3/2)*sqrt(d + e*x)), x)","F",0
892,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(-c*e**2*x**2+c*d**2)**(3/2),x)","\int \frac{1}{\left(- c \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((-c*(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**(3/2)), x)","F",0
893,0,0,0,0.000000," ","integrate(1/(-1+x)**(1/2)/(-x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \sqrt{x - 1}}\, dx"," ",0,"Integral(1/(sqrt(-(x - 1)*(x + 1))*sqrt(x - 1)), x)","F",0
894,-1,0,0,0.000000," ","integrate((e*x+2)**(5/2)*(-3*e**2*x**2+12)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
895,0,0,0,0.000000," ","integrate((e*x+2)**(3/2)*(-3*e**2*x**2+12)**(1/2),x)","\sqrt{3} \left(\int 2 \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4}\, dx + \int e x \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4}\, dx\right)"," ",0,"sqrt(3)*(Integral(2*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4), x) + Integral(e*x*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4), x))","F",0
896,0,0,0,0.000000," ","integrate((e*x+2)**(1/2)*(-3*e**2*x**2+12)**(1/2),x)","\sqrt{3} \int \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4}\, dx"," ",0,"sqrt(3)*Integral(sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4), x)","F",0
897,0,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(1/2)/(e*x+2)**(1/2),x)","\sqrt{3} \int \frac{\sqrt{- e^{2} x^{2} + 4}}{\sqrt{e x + 2}}\, dx"," ",0,"sqrt(3)*Integral(sqrt(-e**2*x**2 + 4)/sqrt(e*x + 2), x)","F",0
898,0,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(1/2)/(e*x+2)**(3/2),x)","\sqrt{3} \int \frac{\sqrt{- e^{2} x^{2} + 4}}{e x \sqrt{e x + 2} + 2 \sqrt{e x + 2}}\, dx"," ",0,"sqrt(3)*Integral(sqrt(-e**2*x**2 + 4)/(e*x*sqrt(e*x + 2) + 2*sqrt(e*x + 2)), x)","F",0
899,0,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(1/2)/(e*x+2)**(5/2),x)","\sqrt{3} \int \frac{\sqrt{- e^{2} x^{2} + 4}}{e^{2} x^{2} \sqrt{e x + 2} + 4 e x \sqrt{e x + 2} + 4 \sqrt{e x + 2}}\, dx"," ",0,"sqrt(3)*Integral(sqrt(-e**2*x**2 + 4)/(e**2*x**2*sqrt(e*x + 2) + 4*e*x*sqrt(e*x + 2) + 4*sqrt(e*x + 2)), x)","F",0
900,-1,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(1/2)/(e*x+2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
901,-1,0,0,0.000000," ","integrate((e*x+2)**(5/2)*(-3*e**2*x**2+12)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
902,-1,0,0,0.000000," ","integrate((e*x+2)**(3/2)*(-3*e**2*x**2+12)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
903,0,0,0,0.000000," ","integrate((e*x+2)**(1/2)*(-3*e**2*x**2+12)**(3/2),x)","3 \sqrt{3} \left(\int 4 \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4}\, dx + \int \left(- e^{2} x^{2} \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4}\right)\, dx\right)"," ",0,"3*sqrt(3)*(Integral(4*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4), x) + Integral(-e**2*x**2*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4), x))","F",0
904,0,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(3/2)/(e*x+2)**(1/2),x)","3 \sqrt{3} \left(\int \frac{4 \sqrt{- e^{2} x^{2} + 4}}{\sqrt{e x + 2}}\, dx + \int \left(- \frac{e^{2} x^{2} \sqrt{- e^{2} x^{2} + 4}}{\sqrt{e x + 2}}\right)\, dx\right)"," ",0,"3*sqrt(3)*(Integral(4*sqrt(-e**2*x**2 + 4)/sqrt(e*x + 2), x) + Integral(-e**2*x**2*sqrt(-e**2*x**2 + 4)/sqrt(e*x + 2), x))","F",0
905,0,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(3/2)/(e*x+2)**(3/2),x)","3 \sqrt{3} \left(\int \frac{4 \sqrt{- e^{2} x^{2} + 4}}{e x \sqrt{e x + 2} + 2 \sqrt{e x + 2}}\, dx + \int \left(- \frac{e^{2} x^{2} \sqrt{- e^{2} x^{2} + 4}}{e x \sqrt{e x + 2} + 2 \sqrt{e x + 2}}\right)\, dx\right)"," ",0,"3*sqrt(3)*(Integral(4*sqrt(-e**2*x**2 + 4)/(e*x*sqrt(e*x + 2) + 2*sqrt(e*x + 2)), x) + Integral(-e**2*x**2*sqrt(-e**2*x**2 + 4)/(e*x*sqrt(e*x + 2) + 2*sqrt(e*x + 2)), x))","F",0
906,-1,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(3/2)/(e*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,-1,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(3/2)/(e*x+2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
908,-1,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(3/2)/(e*x+2)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
909,-1,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(3/2)/(e*x+2)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
910,-1,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(3/2)/(e*x+2)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
911,-1,0,0,0.000000," ","integrate((e*x+2)**(7/2)/(-3*e**2*x**2+12)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
912,0,0,0,0.000000," ","integrate((e*x+2)**(5/2)/(-3*e**2*x**2+12)**(1/2),x)","\frac{\sqrt{3} \left(\int \frac{4 \sqrt{e x + 2}}{\sqrt{- e^{2} x^{2} + 4}}\, dx + \int \frac{4 e x \sqrt{e x + 2}}{\sqrt{- e^{2} x^{2} + 4}}\, dx + \int \frac{e^{2} x^{2} \sqrt{e x + 2}}{\sqrt{- e^{2} x^{2} + 4}}\, dx\right)}{3}"," ",0,"sqrt(3)*(Integral(4*sqrt(e*x + 2)/sqrt(-e**2*x**2 + 4), x) + Integral(4*e*x*sqrt(e*x + 2)/sqrt(-e**2*x**2 + 4), x) + Integral(e**2*x**2*sqrt(e*x + 2)/sqrt(-e**2*x**2 + 4), x))/3","F",0
913,0,0,0,0.000000," ","integrate((e*x+2)**(3/2)/(-3*e**2*x**2+12)**(1/2),x)","\frac{\sqrt{3} \left(\int \frac{2 \sqrt{e x + 2}}{\sqrt{- e^{2} x^{2} + 4}}\, dx + \int \frac{e x \sqrt{e x + 2}}{\sqrt{- e^{2} x^{2} + 4}}\, dx\right)}{3}"," ",0,"sqrt(3)*(Integral(2*sqrt(e*x + 2)/sqrt(-e**2*x**2 + 4), x) + Integral(e*x*sqrt(e*x + 2)/sqrt(-e**2*x**2 + 4), x))/3","F",0
914,0,0,0,0.000000," ","integrate((e*x+2)**(1/2)/(-3*e**2*x**2+12)**(1/2),x)","\frac{\sqrt{3} \int \frac{\sqrt{e x + 2}}{\sqrt{- e^{2} x^{2} + 4}}\, dx}{3}"," ",0,"sqrt(3)*Integral(sqrt(e*x + 2)/sqrt(-e**2*x**2 + 4), x)/3","F",0
915,0,0,0,0.000000," ","integrate(1/(e*x+2)**(1/2)/(-3*e**2*x**2+12)**(1/2),x)","\frac{\sqrt{3} \int \frac{1}{\sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4}}\, dx}{3}"," ",0,"sqrt(3)*Integral(1/(sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4)), x)/3","F",0
916,0,0,0,0.000000," ","integrate(1/(e*x+2)**(3/2)/(-3*e**2*x**2+12)**(1/2),x)","\frac{\sqrt{3} \int \frac{1}{e x \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4} + 2 \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4}}\, dx}{3}"," ",0,"sqrt(3)*Integral(1/(e*x*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4) + 2*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4)), x)/3","F",0
917,0,0,0,0.000000," ","integrate(1/(e*x+2)**(5/2)/(-3*e**2*x**2+12)**(1/2),x)","\frac{\sqrt{3} \int \frac{1}{e^{2} x^{2} \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4} + 4 e x \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4} + 4 \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4}}\, dx}{3}"," ",0,"sqrt(3)*Integral(1/(e**2*x**2*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4) + 4*e*x*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4) + 4*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4)), x)/3","F",0
918,-1,0,0,0.000000," ","integrate((e*x+2)**(11/2)/(-3*e**2*x**2+12)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
919,-1,0,0,0.000000," ","integrate((e*x+2)**(9/2)/(-3*e**2*x**2+12)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
920,-1,0,0,0.000000," ","integrate((e*x+2)**(7/2)/(-3*e**2*x**2+12)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
921,0,0,0,0.000000," ","integrate((e*x+2)**(5/2)/(-3*e**2*x**2+12)**(3/2),x)","\frac{\sqrt{3} \left(\int \frac{4 \sqrt{e x + 2}}{- e^{2} x^{2} \sqrt{- e^{2} x^{2} + 4} + 4 \sqrt{- e^{2} x^{2} + 4}}\, dx + \int \frac{4 e x \sqrt{e x + 2}}{- e^{2} x^{2} \sqrt{- e^{2} x^{2} + 4} + 4 \sqrt{- e^{2} x^{2} + 4}}\, dx + \int \frac{e^{2} x^{2} \sqrt{e x + 2}}{- e^{2} x^{2} \sqrt{- e^{2} x^{2} + 4} + 4 \sqrt{- e^{2} x^{2} + 4}}\, dx\right)}{9}"," ",0,"sqrt(3)*(Integral(4*sqrt(e*x + 2)/(-e**2*x**2*sqrt(-e**2*x**2 + 4) + 4*sqrt(-e**2*x**2 + 4)), x) + Integral(4*e*x*sqrt(e*x + 2)/(-e**2*x**2*sqrt(-e**2*x**2 + 4) + 4*sqrt(-e**2*x**2 + 4)), x) + Integral(e**2*x**2*sqrt(e*x + 2)/(-e**2*x**2*sqrt(-e**2*x**2 + 4) + 4*sqrt(-e**2*x**2 + 4)), x))/9","F",0
922,0,0,0,0.000000," ","integrate((e*x+2)**(3/2)/(-3*e**2*x**2+12)**(3/2),x)","\frac{\sqrt{3} \left(\int \frac{2 \sqrt{e x + 2}}{- e^{2} x^{2} \sqrt{- e^{2} x^{2} + 4} + 4 \sqrt{- e^{2} x^{2} + 4}}\, dx + \int \frac{e x \sqrt{e x + 2}}{- e^{2} x^{2} \sqrt{- e^{2} x^{2} + 4} + 4 \sqrt{- e^{2} x^{2} + 4}}\, dx\right)}{9}"," ",0,"sqrt(3)*(Integral(2*sqrt(e*x + 2)/(-e**2*x**2*sqrt(-e**2*x**2 + 4) + 4*sqrt(-e**2*x**2 + 4)), x) + Integral(e*x*sqrt(e*x + 2)/(-e**2*x**2*sqrt(-e**2*x**2 + 4) + 4*sqrt(-e**2*x**2 + 4)), x))/9","F",0
923,0,0,0,0.000000," ","integrate((e*x+2)**(1/2)/(-3*e**2*x**2+12)**(3/2),x)","\frac{\sqrt{3} \int \frac{\sqrt{e x + 2}}{- e^{2} x^{2} \sqrt{- e^{2} x^{2} + 4} + 4 \sqrt{- e^{2} x^{2} + 4}}\, dx}{9}"," ",0,"sqrt(3)*Integral(sqrt(e*x + 2)/(-e**2*x**2*sqrt(-e**2*x**2 + 4) + 4*sqrt(-e**2*x**2 + 4)), x)/9","F",0
924,0,0,0,0.000000," ","integrate(1/(e*x+2)**(1/2)/(-3*e**2*x**2+12)**(3/2),x)","\frac{\sqrt{3} \int \frac{1}{- e^{2} x^{2} \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4} + 4 \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4}}\, dx}{9}"," ",0,"sqrt(3)*Integral(1/(-e**2*x**2*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4) + 4*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4)), x)/9","F",0
925,0,0,0,0.000000," ","integrate(1/(e*x+2)**(3/2)/(-3*e**2*x**2+12)**(3/2),x)","\frac{\sqrt{3} \int \frac{1}{- e^{3} x^{3} \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4} - 2 e^{2} x^{2} \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4} + 4 e x \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4} + 8 \sqrt{e x + 2} \sqrt{- e^{2} x^{2} + 4}}\, dx}{9}"," ",0,"sqrt(3)*Integral(1/(-e**3*x**3*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4) - 2*e**2*x**2*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4) + 4*e*x*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4) + 8*sqrt(e*x + 2)*sqrt(-e**2*x**2 + 4)), x)/9","F",0
926,1,44,0,1.023578," ","integrate(1/(1+x)/(1-x)**(1/2),x)","\begin{cases} - \sqrt{2} \operatorname{acosh}{\left(\frac{\sqrt{2}}{\sqrt{x + 1}} \right)} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\\sqrt{2} i \operatorname{asin}{\left(\frac{\sqrt{2}}{\sqrt{x + 1}} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(2)*acosh(sqrt(2)/sqrt(x + 1)), 2/Abs(x + 1) > 1), (sqrt(2)*I*asin(sqrt(2)/sqrt(x + 1)), True))","A",0
927,0,0,0,0.000000," ","integrate(1/(1+x)**(1/2)/(-x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \sqrt{x + 1}}\, dx"," ",0,"Integral(1/(sqrt(-(x - 1)*(x + 1))*sqrt(x + 1)), x)","F",0
928,1,65,0,6.182337," ","integrate(1/(a*x+1)/(-a*x+1)**(1/2),x)","\begin{cases} \frac{2 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2}}{\sqrt{- a x + 1}} \right)}}{2} & \text{for}\: \frac{1}{- a x + 1} > \frac{1}{2} \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2}}{\sqrt{- a x + 1}} \right)}}{2} & \text{for}\: \frac{1}{- a x + 1} < \frac{1}{2} \end{cases}\right)}{a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*Piecewise((-sqrt(2)*acoth(sqrt(2)/sqrt(-a*x + 1))/2, 1/(-a*x + 1) > 1/2), (-sqrt(2)*atanh(sqrt(2)/sqrt(-a*x + 1))/2, 1/(-a*x + 1) < 1/2))/a, Ne(a, 0)), (x, True))","A",0
929,0,0,0,0.000000," ","integrate(1/(a*x+1)**(1/2)/(-a**2*x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \sqrt{a x + 1}}\, dx"," ",0,"Integral(1/(sqrt(-(a*x - 1)*(a*x + 1))*sqrt(a*x + 1)), x)","F",0
930,0,0,0,0.000000," ","integrate((e*x+2)**(1/2)*(-3*e**2*x**2+12)**(1/4),x)","\sqrt[4]{3} \int \sqrt{e x + 2} \sqrt[4]{- e^{2} x^{2} + 4}\, dx"," ",0,"3**(1/4)*Integral(sqrt(e*x + 2)*(-e**2*x**2 + 4)**(1/4), x)","F",0
931,0,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(1/4)/(e*x+2)**(1/2),x)","\sqrt[4]{3} \int \frac{\sqrt[4]{- e^{2} x^{2} + 4}}{\sqrt{e x + 2}}\, dx"," ",0,"3**(1/4)*Integral((-e**2*x**2 + 4)**(1/4)/sqrt(e*x + 2), x)","F",0
932,0,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(1/4)/(e*x+2)**(3/2),x)","\sqrt[4]{3} \int \frac{\sqrt[4]{- e^{2} x^{2} + 4}}{e x \sqrt{e x + 2} + 2 \sqrt{e x + 2}}\, dx"," ",0,"3**(1/4)*Integral((-e**2*x**2 + 4)**(1/4)/(e*x*sqrt(e*x + 2) + 2*sqrt(e*x + 2)), x)","F",0
933,0,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(1/4)/(e*x+2)**(5/2),x)","\sqrt[4]{3} \int \frac{\sqrt[4]{- e^{2} x^{2} + 4}}{e^{2} x^{2} \sqrt{e x + 2} + 4 e x \sqrt{e x + 2} + 4 \sqrt{e x + 2}}\, dx"," ",0,"3**(1/4)*Integral((-e**2*x**2 + 4)**(1/4)/(e**2*x**2*sqrt(e*x + 2) + 4*e*x*sqrt(e*x + 2) + 4*sqrt(e*x + 2)), x)","F",0
934,-1,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(1/4)/(e*x+2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
935,-1,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(1/4)/(e*x+2)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
936,-1,0,0,0.000000," ","integrate((-3*e**2*x**2+12)**(1/4)/(e*x+2)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
937,0,0,0,0.000000," ","integrate((e*x+2)**(5/2)/(-3*e**2*x**2+12)**(1/4),x)","\frac{3^{\frac{3}{4}} \left(\int \frac{4 \sqrt{e x + 2}}{\sqrt[4]{- e^{2} x^{2} + 4}}\, dx + \int \frac{4 e x \sqrt{e x + 2}}{\sqrt[4]{- e^{2} x^{2} + 4}}\, dx + \int \frac{e^{2} x^{2} \sqrt{e x + 2}}{\sqrt[4]{- e^{2} x^{2} + 4}}\, dx\right)}{3}"," ",0,"3**(3/4)*(Integral(4*sqrt(e*x + 2)/(-e**2*x**2 + 4)**(1/4), x) + Integral(4*e*x*sqrt(e*x + 2)/(-e**2*x**2 + 4)**(1/4), x) + Integral(e**2*x**2*sqrt(e*x + 2)/(-e**2*x**2 + 4)**(1/4), x))/3","F",0
938,0,0,0,0.000000," ","integrate((e*x+2)**(3/2)/(-3*e**2*x**2+12)**(1/4),x)","\frac{3^{\frac{3}{4}} \left(\int \frac{2 \sqrt{e x + 2}}{\sqrt[4]{- e^{2} x^{2} + 4}}\, dx + \int \frac{e x \sqrt{e x + 2}}{\sqrt[4]{- e^{2} x^{2} + 4}}\, dx\right)}{3}"," ",0,"3**(3/4)*(Integral(2*sqrt(e*x + 2)/(-e**2*x**2 + 4)**(1/4), x) + Integral(e*x*sqrt(e*x + 2)/(-e**2*x**2 + 4)**(1/4), x))/3","F",0
939,0,0,0,0.000000," ","integrate((e*x+2)**(1/2)/(-3*e**2*x**2+12)**(1/4),x)","\frac{3^{\frac{3}{4}} \int \frac{\sqrt{e x + 2}}{\sqrt[4]{- e^{2} x^{2} + 4}}\, dx}{3}"," ",0,"3**(3/4)*Integral(sqrt(e*x + 2)/(-e**2*x**2 + 4)**(1/4), x)/3","F",0
940,0,0,0,0.000000," ","integrate(1/(e*x+2)**(1/2)/(-3*e**2*x**2+12)**(1/4),x)","\frac{3^{\frac{3}{4}} \int \frac{1}{\sqrt{e x + 2} \sqrt[4]{- e^{2} x^{2} + 4}}\, dx}{3}"," ",0,"3**(3/4)*Integral(1/(sqrt(e*x + 2)*(-e**2*x**2 + 4)**(1/4)), x)/3","F",0
941,0,0,0,0.000000," ","integrate(1/(e*x+2)**(3/2)/(-3*e**2*x**2+12)**(1/4),x)","\frac{3^{\frac{3}{4}} \int \frac{1}{e x \sqrt{e x + 2} \sqrt[4]{- e^{2} x^{2} + 4} + 2 \sqrt{e x + 2} \sqrt[4]{- e^{2} x^{2} + 4}}\, dx}{3}"," ",0,"3**(3/4)*Integral(1/(e*x*sqrt(e*x + 2)*(-e**2*x**2 + 4)**(1/4) + 2*sqrt(e*x + 2)*(-e**2*x**2 + 4)**(1/4)), x)/3","F",0
942,0,0,0,0.000000," ","integrate(1/(e*x+2)**(5/2)/(-3*e**2*x**2+12)**(1/4),x)","\frac{3^{\frac{3}{4}} \int \frac{1}{e^{2} x^{2} \sqrt{e x + 2} \sqrt[4]{- e^{2} x^{2} + 4} + 4 e x \sqrt{e x + 2} \sqrt[4]{- e^{2} x^{2} + 4} + 4 \sqrt{e x + 2} \sqrt[4]{- e^{2} x^{2} + 4}}\, dx}{3}"," ",0,"3**(3/4)*Integral(1/(e**2*x**2*sqrt(e*x + 2)*(-e**2*x**2 + 4)**(1/4) + 4*e*x*sqrt(e*x + 2)*(-e**2*x**2 + 4)**(1/4) + 4*sqrt(e*x + 2)*(-e**2*x**2 + 4)**(1/4)), x)/3","F",0
943,-1,0,0,0.000000," ","integrate(1/(e*x+2)**(7/2)/(-3*e**2*x**2+12)**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
944,-1,0,0,0.000000," ","integrate(1/(e*x+2)**(9/2)/(-3*e**2*x**2+12)**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
945,1,2059,0,6.152098," ","integrate((b*x+a)**m*(-b**2*x**2+a**2)**3,x)","\begin{cases} a^{6} a^{m} x & \text{for}\: b = 0 \\- \frac{3 a^{3} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b + 9 a^{2} b^{2} x + 9 a b^{3} x^{2} + 3 b^{4} x^{3}} - \frac{8 a^{3}}{3 a^{3} b + 9 a^{2} b^{2} x + 9 a b^{3} x^{2} + 3 b^{4} x^{3}} - \frac{9 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b + 9 a^{2} b^{2} x + 9 a b^{3} x^{2} + 3 b^{4} x^{3}} - \frac{18 a^{2} b x}{3 a^{3} b + 9 a^{2} b^{2} x + 9 a b^{3} x^{2} + 3 b^{4} x^{3}} - \frac{9 a b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b + 9 a^{2} b^{2} x + 9 a b^{3} x^{2} + 3 b^{4} x^{3}} - \frac{18 a b^{2} x^{2}}{3 a^{3} b + 9 a^{2} b^{2} x + 9 a b^{3} x^{2} + 3 b^{4} x^{3}} - \frac{3 b^{3} x^{3} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b + 9 a^{2} b^{2} x + 9 a b^{3} x^{2} + 3 b^{4} x^{3}} & \text{for}\: m = -7 \\\frac{6 a^{3} \log{\left(\frac{a}{b} + x \right)}}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} + \frac{13 a^{3}}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} + \frac{12 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} + \frac{21 a^{2} b x}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} + \frac{6 a b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} + \frac{3 a b^{2} x^{2}}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} - \frac{b^{3} x^{3}}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} & \text{for}\: m = -6 \\- \frac{24 a^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a b + 2 b^{2} x} - \frac{50 a^{3}}{2 a b + 2 b^{2} x} - \frac{24 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{2 a b + 2 b^{2} x} - \frac{24 a^{2} b x}{2 a b + 2 b^{2} x} + \frac{9 a b^{2} x^{2}}{2 a b + 2 b^{2} x} - \frac{b^{3} x^{3}}{2 a b + 2 b^{2} x} & \text{for}\: m = -5 \\\frac{8 a^{3} \log{\left(\frac{a}{b} + x \right)}}{b} - 7 a^{2} x + 2 a b x^{2} - \frac{b^{2} x^{3}}{3} & \text{for}\: m = -4 \\\frac{a^{7} m^{3} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{21 a^{7} m^{2} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{152 a^{7} m \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{384 a^{7} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{a^{6} b m^{3} x \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{27 a^{6} b m^{2} x \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{254 a^{6} b m x \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{840 a^{6} b x \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{3 a^{5} b^{2} m^{3} x^{2} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{51 a^{5} b^{2} m^{2} x^{2} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{228 a^{5} b^{2} m x^{2} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{3 a^{4} b^{3} m^{3} x^{3} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{69 a^{4} b^{3} m^{2} x^{3} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{486 a^{4} b^{3} m x^{3} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{840 a^{4} b^{3} x^{3} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{3 a^{3} b^{4} m^{3} x^{4} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{39 a^{3} b^{4} m^{2} x^{4} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{96 a^{3} b^{4} m x^{4} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{3 a^{2} b^{5} m^{3} x^{5} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{57 a^{2} b^{5} m^{2} x^{5} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{306 a^{2} b^{5} m x^{5} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} + \frac{504 a^{2} b^{5} x^{5} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{a b^{6} m^{3} x^{6} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{9 a b^{6} m^{2} x^{6} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{20 a b^{6} m x^{6} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{b^{7} m^{3} x^{7} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{15 b^{7} m^{2} x^{7} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{74 b^{7} m x^{7} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} - \frac{120 b^{7} x^{7} \left(a + b x\right)^{m}}{b m^{4} + 22 b m^{3} + 179 b m^{2} + 638 b m + 840 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*a**m*x, Eq(b, 0)), (-3*a**3*log(a/b + x)/(3*a**3*b + 9*a**2*b**2*x + 9*a*b**3*x**2 + 3*b**4*x**3) - 8*a**3/(3*a**3*b + 9*a**2*b**2*x + 9*a*b**3*x**2 + 3*b**4*x**3) - 9*a**2*b*x*log(a/b + x)/(3*a**3*b + 9*a**2*b**2*x + 9*a*b**3*x**2 + 3*b**4*x**3) - 18*a**2*b*x/(3*a**3*b + 9*a**2*b**2*x + 9*a*b**3*x**2 + 3*b**4*x**3) - 9*a*b**2*x**2*log(a/b + x)/(3*a**3*b + 9*a**2*b**2*x + 9*a*b**3*x**2 + 3*b**4*x**3) - 18*a*b**2*x**2/(3*a**3*b + 9*a**2*b**2*x + 9*a*b**3*x**2 + 3*b**4*x**3) - 3*b**3*x**3*log(a/b + x)/(3*a**3*b + 9*a**2*b**2*x + 9*a*b**3*x**2 + 3*b**4*x**3), Eq(m, -7)), (6*a**3*log(a/b + x)/(a**2*b + 2*a*b**2*x + b**3*x**2) + 13*a**3/(a**2*b + 2*a*b**2*x + b**3*x**2) + 12*a**2*b*x*log(a/b + x)/(a**2*b + 2*a*b**2*x + b**3*x**2) + 21*a**2*b*x/(a**2*b + 2*a*b**2*x + b**3*x**2) + 6*a*b**2*x**2*log(a/b + x)/(a**2*b + 2*a*b**2*x + b**3*x**2) + 3*a*b**2*x**2/(a**2*b + 2*a*b**2*x + b**3*x**2) - b**3*x**3/(a**2*b + 2*a*b**2*x + b**3*x**2), Eq(m, -6)), (-24*a**3*log(a/b + x)/(2*a*b + 2*b**2*x) - 50*a**3/(2*a*b + 2*b**2*x) - 24*a**2*b*x*log(a/b + x)/(2*a*b + 2*b**2*x) - 24*a**2*b*x/(2*a*b + 2*b**2*x) + 9*a*b**2*x**2/(2*a*b + 2*b**2*x) - b**3*x**3/(2*a*b + 2*b**2*x), Eq(m, -5)), (8*a**3*log(a/b + x)/b - 7*a**2*x + 2*a*b*x**2 - b**2*x**3/3, Eq(m, -4)), (a**7*m**3*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 21*a**7*m**2*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 152*a**7*m*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 384*a**7*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + a**6*b*m**3*x*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 27*a**6*b*m**2*x*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 254*a**6*b*m*x*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 840*a**6*b*x*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 3*a**5*b**2*m**3*x**2*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 51*a**5*b**2*m**2*x**2*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 228*a**5*b**2*m*x**2*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 3*a**4*b**3*m**3*x**3*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 69*a**4*b**3*m**2*x**3*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 486*a**4*b**3*m*x**3*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 840*a**4*b**3*x**3*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 3*a**3*b**4*m**3*x**4*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 39*a**3*b**4*m**2*x**4*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 96*a**3*b**4*m*x**4*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 3*a**2*b**5*m**3*x**5*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 57*a**2*b**5*m**2*x**5*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 306*a**2*b**5*m*x**5*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) + 504*a**2*b**5*x**5*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - a*b**6*m**3*x**6*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 9*a*b**6*m**2*x**6*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 20*a*b**6*m*x**6*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - b**7*m**3*x**7*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 15*b**7*m**2*x**7*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 74*b**7*m*x**7*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b) - 120*b**7*x**7*(a + b*x)**m/(b*m**4 + 22*b*m**3 + 179*b*m**2 + 638*b*m + 840*b), True))","A",0
946,1,876,0,3.054029," ","integrate((b*x+a)**m*(-b**2*x**2+a**2)**2,x)","\begin{cases} a^{4} a^{m} x & \text{for}\: b = 0 \\\frac{a^{2} \log{\left(\frac{a}{b} + x \right)}}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} + \frac{2 a^{2}}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} + \frac{2 a b x \log{\left(\frac{a}{b} + x \right)}}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} + \frac{4 a b x}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} + \frac{b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{a^{2} b + 2 a b^{2} x + b^{3} x^{2}} & \text{for}\: m = -5 \\- \frac{4 a^{2} \log{\left(\frac{a}{b} + x \right)}}{a b + b^{2} x} - \frac{7 a^{2}}{a b + b^{2} x} - \frac{4 a b x \log{\left(\frac{a}{b} + x \right)}}{a b + b^{2} x} - \frac{2 a b x}{a b + b^{2} x} + \frac{b^{2} x^{2}}{a b + b^{2} x} & \text{for}\: m = -4 \\\frac{4 a^{2} \log{\left(\frac{a}{b} + x \right)}}{b} - 3 a x + \frac{b x^{2}}{2} & \text{for}\: m = -3 \\\frac{a^{5} m^{2} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} + \frac{11 a^{5} m \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} + \frac{32 a^{5} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} + \frac{a^{4} b m^{2} x \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} + \frac{15 a^{4} b m x \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} + \frac{60 a^{4} b x \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} - \frac{2 a^{3} b^{2} m^{2} x^{2} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} - \frac{14 a^{3} b^{2} m x^{2} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} - \frac{2 a^{2} b^{3} m^{2} x^{3} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} - \frac{22 a^{2} b^{3} m x^{3} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} - \frac{40 a^{2} b^{3} x^{3} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} + \frac{a b^{4} m^{2} x^{4} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} + \frac{3 a b^{4} m x^{4} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} + \frac{b^{5} m^{2} x^{5} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} + \frac{7 b^{5} m x^{5} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} + \frac{12 b^{5} x^{5} \left(a + b x\right)^{m}}{b m^{3} + 12 b m^{2} + 47 b m + 60 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*a**m*x, Eq(b, 0)), (a**2*log(a/b + x)/(a**2*b + 2*a*b**2*x + b**3*x**2) + 2*a**2/(a**2*b + 2*a*b**2*x + b**3*x**2) + 2*a*b*x*log(a/b + x)/(a**2*b + 2*a*b**2*x + b**3*x**2) + 4*a*b*x/(a**2*b + 2*a*b**2*x + b**3*x**2) + b**2*x**2*log(a/b + x)/(a**2*b + 2*a*b**2*x + b**3*x**2), Eq(m, -5)), (-4*a**2*log(a/b + x)/(a*b + b**2*x) - 7*a**2/(a*b + b**2*x) - 4*a*b*x*log(a/b + x)/(a*b + b**2*x) - 2*a*b*x/(a*b + b**2*x) + b**2*x**2/(a*b + b**2*x), Eq(m, -4)), (4*a**2*log(a/b + x)/b - 3*a*x + b*x**2/2, Eq(m, -3)), (a**5*m**2*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) + 11*a**5*m*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) + 32*a**5*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) + a**4*b*m**2*x*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) + 15*a**4*b*m*x*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) + 60*a**4*b*x*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) - 2*a**3*b**2*m**2*x**2*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) - 14*a**3*b**2*m*x**2*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) - 2*a**2*b**3*m**2*x**3*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) - 22*a**2*b**3*m*x**3*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) - 40*a**2*b**3*x**3*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) + a*b**4*m**2*x**4*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) + 3*a*b**4*m*x**4*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) + b**5*m**2*x**5*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) + 7*b**5*m*x**5*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b) + 12*b**5*x**5*(a + b*x)**m/(b*m**3 + 12*b*m**2 + 47*b*m + 60*b), True))","A",0
947,1,267,0,1.092192," ","integrate((b*x+a)**m*(-b**2*x**2+a**2),x)","\begin{cases} a^{2} a^{m} x & \text{for}\: b = 0 \\- \frac{a \log{\left(\frac{a}{b} + x \right)}}{a b + b^{2} x} - \frac{2 a}{a b + b^{2} x} - \frac{b x \log{\left(\frac{a}{b} + x \right)}}{a b + b^{2} x} & \text{for}\: m = -3 \\\frac{2 a \log{\left(\frac{a}{b} + x \right)}}{b} - x & \text{for}\: m = -2 \\\frac{a^{3} m \left(a + b x\right)^{m}}{b m^{2} + 5 b m + 6 b} + \frac{4 a^{3} \left(a + b x\right)^{m}}{b m^{2} + 5 b m + 6 b} + \frac{a^{2} b m x \left(a + b x\right)^{m}}{b m^{2} + 5 b m + 6 b} + \frac{6 a^{2} b x \left(a + b x\right)^{m}}{b m^{2} + 5 b m + 6 b} - \frac{a b^{2} m x^{2} \left(a + b x\right)^{m}}{b m^{2} + 5 b m + 6 b} - \frac{b^{3} m x^{3} \left(a + b x\right)^{m}}{b m^{2} + 5 b m + 6 b} - \frac{2 b^{3} x^{3} \left(a + b x\right)^{m}}{b m^{2} + 5 b m + 6 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*a**m*x, Eq(b, 0)), (-a*log(a/b + x)/(a*b + b**2*x) - 2*a/(a*b + b**2*x) - b*x*log(a/b + x)/(a*b + b**2*x), Eq(m, -3)), (2*a*log(a/b + x)/b - x, Eq(m, -2)), (a**3*m*(a + b*x)**m/(b*m**2 + 5*b*m + 6*b) + 4*a**3*(a + b*x)**m/(b*m**2 + 5*b*m + 6*b) + a**2*b*m*x*(a + b*x)**m/(b*m**2 + 5*b*m + 6*b) + 6*a**2*b*x*(a + b*x)**m/(b*m**2 + 5*b*m + 6*b) - a*b**2*m*x**2*(a + b*x)**m/(b*m**2 + 5*b*m + 6*b) - b**3*m*x**3*(a + b*x)**m/(b*m**2 + 5*b*m + 6*b) - 2*b**3*x**3*(a + b*x)**m/(b*m**2 + 5*b*m + 6*b), True))","A",0
948,0,0,0,0.000000," ","integrate((b*x+a)**m/(-b**2*x**2+a**2),x)","- \int \frac{\left(a + b x\right)^{m}}{- a^{2} + b^{2} x^{2}}\, dx"," ",0,"-Integral((a + b*x)**m/(-a**2 + b**2*x**2), x)","F",0
949,0,0,0,0.000000," ","integrate((b*x+a)**m/(-b**2*x**2+a**2)**2,x)","\int \frac{\left(a + b x\right)^{m}}{\left(- a + b x\right)^{2} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral((a + b*x)**m/((-a + b*x)**2*(a + b*x)**2), x)","F",0
950,0,0,0,0.000000," ","integrate((b*x+a)**m/(-b**2*x**2+a**2)**3,x)","- \int \frac{\left(a + b x\right)^{m}}{- a^{6} + 3 a^{4} b^{2} x^{2} - 3 a^{2} b^{4} x^{4} + b^{6} x^{6}}\, dx"," ",0,"-Integral((a + b*x)**m/(-a**6 + 3*a**4*b**2*x**2 - 3*a**2*b**4*x**4 + b**6*x**6), x)","F",0
951,-1,0,0,0.000000," ","integrate((e*x+d)**m*(-e**2*x**2+d**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
952,0,0,0,0.000000," ","integrate((e*x+d)**m*(-e**2*x**2+d**2)**(5/2),x)","\int \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{m}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)**m, x)","F",0
953,0,0,0,0.000000," ","integrate((e*x+d)**m*(-e**2*x**2+d**2)**(3/2),x)","\int \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{m}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**m, x)","F",0
954,0,0,0,0.000000," ","integrate((e*x+d)**m*(-e**2*x**2+d**2)**(1/2),x)","\int \sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{m}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**m, x)","F",0
955,0,0,0,0.000000," ","integrate((e*x+d)**m/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{m}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}\, dx"," ",0,"Integral((d + e*x)**m/sqrt(-(-d + e*x)*(d + e*x)), x)","F",0
956,0,0,0,0.000000," ","integrate((e*x+d)**m/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**m/(-(-d + e*x)*(d + e*x))**(3/2), x)","F",0
957,0,0,0,0.000000," ","integrate((e*x+d)**m/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**m/(-(-d + e*x)*(d + e*x))**(5/2), x)","F",0
958,0,0,0,0.000000," ","integrate((e*x+d)**m/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**m/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
959,0,0,0,0.000000," ","integrate((b*x+a)**m*(-b**2*x**2+a**2)**p,x)","\int \left(- \left(- a + b x\right) \left(a + b x\right)\right)^{p} \left(a + b x\right)^{m}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**p*(a + b*x)**m, x)","F",0
960,1,479,0,6.661149," ","integrate((e*x+d)**3*(1-e**2*x**2/d**2)**p,x)","d^{3} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + 3 d^{2} e \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: e^{2} = 0 \\- \frac{d^{2} \left(\begin{cases} \frac{\left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(1 - \frac{e^{2} x^{2}}{d^{2}} \right)} & \text{otherwise} \end{cases}\right)}{2 e^{2}} & \text{otherwise} \end{cases}\right) + d e^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + e^{3} \left(\begin{cases} \frac{x^{4}}{4} & \text{for}\: e = 0 \\- \frac{d^{6} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{6} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{6}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{d^{4} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{4} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{2} x^{2}}{2 e^{2}} & \text{for}\: p = -1 \\- \frac{d^{4} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} - \frac{d^{2} e^{2} p x^{2} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} p x^{4} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} x^{4} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + 3*d**2*e*Piecewise((x**2/2, Eq(e**2, 0)), (-d**2*Piecewise(((1 - e**2*x**2/d**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(1 - e**2*x**2/d**2), True))/(2*e**2), True)) + d*e**2*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + e**3*Piecewise((x**4/4, Eq(e, 0)), (-d**6*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**6*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**6/(-2*d**2*e**4 + 2*e**6*x**2) + d**4*e**2*x**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) + d**4*e**2*x**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2), Eq(p, -2)), (-d**4*log(-d/e + x)/(2*e**4) - d**4*log(d/e + x)/(2*e**4) - d**2*x**2/(2*e**2), Eq(p, -1)), (-d**4*(1 - e**2*x**2/d**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) - d**2*e**2*p*x**2*(1 - e**2*x**2/d**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*p*x**4*(1 - e**2*x**2/d**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*x**4*(1 - e**2*x**2/d**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4), True))","B",0
961,1,116,0,4.575672," ","integrate((e*x+d)**2*(1-e**2*x**2/d**2)**p,x)","d^{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + 2 d e \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: e^{2} = 0 \\- \frac{d^{2} \left(\begin{cases} \frac{\left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(1 - \frac{e^{2} x^{2}}{d^{2}} \right)} & \text{otherwise} \end{cases}\right)}{2 e^{2}} & \text{otherwise} \end{cases}\right) + \frac{e^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{3}"," ",0,"d**2*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + 2*d*e*Piecewise((x**2/2, Eq(e**2, 0)), (-d**2*Piecewise(((1 - e**2*x**2/d**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(1 - e**2*x**2/d**2), True))/(2*e**2), True)) + e**2*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/3","C",0
962,1,78,0,3.720462," ","integrate((e*x+d)*(1-e**2*x**2/d**2)**p,x)","d x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + e \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: e^{2} = 0 \\- \frac{d^{2} \left(\begin{cases} \frac{\left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(1 - \frac{e^{2} x^{2}}{d^{2}} \right)} & \text{otherwise} \end{cases}\right)}{2 e^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + e*Piecewise((x**2/2, Eq(e**2, 0)), (-d**2*Piecewise(((1 - e**2*x**2/d**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(1 - e**2*x**2/d**2), True))/(2*e**2), True))","A",0
963,1,24,0,1.066473," ","integrate((1-e**2*x**2/d**2)**p,x)","x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}"," ",0,"x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)","C",0
964,1,321,0,6.499875," ","integrate((1-e**2*x**2/d**2)**p/(e*x+d),x)","\begin{cases} \frac{0^{p} \log{\left(-1 + \frac{e^{2} x^{2}}{d^{2}} \right)}}{2 e} + \frac{0^{p} \operatorname{acoth}{\left(\frac{e x}{d} \right)}}{e} + \frac{d d^{- 2 p} e^{2 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{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{e 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| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 d^{2} \Gamma\left(- p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{0^{p} \log{\left(1 - \frac{e^{2} x^{2}}{d^{2}} \right)}}{2 e} + \frac{0^{p} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{e} + \frac{d d^{- 2 p} e^{2 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{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{e 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| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 d^{2} \Gamma\left(- p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0**p*log(-1 + e**2*x**2/d**2)/(2*e) + 0**p*acoth(e*x/d)/e + d*d**(-2*p)*e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), d**2/(e**2*x**2))/(2*e**2*x*gamma(3/2 - p)*gamma(p + 1)) + e*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*d**2*gamma(-p)*gamma(p + 1)), Abs(e**2*x**2/d**2) > 1), (0**p*log(1 - e**2*x**2/d**2)/(2*e) + 0**p*atanh(e*x/d)/e + d*d**(-2*p)*e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), d**2/(e**2*x**2))/(2*e**2*x*gamma(3/2 - p)*gamma(p + 1)) + e*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*d**2*gamma(-p)*gamma(p + 1)), True))","C",0
965,0,0,0,0.000000," ","integrate((1-e**2*x**2/d**2)**p/(e*x+d)**2,x)","\int \frac{\left(- \left(-1 + \frac{e x}{d}\right) \left(1 + \frac{e x}{d}\right)\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((-(-1 + e*x/d)*(1 + e*x/d))**p/(d + e*x)**2, x)","F",0
966,0,0,0,0.000000," ","integrate((1-e**2*x**2/d**2)**p/(e*x+d)**3,x)","\int \frac{\left(- \left(-1 + \frac{e x}{d}\right) \left(1 + \frac{e x}{d}\right)\right)^{p}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((-(-1 + e*x/d)*(1 + e*x/d))**p/(d + e*x)**3, x)","F",0
967,1,476,0,6.455836," ","integrate((b*x+a)**3*(-b**2*x**2+a**2)**p,x)","a^{3} a^{2 p} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b^{2} x^{2} e^{2 i \pi}}{a^{2}}} \right)} + 3 a^{2} b \left(\begin{cases} \frac{x^{2} \left(a^{2}\right)^{p}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\begin{cases} \frac{\left(a^{2} - b^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a^{2} - b^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 b^{2}} & \text{otherwise} \end{cases}\right) + a a^{2 p} b^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b^{2} x^{2} e^{2 i \pi}}{a^{2}}} \right)} + b^{3} \left(\begin{cases} \frac{x^{4} \left(a^{2}\right)^{p}}{4} & \text{for}\: b = 0 \\- \frac{a^{2} \log{\left(- \frac{a}{b} + x \right)}}{- 2 a^{2} b^{4} + 2 b^{6} x^{2}} - \frac{a^{2} \log{\left(\frac{a}{b} + x \right)}}{- 2 a^{2} b^{4} + 2 b^{6} x^{2}} - \frac{a^{2}}{- 2 a^{2} b^{4} + 2 b^{6} x^{2}} + \frac{b^{2} x^{2} \log{\left(- \frac{a}{b} + x \right)}}{- 2 a^{2} b^{4} + 2 b^{6} x^{2}} + \frac{b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{- 2 a^{2} b^{4} + 2 b^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{a^{2} \log{\left(- \frac{a}{b} + x \right)}}{2 b^{4}} - \frac{a^{2} \log{\left(\frac{a}{b} + x \right)}}{2 b^{4}} - \frac{x^{2}}{2 b^{2}} & \text{for}\: p = -1 \\- \frac{a^{4} \left(a^{2} - b^{2} x^{2}\right)^{p}}{2 b^{4} p^{2} + 6 b^{4} p + 4 b^{4}} - \frac{a^{2} b^{2} p x^{2} \left(a^{2} - b^{2} x^{2}\right)^{p}}{2 b^{4} p^{2} + 6 b^{4} p + 4 b^{4}} + \frac{b^{4} p x^{4} \left(a^{2} - b^{2} x^{2}\right)^{p}}{2 b^{4} p^{2} + 6 b^{4} p + 4 b^{4}} + \frac{b^{4} x^{4} \left(a^{2} - b^{2} x^{2}\right)^{p}}{2 b^{4} p^{2} + 6 b^{4} p + 4 b^{4}} & \text{otherwise} \end{cases}\right)"," ",0,"a**3*a**(2*p)*x*hyper((1/2, -p), (3/2,), b**2*x**2*exp_polar(2*I*pi)/a**2) + 3*a**2*b*Piecewise((x**2*(a**2)**p/2, Eq(b**2, 0)), (-Piecewise(((a**2 - b**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a**2 - b**2*x**2), True))/(2*b**2), True)) + a*a**(2*p)*b**2*x**3*hyper((3/2, -p), (5/2,), b**2*x**2*exp_polar(2*I*pi)/a**2) + b**3*Piecewise((x**4*(a**2)**p/4, Eq(b, 0)), (-a**2*log(-a/b + x)/(-2*a**2*b**4 + 2*b**6*x**2) - a**2*log(a/b + x)/(-2*a**2*b**4 + 2*b**6*x**2) - a**2/(-2*a**2*b**4 + 2*b**6*x**2) + b**2*x**2*log(-a/b + x)/(-2*a**2*b**4 + 2*b**6*x**2) + b**2*x**2*log(a/b + x)/(-2*a**2*b**4 + 2*b**6*x**2), Eq(p, -2)), (-a**2*log(-a/b + x)/(2*b**4) - a**2*log(a/b + x)/(2*b**4) - x**2/(2*b**2), Eq(p, -1)), (-a**4*(a**2 - b**2*x**2)**p/(2*b**4*p**2 + 6*b**4*p + 4*b**4) - a**2*b**2*p*x**2*(a**2 - b**2*x**2)**p/(2*b**4*p**2 + 6*b**4*p + 4*b**4) + b**4*p*x**4*(a**2 - b**2*x**2)**p/(2*b**4*p**2 + 6*b**4*p + 4*b**4) + b**4*x**4*(a**2 - b**2*x**2)**p/(2*b**4*p**2 + 6*b**4*p + 4*b**4), True))","B",0
968,1,124,0,5.072417," ","integrate((b*x+a)**2*(-b**2*x**2+a**2)**p,x)","a^{2} a^{2 p} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b^{2} x^{2} e^{2 i \pi}}{a^{2}}} \right)} + 2 a b \left(\begin{cases} \frac{x^{2} \left(a^{2}\right)^{p}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\begin{cases} \frac{\left(a^{2} - b^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a^{2} - b^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 b^{2}} & \text{otherwise} \end{cases}\right) + \frac{a^{2 p} b^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b^{2} x^{2} e^{2 i \pi}}{a^{2}}} \right)}}{3}"," ",0,"a**2*a**(2*p)*x*hyper((1/2, -p), (3/2,), b**2*x**2*exp_polar(2*I*pi)/a**2) + 2*a*b*Piecewise((x**2*(a**2)**p/2, Eq(b**2, 0)), (-Piecewise(((a**2 - b**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a**2 - b**2*x**2), True))/(2*b**2), True)) + a**(2*p)*b**2*x**3*hyper((3/2, -p), (5/2,), b**2*x**2*exp_polar(2*I*pi)/a**2)/3","A",0
969,1,82,0,4.200005," ","integrate((b*x+a)*(-b**2*x**2+a**2)**p,x)","a a^{2 p} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b^{2} x^{2} e^{2 i \pi}}{a^{2}}} \right)} + b \left(\begin{cases} \frac{x^{2} \left(a^{2}\right)^{p}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\begin{cases} \frac{\left(a^{2} - b^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a^{2} - b^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a*a**(2*p)*x*hyper((1/2, -p), (3/2,), b**2*x**2*exp_polar(2*I*pi)/a**2) + b*Piecewise((x**2*(a**2)**p/2, Eq(b**2, 0)), (-Piecewise(((a**2 - b**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a**2 - b**2*x**2), True))/(2*b**2), True))","A",0
970,1,321,0,6.682334," ","integrate((-b**2*x**2+a**2)**p/(b*x+a),x)","\begin{cases} \frac{0^{p} \log{\left(-1 + \frac{b^{2} x^{2}}{a^{2}} \right)}}{2 b} + \frac{0^{p} \operatorname{acoth}{\left(\frac{b x}{a} \right)}}{b} + \frac{a b^{2 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{a^{2}}{b^{2} x^{2}}} \right)}}{2 b^{2} x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{a^{2 p} b 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| {\frac{b^{2} x^{2} e^{2 i \pi}}{a^{2}}} \right)}}{2 a^{2} \Gamma\left(- p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{b^{2} x^{2}}{a^{2}}}\right| > 1 \\\frac{0^{p} \log{\left(1 - \frac{b^{2} x^{2}}{a^{2}} \right)}}{2 b} + \frac{0^{p} \operatorname{atanh}{\left(\frac{b x}{a} \right)}}{b} + \frac{a b^{2 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{a^{2}}{b^{2} x^{2}}} \right)}}{2 b^{2} x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{a^{2 p} b 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| {\frac{b^{2} x^{2} e^{2 i \pi}}{a^{2}}} \right)}}{2 a^{2} \Gamma\left(- p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0**p*log(-1 + b**2*x**2/a**2)/(2*b) + 0**p*acoth(b*x/a)/b + a*b**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), a**2/(b**2*x**2))/(2*b**2*x*gamma(3/2 - p)*gamma(p + 1)) + a**(2*p)*b*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), b**2*x**2*exp_polar(2*I*pi)/a**2)/(2*a**2*gamma(-p)*gamma(p + 1)), Abs(b**2*x**2/a**2) > 1), (0**p*log(1 - b**2*x**2/a**2)/(2*b) + 0**p*atanh(b*x/a)/b + a*b**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), a**2/(b**2*x**2))/(2*b**2*x*gamma(3/2 - p)*gamma(p + 1)) + a**(2*p)*b*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), b**2*x**2*exp_polar(2*I*pi)/a**2)/(2*a**2*gamma(-p)*gamma(p + 1)), True))","C",0
971,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**p/(b*x+a)**2,x)","\int \frac{\left(- \left(- a + b x\right) \left(a + b x\right)\right)^{p}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**p/(a + b*x)**2, x)","F",0
972,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**p/(b*x+a)**3,x)","\int \frac{\left(- \left(- a + b x\right) \left(a + b x\right)\right)^{p}}{\left(a + b x\right)^{3}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**p/(a + b*x)**3, x)","F",0
973,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(-b**2*x**2+a**2)**p,x)","\int \left(- \left(- a + b x\right) \left(a + b x\right)\right)^{p} \left(a + b x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**p*(a + b*x)**(3/2), x)","F",0
974,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(-b**2*x**2+a**2)**p,x)","\int \left(- \left(- a + b x\right) \left(a + b x\right)\right)^{p} \sqrt{a + b x}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**p*sqrt(a + b*x), x)","F",0
975,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**p/(b*x+a)**(1/2),x)","\int \frac{\left(- \left(- a + b x\right) \left(a + b x\right)\right)^{p}}{\sqrt{a + b x}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**p/sqrt(a + b*x), x)","F",0
976,0,0,0,0.000000," ","integrate((-b**2*x**2+a**2)**p/(b*x+a)**(3/2),x)","\int \frac{\left(- \left(- a + b x\right) \left(a + b x\right)\right)^{p}}{\left(a + b x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-(-a + b*x)*(a + b*x))**p/(a + b*x)**(3/2), x)","F",0
977,1,49,0,4.024646," ","integrate(-a*(-b**2*x**2+a**2)**p+(b*x+a)*(-b**2*x**2+a**2)**p,x)","b \left(\begin{cases} \frac{x^{2} \left(a^{2}\right)^{p}}{2} & \text{for}\: b^{2} = 0 \\- \frac{\begin{cases} \frac{\left(a^{2} - b^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a^{2} - b^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"b*Piecewise((x**2*(a**2)**p/2, Eq(b**2, 0)), (-Piecewise(((a**2 - b**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a**2 - b**2*x**2), True))/(2*b**2), True))","A",0
978,1,51,0,0.076016," ","integrate((e*x+d)**2*(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","c d^{4} x + 2 c d^{3} e x^{2} + 2 c d^{2} e^{2} x^{3} + c d e^{3} x^{4} + \frac{c e^{4} x^{5}}{5}"," ",0,"c*d**4*x + 2*c*d**3*e*x**2 + 2*c*d**2*e**2*x**3 + c*d*e**3*x**4 + c*e**4*x**5/5","B",0
979,1,39,0,0.068602," ","integrate((e*x+d)*(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","c d^{3} x + \frac{3 c d^{2} e x^{2}}{2} + c d e^{2} x^{3} + \frac{c e^{3} x^{4}}{4}"," ",0,"c*d**3*x + 3*c*d**2*e*x**2/2 + c*d*e**2*x**3 + c*e**3*x**4/4","B",0
980,1,24,0,0.066448," ","integrate(c*e**2*x**2+2*c*d*e*x+c*d**2,x)","c d^{2} x + c d e x^{2} + \frac{c e^{2} x^{3}}{3}"," ",0,"c*d**2*x + c*d*e*x**2 + c*e**2*x**3/3","A",0
981,1,12,0,0.076860," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)/(e*x+d),x)","c d x + \frac{c e x^{2}}{2}"," ",0,"c*d*x + c*e*x**2/2","A",0
982,1,2,0,0.079350," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)/(e*x+d)**2,x)","c x"," ",0,"c*x","A",0
983,1,8,0,0.094747," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)/(e*x+d)**3,x)","\frac{c \log{\left(d + e x \right)}}{e}"," ",0,"c*log(d + e*x)/e","A",0
984,1,10,0,0.154384," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)/(e*x+d)**4,x)","- \frac{c}{d e + e^{2} x}"," ",0,"-c/(d*e + e**2*x)","A",0
985,1,26,0,0.223935," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)/(e*x+d)**5,x)","- \frac{c}{2 d^{2} e + 4 d e^{2} x + 2 e^{3} x^{2}}"," ",0,"-c/(2*d**2*e + 4*d*e**2*x + 2*e**3*x**2)","B",0
986,1,37,0,0.280234," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)/(e*x+d)**6,x)","- \frac{c}{3 d^{3} e + 9 d^{2} e^{2} x + 9 d e^{3} x^{2} + 3 e^{4} x^{3}}"," ",0,"-c/(3*d**3*e + 9*d**2*e**2*x + 9*d*e**3*x**2 + 3*e**4*x**3)","B",0
987,1,90,0,0.096856," ","integrate((e*x+d)**2*(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","c^{2} d^{6} x + 3 c^{2} d^{5} e x^{2} + 5 c^{2} d^{4} e^{2} x^{3} + 5 c^{2} d^{3} e^{3} x^{4} + 3 c^{2} d^{2} e^{4} x^{5} + c^{2} d e^{5} x^{6} + \frac{c^{2} e^{6} x^{7}}{7}"," ",0,"c**2*d**6*x + 3*c**2*d**5*e*x**2 + 5*c**2*d**4*e**2*x**3 + 5*c**2*d**3*e**3*x**4 + 3*c**2*d**2*e**4*x**5 + c**2*d*e**5*x**6 + c**2*e**6*x**7/7","B",0
988,1,80,0,0.119515," ","integrate((e*x+d)*(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","c^{2} d^{5} x + \frac{5 c^{2} d^{4} e x^{2}}{2} + \frac{10 c^{2} d^{3} e^{2} x^{3}}{3} + \frac{5 c^{2} d^{2} e^{3} x^{4}}{2} + c^{2} d e^{4} x^{5} + \frac{c^{2} e^{5} x^{6}}{6}"," ",0,"c**2*d**5*x + 5*c**2*d**4*e*x**2/2 + 10*c**2*d**3*e**2*x**3/3 + 5*c**2*d**2*e**3*x**4/2 + c**2*d*e**4*x**5 + c**2*e**5*x**6/6","B",0
989,1,60,0,0.079277," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","c^{2} d^{4} x + 2 c^{2} d^{3} e x^{2} + 2 c^{2} d^{2} e^{2} x^{3} + c^{2} d e^{3} x^{4} + \frac{c^{2} e^{4} x^{5}}{5}"," ",0,"c**2*d**4*x + 2*c**2*d**3*e*x**2 + 2*c**2*d**2*e**2*x**3 + c**2*d*e**3*x**4 + c**2*e**4*x**5/5","B",0
990,1,46,0,0.104052," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2/(e*x+d),x)","c^{2} d^{3} x + \frac{3 c^{2} d^{2} e x^{2}}{2} + c^{2} d e^{2} x^{3} + \frac{c^{2} e^{3} x^{4}}{4}"," ",0,"c**2*d**3*x + 3*c**2*d**2*e*x**2/2 + c**2*d*e**2*x**3 + c**2*e**3*x**4/4","B",0
991,1,29,0,0.108071," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2/(e*x+d)**2,x)","c^{2} d^{2} x + c^{2} d e x^{2} + \frac{c^{2} e^{2} x^{3}}{3}"," ",0,"c**2*d**2*x + c**2*d*e*x**2 + c**2*e**2*x**3/3","B",0
992,1,15,0,0.105563," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2/(e*x+d)**3,x)","c^{2} d x + \frac{c^{2} e x^{2}}{2}"," ",0,"c**2*d*x + c**2*e*x**2/2","A",0
993,1,3,0,0.106834," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2/(e*x+d)**4,x)","c^{2} x"," ",0,"c**2*x","A",0
994,1,10,0,0.124072," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2/(e*x+d)**5,x)","\frac{c^{2} \log{\left(d + e x \right)}}{e}"," ",0,"c**2*log(d + e*x)/e","A",0
995,1,12,0,0.185925," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2/(e*x+d)**6,x)","- \frac{c^{2}}{d e + e^{2} x}"," ",0,"-c**2/(d*e + e**2*x)","A",0
996,1,27,0,0.239429," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2/(e*x+d)**7,x)","- \frac{c^{2}}{2 d^{2} e + 4 d e^{2} x + 2 e^{3} x^{2}}"," ",0,"-c**2/(2*d**2*e + 4*d*e**2*x + 2*e**3*x**2)","A",0
997,1,39,0,0.287187," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**2/(e*x+d)**8,x)","- \frac{c^{2}}{3 d^{3} e + 9 d^{2} e^{2} x + 9 d e^{3} x^{2} + 3 e^{4} x^{3}}"," ",0,"-c**2/(3*d**3*e + 9*d**2*e**2*x + 9*d*e**3*x**2 + 3*e**4*x**3)","B",0
998,1,39,0,0.103958," ","integrate((e*x+d)**5/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","\frac{d^{3} x}{c} + \frac{3 d^{2} e x^{2}}{2 c} + \frac{d e^{2} x^{3}}{c} + \frac{e^{3} x^{4}}{4 c}"," ",0,"d**3*x/c + 3*d**2*e*x**2/(2*c) + d*e**2*x**3/c + e**3*x**4/(4*c)","B",0
999,1,24,0,0.095850," ","integrate((e*x+d)**4/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","\frac{d^{2} x}{c} + \frac{d e x^{2}}{c} + \frac{e^{2} x^{3}}{3 c}"," ",0,"d**2*x/c + d*e*x**2/c + e**2*x**3/(3*c)","B",0
1000,1,12,0,0.089858," ","integrate((e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","\frac{d x}{c} + \frac{e x^{2}}{2 c}"," ",0,"d*x/c + e*x**2/(2*c)","A",0
1001,1,2,0,0.079534," ","integrate((e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","\frac{x}{c}"," ",0,"x/c","A",0
1002,1,12,0,0.085861," ","integrate((e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","\frac{\log{\left(c d + c e x \right)}}{c e}"," ",0,"log(c*d + c*e*x)/(c*e)","A",0
1003,1,14,0,0.144085," ","integrate(1/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","- \frac{1}{c d e + c e^{2} x}"," ",0,"-1/(c*d*e + c*e**2*x)","A",0
1004,1,31,0,0.212705," ","integrate(1/(e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","- \frac{1}{2 c d^{2} e + 4 c d e^{2} x + 2 c e^{3} x^{2}}"," ",0,"-1/(2*c*d**2*e + 4*c*d*e**2*x + 2*c*e**3*x**2)","B",0
1005,1,44,0,0.265408," ","integrate(1/(e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","- \frac{1}{3 c d^{3} e + 9 c d^{2} e^{2} x + 9 c d e^{3} x^{2} + 3 c e^{4} x^{3}}"," ",0,"-1/(3*c*d**3*e + 9*c*d**2*e**2*x + 9*c*d*e**3*x**2 + 3*c*e**4*x**3)","B",0
1006,1,58,0,0.329091," ","integrate(1/(e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","- \frac{1}{4 c d^{4} e + 16 c d^{3} e^{2} x + 24 c d^{2} e^{3} x^{2} + 16 c d e^{4} x^{3} + 4 c e^{5} x^{4}}"," ",0,"-1/(4*c*d**4*e + 16*c*d**3*e**2*x + 24*c*d**2*e**3*x**2 + 16*c*d*e**4*x**3 + 4*c*e**5*x**4)","B",0
1007,1,46,0,0.123706," ","integrate((e*x+d)**7/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","\frac{d^{3} x}{c^{2}} + \frac{3 d^{2} e x^{2}}{2 c^{2}} + \frac{d e^{2} x^{3}}{c^{2}} + \frac{e^{3} x^{4}}{4 c^{2}}"," ",0,"d**3*x/c**2 + 3*d**2*e*x**2/(2*c**2) + d*e**2*x**3/c**2 + e**3*x**4/(4*c**2)","B",0
1008,1,29,0,0.118448," ","integrate((e*x+d)**6/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","\frac{d^{2} x}{c^{2}} + \frac{d e x^{2}}{c^{2}} + \frac{e^{2} x^{3}}{3 c^{2}}"," ",0,"d**2*x/c**2 + d*e*x**2/c**2 + e**2*x**3/(3*c**2)","B",0
1009,1,15,0,0.109651," ","integrate((e*x+d)**5/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","\frac{d x}{c^{2}} + \frac{e x^{2}}{2 c^{2}}"," ",0,"d*x/c**2 + e*x**2/(2*c**2)","A",0
1010,1,3,0,0.100990," ","integrate((e*x+d)**4/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","\frac{x}{c^{2}}"," ",0,"x/c**2","A",0
1011,1,17,0,0.105121," ","integrate((e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","\frac{\log{\left(c^{2} d + c^{2} e x \right)}}{c^{2} e}"," ",0,"log(c**2*d + c**2*e*x)/(c**2*e)","A",0
1012,1,17,0,0.172367," ","integrate((e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","- \frac{1}{c^{2} d e + c^{2} e^{2} x}"," ",0,"-1/(c**2*d*e + c**2*e**2*x)","A",0
1013,1,36,0,0.229584," ","integrate((e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","- \frac{1}{2 c^{2} d^{2} e + 4 c^{2} d e^{2} x + 2 c^{2} e^{3} x^{2}}"," ",0,"-1/(2*c**2*d**2*e + 4*c**2*d*e**2*x + 2*c**2*e**3*x**2)","B",0
1014,1,51,0,0.274708," ","integrate(1/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","- \frac{1}{3 c^{2} d^{3} e + 9 c^{2} d^{2} e^{2} x + 9 c^{2} d e^{3} x^{2} + 3 c^{2} e^{4} x^{3}}"," ",0,"-1/(3*c**2*d**3*e + 9*c**2*d**2*e**2*x + 9*c**2*d*e**3*x**2 + 3*c**2*e**4*x**3)","B",0
1015,1,66,0,0.338811," ","integrate(1/(e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","- \frac{1}{4 c^{2} d^{4} e + 16 c^{2} d^{3} e^{2} x + 24 c^{2} d^{2} e^{3} x^{2} + 16 c^{2} d e^{4} x^{3} + 4 c^{2} e^{5} x^{4}}"," ",0,"-1/(4*c**2*d**4*e + 16*c**2*d**3*e**2*x + 24*c**2*d**2*e**3*x**2 + 16*c**2*d*e**4*x**3 + 4*c**2*e**5*x**4)","B",0
1016,1,82,0,0.417128," ","integrate(1/(e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","- \frac{1}{5 c^{2} d^{5} e + 25 c^{2} d^{4} e^{2} x + 50 c^{2} d^{3} e^{3} x^{2} + 50 c^{2} d^{2} e^{4} x^{3} + 25 c^{2} d e^{5} x^{4} + 5 c^{2} e^{6} x^{5}}"," ",0,"-1/(5*c**2*d**5*e + 25*c**2*d**4*e**2*x + 50*c**2*d**3*e**3*x**2 + 50*c**2*d**2*e**4*x**3 + 25*c**2*d*e**5*x**4 + 5*c**2*e**6*x**5)","B",0
1017,1,46,0,0.144088," ","integrate((e*x+d)**9/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","\frac{d^{3} x}{c^{3}} + \frac{3 d^{2} e x^{2}}{2 c^{3}} + \frac{d e^{2} x^{3}}{c^{3}} + \frac{e^{3} x^{4}}{4 c^{3}}"," ",0,"d**3*x/c**3 + 3*d**2*e*x**2/(2*c**3) + d*e**2*x**3/c**3 + e**3*x**4/(4*c**3)","B",0
1018,1,29,0,0.135625," ","integrate((e*x+d)**8/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","\frac{d^{2} x}{c^{3}} + \frac{d e x^{2}}{c^{3}} + \frac{e^{2} x^{3}}{3 c^{3}}"," ",0,"d**2*x/c**3 + d*e*x**2/c**3 + e**2*x**3/(3*c**3)","B",0
1019,1,15,0,0.129075," ","integrate((e*x+d)**7/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","\frac{d x}{c^{3}} + \frac{e x^{2}}{2 c^{3}}"," ",0,"d*x/c**3 + e*x**2/(2*c**3)","A",0
1020,1,3,0,0.151423," ","integrate((e*x+d)**6/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","\frac{x}{c^{3}}"," ",0,"x/c**3","A",0
1021,1,17,0,0.124933," ","integrate((e*x+d)**5/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","\frac{\log{\left(c^{3} d + c^{3} e x \right)}}{c^{3} e}"," ",0,"log(c**3*d + c**3*e*x)/(c**3*e)","A",0
1022,1,17,0,0.193303," ","integrate((e*x+d)**4/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","- \frac{1}{c^{3} d e + c^{3} e^{2} x}"," ",0,"-1/(c**3*d*e + c**3*e**2*x)","A",0
1023,1,36,0,0.242002," ","integrate((e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","- \frac{1}{2 c^{3} d^{2} e + 4 c^{3} d e^{2} x + 2 c^{3} e^{3} x^{2}}"," ",0,"-1/(2*c**3*d**2*e + 4*c**3*d*e**2*x + 2*c**3*e**3*x**2)","B",0
1024,1,51,0,0.307945," ","integrate((e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","- \frac{1}{3 c^{3} d^{3} e + 9 c^{3} d^{2} e^{2} x + 9 c^{3} d e^{3} x^{2} + 3 c^{3} e^{4} x^{3}}"," ",0,"-1/(3*c**3*d**3*e + 9*c**3*d**2*e**2*x + 9*c**3*d*e**3*x**2 + 3*c**3*e**4*x**3)","B",0
1025,1,66,0,0.351839," ","integrate((e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","- \frac{1}{4 c^{3} d^{4} e + 16 c^{3} d^{3} e^{2} x + 24 c^{3} d^{2} e^{3} x^{2} + 16 c^{3} d e^{4} x^{3} + 4 c^{3} e^{5} x^{4}}"," ",0,"-1/(4*c**3*d**4*e + 16*c**3*d**3*e**2*x + 24*c**3*d**2*e**3*x**2 + 16*c**3*d*e**4*x**3 + 4*c**3*e**5*x**4)","B",0
1026,1,82,0,0.469090," ","integrate(1/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","- \frac{1}{5 c^{3} d^{5} e + 25 c^{3} d^{4} e^{2} x + 50 c^{3} d^{3} e^{3} x^{2} + 50 c^{3} d^{2} e^{4} x^{3} + 25 c^{3} d e^{5} x^{4} + 5 c^{3} e^{6} x^{5}}"," ",0,"-1/(5*c**3*d**5*e + 25*c**3*d**4*e**2*x + 50*c**3*d**3*e**3*x**2 + 50*c**3*d**2*e**4*x**3 + 25*c**3*d*e**5*x**4 + 5*c**3*e**6*x**5)","B",0
1027,1,97,0,0.488246," ","integrate(1/(e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","- \frac{1}{6 c^{3} d^{6} e + 36 c^{3} d^{5} e^{2} x + 90 c^{3} d^{4} e^{3} x^{2} + 120 c^{3} d^{3} e^{4} x^{3} + 90 c^{3} d^{2} e^{5} x^{4} + 36 c^{3} d e^{6} x^{5} + 6 c^{3} e^{7} x^{6}}"," ",0,"-1/(6*c**3*d**6*e + 36*c**3*d**5*e**2*x + 90*c**3*d**4*e**3*x**2 + 120*c**3*d**3*e**4*x**3 + 90*c**3*d**2*e**5*x**4 + 36*c**3*d*e**6*x**5 + 6*c**3*e**7*x**6)","B",0
1028,1,112,0,0.553418," ","integrate(1/(e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","- \frac{1}{7 c^{3} d^{7} e + 49 c^{3} d^{6} e^{2} x + 147 c^{3} d^{5} e^{3} x^{2} + 245 c^{3} d^{4} e^{4} x^{3} + 245 c^{3} d^{3} e^{5} x^{4} + 147 c^{3} d^{2} e^{6} x^{5} + 49 c^{3} d e^{7} x^{6} + 7 c^{3} e^{8} x^{7}}"," ",0,"-1/(7*c**3*d**7*e + 49*c**3*d**6*e**2*x + 147*c**3*d**5*e**3*x**2 + 245*c**3*d**4*e**4*x**3 + 245*c**3*d**3*e**5*x**4 + 147*c**3*d**2*e**6*x**5 + 49*c**3*d*e**7*x**6 + 7*c**3*e**8*x**7)","B",0
1029,1,187,0,0.551050," ","integrate((e*x+d)**3*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\begin{cases} \frac{d^{4} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{5 e} + \frac{4 d^{3} x \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{5} + \frac{6 d^{2} e x^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{5} + \frac{4 d e^{2} x^{3} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{5} + \frac{e^{3} x^{4} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\d^{3} x \sqrt{c d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**4*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(5*e) + 4*d**3*x*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/5 + 6*d**2*e*x**2*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/5 + 4*d*e**2*x**3*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/5 + e**3*x**4*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/5, Ne(e, 0)), (d**3*x*sqrt(c*d**2), True))","A",0
1030,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\int \sqrt{c \left(d + e x\right)^{2}} \left(d + e x\right)^{2}\, dx"," ",0,"Integral(sqrt(c*(d + e*x)**2)*(d + e*x)**2, x)","F",0
1031,1,107,0,0.339907," ","integrate((e*x+d)*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\begin{cases} \frac{d^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{3 e} + \frac{2 d x \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{3} + \frac{e x^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{3} & \text{for}\: e \neq 0 \\d x \sqrt{c d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**2*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(3*e) + 2*d*x*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/3 + e*x**2*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/3, Ne(e, 0)), (d*x*sqrt(c*d**2), True))","A",0
1032,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\int \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}\, dx"," ",0,"Integral(sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2), x)","F",0
1033,1,37,0,2.601045," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2)/(e*x+d),x)","\begin{cases} \frac{\sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{e} & \text{for}\: e \neq 0 \\\frac{x \sqrt{c d^{2}}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/e, Ne(e, 0)), (x*sqrt(c*d**2)/d, True))","A",0
1034,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{c \left(d + e x\right)^{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(c*(d + e*x)**2)/(d + e*x)**2, x)","F",0
1035,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2)/(e*x+d)**3,x)","\int \frac{\sqrt{c \left(d + e x\right)^{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(sqrt(c*(d + e*x)**2)/(d + e*x)**3, x)","F",0
1036,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2)/(e*x+d)**4,x)","\int \frac{\sqrt{c \left(d + e x\right)^{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(c*(d + e*x)**2)/(d + e*x)**4, x)","F",0
1037,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2)/(e*x+d)**5,x)","\int \frac{\sqrt{c \left(d + e x\right)^{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(sqrt(c*(d + e*x)**2)/(d + e*x)**5, x)","F",0
1038,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2)/(e*x+d)**6,x)","\int \frac{\sqrt{c \left(d + e x\right)^{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral(sqrt(c*(d + e*x)**2)/(d + e*x)**6, x)","F",0
1039,1,277,0,3.296518," ","integrate((e*x+d)**3*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\begin{cases} \frac{c d^{6} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7 e} + \frac{6 c d^{5} x \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{15 c d^{4} e x^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{20 c d^{3} e^{2} x^{3} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{15 c d^{2} e^{3} x^{4} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{6 c d e^{4} x^{5} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{c e^{5} x^{6} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\d^{3} x \left(c d^{2}\right)^{\frac{3}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*d**6*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(7*e) + 6*c*d**5*x*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7 + 15*c*d**4*e*x**2*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7 + 20*c*d**3*e**2*x**3*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7 + 15*c*d**2*e**3*x**4*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7 + 6*c*d*e**4*x**5*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7 + c*e**5*x**6*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7, Ne(e, 0)), (d**3*x*(c*d**2)**(3/2), True))","A",0
1040,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\int \left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{2}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(3/2)*(d + e*x)**2, x)","F",0
1041,1,194,0,1.206283," ","integrate((e*x+d)*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\begin{cases} \frac{c d^{4} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{5 e} + \frac{4 c d^{3} x \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{5} + \frac{6 c d^{2} e x^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{5} + \frac{4 c d e^{2} x^{3} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{5} + \frac{c e^{3} x^{4} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\d x \left(c d^{2}\right)^{\frac{3}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*d**4*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(5*e) + 4*c*d**3*x*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/5 + 6*c*d**2*e*x**2*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/5 + 4*c*d*e**2*x**3*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/5 + c*e**3*x**4*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/5, Ne(e, 0)), (d*x*(c*d**2)**(3/2), True))","A",0
1042,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\int \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c*d**2 + 2*c*d*e*x + c*e**2*x**2)**(3/2), x)","F",0
1043,1,39,0,3.888546," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2)/(e*x+d),x)","\begin{cases} \frac{\left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e} & \text{for}\: e \neq 0 \\\frac{x \left(c d^{2}\right)^{\frac{3}{2}}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((c*d**2 + 2*c*d*e*x + c*e**2*x**2)**(3/2)/(3*e), Ne(e, 0)), (x*(c*d**2)**(3/2)/d, True))","A",0
1044,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(3/2)/(d + e*x)**2, x)","F",0
1045,1,39,0,4.547195," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2)/(e*x+d)**3,x)","c \left(\begin{cases} \frac{x \sqrt{c d^{2}}}{d} & \text{for}\: e = 0 \\\frac{\sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{e} & \text{otherwise} \end{cases}\right)"," ",0,"c*Piecewise((x*sqrt(c*d**2)/d, Eq(e, 0)), (sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/e, True))","A",0
1046,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2)/(e*x+d)**4,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(3/2)/(d + e*x)**4, x)","F",0
1047,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2)/(e*x+d)**5,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(3/2)/(d + e*x)**5, x)","F",0
1048,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2)/(e*x+d)**6,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(3/2)/(d + e*x)**6, x)","F",0
1049,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2)/(e*x+d)**7,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(3/2)/(d + e*x)**7, x)","F",0
1050,1,374,0,13.495085," ","integrate((e*x+d)**3*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\begin{cases} \frac{c^{2} d^{8} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{9 e} + \frac{8 c^{2} d^{7} x \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{9} + \frac{28 c^{2} d^{6} e x^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{9} + \frac{56 c^{2} d^{5} e^{2} x^{3} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{9} + \frac{70 c^{2} d^{4} e^{3} x^{4} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{9} + \frac{56 c^{2} d^{3} e^{4} x^{5} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{9} + \frac{28 c^{2} d^{2} e^{5} x^{6} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{9} + \frac{8 c^{2} d e^{6} x^{7} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{9} + \frac{c^{2} e^{7} x^{8} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\d^{3} x \left(c d^{2}\right)^{\frac{5}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*d**8*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(9*e) + 8*c**2*d**7*x*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/9 + 28*c**2*d**6*e*x**2*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/9 + 56*c**2*d**5*e**2*x**3*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/9 + 70*c**2*d**4*e**3*x**4*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/9 + 56*c**2*d**3*e**4*x**5*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/9 + 28*c**2*d**2*e**5*x**6*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/9 + 8*c**2*d*e**6*x**7*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/9 + c**2*e**7*x**8*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/9, Ne(e, 0)), (d**3*x*(c*d**2)**(5/2), True))","A",0
1051,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\int \left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}} \left(d + e x\right)^{2}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(5/2)*(d + e*x)**2, x)","F",0
1052,1,287,0,6.714792," ","integrate((e*x+d)*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\begin{cases} \frac{c^{2} d^{6} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7 e} + \frac{6 c^{2} d^{5} x \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{15 c^{2} d^{4} e x^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{20 c^{2} d^{3} e^{2} x^{3} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{15 c^{2} d^{2} e^{3} x^{4} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{6 c^{2} d e^{4} x^{5} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{c^{2} e^{5} x^{6} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\d x \left(c d^{2}\right)^{\frac{5}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*d**6*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(7*e) + 6*c**2*d**5*x*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7 + 15*c**2*d**4*e*x**2*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7 + 20*c**2*d**3*e**2*x**3*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7 + 15*c**2*d**2*e**3*x**4*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7 + 6*c**2*d*e**4*x**5*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7 + c**2*e**5*x**6*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/7, Ne(e, 0)), (d*x*(c*d**2)**(5/2), True))","A",0
1053,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\int \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((c*d**2 + 2*c*d*e*x + c*e**2*x**2)**(5/2), x)","F",0
1054,1,39,0,5.087742," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2)/(e*x+d),x)","\begin{cases} \frac{\left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{\frac{5}{2}}}{5 e} & \text{for}\: e \neq 0 \\\frac{x \left(c d^{2}\right)^{\frac{5}{2}}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((c*d**2 + 2*c*d*e*x + c*e**2*x**2)**(5/2)/(5*e), Ne(e, 0)), (x*(c*d**2)**(5/2)/d, True))","A",0
1055,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2)/(e*x+d)**2,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(5/2)/(d + e*x)**2, x)","F",0
1056,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(5/2)/(d + e*x)**3, x)","F",0
1057,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(5/2)/(d + e*x)**4, x)","F",0
1058,1,41,0,7.739743," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2)/(e*x+d)**5,x)","c^{2} \left(\begin{cases} \frac{x \sqrt{c d^{2}}}{d} & \text{for}\: e = 0 \\\frac{\sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{e} & \text{otherwise} \end{cases}\right)"," ",0,"c**2*Piecewise((x*sqrt(c*d**2)/d, Eq(e, 0)), (sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/e, True))","A",0
1059,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2)/(e*x+d)**6,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(5/2)/(d + e*x)**6, x)","F",0
1060,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2)/(e*x+d)**7,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(5/2)/(d + e*x)**7, x)","F",0
1061,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2)/(e*x+d)**8,x)","\int \frac{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{8}}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(5/2)/(d + e*x)**8, x)","F",0
1062,0,0,0,0.000000," ","integrate((e*x+d)**4/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{4}}{\sqrt{c \left(d + e x\right)^{2}}}\, dx"," ",0,"Integral((d + e*x)**4/sqrt(c*(d + e*x)**2), x)","F",0
1063,1,114,0,1.188201," ","integrate((e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\begin{cases} \frac{d^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{3 c e} + \frac{2 d x \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{3 c} + \frac{e x^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{3 c} & \text{for}\: e \neq 0 \\\frac{d^{3} x}{\sqrt{c d^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**2*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(3*c*e) + 2*d*x*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(3*c) + e*x**2*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(3*c), Ne(e, 0)), (d**3*x/sqrt(c*d**2), True))","A",0
1064,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{2}}{\sqrt{c \left(d + e x\right)^{2}}}\, dx"," ",0,"Integral((d + e*x)**2/sqrt(c*(d + e*x)**2), x)","F",0
1065,1,39,0,0.888395," ","integrate((e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\begin{cases} \frac{\sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{c e} & \text{for}\: e \neq 0 \\\frac{d x}{\sqrt{c d^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(c*e), Ne(e, 0)), (d*x/sqrt(c*d**2), True))","A",0
1066,0,0,0,0.000000," ","integrate(1/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\int \frac{1}{\sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}\, dx"," ",0,"Integral(1/sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2), x)","F",0
1067,1,41,0,3.829740," ","integrate(1/(e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\begin{cases} - \frac{1}{e \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x}{d \sqrt{c d^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(e*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)), Ne(e, 0)), (x/(d*sqrt(c*d**2)), True))","A",0
1068,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\int \frac{1}{\sqrt{c \left(d + e x\right)^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(c*(d + e*x)**2)*(d + e*x)**2), x)","F",0
1069,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\int \frac{1}{\sqrt{c \left(d + e x\right)^{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(c*(d + e*x)**2)*(d + e*x)**3), x)","F",0
1070,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\int \frac{1}{\sqrt{c \left(d + e x\right)^{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/(sqrt(c*(d + e*x)**2)*(d + e*x)**4), x)","F",0
1071,0,0,0,0.000000," ","integrate((e*x+d)**4/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/(c*(d + e*x)**2)**(3/2), x)","F",0
1072,1,42,0,0.803073," ","integrate((e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\begin{cases} \frac{\sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{c^{2} e} & \text{for}\: e \neq 0 \\\frac{d^{3} x}{\left(c d^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(c**2*e), Ne(e, 0)), (d**3*x/(c*d**2)**(3/2), True))","A",0
1073,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(c*(d + e*x)**2)**(3/2), x)","F",0
1074,1,42,0,1.228550," ","integrate((e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\begin{cases} - \frac{1}{c e \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{d x}{\left(c d^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(c*e*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)), Ne(e, 0)), (d*x/(c*d**2)**(3/2), True))","A",0
1075,0,0,0,0.000000," ","integrate(1/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\int \frac{1}{\left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*d**2 + 2*c*d*e*x + c*e**2*x**2)**(-3/2), x)","F",0
1076,1,42,0,5.428481," ","integrate(1/(e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\begin{cases} - \frac{1}{3 e \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{\frac{3}{2}}} & \text{for}\: e \neq 0 \\\frac{x}{d \left(c d^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(3*e*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**(3/2)), Ne(e, 0)), (x/(d*(c*d**2)**(3/2)), True))","A",0
1077,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\int \frac{1}{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((c*(d + e*x)**2)**(3/2)*(d + e*x)**2), x)","F",0
1078,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\int \frac{1}{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/((c*(d + e*x)**2)**(3/2)*(d + e*x)**3), x)","F",0
1079,0,0,0,0.000000," ","integrate((e*x+d)**6/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{6}}{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**6/(c*(d + e*x)**2)**(5/2), x)","F",0
1080,1,42,0,1.635476," ","integrate((e*x+d)**5/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\begin{cases} \frac{\sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{c^{3} e} & \text{for}\: e \neq 0 \\\frac{d^{5} x}{\left(c d^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(c**3*e), Ne(e, 0)), (d**5*x/(c*d**2)**(5/2), True))","A",0
1081,0,0,0,0.000000," ","integrate((e*x+d)**4/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/(c*(d + e*x)**2)**(5/2), x)","F",0
1082,1,70,0,1.456258," ","integrate((e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\begin{cases} - \frac{\sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{c^{3} d^{2} e + 2 c^{3} d e^{2} x + c^{3} e^{3} x^{2}} & \text{for}\: e \neq 0 \\\frac{d^{3} x}{\left(c d^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)/(c**3*d**2*e + 2*c**3*d*e**2*x + c**3*e**3*x**2), Ne(e, 0)), (d**3*x/(c*d**2)**(5/2), True))","A",0
1083,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(c*(d + e*x)**2)**(5/2), x)","F",0
1084,1,124,0,1.604715," ","integrate((e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\begin{cases} - \frac{1}{3 c^{2} d^{2} e \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}} + 6 c^{2} d e^{2} x \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}} + 3 c^{2} e^{3} x^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{d x}{\left(c d^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(3*c**2*d**2*e*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2) + 6*c**2*d*e**2*x*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2) + 3*c**2*e**3*x**2*sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2)), Ne(e, 0)), (d*x/(c*d**2)**(5/2), True))","A",0
1085,0,0,0,0.000000," ","integrate(1/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\int \frac{1}{\left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c*d**2 + 2*c*d*e*x + c*e**2*x**2)**(-5/2), x)","F",0
1086,1,42,0,7.215394," ","integrate(1/(e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\begin{cases} - \frac{1}{5 e \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{\frac{5}{2}}} & \text{for}\: e \neq 0 \\\frac{x}{d \left(c d^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(5*e*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**(5/2)), Ne(e, 0)), (x/(d*(c*d**2)**(5/2)), True))","A",0
1087,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\int \frac{1}{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((c*(d + e*x)**2)**(5/2)*(d + e*x)**2), x)","F",0
1088,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)","\int \frac{1}{\left(c \left(d + e x\right)^{2}\right)^{\frac{5}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/((c*(d + e*x)**2)**(5/2)*(d + e*x)**3), x)","F",0
1089,1,185,0,1.747626," ","integrate((e*x+d)**m*(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","\begin{cases} \frac{c^{2} x}{d} & \text{for}\: e = 0 \wedge m = -5 \\c^{2} d^{4} d^{m} x & \text{for}\: e = 0 \\\frac{c^{2} \log{\left(\frac{d}{e} + x \right)}}{e} & \text{for}\: m = -5 \\\frac{c^{2} d^{5} \left(d + e x\right)^{m}}{e m + 5 e} + \frac{5 c^{2} d^{4} e x \left(d + e x\right)^{m}}{e m + 5 e} + \frac{10 c^{2} d^{3} e^{2} x^{2} \left(d + e x\right)^{m}}{e m + 5 e} + \frac{10 c^{2} d^{2} e^{3} x^{3} \left(d + e x\right)^{m}}{e m + 5 e} + \frac{5 c^{2} d e^{4} x^{4} \left(d + e x\right)^{m}}{e m + 5 e} + \frac{c^{2} e^{5} x^{5} \left(d + e x\right)^{m}}{e m + 5 e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*x/d, Eq(e, 0) & Eq(m, -5)), (c**2*d**4*d**m*x, Eq(e, 0)), (c**2*log(d/e + x)/e, Eq(m, -5)), (c**2*d**5*(d + e*x)**m/(e*m + 5*e) + 5*c**2*d**4*e*x*(d + e*x)**m/(e*m + 5*e) + 10*c**2*d**3*e**2*x**2*(d + e*x)**m/(e*m + 5*e) + 10*c**2*d**2*e**3*x**3*(d + e*x)**m/(e*m + 5*e) + 5*c**2*d*e**4*x**4*(d + e*x)**m/(e*m + 5*e) + c**2*e**5*x**5*(d + e*x)**m/(e*m + 5*e), True))","A",0
1090,1,116,0,0.764381," ","integrate((e*x+d)**m*(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","\begin{cases} \frac{c x}{d} & \text{for}\: e = 0 \wedge m = -3 \\c d^{2} d^{m} x & \text{for}\: e = 0 \\\frac{c \log{\left(\frac{d}{e} + x \right)}}{e} & \text{for}\: m = -3 \\\frac{c d^{3} \left(d + e x\right)^{m}}{e m + 3 e} + \frac{3 c d^{2} e x \left(d + e x\right)^{m}}{e m + 3 e} + \frac{3 c d e^{2} x^{2} \left(d + e x\right)^{m}}{e m + 3 e} + \frac{c e^{3} x^{3} \left(d + e x\right)^{m}}{e m + 3 e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*x/d, Eq(e, 0) & Eq(m, -3)), (c*d**2*d**m*x, Eq(e, 0)), (c*log(d/e + x)/e, Eq(m, -3)), (c*d**3*(d + e*x)**m/(e*m + 3*e) + 3*c*d**2*e*x*(d + e*x)**m/(e*m + 3*e) + 3*c*d*e**2*x**2*(d + e*x)**m/(e*m + 3*e) + c*e**3*x**3*(d + e*x)**m/(e*m + 3*e), True))","A",0
1091,1,63,0,1.055319," ","integrate((e*x+d)**m/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)","\begin{cases} \text{NaN} & \text{for}\: d = 0 \wedge e = 0 \wedge m = 1 \\0^{m} \tilde{\infty} x & \text{for}\: d = - e x \\\frac{d^{m} x}{c d^{2}} & \text{for}\: e = 0 \\\frac{\log{\left(\frac{d}{e} + x \right)}}{c e} & \text{for}\: m = 1 \\\frac{\left(d + e x\right)^{m}}{c d e m - c d e + c e^{2} m x - c e^{2} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(d, 0) & Eq(e, 0) & Eq(m, 1)), (0**m*zoo*x, Eq(d, -e*x)), (d**m*x/(c*d**2), Eq(e, 0)), (log(d/e + x)/(c*e), Eq(m, 1)), ((d + e*x)**m/(c*d*e*m - c*d*e + c*e**2*m*x - c*e**2*x), True))","A",0
1092,1,136,0,2.129837," ","integrate((e*x+d)**m/(c*e**2*x**2+2*c*d*e*x+c*d**2)**2,x)","\begin{cases} \frac{x}{c^{2} d} & \text{for}\: e = 0 \wedge m = 3 \\\frac{d^{m} x}{c^{2} d^{4}} & \text{for}\: e = 0 \\\frac{\log{\left(\frac{d}{e} + x \right)}}{c^{2} e} & \text{for}\: m = 3 \\\frac{\left(d + e x\right)^{m}}{c^{2} d^{3} e m - 3 c^{2} d^{3} e + 3 c^{2} d^{2} e^{2} m x - 9 c^{2} d^{2} e^{2} x + 3 c^{2} d e^{3} m x^{2} - 9 c^{2} d e^{3} x^{2} + c^{2} e^{4} m x^{3} - 3 c^{2} e^{4} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(c**2*d), Eq(e, 0) & Eq(m, 3)), (d**m*x/(c**2*d**4), Eq(e, 0)), (log(d/e + x)/(c**2*e), Eq(m, 3)), ((d + e*x)**m/(c**2*d**3*e*m - 3*c**2*d**3*e + 3*c**2*d**2*e**2*m*x - 9*c**2*d**2*e**2*x + 3*c**2*d*e**3*m*x**2 - 9*c**2*d*e**3*x**2 + c**2*e**4*m*x**3 - 3*c**2*e**4*x**3), True))","A",0
1093,1,201,0,4.624805," ","integrate((e*x+d)**m/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)","\begin{cases} \frac{x}{c^{3} d} & \text{for}\: e = 0 \wedge m = 5 \\\frac{d^{m} x}{c^{3} d^{6}} & \text{for}\: e = 0 \\\frac{\log{\left(\frac{d}{e} + x \right)}}{c^{3} e} & \text{for}\: m = 5 \\\frac{\left(d + e x\right)^{m}}{c^{3} d^{5} e m - 5 c^{3} d^{5} e + 5 c^{3} d^{4} e^{2} m x - 25 c^{3} d^{4} e^{2} x + 10 c^{3} d^{3} e^{3} m x^{2} - 50 c^{3} d^{3} e^{3} x^{2} + 10 c^{3} d^{2} e^{4} m x^{3} - 50 c^{3} d^{2} e^{4} x^{3} + 5 c^{3} d e^{5} m x^{4} - 25 c^{3} d e^{5} x^{4} + c^{3} e^{6} m x^{5} - 5 c^{3} e^{6} x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(c**3*d), Eq(e, 0) & Eq(m, 5)), (d**m*x/(c**3*d**6), Eq(e, 0)), (log(d/e + x)/(c**3*e), Eq(m, 5)), ((d + e*x)**m/(c**3*d**5*e*m - 5*c**3*d**5*e + 5*c**3*d**4*e**2*m*x - 25*c**3*d**4*e**2*x + 10*c**3*d**3*e**3*m*x**2 - 50*c**3*d**3*e**3*x**2 + 10*c**3*d**2*e**4*m*x**3 - 50*c**3*d**2*e**4*x**3 + 5*c**3*d*e**5*m*x**4 - 25*c**3*d*e**5*x**4 + c**3*e**6*m*x**5 - 5*c**3*e**6*x**5), True))","A",0
1094,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\int \left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}} \left(d + e x\right)^{m}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(3/2)*(d + e*x)**m, x)","F",0
1095,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\int \sqrt{c \left(d + e x\right)^{2}} \left(d + e x\right)^{m}\, dx"," ",0,"Integral(sqrt(c*(d + e*x)**2)*(d + e*x)**m, x)","F",0
1096,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{m}}{\sqrt{c \left(d + e x\right)^{2}}}\, dx"," ",0,"Integral((d + e*x)**m/sqrt(c*(d + e*x)**2), x)","F",0
1097,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*e**2*x**2+2*c*d*e*x+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**m/(c*(d + e*x)**2)**(3/2), x)","F",0
1098,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*e**2*x**2+2*c*d*e*x+c*d**2)**p,x)","\begin{cases} d^{- 2 p - 1} x \left(c d^{2}\right)^{p} & \text{for}\: e = 0 \wedge m = - 2 p - 1 \\d^{m} x \left(c d^{2}\right)^{p} & \text{for}\: e = 0 \\\int \left(c \left(d + e x\right)^{2}\right)^{p} \left(d + e x\right)^{- 2 p - 1}\, dx & \text{for}\: m = - 2 p - 1 \\\frac{d \left(d + e x\right)^{m} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{e m + 2 e p + e} + \frac{e x \left(d + e x\right)^{m} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{e m + 2 e p + e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**(-2*p - 1)*x*(c*d**2)**p, Eq(e, 0) & Eq(m, -2*p - 1)), (d**m*x*(c*d**2)**p, Eq(e, 0)), (Integral((c*(d + e*x)**2)**p*(d + e*x)**(-2*p - 1), x), Eq(m, -2*p - 1)), (d*(d + e*x)**m*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(e*m + 2*e*p + e) + e*x*(d + e*x)**m*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(e*m + 2*e*p + e), True))","F",0
1099,-2,0,0,0.000000," ","integrate((e*x+d)**p/((c*e**2*x**2+2*c*d*e*x+c*d**2)**p),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
1100,1,233,0,1.137217," ","integrate((e*x+d)**3*(c*e**2*x**2+2*c*d*e*x+c*d**2)**p,x)","\begin{cases} \frac{x}{c^{2} d} & \text{for}\: e = 0 \wedge p = -2 \\d^{3} x \left(c d^{2}\right)^{p} & \text{for}\: e = 0 \\\frac{\log{\left(\frac{d}{e} + x \right)}}{c^{2} e} & \text{for}\: p = -2 \\\frac{d^{4} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 4 e} + \frac{4 d^{3} e x \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 4 e} + \frac{6 d^{2} e^{2} x^{2} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 4 e} + \frac{4 d e^{3} x^{3} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 4 e} + \frac{e^{4} x^{4} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 4 e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(c**2*d), Eq(e, 0) & Eq(p, -2)), (d**3*x*(c*d**2)**p, Eq(e, 0)), (log(d/e + x)/(c**2*e), Eq(p, -2)), (d**4*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 4*e) + 4*d**3*e*x*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 4*e) + 6*d**2*e**2*x**2*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 4*e) + 4*d*e**3*x**3*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 4*e) + e**4*x**4*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 4*e), True))","A",0
1101,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*e**2*x**2+2*c*d*e*x+c*d**2)**p,x)","\begin{cases} \frac{d^{2} x}{\left(c d^{2}\right)^{\frac{3}{2}}} & \text{for}\: e = 0 \wedge p = - \frac{3}{2} \\d^{2} x \left(c d^{2}\right)^{p} & \text{for}\: e = 0 \\\int \frac{\left(d + e x\right)^{2}}{\left(c \left(d + e x\right)^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: p = - \frac{3}{2} \\\frac{d^{3} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 3 e} + \frac{3 d^{2} e x \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 3 e} + \frac{3 d e^{2} x^{2} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 3 e} + \frac{e^{3} x^{3} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 3 e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**2*x/(c*d**2)**(3/2), Eq(e, 0) & Eq(p, -3/2)), (d**2*x*(c*d**2)**p, Eq(e, 0)), (Integral((d + e*x)**2/(c*(d + e*x)**2)**(3/2), x), Eq(p, -3/2)), (d**3*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 3*e) + 3*d**2*e*x*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 3*e) + 3*d*e**2*x**2*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 3*e) + e**3*x**3*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 3*e), True))","F",0
1102,1,139,0,0.547224," ","integrate((e*x+d)*(c*e**2*x**2+2*c*d*e*x+c*d**2)**p,x)","\begin{cases} \frac{x}{c d} & \text{for}\: e = 0 \wedge p = -1 \\d x \left(c d^{2}\right)^{p} & \text{for}\: e = 0 \\\frac{\log{\left(\frac{d}{e} + x \right)}}{c e} & \text{for}\: p = -1 \\\frac{d^{2} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 2 e} + \frac{2 d e x \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 2 e} + \frac{e^{2} x^{2} \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + 2 e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(c*d), Eq(e, 0) & Eq(p, -1)), (d*x*(c*d**2)**p, Eq(e, 0)), (log(d/e + x)/(c*e), Eq(p, -1)), (d**2*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 2*e) + 2*d*e*x*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 2*e) + e**2*x**2*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + 2*e), True))","A",0
1103,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**p,x)","\begin{cases} \frac{x}{\sqrt{c d^{2}}} & \text{for}\: e = 0 \wedge p = - \frac{1}{2} \\x \left(c d^{2}\right)^{p} & \text{for}\: e = 0 \\\int \frac{1}{\sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{d \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + e} + \frac{e x \left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p + e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/sqrt(c*d**2), Eq(e, 0) & Eq(p, -1/2)), (x*(c*d**2)**p, Eq(e, 0)), (Integral(1/sqrt(c*d**2 + 2*c*d*e*x + c*e**2*x**2), x), Eq(p, -1/2)), (d*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + e) + e*x*(c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p + e), True))","F",0
1104,1,48,0,0.366850," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**p/(e*x+d),x)","\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \wedge p = 0 \\\frac{\log{\left(\frac{d}{e} + x \right)}}{e} & \text{for}\: p = 0 \\\frac{x \left(c d^{2}\right)^{p}}{d} & \text{for}\: e = 0 \\\frac{\left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 e p} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/d, Eq(e, 0) & Eq(p, 0)), (log(d/e + x)/e, Eq(p, 0)), (x*(c*d**2)**p/d, Eq(e, 0)), ((c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*e*p), True))","A",0
1105,0,0,0,0.000000," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**p/(e*x+d)**2,x)","\begin{cases} \text{NaN} & \text{for}\: d = 0 \wedge e = 0 \wedge p = \frac{1}{2} \\0^{p} \tilde{\infty} x & \text{for}\: d = - e x \\\frac{x \left(c d^{2}\right)^{p}}{d^{2}} & \text{for}\: e = 0 \\\int \frac{\sqrt{c \left(d + e x\right)^{2}}}{\left(d + e x\right)^{2}}\, dx & \text{for}\: p = \frac{1}{2} \\\frac{\left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 d e p - d e + 2 e^{2} p x - e^{2} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(d, 0) & Eq(e, 0) & Eq(p, 1/2)), (0**p*zoo*x, Eq(d, -e*x)), (x*(c*d**2)**p/d**2, Eq(e, 0)), (Integral(sqrt(c*(d + e*x)**2)/(d + e*x)**2, x), Eq(p, 1/2)), ((c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*d*e*p - d*e + 2*e**2*p*x - e**2*x), True))","F",0
1106,1,100,0,1.247168," ","integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**p/(e*x+d)**3,x)","\begin{cases} \frac{c x}{d} & \text{for}\: e = 0 \wedge p = 1 \\\frac{x \left(c d^{2}\right)^{p}}{d^{3}} & \text{for}\: e = 0 \\\frac{c \log{\left(\frac{d}{e} + x \right)}}{e} & \text{for}\: p = 1 \\\frac{\left(c d^{2} + 2 c d e x + c e^{2} x^{2}\right)^{p}}{2 d^{2} e p - 2 d^{2} e + 4 d e^{2} p x - 4 d e^{2} x + 2 e^{3} p x^{2} - 2 e^{3} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*x/d, Eq(e, 0) & Eq(p, 1)), (x*(c*d**2)**p/d**3, Eq(e, 0)), (c*log(d/e + x)/e, Eq(p, 1)), ((c*d**2 + 2*c*d*e*x + c*e**2*x**2)**p/(2*d**2*e*p - 2*d**2*e + 4*d*e**2*p*x - 4*d*e**2*x + 2*e**3*p*x**2 - 2*e**3*x**2), True))","A",0
1107,0,0,0,0.000000," ","integrate((e*x+d)**(-1-2*p)*(c*e**2*x**2+2*c*d*e*x+c*d**2)**p,x)","\int \left(c \left(d + e x\right)^{2}\right)^{p} \left(d + e x\right)^{- 2 p - 1}\, dx"," ",0,"Integral((c*(d + e*x)**2)**p*(d + e*x)**(-2*p - 1), x)","F",0
1108,0,0,0,0.000000," ","integrate((e*x+d)**(-1+2*p)/((c*e**2*x**2+2*c*d*e*x+c*d**2)**p),x)","\int \left(c \left(d + e x\right)^{2}\right)^{- p} \left(d + e x\right)^{2 p - 1}\, dx"," ",0,"Integral((c*(d + e*x)**2)**(-p)*(d + e*x)**(2*p - 1), x)","F",0
1109,1,143,0,0.098479," ","integrate((2*c*d*x+b*d)**4*(c*x**2+b*x+a),x)","a b^{4} d^{4} x + 8 b c^{4} d^{4} x^{6} + \frac{16 c^{5} d^{4} x^{7}}{7} + x^{5} \left(\frac{16 a c^{4} d^{4}}{5} + \frac{56 b^{2} c^{3} d^{4}}{5}\right) + x^{4} \left(8 a b c^{3} d^{4} + 8 b^{3} c^{2} d^{4}\right) + x^{3} \left(8 a b^{2} c^{2} d^{4} + 3 b^{4} c d^{4}\right) + x^{2} \left(4 a b^{3} c d^{4} + \frac{b^{5} d^{4}}{2}\right)"," ",0,"a*b**4*d**4*x + 8*b*c**4*d**4*x**6 + 16*c**5*d**4*x**7/7 + x**5*(16*a*c**4*d**4/5 + 56*b**2*c**3*d**4/5) + x**4*(8*a*b*c**3*d**4 + 8*b**3*c**2*d**4) + x**3*(8*a*b**2*c**2*d**4 + 3*b**4*c*d**4) + x**2*(4*a*b**3*c*d**4 + b**5*d**4/2)","B",0
1110,1,114,0,0.087798," ","integrate((2*c*d*x+b*d)**3*(c*x**2+b*x+a),x)","a b^{3} d^{3} x + 4 b c^{3} d^{3} x^{5} + \frac{4 c^{4} d^{3} x^{6}}{3} + x^{4} \left(2 a c^{3} d^{3} + \frac{9 b^{2} c^{2} d^{3}}{2}\right) + x^{3} \left(4 a b c^{2} d^{3} + \frac{7 b^{3} c d^{3}}{3}\right) + x^{2} \left(3 a b^{2} c d^{3} + \frac{b^{4} d^{3}}{2}\right)"," ",0,"a*b**3*d**3*x + 4*b*c**3*d**3*x**5 + 4*c**4*d**3*x**6/3 + x**4*(2*a*c**3*d**3 + 9*b**2*c**2*d**3/2) + x**3*(4*a*b*c**2*d**3 + 7*b**3*c*d**3/3) + x**2*(3*a*b**2*c*d**3 + b**4*d**3/2)","B",0
1111,1,85,0,0.085344," ","integrate((2*c*d*x+b*d)**2*(c*x**2+b*x+a),x)","a b^{2} d^{2} x + 2 b c^{2} d^{2} x^{4} + \frac{4 c^{3} d^{2} x^{5}}{5} + x^{3} \left(\frac{4 a c^{2} d^{2}}{3} + \frac{5 b^{2} c d^{2}}{3}\right) + x^{2} \left(2 a b c d^{2} + \frac{b^{3} d^{2}}{2}\right)"," ",0,"a*b**2*d**2*x + 2*b*c**2*d**2*x**4 + 4*c**3*d**2*x**5/5 + x**3*(4*a*c**2*d**2/3 + 5*b**2*c*d**2/3) + x**2*(2*a*b*c*d**2 + b**3*d**2/2)","B",0
1112,1,39,0,0.071094," ","integrate((2*c*d*x+b*d)*(c*x**2+b*x+a),x)","a b d x + b c d x^{3} + \frac{c^{2} d x^{4}}{2} + x^{2} \left(a c d + \frac{b^{2} d}{2}\right)"," ",0,"a*b*d*x + b*c*d*x**3 + c**2*d*x**4/2 + x**2*(a*c*d + b**2*d/2)","B",0
1113,1,37,0,0.206026," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d),x)","\frac{b x}{4 c d} + \frac{x^{2}}{4 d} + \frac{\left(4 a c - b^{2}\right) \log{\left(b + 2 c x \right)}}{8 c^{2} d}"," ",0,"b*x/(4*c*d) + x**2/(4*d) + (4*a*c - b**2)*log(b + 2*c*x)/(8*c**2*d)","A",0
1114,1,36,0,0.233110," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**2,x)","\frac{- 4 a c + b^{2}}{8 b c^{2} d^{2} + 16 c^{3} d^{2} x} + \frac{x}{4 c d^{2}}"," ",0,"(-4*a*c + b**2)/(8*b*c**2*d**2 + 16*c**3*d**2*x) + x/(4*c*d**2)","A",0
1115,1,60,0,0.379766," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**3,x)","\frac{- 4 a c + b^{2}}{16 b^{2} c^{2} d^{3} + 64 b c^{3} d^{3} x + 64 c^{4} d^{3} x^{2}} + \frac{\log{\left(b + 2 c x \right)}}{8 c^{2} d^{3}}"," ",0,"(-4*a*c + b**2)/(16*b**2*c**2*d**3 + 64*b*c**3*d**3*x + 64*c**4*d**3*x**2) + log(b + 2*c*x)/(8*c**2*d**3)","A",0
1116,1,75,0,0.437840," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**4,x)","\frac{- 2 a c - b^{2} - 6 b c x - 6 c^{2} x^{2}}{12 b^{3} c^{2} d^{4} + 72 b^{2} c^{3} d^{4} x + 144 b c^{4} d^{4} x^{2} + 96 c^{5} d^{4} x^{3}}"," ",0,"(-2*a*c - b**2 - 6*b*c*x - 6*c**2*x**2)/(12*b**3*c**2*d**4 + 72*b**2*c**3*d**4*x + 144*b*c**4*d**4*x**2 + 96*c**5*d**4*x**3)","A",0
1117,1,90,0,0.627991," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**5,x)","\frac{- 4 a c - b^{2} - 8 b c x - 8 c^{2} x^{2}}{32 b^{4} c^{2} d^{5} + 256 b^{3} c^{3} d^{5} x + 768 b^{2} c^{4} d^{5} x^{2} + 1024 b c^{5} d^{5} x^{3} + 512 c^{6} d^{5} x^{4}}"," ",0,"(-4*a*c - b**2 - 8*b*c*x - 8*c**2*x**2)/(32*b**4*c**2*d**5 + 256*b**3*c**3*d**5*x + 768*b**2*c**4*d**5*x**2 + 1024*b*c**5*d**5*x**3 + 512*c**6*d**5*x**4)","B",0
1118,1,105,0,0.657875," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**6,x)","\frac{- 6 a c - b^{2} - 10 b c x - 10 c^{2} x^{2}}{60 b^{5} c^{2} d^{6} + 600 b^{4} c^{3} d^{6} x + 2400 b^{3} c^{4} d^{6} x^{2} + 4800 b^{2} c^{5} d^{6} x^{3} + 4800 b c^{6} d^{6} x^{4} + 1920 c^{7} d^{6} x^{5}}"," ",0,"(-6*a*c - b**2 - 10*b*c*x - 10*c**2*x**2)/(60*b**5*c**2*d**6 + 600*b**4*c**3*d**6*x + 2400*b**3*c**4*d**6*x**2 + 4800*b**2*c**5*d**6*x**3 + 4800*b*c**6*d**6*x**4 + 1920*c**7*d**6*x**5)","B",0
1119,1,121,0,0.897332," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**7,x)","\frac{- 8 a c - b^{2} - 12 b c x - 12 c^{2} x^{2}}{96 b^{6} c^{2} d^{7} + 1152 b^{5} c^{3} d^{7} x + 5760 b^{4} c^{4} d^{7} x^{2} + 15360 b^{3} c^{5} d^{7} x^{3} + 23040 b^{2} c^{6} d^{7} x^{4} + 18432 b c^{7} d^{7} x^{5} + 6144 c^{8} d^{7} x^{6}}"," ",0,"(-8*a*c - b**2 - 12*b*c*x - 12*c**2*x**2)/(96*b**6*c**2*d**7 + 1152*b**5*c**3*d**7*x + 5760*b**4*c**4*d**7*x**2 + 15360*b**3*c**5*d**7*x**3 + 23040*b**2*c**6*d**7*x**4 + 18432*b*c**7*d**7*x**5 + 6144*c**8*d**7*x**6)","B",0
1120,1,136,0,0.926755," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**8,x)","\frac{- 10 a c - b^{2} - 14 b c x - 14 c^{2} x^{2}}{140 b^{7} c^{2} d^{8} + 1960 b^{6} c^{3} d^{8} x + 11760 b^{5} c^{4} d^{8} x^{2} + 39200 b^{4} c^{5} d^{8} x^{3} + 78400 b^{3} c^{6} d^{8} x^{4} + 94080 b^{2} c^{7} d^{8} x^{5} + 62720 b c^{8} d^{8} x^{6} + 17920 c^{9} d^{8} x^{7}}"," ",0,"(-10*a*c - b**2 - 14*b*c*x - 14*c**2*x**2)/(140*b**7*c**2*d**8 + 1960*b**6*c**3*d**8*x + 11760*b**5*c**4*d**8*x**2 + 39200*b**4*c**5*d**8*x**3 + 78400*b**3*c**6*d**8*x**4 + 94080*b**2*c**7*d**8*x**5 + 62720*b*c**8*d**8*x**6 + 17920*c**9*d**8*x**7)","B",0
1121,1,291,0,0.140023," ","integrate((2*c*d*x+b*d)**5*(c*x**2+b*x+a)**2,x)","a^{2} b^{5} d^{5} x + 16 b c^{6} d^{5} x^{9} + \frac{16 c^{7} d^{5} x^{10}}{5} + x^{8} \left(8 a c^{6} d^{5} + 34 b^{2} c^{5} d^{5}\right) + x^{7} \left(32 a b c^{5} d^{5} + 40 b^{3} c^{4} d^{5}\right) + x^{6} \left(\frac{16 a^{2} c^{5} d^{5}}{3} + \frac{160 a b^{2} c^{4} d^{5}}{3} + \frac{85 b^{4} c^{3} d^{5}}{3}\right) + x^{5} \left(16 a^{2} b c^{4} d^{5} + 48 a b^{3} c^{3} d^{5} + \frac{61 b^{5} c^{2} d^{5}}{5}\right) + x^{4} \left(20 a^{2} b^{2} c^{3} d^{5} + 25 a b^{4} c^{2} d^{5} + 3 b^{6} c d^{5}\right) + x^{3} \left(\frac{40 a^{2} b^{3} c^{2} d^{5}}{3} + \frac{22 a b^{5} c d^{5}}{3} + \frac{b^{7} d^{5}}{3}\right) + x^{2} \left(5 a^{2} b^{4} c d^{5} + a b^{6} d^{5}\right)"," ",0,"a**2*b**5*d**5*x + 16*b*c**6*d**5*x**9 + 16*c**7*d**5*x**10/5 + x**8*(8*a*c**6*d**5 + 34*b**2*c**5*d**5) + x**7*(32*a*b*c**5*d**5 + 40*b**3*c**4*d**5) + x**6*(16*a**2*c**5*d**5/3 + 160*a*b**2*c**4*d**5/3 + 85*b**4*c**3*d**5/3) + x**5*(16*a**2*b*c**4*d**5 + 48*a*b**3*c**3*d**5 + 61*b**5*c**2*d**5/5) + x**4*(20*a**2*b**2*c**3*d**5 + 25*a*b**4*c**2*d**5 + 3*b**6*c*d**5) + x**3*(40*a**2*b**3*c**2*d**5/3 + 22*a*b**5*c*d**5/3 + b**7*d**5/3) + x**2*(5*a**2*b**4*c*d**5 + a*b**6*d**5)","B",0
1122,1,248,0,0.114497," ","integrate((2*c*d*x+b*d)**4*(c*x**2+b*x+a)**2,x)","a^{2} b^{4} d^{4} x + 8 b c^{5} d^{4} x^{8} + \frac{16 c^{6} d^{4} x^{9}}{9} + x^{7} \left(\frac{32 a c^{5} d^{4}}{7} + \frac{104 b^{2} c^{4} d^{4}}{7}\right) + x^{6} \left(16 a b c^{4} d^{4} + \frac{44 b^{3} c^{3} d^{4}}{3}\right) + x^{5} \left(\frac{16 a^{2} c^{4} d^{4}}{5} + \frac{112 a b^{2} c^{3} d^{4}}{5} + \frac{41 b^{4} c^{2} d^{4}}{5}\right) + x^{4} \left(8 a^{2} b c^{3} d^{4} + 16 a b^{3} c^{2} d^{4} + \frac{5 b^{5} c d^{4}}{2}\right) + x^{3} \left(8 a^{2} b^{2} c^{2} d^{4} + 6 a b^{4} c d^{4} + \frac{b^{6} d^{4}}{3}\right) + x^{2} \left(4 a^{2} b^{3} c d^{4} + a b^{5} d^{4}\right)"," ",0,"a**2*b**4*d**4*x + 8*b*c**5*d**4*x**8 + 16*c**6*d**4*x**9/9 + x**7*(32*a*c**5*d**4/7 + 104*b**2*c**4*d**4/7) + x**6*(16*a*b*c**4*d**4 + 44*b**3*c**3*d**4/3) + x**5*(16*a**2*c**4*d**4/5 + 112*a*b**2*c**3*d**4/5 + 41*b**4*c**2*d**4/5) + x**4*(8*a**2*b*c**3*d**4 + 16*a*b**3*c**2*d**4 + 5*b**5*c*d**4/2) + x**3*(8*a**2*b**2*c**2*d**4 + 6*a*b**4*c*d**4 + b**6*d**4/3) + x**2*(4*a**2*b**3*c*d**4 + a*b**5*d**4)","B",0
1123,1,194,0,0.105970," ","integrate((2*c*d*x+b*d)**3*(c*x**2+b*x+a)**2,x)","a^{2} b^{3} d^{3} x + 4 b c^{4} d^{3} x^{7} + c^{5} d^{3} x^{8} + x^{6} \left(\frac{8 a c^{4} d^{3}}{3} + \frac{19 b^{2} c^{3} d^{3}}{3}\right) + x^{5} \left(8 a b c^{3} d^{3} + 5 b^{3} c^{2} d^{3}\right) + x^{4} \left(2 a^{2} c^{3} d^{3} + 9 a b^{2} c^{2} d^{3} + 2 b^{4} c d^{3}\right) + x^{3} \left(4 a^{2} b c^{2} d^{3} + \frac{14 a b^{3} c d^{3}}{3} + \frac{b^{5} d^{3}}{3}\right) + x^{2} \left(3 a^{2} b^{2} c d^{3} + a b^{4} d^{3}\right)"," ",0,"a**2*b**3*d**3*x + 4*b*c**4*d**3*x**7 + c**5*d**3*x**8 + x**6*(8*a*c**4*d**3/3 + 19*b**2*c**3*d**3/3) + x**5*(8*a*b*c**3*d**3 + 5*b**3*c**2*d**3) + x**4*(2*a**2*c**3*d**3 + 9*a*b**2*c**2*d**3 + 2*b**4*c*d**3) + x**3*(4*a**2*b*c**2*d**3 + 14*a*b**3*c*d**3/3 + b**5*d**3/3) + x**2*(3*a**2*b**2*c*d**3 + a*b**4*d**3)","B",0
1124,1,156,0,0.097801," ","integrate((2*c*d*x+b*d)**2*(c*x**2+b*x+a)**2,x)","a^{2} b^{2} d^{2} x + 2 b c^{3} d^{2} x^{6} + \frac{4 c^{4} d^{2} x^{7}}{7} + x^{5} \left(\frac{8 a c^{3} d^{2}}{5} + \frac{13 b^{2} c^{2} d^{2}}{5}\right) + x^{4} \left(4 a b c^{2} d^{2} + \frac{3 b^{3} c d^{2}}{2}\right) + x^{3} \left(\frac{4 a^{2} c^{2} d^{2}}{3} + \frac{10 a b^{2} c d^{2}}{3} + \frac{b^{4} d^{2}}{3}\right) + x^{2} \left(2 a^{2} b c d^{2} + a b^{3} d^{2}\right)"," ",0,"a**2*b**2*d**2*x + 2*b*c**3*d**2*x**6 + 4*c**4*d**2*x**7/7 + x**5*(8*a*c**3*d**2/5 + 13*b**2*c**2*d**2/5) + x**4*(4*a*b*c**2*d**2 + 3*b**3*c*d**2/2) + x**3*(4*a**2*c**2*d**2/3 + 10*a*b**2*c*d**2/3 + b**4*d**2/3) + x**2*(2*a**2*b*c*d**2 + a*b**3*d**2)","B",0
1125,1,80,0,0.083441," ","integrate((2*c*d*x+b*d)*(c*x**2+b*x+a)**2,x)","a^{2} b d x + b c^{2} d x^{5} + \frac{c^{3} d x^{6}}{3} + x^{4} \left(a c^{2} d + b^{2} c d\right) + x^{3} \left(2 a b c d + \frac{b^{3} d}{3}\right) + x^{2} \left(a^{2} c d + a b^{2} d\right)"," ",0,"a**2*b*d*x + b*c**2*d*x**5 + c**3*d*x**6/3 + x**4*(a*c**2*d + b**2*c*d) + x**3*(2*a*b*c*d + b**3*d/3) + x**2*(a**2*c*d + a*b**2*d)","B",0
1126,1,78,0,0.329477," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d),x)","\frac{b x^{3}}{4 d} + \frac{c x^{4}}{8 d} + x^{2} \left(\frac{a}{2 d} + \frac{b^{2}}{16 c d}\right) + x \left(\frac{a b}{2 c d} - \frac{b^{3}}{16 c^{2} d}\right) + \frac{\left(4 a c - b^{2}\right)^{2} \log{\left(b + 2 c x \right)}}{32 c^{3} d}"," ",0,"b*x**3/(4*d) + c*x**4/(8*d) + x**2*(a/(2*d) + b**2/(16*c*d)) + x*(a*b/(2*c*d) - b**3/(16*c**2*d)) + (4*a*c - b**2)**2*log(b + 2*c*x)/(32*c**3*d)","A",0
1127,1,82,0,0.389221," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**2,x)","\frac{b x^{2}}{8 c d^{2}} + x \left(\frac{a}{2 c d^{2}} - \frac{b^{2}}{16 c^{2} d^{2}}\right) + \frac{- 16 a^{2} c^{2} + 8 a b^{2} c - b^{4}}{32 b c^{3} d^{2} + 64 c^{4} d^{2} x} + \frac{x^{3}}{12 d^{2}}"," ",0,"b*x**2/(8*c*d**2) + x*(a/(2*c*d**2) - b**2/(16*c**2*d**2)) + (-16*a**2*c**2 + 8*a*b**2*c - b**4)/(32*b*c**3*d**2 + 64*c**4*d**2*x) + x**3/(12*d**2)","A",0
1128,1,102,0,0.789280," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**3,x)","\frac{b x}{16 c^{2} d^{3}} + \frac{- 16 a^{2} c^{2} + 8 a b^{2} c - b^{4}}{64 b^{2} c^{3} d^{3} + 256 b c^{4} d^{3} x + 256 c^{5} d^{3} x^{2}} + \frac{x^{2}}{16 c d^{3}} + \frac{\left(4 a c - b^{2}\right) \log{\left(b + 2 c x \right)}}{16 c^{3} d^{3}}"," ",0,"b*x/(16*c**2*d**3) + (-16*a**2*c**2 + 8*a*b**2*c - b**4)/(64*b**2*c**3*d**3 + 256*b*c**4*d**3*x + 256*c**5*d**3*x**2) + x**2/(16*c*d**3) + (4*a*c - b**2)*log(b + 2*c*x)/(16*c**3*d**3)","A",0
1129,1,117,0,0.858191," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**4,x)","\frac{- 16 a^{2} c^{2} - 16 a b^{2} c + 5 b^{4} + x^{2} \left(- 96 a c^{3} + 24 b^{2} c^{2}\right) + x \left(- 96 a b c^{2} + 24 b^{3} c\right)}{96 b^{3} c^{3} d^{4} + 576 b^{2} c^{4} d^{4} x + 1152 b c^{5} d^{4} x^{2} + 768 c^{6} d^{4} x^{3}} + \frac{x}{16 c^{2} d^{4}}"," ",0,"(-16*a**2*c**2 - 16*a*b**2*c + 5*b**4 + x**2*(-96*a*c**3 + 24*b**2*c**2) + x*(-96*a*b*c**2 + 24*b**3*c))/(96*b**3*c**3*d**4 + 576*b**2*c**4*d**4*x + 1152*b*c**5*d**4*x**2 + 768*c**6*d**4*x**3) + x/(16*c**2*d**4)","A",0
1130,1,139,0,1.538541," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**5,x)","\frac{- 16 a^{2} c^{2} - 8 a b^{2} c + 3 b^{4} + x^{2} \left(- 64 a c^{3} + 16 b^{2} c^{2}\right) + x \left(- 64 a b c^{2} + 16 b^{3} c\right)}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} + \frac{\log{\left(b + 2 c x \right)}}{32 c^{3} d^{5}}"," ",0,"(-16*a**2*c**2 - 8*a*b**2*c + 3*b**4 + x**2*(-64*a*c**3 + 16*b**2*c**2) + x*(-64*a*b*c**2 + 16*b**3*c))/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) + log(b + 2*c*x)/(32*c**3*d**5)","B",0
1131,1,158,0,1.362287," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**6,x)","\frac{- 6 a^{2} c^{2} - 2 a b^{2} c - b^{4} - 60 b c^{3} x^{3} - 30 c^{4} x^{4} + x^{2} \left(- 20 a c^{3} - 40 b^{2} c^{2}\right) + x \left(- 20 a b c^{2} - 10 b^{3} c\right)}{60 b^{5} c^{3} d^{6} + 600 b^{4} c^{4} d^{6} x + 2400 b^{3} c^{5} d^{6} x^{2} + 4800 b^{2} c^{6} d^{6} x^{3} + 4800 b c^{7} d^{6} x^{4} + 1920 c^{8} d^{6} x^{5}}"," ",0,"(-6*a**2*c**2 - 2*a*b**2*c - b**4 - 60*b*c**3*x**3 - 30*c**4*x**4 + x**2*(-20*a*c**3 - 40*b**2*c**2) + x*(-20*a*b*c**2 - 10*b**3*c))/(60*b**5*c**3*d**6 + 600*b**4*c**4*d**6*x + 2400*b**3*c**5*d**6*x**2 + 4800*b**2*c**6*d**6*x**3 + 4800*b*c**7*d**6*x**4 + 1920*c**8*d**6*x**5)","B",0
1132,1,173,0,2.371278," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**7,x)","\frac{- 16 a^{2} c^{2} - 4 a b^{2} c - b^{4} - 96 b c^{3} x^{3} - 48 c^{4} x^{4} + x^{2} \left(- 48 a c^{3} - 60 b^{2} c^{2}\right) + x \left(- 48 a b c^{2} - 12 b^{3} c\right)}{192 b^{6} c^{3} d^{7} + 2304 b^{5} c^{4} d^{7} x + 11520 b^{4} c^{5} d^{7} x^{2} + 30720 b^{3} c^{6} d^{7} x^{3} + 46080 b^{2} c^{7} d^{7} x^{4} + 36864 b c^{8} d^{7} x^{5} + 12288 c^{9} d^{7} x^{6}}"," ",0,"(-16*a**2*c**2 - 4*a*b**2*c - b**4 - 96*b*c**3*x**3 - 48*c**4*x**4 + x**2*(-48*a*c**3 - 60*b**2*c**2) + x*(-48*a*b*c**2 - 12*b**3*c))/(192*b**6*c**3*d**7 + 2304*b**5*c**4*d**7*x + 11520*b**4*c**5*d**7*x**2 + 30720*b**3*c**6*d**7*x**3 + 46080*b**2*c**7*d**7*x**4 + 36864*b*c**8*d**7*x**5 + 12288*c**9*d**7*x**6)","B",0
1133,1,189,0,1.998764," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**8,x)","\frac{- 30 a^{2} c^{2} - 6 a b^{2} c - b^{4} - 140 b c^{3} x^{3} - 70 c^{4} x^{4} + x^{2} \left(- 84 a c^{3} - 84 b^{2} c^{2}\right) + x \left(- 84 a b c^{2} - 14 b^{3} c\right)}{420 b^{7} c^{3} d^{8} + 5880 b^{6} c^{4} d^{8} x + 35280 b^{5} c^{5} d^{8} x^{2} + 117600 b^{4} c^{6} d^{8} x^{3} + 235200 b^{3} c^{7} d^{8} x^{4} + 282240 b^{2} c^{8} d^{8} x^{5} + 188160 b c^{9} d^{8} x^{6} + 53760 c^{10} d^{8} x^{7}}"," ",0,"(-30*a**2*c**2 - 6*a*b**2*c - b**4 - 140*b*c**3*x**3 - 70*c**4*x**4 + x**2*(-84*a*c**3 - 84*b**2*c**2) + x*(-84*a*b*c**2 - 14*b**3*c))/(420*b**7*c**3*d**8 + 5880*b**6*c**4*d**8*x + 35280*b**5*c**5*d**8*x**2 + 117600*b**4*c**6*d**8*x**3 + 235200*b**3*c**7*d**8*x**4 + 282240*b**2*c**8*d**8*x**5 + 188160*b*c**9*d**8*x**6 + 53760*c**10*d**8*x**7)","B",0
1134,1,204,0,3.549821," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**9,x)","\frac{- 48 a^{2} c^{2} - 8 a b^{2} c - b^{4} - 192 b c^{3} x^{3} - 96 c^{4} x^{4} + x^{2} \left(- 128 a c^{3} - 112 b^{2} c^{2}\right) + x \left(- 128 a b c^{2} - 16 b^{3} c\right)}{768 b^{8} c^{3} d^{9} + 12288 b^{7} c^{4} d^{9} x + 86016 b^{6} c^{5} d^{9} x^{2} + 344064 b^{5} c^{6} d^{9} x^{3} + 860160 b^{4} c^{7} d^{9} x^{4} + 1376256 b^{3} c^{8} d^{9} x^{5} + 1376256 b^{2} c^{9} d^{9} x^{6} + 786432 b c^{10} d^{9} x^{7} + 196608 c^{11} d^{9} x^{8}}"," ",0,"(-48*a**2*c**2 - 8*a*b**2*c - b**4 - 192*b*c**3*x**3 - 96*c**4*x**4 + x**2*(-128*a*c**3 - 112*b**2*c**2) + x*(-128*a*b*c**2 - 16*b**3*c))/(768*b**8*c**3*d**9 + 12288*b**7*c**4*d**9*x + 86016*b**6*c**5*d**9*x**2 + 344064*b**5*c**6*d**9*x**3 + 860160*b**4*c**7*d**9*x**4 + 1376256*b**3*c**8*d**9*x**5 + 1376256*b**2*c**9*d**9*x**6 + 786432*b*c**10*d**9*x**7 + 196608*c**11*d**9*x**8)","B",0
1135,1,219,0,2.730470," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**10,x)","\frac{- 70 a^{2} c^{2} - 10 a b^{2} c - b^{4} - 252 b c^{3} x^{3} - 126 c^{4} x^{4} + x^{2} \left(- 180 a c^{3} - 144 b^{2} c^{2}\right) + x \left(- 180 a b c^{2} - 18 b^{3} c\right)}{1260 b^{9} c^{3} d^{10} + 22680 b^{8} c^{4} d^{10} x + 181440 b^{7} c^{5} d^{10} x^{2} + 846720 b^{6} c^{6} d^{10} x^{3} + 2540160 b^{5} c^{7} d^{10} x^{4} + 5080320 b^{4} c^{8} d^{10} x^{5} + 6773760 b^{3} c^{9} d^{10} x^{6} + 5806080 b^{2} c^{10} d^{10} x^{7} + 2903040 b c^{11} d^{10} x^{8} + 645120 c^{12} d^{10} x^{9}}"," ",0,"(-70*a**2*c**2 - 10*a*b**2*c - b**4 - 252*b*c**3*x**3 - 126*c**4*x**4 + x**2*(-180*a*c**3 - 144*b**2*c**2) + x*(-180*a*b*c**2 - 18*b**3*c))/(1260*b**9*c**3*d**10 + 22680*b**8*c**4*d**10*x + 181440*b**7*c**5*d**10*x**2 + 846720*b**6*c**6*d**10*x**3 + 2540160*b**5*c**7*d**10*x**4 + 5080320*b**4*c**8*d**10*x**5 + 6773760*b**3*c**9*d**10*x**6 + 5806080*b**2*c**10*d**10*x**7 + 2903040*b*c**11*d**10*x**8 + 645120*c**12*d**10*x**9)","B",0
1136,1,235,0,4.852689," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**11,x)","\frac{- 96 a^{2} c^{2} - 12 a b^{2} c - b^{4} - 320 b c^{3} x^{3} - 160 c^{4} x^{4} + x^{2} \left(- 240 a c^{3} - 180 b^{2} c^{2}\right) + x \left(- 240 a b c^{2} - 20 b^{3} c\right)}{1920 b^{10} c^{3} d^{11} + 38400 b^{9} c^{4} d^{11} x + 345600 b^{8} c^{5} d^{11} x^{2} + 1843200 b^{7} c^{6} d^{11} x^{3} + 6451200 b^{6} c^{7} d^{11} x^{4} + 15482880 b^{5} c^{8} d^{11} x^{5} + 25804800 b^{4} c^{9} d^{11} x^{6} + 29491200 b^{3} c^{10} d^{11} x^{7} + 22118400 b^{2} c^{11} d^{11} x^{8} + 9830400 b c^{12} d^{11} x^{9} + 1966080 c^{13} d^{11} x^{10}}"," ",0,"(-96*a**2*c**2 - 12*a*b**2*c - b**4 - 320*b*c**3*x**3 - 160*c**4*x**4 + x**2*(-240*a*c**3 - 180*b**2*c**2) + x*(-240*a*b*c**2 - 20*b**3*c))/(1920*b**10*c**3*d**11 + 38400*b**9*c**4*d**11*x + 345600*b**8*c**5*d**11*x**2 + 1843200*b**7*c**6*d**11*x**3 + 6451200*b**6*c**7*d**11*x**4 + 15482880*b**5*c**8*d**11*x**5 + 25804800*b**4*c**9*d**11*x**6 + 29491200*b**3*c**10*d**11*x**7 + 22118400*b**2*c**11*d**11*x**8 + 9830400*b*c**12*d**11*x**9 + 1966080*c**13*d**11*x**10)","B",0
1137,1,428,0,0.145134," ","integrate((2*c*d*x+b*d)**5*(c*x**2+b*x+a)**3,x)","a^{3} b^{5} d^{5} x + 16 b c^{7} d^{5} x^{11} + \frac{8 c^{8} d^{5} x^{12}}{3} + x^{10} \left(\frac{48 a c^{7} d^{5}}{5} + \frac{208 b^{2} c^{6} d^{5}}{5}\right) + x^{9} \left(48 a b c^{6} d^{5} + \frac{184 b^{3} c^{5} d^{5}}{3}\right) + x^{8} \left(12 a^{2} c^{6} d^{5} + 102 a b^{2} c^{5} d^{5} + \frac{225 b^{4} c^{4} d^{5}}{4}\right) + x^{7} \left(48 a^{2} b c^{5} d^{5} + 120 a b^{3} c^{4} d^{5} + 33 b^{5} c^{3} d^{5}\right) + x^{6} \left(\frac{16 a^{3} c^{5} d^{5}}{3} + 80 a^{2} b^{2} c^{4} d^{5} + 85 a b^{4} c^{3} d^{5} + \frac{73 b^{6} c^{2} d^{5}}{6}\right) + x^{5} \left(16 a^{3} b c^{4} d^{5} + 72 a^{2} b^{3} c^{3} d^{5} + \frac{183 a b^{5} c^{2} d^{5}}{5} + \frac{13 b^{7} c d^{5}}{5}\right) + x^{4} \left(20 a^{3} b^{2} c^{3} d^{5} + \frac{75 a^{2} b^{4} c^{2} d^{5}}{2} + 9 a b^{6} c d^{5} + \frac{b^{8} d^{5}}{4}\right) + x^{3} \left(\frac{40 a^{3} b^{3} c^{2} d^{5}}{3} + 11 a^{2} b^{5} c d^{5} + a b^{7} d^{5}\right) + x^{2} \left(5 a^{3} b^{4} c d^{5} + \frac{3 a^{2} b^{6} d^{5}}{2}\right)"," ",0,"a**3*b**5*d**5*x + 16*b*c**7*d**5*x**11 + 8*c**8*d**5*x**12/3 + x**10*(48*a*c**7*d**5/5 + 208*b**2*c**6*d**5/5) + x**9*(48*a*b*c**6*d**5 + 184*b**3*c**5*d**5/3) + x**8*(12*a**2*c**6*d**5 + 102*a*b**2*c**5*d**5 + 225*b**4*c**4*d**5/4) + x**7*(48*a**2*b*c**5*d**5 + 120*a*b**3*c**4*d**5 + 33*b**5*c**3*d**5) + x**6*(16*a**3*c**5*d**5/3 + 80*a**2*b**2*c**4*d**5 + 85*a*b**4*c**3*d**5 + 73*b**6*c**2*d**5/6) + x**5*(16*a**3*b*c**4*d**5 + 72*a**2*b**3*c**3*d**5 + 183*a*b**5*c**2*d**5/5 + 13*b**7*c*d**5/5) + x**4*(20*a**3*b**2*c**3*d**5 + 75*a**2*b**4*c**2*d**5/2 + 9*a*b**6*c*d**5 + b**8*d**5/4) + x**3*(40*a**3*b**3*c**2*d**5/3 + 11*a**2*b**5*c*d**5 + a*b**7*d**5) + x**2*(5*a**3*b**4*c*d**5 + 3*a**2*b**6*d**5/2)","B",0
1138,1,371,0,0.132430," ","integrate((2*c*d*x+b*d)**4*(c*x**2+b*x+a)**3,x)","a^{3} b^{4} d^{4} x + 8 b c^{6} d^{4} x^{10} + \frac{16 c^{7} d^{4} x^{11}}{11} + x^{9} \left(\frac{16 a c^{6} d^{4}}{3} + \frac{56 b^{2} c^{5} d^{4}}{3}\right) + x^{8} \left(24 a b c^{5} d^{4} + 24 b^{3} c^{4} d^{4}\right) + x^{7} \left(\frac{48 a^{2} c^{5} d^{4}}{7} + \frac{312 a b^{2} c^{4} d^{4}}{7} + \frac{129 b^{4} c^{3} d^{4}}{7}\right) + x^{6} \left(24 a^{2} b c^{4} d^{4} + 44 a b^{3} c^{3} d^{4} + \frac{17 b^{5} c^{2} d^{4}}{2}\right) + x^{5} \left(\frac{16 a^{3} c^{4} d^{4}}{5} + \frac{168 a^{2} b^{2} c^{3} d^{4}}{5} + \frac{123 a b^{4} c^{2} d^{4}}{5} + \frac{11 b^{6} c d^{4}}{5}\right) + x^{4} \left(8 a^{3} b c^{3} d^{4} + 24 a^{2} b^{3} c^{2} d^{4} + \frac{15 a b^{5} c d^{4}}{2} + \frac{b^{7} d^{4}}{4}\right) + x^{3} \left(8 a^{3} b^{2} c^{2} d^{4} + 9 a^{2} b^{4} c d^{4} + a b^{6} d^{4}\right) + x^{2} \left(4 a^{3} b^{3} c d^{4} + \frac{3 a^{2} b^{5} d^{4}}{2}\right)"," ",0,"a**3*b**4*d**4*x + 8*b*c**6*d**4*x**10 + 16*c**7*d**4*x**11/11 + x**9*(16*a*c**6*d**4/3 + 56*b**2*c**5*d**4/3) + x**8*(24*a*b*c**5*d**4 + 24*b**3*c**4*d**4) + x**7*(48*a**2*c**5*d**4/7 + 312*a*b**2*c**4*d**4/7 + 129*b**4*c**3*d**4/7) + x**6*(24*a**2*b*c**4*d**4 + 44*a*b**3*c**3*d**4 + 17*b**5*c**2*d**4/2) + x**5*(16*a**3*c**4*d**4/5 + 168*a**2*b**2*c**3*d**4/5 + 123*a*b**4*c**2*d**4/5 + 11*b**6*c*d**4/5) + x**4*(8*a**3*b*c**3*d**4 + 24*a**2*b**3*c**2*d**4 + 15*a*b**5*c*d**4/2 + b**7*d**4/4) + x**3*(8*a**3*b**2*c**2*d**4 + 9*a**2*b**4*c*d**4 + a*b**6*d**4) + x**2*(4*a**3*b**3*c*d**4 + 3*a**2*b**5*d**4/2)","B",0
1139,1,299,0,0.122097," ","integrate((2*c*d*x+b*d)**3*(c*x**2+b*x+a)**3,x)","a^{3} b^{3} d^{3} x + 4 b c^{5} d^{3} x^{9} + \frac{4 c^{6} d^{3} x^{10}}{5} + x^{8} \left(3 a c^{5} d^{3} + \frac{33 b^{2} c^{4} d^{3}}{4}\right) + x^{7} \left(12 a b c^{4} d^{3} + 9 b^{3} c^{3} d^{3}\right) + x^{6} \left(4 a^{2} c^{4} d^{3} + 19 a b^{2} c^{3} d^{3} + \frac{11 b^{4} c^{2} d^{3}}{2}\right) + x^{5} \left(12 a^{2} b c^{3} d^{3} + 15 a b^{3} c^{2} d^{3} + \frac{9 b^{5} c d^{3}}{5}\right) + x^{4} \left(2 a^{3} c^{3} d^{3} + \frac{27 a^{2} b^{2} c^{2} d^{3}}{2} + 6 a b^{4} c d^{3} + \frac{b^{6} d^{3}}{4}\right) + x^{3} \left(4 a^{3} b c^{2} d^{3} + 7 a^{2} b^{3} c d^{3} + a b^{5} d^{3}\right) + x^{2} \left(3 a^{3} b^{2} c d^{3} + \frac{3 a^{2} b^{4} d^{3}}{2}\right)"," ",0,"a**3*b**3*d**3*x + 4*b*c**5*d**3*x**9 + 4*c**6*d**3*x**10/5 + x**8*(3*a*c**5*d**3 + 33*b**2*c**4*d**3/4) + x**7*(12*a*b*c**4*d**3 + 9*b**3*c**3*d**3) + x**6*(4*a**2*c**4*d**3 + 19*a*b**2*c**3*d**3 + 11*b**4*c**2*d**3/2) + x**5*(12*a**2*b*c**3*d**3 + 15*a*b**3*c**2*d**3 + 9*b**5*c*d**3/5) + x**4*(2*a**3*c**3*d**3 + 27*a**2*b**2*c**2*d**3/2 + 6*a*b**4*c*d**3 + b**6*d**3/4) + x**3*(4*a**3*b*c**2*d**3 + 7*a**2*b**3*c*d**3 + a*b**5*d**3) + x**2*(3*a**3*b**2*c*d**3 + 3*a**2*b**4*d**3/2)","B",0
1140,1,246,0,0.113327," ","integrate((2*c*d*x+b*d)**2*(c*x**2+b*x+a)**3,x)","a^{3} b^{2} d^{2} x + 2 b c^{4} d^{2} x^{8} + \frac{4 c^{5} d^{2} x^{9}}{9} + x^{7} \left(\frac{12 a c^{4} d^{2}}{7} + \frac{25 b^{2} c^{3} d^{2}}{7}\right) + x^{6} \left(6 a b c^{3} d^{2} + \frac{19 b^{3} c^{2} d^{2}}{6}\right) + x^{5} \left(\frac{12 a^{2} c^{3} d^{2}}{5} + \frac{39 a b^{2} c^{2} d^{2}}{5} + \frac{7 b^{4} c d^{2}}{5}\right) + x^{4} \left(6 a^{2} b c^{2} d^{2} + \frac{9 a b^{3} c d^{2}}{2} + \frac{b^{5} d^{2}}{4}\right) + x^{3} \left(\frac{4 a^{3} c^{2} d^{2}}{3} + 5 a^{2} b^{2} c d^{2} + a b^{4} d^{2}\right) + x^{2} \left(2 a^{3} b c d^{2} + \frac{3 a^{2} b^{3} d^{2}}{2}\right)"," ",0,"a**3*b**2*d**2*x + 2*b*c**4*d**2*x**8 + 4*c**5*d**2*x**9/9 + x**7*(12*a*c**4*d**2/7 + 25*b**2*c**3*d**2/7) + x**6*(6*a*b*c**3*d**2 + 19*b**3*c**2*d**2/6) + x**5*(12*a**2*c**3*d**2/5 + 39*a*b**2*c**2*d**2/5 + 7*b**4*c*d**2/5) + x**4*(6*a**2*b*c**2*d**2 + 9*a*b**3*c*d**2/2 + b**5*d**2/4) + x**3*(4*a**3*c**2*d**2/3 + 5*a**2*b**2*c*d**2 + a*b**4*d**2) + x**2*(2*a**3*b*c*d**2 + 3*a**2*b**3*d**2/2)","B",0
1141,1,144,0,0.098624," ","integrate((2*c*d*x+b*d)*(c*x**2+b*x+a)**3,x)","a^{3} b d x + b c^{3} d x^{7} + \frac{c^{4} d x^{8}}{4} + x^{6} \left(a c^{3} d + \frac{3 b^{2} c^{2} d}{2}\right) + x^{5} \left(3 a b c^{2} d + b^{3} c d\right) + x^{4} \left(\frac{3 a^{2} c^{2} d}{2} + 3 a b^{2} c d + \frac{b^{4} d}{4}\right) + x^{3} \left(3 a^{2} b c d + a b^{3} d\right) + x^{2} \left(a^{3} c d + \frac{3 a^{2} b^{2} d}{2}\right)"," ",0,"a**3*b*d*x + b*c**3*d*x**7 + c**4*d*x**8/4 + x**6*(a*c**3*d + 3*b**2*c**2*d/2) + x**5*(3*a*b*c**2*d + b**3*c*d) + x**4*(3*a**2*c**2*d/2 + 3*a*b**2*c*d + b**4*d/4) + x**3*(3*a**2*b*c*d + a*b**3*d) + x**2*(a**3*c*d + 3*a**2*b**2*d/2)","B",0
1142,1,156,0,0.539665," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d),x)","\frac{b c x^{5}}{4 d} + \frac{c^{2} x^{6}}{12 d} + x^{4} \left(\frac{3 a c}{8 d} + \frac{7 b^{2}}{32 d}\right) + x^{3} \left(\frac{3 a b}{4 d} + \frac{b^{3}}{48 c d}\right) + x^{2} \left(\frac{3 a^{2}}{4 d} + \frac{3 a b^{2}}{16 c d} - \frac{b^{4}}{64 c^{2} d}\right) + x \left(\frac{3 a^{2} b}{4 c d} - \frac{3 a b^{3}}{16 c^{2} d} + \frac{b^{5}}{64 c^{3} d}\right) + \frac{\left(4 a c - b^{2}\right)^{3} \log{\left(b + 2 c x \right)}}{128 c^{4} d}"," ",0,"b*c*x**5/(4*d) + c**2*x**6/(12*d) + x**4*(3*a*c/(8*d) + 7*b**2/(32*d)) + x**3*(3*a*b/(4*d) + b**3/(48*c*d)) + x**2*(3*a**2/(4*d) + 3*a*b**2/(16*c*d) - b**4/(64*c**2*d)) + x*(3*a**2*b/(4*c*d) - 3*a*b**3/(16*c**2*d) + b**5/(64*c**3*d)) + (4*a*c - b**2)**3*log(b + 2*c*x)/(128*c**4*d)","A",0
1143,1,160,0,0.636170," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**2,x)","\frac{b x^{4}}{8 d^{2}} + \frac{c x^{5}}{20 d^{2}} + x^{3} \left(\frac{a}{4 d^{2}} + \frac{b^{2}}{16 c d^{2}}\right) + x^{2} \left(\frac{3 a b}{8 c d^{2}} - \frac{b^{3}}{32 c^{2} d^{2}}\right) + x \left(\frac{3 a^{2}}{4 c d^{2}} - \frac{3 a b^{2}}{16 c^{2} d^{2}} + \frac{b^{4}}{64 c^{3} d^{2}}\right) + \frac{- 64 a^{3} c^{3} + 48 a^{2} b^{2} c^{2} - 12 a b^{4} c + b^{6}}{128 b c^{4} d^{2} + 256 c^{5} d^{2} x}"," ",0,"b*x**4/(8*d**2) + c*x**5/(20*d**2) + x**3*(a/(4*d**2) + b**2/(16*c*d**2)) + x**2*(3*a*b/(8*c*d**2) - b**3/(32*c**2*d**2)) + x*(3*a**2/(4*c*d**2) - 3*a*b**2/(16*c**2*d**2) + b**4/(64*c**3*d**2)) + (-64*a**3*c**3 + 48*a**2*b**2*c**2 - 12*a*b**4*c + b**6)/(128*b*c**4*d**2 + 256*c**5*d**2*x)","A",0
1144,1,156,0,1.269574," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**3,x)","\frac{3 a x^{2}}{16 c d^{3}} + \frac{b x^{3}}{16 c d^{3}} + x \left(\frac{3 a b}{16 c^{2} d^{3}} - \frac{b^{3}}{32 c^{3} d^{3}}\right) + \frac{- 64 a^{3} c^{3} + 48 a^{2} b^{2} c^{2} - 12 a b^{4} c + b^{6}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{x^{4}}{32 d^{3}} + \frac{3 \left(4 a c - b^{2}\right)^{2} \log{\left(b + 2 c x \right)}}{128 c^{4} d^{3}}"," ",0,"3*a*x**2/(16*c*d**3) + b*x**3/(16*c*d**3) + x*(3*a*b/(16*c**2*d**3) - b**3/(32*c**3*d**3)) + (-64*a**3*c**3 + 48*a**2*b**2*c**2 - 12*a*b**4*c + b**6)/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + x**4/(32*d**3) + 3*(4*a*c - b**2)**2*log(b + 2*c*x)/(128*c**4*d**3)","A",0
1145,1,192,0,1.412349," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**4,x)","\frac{b x^{2}}{32 c^{2} d^{4}} + x \left(\frac{3 a}{16 c^{2} d^{4}} - \frac{b^{2}}{32 c^{3} d^{4}}\right) + \frac{- 16 a^{3} c^{3} - 24 a^{2} b^{2} c^{2} + 15 a b^{4} c - 2 b^{6} + x^{2} \left(- 144 a^{2} c^{4} + 72 a b^{2} c^{3} - 9 b^{4} c^{2}\right) + x \left(- 144 a^{2} b c^{3} + 72 a b^{3} c^{2} - 9 b^{5} c\right)}{96 b^{3} c^{4} d^{4} + 576 b^{2} c^{5} d^{4} x + 1152 b c^{6} d^{4} x^{2} + 768 c^{7} d^{4} x^{3}} + \frac{x^{3}}{48 c d^{4}}"," ",0,"b*x**2/(32*c**2*d**4) + x*(3*a/(16*c**2*d**4) - b**2/(32*c**3*d**4)) + (-16*a**3*c**3 - 24*a**2*b**2*c**2 + 15*a*b**4*c - 2*b**6 + x**2*(-144*a**2*c**4 + 72*a*b**2*c**3 - 9*b**4*c**2) + x*(-144*a**2*b*c**3 + 72*a*b**3*c**2 - 9*b**5*c))/(96*b**3*c**4*d**4 + 576*b**2*c**5*d**4*x + 1152*b*c**6*d**4*x**2 + 768*c**7*d**4*x**3) + x**3/(48*c*d**4)","A",0
1146,1,209,0,3.032660," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**5,x)","\frac{b x}{64 c^{3} d^{5}} + \frac{- 64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 36 a b^{4} c - 5 b^{6} + x^{2} \left(- 384 a^{2} c^{4} + 192 a b^{2} c^{3} - 24 b^{4} c^{2}\right) + x \left(- 384 a^{2} b c^{3} + 192 a b^{3} c^{2} - 24 b^{5} c\right)}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{x^{2}}{64 c^{2} d^{5}} + \frac{3 \left(4 a c - b^{2}\right) \log{\left(b + 2 c x \right)}}{128 c^{4} d^{5}}"," ",0,"b*x/(64*c**3*d**5) + (-64*a**3*c**3 - 48*a**2*b**2*c**2 + 36*a*b**4*c - 5*b**6 + x**2*(-384*a**2*c**4 + 192*a*b**2*c**3 - 24*b**4*c**2) + x*(-384*a**2*b*c**3 + 192*a*b**3*c**2 - 24*b**5*c))/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + x**2/(64*c**2*d**5) + 3*(4*a*c - b**2)*log(b + 2*c*x)/(128*c**4*d**5)","A",0
1147,1,223,0,2.851287," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**6,x)","\frac{- 64 a^{3} c^{3} - 32 a^{2} b^{2} c^{2} - 32 a b^{4} c + 11 b^{6} + x^{4} \left(- 960 a c^{5} + 240 b^{2} c^{4}\right) + x^{3} \left(- 1920 a b c^{4} + 480 b^{3} c^{3}\right) + x^{2} \left(- 320 a^{2} c^{4} - 1280 a b^{2} c^{3} + 340 b^{4} c^{2}\right) + x \left(- 320 a^{2} b c^{3} - 320 a b^{3} c^{2} + 100 b^{5} c\right)}{640 b^{5} c^{4} d^{6} + 6400 b^{4} c^{5} d^{6} x + 25600 b^{3} c^{6} d^{6} x^{2} + 51200 b^{2} c^{7} d^{6} x^{3} + 51200 b c^{8} d^{6} x^{4} + 20480 c^{9} d^{6} x^{5}} + \frac{x}{64 c^{3} d^{6}}"," ",0,"(-64*a**3*c**3 - 32*a**2*b**2*c**2 - 32*a*b**4*c + 11*b**6 + x**4*(-960*a*c**5 + 240*b**2*c**4) + x**3*(-1920*a*b*c**4 + 480*b**3*c**3) + x**2*(-320*a**2*c**4 - 1280*a*b**2*c**3 + 340*b**4*c**2) + x*(-320*a**2*b*c**3 - 320*a*b**3*c**2 + 100*b**5*c))/(640*b**5*c**4*d**6 + 6400*b**4*c**5*d**6*x + 25600*b**3*c**6*d**6*x**2 + 51200*b**2*c**7*d**6*x**3 + 51200*b*c**8*d**6*x**4 + 20480*c**9*d**6*x**5) + x/(64*c**3*d**6)","B",0
1148,1,245,0,5.857569," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**7,x)","\frac{- 128 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} - 24 a b^{4} c + 11 b^{6} + x^{4} \left(- 1152 a c^{5} + 288 b^{2} c^{4}\right) + x^{3} \left(- 2304 a b c^{4} + 576 b^{3} c^{3}\right) + x^{2} \left(- 576 a^{2} c^{4} - 1440 a b^{2} c^{3} + 396 b^{4} c^{2}\right) + x \left(- 576 a^{2} b c^{3} - 288 a b^{3} c^{2} + 108 b^{5} c\right)}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{\log{\left(b + 2 c x \right)}}{128 c^{4} d^{7}}"," ",0,"(-128*a**3*c**3 - 48*a**2*b**2*c**2 - 24*a*b**4*c + 11*b**6 + x**4*(-1152*a*c**5 + 288*b**2*c**4) + x**3*(-2304*a*b*c**4 + 576*b**3*c**3) + x**2*(-576*a**2*c**4 - 1440*a*b**2*c**3 + 396*b**4*c**2) + x*(-576*a**2*b*c**3 - 288*a*b**3*c**2 + 108*b**5*c))/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + log(b + 2*c*x)/(128*c**4*d**7)","B",0
1149,1,267,0,4.629491," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**8,x)","\frac{- 20 a^{3} c^{3} - 6 a^{2} b^{2} c^{2} - 2 a b^{4} c - b^{6} - 420 b c^{5} x^{5} - 140 c^{6} x^{6} + x^{4} \left(- 140 a c^{5} - 490 b^{2} c^{4}\right) + x^{3} \left(- 280 a b c^{4} - 280 b^{3} c^{3}\right) + x^{2} \left(- 84 a^{2} c^{4} - 168 a b^{2} c^{3} - 84 b^{4} c^{2}\right) + x \left(- 84 a^{2} b c^{3} - 28 a b^{3} c^{2} - 14 b^{5} c\right)}{280 b^{7} c^{4} d^{8} + 3920 b^{6} c^{5} d^{8} x + 23520 b^{5} c^{6} d^{8} x^{2} + 78400 b^{4} c^{7} d^{8} x^{3} + 156800 b^{3} c^{8} d^{8} x^{4} + 188160 b^{2} c^{9} d^{8} x^{5} + 125440 b c^{10} d^{8} x^{6} + 35840 c^{11} d^{8} x^{7}}"," ",0,"(-20*a**3*c**3 - 6*a**2*b**2*c**2 - 2*a*b**4*c - b**6 - 420*b*c**5*x**5 - 140*c**6*x**6 + x**4*(-140*a*c**5 - 490*b**2*c**4) + x**3*(-280*a*b*c**4 - 280*b**3*c**3) + x**2*(-84*a**2*c**4 - 168*a*b**2*c**3 - 84*b**4*c**2) + x*(-84*a**2*b*c**3 - 28*a*b**3*c**2 - 14*b**5*c))/(280*b**7*c**4*d**8 + 3920*b**6*c**5*d**8*x + 23520*b**5*c**6*d**8*x**2 + 78400*b**4*c**7*d**8*x**3 + 156800*b**3*c**8*d**8*x**4 + 188160*b**2*c**9*d**8*x**5 + 125440*b*c**10*d**8*x**6 + 35840*c**11*d**8*x**7)","B",0
1150,1,282,0,10.110864," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**9,x)","\frac{- 64 a^{3} c^{3} - 16 a^{2} b^{2} c^{2} - 4 a b^{4} c - b^{6} - 768 b c^{5} x^{5} - 256 c^{6} x^{6} + x^{4} \left(- 384 a c^{5} - 864 b^{2} c^{4}\right) + x^{3} \left(- 768 a b c^{4} - 448 b^{3} c^{3}\right) + x^{2} \left(- 256 a^{2} c^{4} - 448 a b^{2} c^{3} - 112 b^{4} c^{2}\right) + x \left(- 256 a^{2} b c^{3} - 64 a b^{3} c^{2} - 16 b^{5} c\right)}{1024 b^{8} c^{4} d^{9} + 16384 b^{7} c^{5} d^{9} x + 114688 b^{6} c^{6} d^{9} x^{2} + 458752 b^{5} c^{7} d^{9} x^{3} + 1146880 b^{4} c^{8} d^{9} x^{4} + 1835008 b^{3} c^{9} d^{9} x^{5} + 1835008 b^{2} c^{10} d^{9} x^{6} + 1048576 b c^{11} d^{9} x^{7} + 262144 c^{12} d^{9} x^{8}}"," ",0,"(-64*a**3*c**3 - 16*a**2*b**2*c**2 - 4*a*b**4*c - b**6 - 768*b*c**5*x**5 - 256*c**6*x**6 + x**4*(-384*a*c**5 - 864*b**2*c**4) + x**3*(-768*a*b*c**4 - 448*b**3*c**3) + x**2*(-256*a**2*c**4 - 448*a*b**2*c**3 - 112*b**4*c**2) + x*(-256*a**2*b*c**3 - 64*a*b**3*c**2 - 16*b**5*c))/(1024*b**8*c**4*d**9 + 16384*b**7*c**5*d**9*x + 114688*b**6*c**6*d**9*x**2 + 458752*b**5*c**7*d**9*x**3 + 1146880*b**4*c**8*d**9*x**4 + 1835008*b**3*c**9*d**9*x**5 + 1835008*b**2*c**10*d**9*x**6 + 1048576*b*c**11*d**9*x**7 + 262144*c**12*d**9*x**8)","B",0
1151,1,298,0,7.009254," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**10,x)","\frac{- 140 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} - 6 a b^{4} c - b^{6} - 1260 b c^{5} x^{5} - 420 c^{6} x^{6} + x^{4} \left(- 756 a c^{5} - 1386 b^{2} c^{4}\right) + x^{3} \left(- 1512 a b c^{4} - 672 b^{3} c^{3}\right) + x^{2} \left(- 540 a^{2} c^{4} - 864 a b^{2} c^{3} - 144 b^{4} c^{2}\right) + x \left(- 540 a^{2} b c^{3} - 108 a b^{3} c^{2} - 18 b^{5} c\right)}{2520 b^{9} c^{4} d^{10} + 45360 b^{8} c^{5} d^{10} x + 362880 b^{7} c^{6} d^{10} x^{2} + 1693440 b^{6} c^{7} d^{10} x^{3} + 5080320 b^{5} c^{8} d^{10} x^{4} + 10160640 b^{4} c^{9} d^{10} x^{5} + 13547520 b^{3} c^{10} d^{10} x^{6} + 11612160 b^{2} c^{11} d^{10} x^{7} + 5806080 b c^{12} d^{10} x^{8} + 1290240 c^{13} d^{10} x^{9}}"," ",0,"(-140*a**3*c**3 - 30*a**2*b**2*c**2 - 6*a*b**4*c - b**6 - 1260*b*c**5*x**5 - 420*c**6*x**6 + x**4*(-756*a*c**5 - 1386*b**2*c**4) + x**3*(-1512*a*b*c**4 - 672*b**3*c**3) + x**2*(-540*a**2*c**4 - 864*a*b**2*c**3 - 144*b**4*c**2) + x*(-540*a**2*b*c**3 - 108*a*b**3*c**2 - 18*b**5*c))/(2520*b**9*c**4*d**10 + 45360*b**8*c**5*d**10*x + 362880*b**7*c**6*d**10*x**2 + 1693440*b**6*c**7*d**10*x**3 + 5080320*b**5*c**8*d**10*x**4 + 10160640*b**4*c**9*d**10*x**5 + 13547520*b**3*c**10*d**10*x**6 + 11612160*b**2*c**11*d**10*x**7 + 5806080*b*c**12*d**10*x**8 + 1290240*c**13*d**10*x**9)","B",0
1152,1,313,0,18.287013," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**11,x)","\frac{- 256 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} - 8 a b^{4} c - b^{6} - 1920 b c^{5} x^{5} - 640 c^{6} x^{6} + x^{4} \left(- 1280 a c^{5} - 2080 b^{2} c^{4}\right) + x^{3} \left(- 2560 a b c^{4} - 960 b^{3} c^{3}\right) + x^{2} \left(- 960 a^{2} c^{4} - 1440 a b^{2} c^{3} - 180 b^{4} c^{2}\right) + x \left(- 960 a^{2} b c^{3} - 160 a b^{3} c^{2} - 20 b^{5} c\right)}{5120 b^{10} c^{4} d^{11} + 102400 b^{9} c^{5} d^{11} x + 921600 b^{8} c^{6} d^{11} x^{2} + 4915200 b^{7} c^{7} d^{11} x^{3} + 17203200 b^{6} c^{8} d^{11} x^{4} + 41287680 b^{5} c^{9} d^{11} x^{5} + 68812800 b^{4} c^{10} d^{11} x^{6} + 78643200 b^{3} c^{11} d^{11} x^{7} + 58982400 b^{2} c^{12} d^{11} x^{8} + 26214400 b c^{13} d^{11} x^{9} + 5242880 c^{14} d^{11} x^{10}}"," ",0,"(-256*a**3*c**3 - 48*a**2*b**2*c**2 - 8*a*b**4*c - b**6 - 1920*b*c**5*x**5 - 640*c**6*x**6 + x**4*(-1280*a*c**5 - 2080*b**2*c**4) + x**3*(-2560*a*b*c**4 - 960*b**3*c**3) + x**2*(-960*a**2*c**4 - 1440*a*b**2*c**3 - 180*b**4*c**2) + x*(-960*a**2*b*c**3 - 160*a*b**3*c**2 - 20*b**5*c))/(5120*b**10*c**4*d**11 + 102400*b**9*c**5*d**11*x + 921600*b**8*c**6*d**11*x**2 + 4915200*b**7*c**7*d**11*x**3 + 17203200*b**6*c**8*d**11*x**4 + 41287680*b**5*c**9*d**11*x**5 + 68812800*b**4*c**10*d**11*x**6 + 78643200*b**3*c**11*d**11*x**7 + 58982400*b**2*c**12*d**11*x**8 + 26214400*b*c**13*d**11*x**9 + 5242880*c**14*d**11*x**10)","B",0
1153,1,328,0,10.003953," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**12,x)","\frac{- 420 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} - 10 a b^{4} c - b^{6} - 2772 b c^{5} x^{5} - 924 c^{6} x^{6} + x^{4} \left(- 1980 a c^{5} - 2970 b^{2} c^{4}\right) + x^{3} \left(- 3960 a b c^{4} - 1320 b^{3} c^{3}\right) + x^{2} \left(- 1540 a^{2} c^{4} - 2200 a b^{2} c^{3} - 220 b^{4} c^{2}\right) + x \left(- 1540 a^{2} b c^{3} - 220 a b^{3} c^{2} - 22 b^{5} c\right)}{9240 b^{11} c^{4} d^{12} + 203280 b^{10} c^{5} d^{12} x + 2032800 b^{9} c^{6} d^{12} x^{2} + 12196800 b^{8} c^{7} d^{12} x^{3} + 48787200 b^{7} c^{8} d^{12} x^{4} + 136604160 b^{6} c^{9} d^{12} x^{5} + 273208320 b^{5} c^{10} d^{12} x^{6} + 390297600 b^{4} c^{11} d^{12} x^{7} + 390297600 b^{3} c^{12} d^{12} x^{8} + 260198400 b^{2} c^{13} d^{12} x^{9} + 104079360 b c^{14} d^{12} x^{10} + 18923520 c^{15} d^{12} x^{11}}"," ",0,"(-420*a**3*c**3 - 70*a**2*b**2*c**2 - 10*a*b**4*c - b**6 - 2772*b*c**5*x**5 - 924*c**6*x**6 + x**4*(-1980*a*c**5 - 2970*b**2*c**4) + x**3*(-3960*a*b*c**4 - 1320*b**3*c**3) + x**2*(-1540*a**2*c**4 - 2200*a*b**2*c**3 - 220*b**4*c**2) + x*(-1540*a**2*b*c**3 - 220*a*b**3*c**2 - 22*b**5*c))/(9240*b**11*c**4*d**12 + 203280*b**10*c**5*d**12*x + 2032800*b**9*c**6*d**12*x**2 + 12196800*b**8*c**7*d**12*x**3 + 48787200*b**7*c**8*d**12*x**4 + 136604160*b**6*c**9*d**12*x**5 + 273208320*b**5*c**10*d**12*x**6 + 390297600*b**4*c**11*d**12*x**7 + 390297600*b**3*c**12*d**12*x**8 + 260198400*b**2*c**13*d**12*x**9 + 104079360*b*c**14*d**12*x**10 + 18923520*c**15*d**12*x**11)","B",0
1154,1,502,0,1.047541," ","integrate((2*c*d*x+b*d)**8/(c*x**2+b*x+a),x)","128 b c^{6} d^{8} x^{6} + \frac{256 c^{7} d^{8} x^{7}}{7} - d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{7}} \log{\left(x + \frac{64 a^{3} b c^{3} d^{8} - 48 a^{2} b^{3} c^{2} d^{8} + 12 a b^{5} c d^{8} - b^{7} d^{8} - d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{7}}}{128 a^{3} c^{4} d^{8} - 96 a^{2} b^{2} c^{3} d^{8} + 24 a b^{4} c^{2} d^{8} - 2 b^{6} c d^{8}} \right)} + d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{7}} \log{\left(x + \frac{64 a^{3} b c^{3} d^{8} - 48 a^{2} b^{3} c^{2} d^{8} + 12 a b^{5} c d^{8} - b^{7} d^{8} + d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{7}}}{128 a^{3} c^{4} d^{8} - 96 a^{2} b^{2} c^{3} d^{8} + 24 a b^{4} c^{2} d^{8} - 2 b^{6} c d^{8}} \right)} + x^{5} \left(- \frac{256 a c^{6} d^{8}}{5} + \frac{1024 b^{2} c^{5} d^{8}}{5}\right) + x^{4} \left(- 128 a b c^{5} d^{8} + 192 b^{3} c^{4} d^{8}\right) + x^{3} \left(\frac{256 a^{2} c^{5} d^{8}}{3} - \frac{512 a b^{2} c^{4} d^{8}}{3} + \frac{352 b^{4} c^{3} d^{8}}{3}\right) + x^{2} \left(128 a^{2} b c^{4} d^{8} - 128 a b^{3} c^{3} d^{8} + 48 b^{5} c^{2} d^{8}\right) + x \left(- 256 a^{3} c^{4} d^{8} + 256 a^{2} b^{2} c^{3} d^{8} - 96 a b^{4} c^{2} d^{8} + 16 b^{6} c d^{8}\right)"," ",0,"128*b*c**6*d**8*x**6 + 256*c**7*d**8*x**7/7 - d**8*sqrt(-(4*a*c - b**2)**7)*log(x + (64*a**3*b*c**3*d**8 - 48*a**2*b**3*c**2*d**8 + 12*a*b**5*c*d**8 - b**7*d**8 - d**8*sqrt(-(4*a*c - b**2)**7))/(128*a**3*c**4*d**8 - 96*a**2*b**2*c**3*d**8 + 24*a*b**4*c**2*d**8 - 2*b**6*c*d**8)) + d**8*sqrt(-(4*a*c - b**2)**7)*log(x + (64*a**3*b*c**3*d**8 - 48*a**2*b**3*c**2*d**8 + 12*a*b**5*c*d**8 - b**7*d**8 + d**8*sqrt(-(4*a*c - b**2)**7))/(128*a**3*c**4*d**8 - 96*a**2*b**2*c**3*d**8 + 24*a*b**4*c**2*d**8 - 2*b**6*c*d**8)) + x**5*(-256*a*c**6*d**8/5 + 1024*b**2*c**5*d**8/5) + x**4*(-128*a*b*c**5*d**8 + 192*b**3*c**4*d**8) + x**3*(256*a**2*c**5*d**8/3 - 512*a*b**2*c**4*d**8/3 + 352*b**4*c**3*d**8/3) + x**2*(128*a**2*b*c**4*d**8 - 128*a*b**3*c**3*d**8 + 48*b**5*c**2*d**8) + x*(-256*a**3*c**4*d**8 + 256*a**2*b**2*c**3*d**8 - 96*a*b**4*c**2*d**8 + 16*b**6*c*d**8)","B",0
1155,1,185,0,0.931600," ","integrate((2*c*d*x+b*d)**7/(c*x**2+b*x+a),x)","64 b c^{5} d^{7} x^{5} + \frac{64 c^{6} d^{7} x^{6}}{3} - d^{7} \left(4 a c - b^{2}\right)^{3} \log{\left(a + b x + c x^{2} \right)} + x^{4} \left(- 32 a c^{5} d^{7} + 88 b^{2} c^{4} d^{7}\right) + x^{3} \left(- 64 a b c^{4} d^{7} + \frac{208 b^{3} c^{3} d^{7}}{3}\right) + x^{2} \left(64 a^{2} c^{4} d^{7} - 80 a b^{2} c^{3} d^{7} + 36 b^{4} c^{2} d^{7}\right) + x \left(64 a^{2} b c^{3} d^{7} - 48 a b^{3} c^{2} d^{7} + 12 b^{5} c d^{7}\right)"," ",0,"64*b*c**5*d**7*x**5 + 64*c**6*d**7*x**6/3 - d**7*(4*a*c - b**2)**3*log(a + b*x + c*x**2) + x**4*(-32*a*c**5*d**7 + 88*b**2*c**4*d**7) + x**3*(-64*a*b*c**4*d**7 + 208*b**3*c**3*d**7/3) + x**2*(64*a**2*c**4*d**7 - 80*a*b**2*c**3*d**7 + 36*b**4*c**2*d**7) + x*(64*a**2*b*c**3*d**7 - 48*a*b**3*c**2*d**7 + 12*b**5*c*d**7)","B",0
1156,1,337,0,0.765993," ","integrate((2*c*d*x+b*d)**6/(c*x**2+b*x+a),x)","32 b c^{4} d^{6} x^{4} + \frac{64 c^{5} d^{6} x^{5}}{5} + d^{6} \sqrt{- \left(4 a c - b^{2}\right)^{5}} \log{\left(x + \frac{16 a^{2} b c^{2} d^{6} - 8 a b^{3} c d^{6} + b^{5} d^{6} - d^{6} \sqrt{- \left(4 a c - b^{2}\right)^{5}}}{32 a^{2} c^{3} d^{6} - 16 a b^{2} c^{2} d^{6} + 2 b^{4} c d^{6}} \right)} - d^{6} \sqrt{- \left(4 a c - b^{2}\right)^{5}} \log{\left(x + \frac{16 a^{2} b c^{2} d^{6} - 8 a b^{3} c d^{6} + b^{5} d^{6} + d^{6} \sqrt{- \left(4 a c - b^{2}\right)^{5}}}{32 a^{2} c^{3} d^{6} - 16 a b^{2} c^{2} d^{6} + 2 b^{4} c d^{6}} \right)} + x^{3} \left(- \frac{64 a c^{4} d^{6}}{3} + \frac{112 b^{2} c^{3} d^{6}}{3}\right) + x^{2} \left(- 32 a b c^{3} d^{6} + 24 b^{3} c^{2} d^{6}\right) + x \left(64 a^{2} c^{3} d^{6} - 48 a b^{2} c^{2} d^{6} + 12 b^{4} c d^{6}\right)"," ",0,"32*b*c**4*d**6*x**4 + 64*c**5*d**6*x**5/5 + d**6*sqrt(-(4*a*c - b**2)**5)*log(x + (16*a**2*b*c**2*d**6 - 8*a*b**3*c*d**6 + b**5*d**6 - d**6*sqrt(-(4*a*c - b**2)**5))/(32*a**2*c**3*d**6 - 16*a*b**2*c**2*d**6 + 2*b**4*c*d**6)) - d**6*sqrt(-(4*a*c - b**2)**5)*log(x + (16*a**2*b*c**2*d**6 - 8*a*b**3*c*d**6 + b**5*d**6 + d**6*sqrt(-(4*a*c - b**2)**5))/(32*a**2*c**3*d**6 - 16*a*b**2*c**2*d**6 + 2*b**4*c*d**6)) + x**3*(-64*a*c**4*d**6/3 + 112*b**2*c**3*d**6/3) + x**2*(-32*a*b*c**3*d**6 + 24*b**3*c**2*d**6) + x*(64*a**2*c**3*d**6 - 48*a*b**2*c**2*d**6 + 12*b**4*c*d**6)","B",0
1157,1,99,0,0.645154," ","integrate((2*c*d*x+b*d)**5/(c*x**2+b*x+a),x)","16 b c^{3} d^{5} x^{3} + 8 c^{4} d^{5} x^{4} + d^{5} \left(4 a c - b^{2}\right)^{2} \log{\left(a + b x + c x^{2} \right)} + x^{2} \left(- 16 a c^{3} d^{5} + 16 b^{2} c^{2} d^{5}\right) + x \left(- 16 a b c^{2} d^{5} + 8 b^{3} c d^{5}\right)"," ",0,"16*b*c**3*d**5*x**3 + 8*c**4*d**5*x**4 + d**5*(4*a*c - b**2)**2*log(a + b*x + c*x**2) + x**2*(-16*a*c**3*d**5 + 16*b**2*c**2*d**5) + x*(-16*a*b*c**2*d**5 + 8*b**3*c*d**5)","A",0
1158,1,204,0,0.517970," ","integrate((2*c*d*x+b*d)**4/(c*x**2+b*x+a),x)","8 b c^{2} d^{4} x^{2} + \frac{16 c^{3} d^{4} x^{3}}{3} - d^{4} \sqrt{- \left(4 a c - b^{2}\right)^{3}} \log{\left(x + \frac{4 a b c d^{4} - b^{3} d^{4} - d^{4} \sqrt{- \left(4 a c - b^{2}\right)^{3}}}{8 a c^{2} d^{4} - 2 b^{2} c d^{4}} \right)} + d^{4} \sqrt{- \left(4 a c - b^{2}\right)^{3}} \log{\left(x + \frac{4 a b c d^{4} - b^{3} d^{4} + d^{4} \sqrt{- \left(4 a c - b^{2}\right)^{3}}}{8 a c^{2} d^{4} - 2 b^{2} c d^{4}} \right)} + x \left(- 16 a c^{2} d^{4} + 8 b^{2} c d^{4}\right)"," ",0,"8*b*c**2*d**4*x**2 + 16*c**3*d**4*x**3/3 - d**4*sqrt(-(4*a*c - b**2)**3)*log(x + (4*a*b*c*d**4 - b**3*d**4 - d**4*sqrt(-(4*a*c - b**2)**3))/(8*a*c**2*d**4 - 2*b**2*c*d**4)) + d**4*sqrt(-(4*a*c - b**2)**3)*log(x + (4*a*b*c*d**4 - b**3*d**4 + d**4*sqrt(-(4*a*c - b**2)**3))/(8*a*c**2*d**4 - 2*b**2*c*d**4)) + x*(-16*a*c**2*d**4 + 8*b**2*c*d**4)","B",0
1159,1,44,0,0.413240," ","integrate((2*c*d*x+b*d)**3/(c*x**2+b*x+a),x)","4 b c d^{3} x + 4 c^{2} d^{3} x^{2} - d^{3} \left(4 a c - b^{2}\right) \log{\left(a + b x + c x^{2} \right)}"," ",0,"4*b*c*d**3*x + 4*c**2*d**3*x**2 - d**3*(4*a*c - b**2)*log(a + b*x + c*x**2)","A",0
1160,1,99,0,0.326157," ","integrate((2*c*d*x+b*d)**2/(c*x**2+b*x+a),x)","4 c d^{2} x + d^{2} \sqrt{- 4 a c + b^{2}} \log{\left(x + \frac{b d^{2} - d^{2} \sqrt{- 4 a c + b^{2}}}{2 c d^{2}} \right)} - d^{2} \sqrt{- 4 a c + b^{2}} \log{\left(x + \frac{b d^{2} + d^{2} \sqrt{- 4 a c + b^{2}}}{2 c d^{2}} \right)}"," ",0,"4*c*d**2*x + d**2*sqrt(-4*a*c + b**2)*log(x + (b*d**2 - d**2*sqrt(-4*a*c + b**2))/(2*c*d**2)) - d**2*sqrt(-4*a*c + b**2)*log(x + (b*d**2 + d**2*sqrt(-4*a*c + b**2))/(2*c*d**2))","B",0
1161,1,12,0,0.196631," ","integrate((2*c*d*x+b*d)/(c*x**2+b*x+a),x)","d \log{\left(a + b x + c x^{2} \right)}"," ",0,"d*log(a + b*x + c*x**2)","A",0
1162,1,42,0,0.752439," ","integrate(1/(2*c*d*x+b*d)/(c*x**2+b*x+a),x)","\frac{2 \log{\left(\frac{b}{2 c} + x \right)}}{d \left(4 a c - b^{2}\right)} - \frac{\log{\left(\frac{a}{c} + \frac{b x}{c} + x^{2} \right)}}{d \left(4 a c - b^{2}\right)}"," ",0,"2*log(b/(2*c) + x)/(d*(4*a*c - b**2)) - log(a/c + b*x/c + x**2)/(d*(4*a*c - b**2))","A",0
1163,1,240,0,0.886686," ","integrate(1/(2*c*d*x+b*d)**2/(c*x**2+b*x+a),x)","- \frac{2}{4 a b c d^{2} - b^{3} d^{2} + x \left(8 a c^{2} d^{2} - 2 b^{2} c d^{2}\right)} + \frac{\sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{- 16 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 8 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b}{2 c} \right)}}{d^{2}} - \frac{\sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{16 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 8 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b}{2 c} \right)}}{d^{2}}"," ",0,"-2/(4*a*b*c*d**2 - b**3*d**2 + x*(8*a*c**2*d**2 - 2*b**2*c*d**2)) + sqrt(-1/(4*a*c - b**2)**3)*log(x + (-16*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3) + 8*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3) - b**4*sqrt(-1/(4*a*c - b**2)**3) + b)/(2*c))/d**2 - sqrt(-1/(4*a*c - b**2)**3)*log(x + (16*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3) - 8*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3) + b**4*sqrt(-1/(4*a*c - b**2)**3) + b)/(2*c))/d**2","B",0
1164,1,119,0,1.668745," ","integrate(1/(2*c*d*x+b*d)**3/(c*x**2+b*x+a),x)","- \frac{1}{4 a b^{2} c d^{3} - b^{4} d^{3} + x^{2} \left(16 a c^{3} d^{3} - 4 b^{2} c^{2} d^{3}\right) + x \left(16 a b c^{2} d^{3} - 4 b^{3} c d^{3}\right)} - \frac{2 \log{\left(\frac{b}{2 c} + x \right)}}{d^{3} \left(4 a c - b^{2}\right)^{2}} + \frac{\log{\left(\frac{a}{c} + \frac{b x}{c} + x^{2} \right)}}{d^{3} \left(4 a c - b^{2}\right)^{2}}"," ",0,"-1/(4*a*b**2*c*d**3 - b**4*d**3 + x**2*(16*a*c**3*d**3 - 4*b**2*c**2*d**3) + x*(16*a*b*c**2*d**3 - 4*b**3*c*d**3)) - 2*log(b/(2*c) + x)/(d**3*(4*a*c - b**2)**2) + log(a/c + b*x/c + x**2)/(d**3*(4*a*c - b**2)**2)","A",0
1165,1,442,0,1.739042," ","integrate(1/(2*c*d*x+b*d)**4/(c*x**2+b*x+a),x)","\frac{- 8 a c + 8 b^{2} + 24 b c x + 24 c^{2} x^{2}}{48 a^{2} b^{3} c^{2} d^{4} - 24 a b^{5} c d^{4} + 3 b^{7} d^{4} + x^{3} \left(384 a^{2} c^{5} d^{4} - 192 a b^{2} c^{4} d^{4} + 24 b^{4} c^{3} d^{4}\right) + x^{2} \left(576 a^{2} b c^{4} d^{4} - 288 a b^{3} c^{3} d^{4} + 36 b^{5} c^{2} d^{4}\right) + x \left(288 a^{2} b^{2} c^{3} d^{4} - 144 a b^{4} c^{2} d^{4} + 18 b^{6} c d^{4}\right)} - \frac{\sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{- 64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + b}{2 c} \right)}}{d^{4}} + \frac{\sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + b}{2 c} \right)}}{d^{4}}"," ",0,"(-8*a*c + 8*b**2 + 24*b*c*x + 24*c**2*x**2)/(48*a**2*b**3*c**2*d**4 - 24*a*b**5*c*d**4 + 3*b**7*d**4 + x**3*(384*a**2*c**5*d**4 - 192*a*b**2*c**4*d**4 + 24*b**4*c**3*d**4) + x**2*(576*a**2*b*c**4*d**4 - 288*a*b**3*c**3*d**4 + 36*b**5*c**2*d**4) + x*(288*a**2*b**2*c**3*d**4 - 144*a*b**4*c**2*d**4 + 18*b**6*c*d**4)) - sqrt(-1/(4*a*c - b**2)**5)*log(x + (-64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5) + 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5) - 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5) + b**6*sqrt(-1/(4*a*c - b**2)**5) + b)/(2*c))/d**4 + sqrt(-1/(4*a*c - b**2)**5)*log(x + (64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5) - 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5) + 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5) - b**6*sqrt(-1/(4*a*c - b**2)**5) + b)/(2*c))/d**4","B",0
1166,1,476,0,2.340914," ","integrate((2*c*d*x+b*d)**8/(c*x**2+b*x+a)**2,x)","128 b c^{5} d^{8} x^{4} + \frac{256 c^{6} d^{8} x^{5}}{5} + 14 c d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{5}} \log{\left(x + \frac{224 a^{2} b c^{3} d^{8} - 112 a b^{3} c^{2} d^{8} + 14 b^{5} c d^{8} - 14 c d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{5}}}{448 a^{2} c^{4} d^{8} - 224 a b^{2} c^{3} d^{8} + 28 b^{4} c^{2} d^{8}} \right)} - 14 c d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{5}} \log{\left(x + \frac{224 a^{2} b c^{3} d^{8} - 112 a b^{3} c^{2} d^{8} + 14 b^{5} c d^{8} + 14 c d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{5}}}{448 a^{2} c^{4} d^{8} - 224 a b^{2} c^{3} d^{8} + 28 b^{4} c^{2} d^{8}} \right)} + x^{3} \left(- \frac{512 a c^{5} d^{8}}{3} + \frac{512 b^{2} c^{4} d^{8}}{3}\right) + x^{2} \left(- 256 a b c^{4} d^{8} + 128 b^{3} c^{3} d^{8}\right) + x \left(768 a^{2} c^{4} d^{8} - 512 a b^{2} c^{3} d^{8} + 96 b^{4} c^{2} d^{8}\right) + \frac{64 a^{3} b c^{3} d^{8} - 48 a^{2} b^{3} c^{2} d^{8} + 12 a b^{5} c d^{8} - b^{7} d^{8} + x \left(128 a^{3} c^{4} d^{8} - 96 a^{2} b^{2} c^{3} d^{8} + 24 a b^{4} c^{2} d^{8} - 2 b^{6} c d^{8}\right)}{a + b x + c x^{2}}"," ",0,"128*b*c**5*d**8*x**4 + 256*c**6*d**8*x**5/5 + 14*c*d**8*sqrt(-(4*a*c - b**2)**5)*log(x + (224*a**2*b*c**3*d**8 - 112*a*b**3*c**2*d**8 + 14*b**5*c*d**8 - 14*c*d**8*sqrt(-(4*a*c - b**2)**5))/(448*a**2*c**4*d**8 - 224*a*b**2*c**3*d**8 + 28*b**4*c**2*d**8)) - 14*c*d**8*sqrt(-(4*a*c - b**2)**5)*log(x + (224*a**2*b*c**3*d**8 - 112*a*b**3*c**2*d**8 + 14*b**5*c*d**8 + 14*c*d**8*sqrt(-(4*a*c - b**2)**5))/(448*a**2*c**4*d**8 - 224*a*b**2*c**3*d**8 + 28*b**4*c**2*d**8)) + x**3*(-512*a*c**5*d**8/3 + 512*b**2*c**4*d**8/3) + x**2*(-256*a*b*c**4*d**8 + 128*b**3*c**3*d**8) + x*(768*a**2*c**4*d**8 - 512*a*b**2*c**3*d**8 + 96*b**4*c**2*d**8) + (64*a**3*b*c**3*d**8 - 48*a**2*b**3*c**2*d**8 + 12*a*b**5*c*d**8 - b**7*d**8 + x*(128*a**3*c**4*d**8 - 96*a**2*b**2*c**3*d**8 + 24*a*b**4*c**2*d**8 - 2*b**6*c*d**8))/(a + b*x + c*x**2)","B",0
1167,1,160,0,2.566568," ","integrate((2*c*d*x+b*d)**7/(c*x**2+b*x+a)**2,x)","64 b c^{4} d^{7} x^{3} + 32 c^{5} d^{7} x^{4} + 12 c d^{7} \left(4 a c - b^{2}\right)^{2} \log{\left(a + b x + c x^{2} \right)} + x^{2} \left(- 128 a c^{4} d^{7} + 80 b^{2} c^{3} d^{7}\right) + x \left(- 128 a b c^{3} d^{7} + 48 b^{3} c^{2} d^{7}\right) + \frac{64 a^{3} c^{3} d^{7} - 48 a^{2} b^{2} c^{2} d^{7} + 12 a b^{4} c d^{7} - b^{6} d^{7}}{a + b x + c x^{2}}"," ",0,"64*b*c**4*d**7*x**3 + 32*c**5*d**7*x**4 + 12*c*d**7*(4*a*c - b**2)**2*log(a + b*x + c*x**2) + x**2*(-128*a*c**4*d**7 + 80*b**2*c**3*d**7) + x*(-128*a*b*c**3*d**7 + 48*b**3*c**2*d**7) + (64*a**3*c**3*d**7 - 48*a**2*b**2*c**2*d**7 + 12*a*b**4*c*d**7 - b**6*d**7)/(a + b*x + c*x**2)","A",0
1168,1,313,0,1.640851," ","integrate((2*c*d*x+b*d)**6/(c*x**2+b*x+a)**2,x)","32 b c^{3} d^{6} x^{2} + \frac{64 c^{4} d^{6} x^{3}}{3} - 10 c d^{6} \sqrt{- \left(4 a c - b^{2}\right)^{3}} \log{\left(x + \frac{40 a b c^{2} d^{6} - 10 b^{3} c d^{6} - 10 c d^{6} \sqrt{- \left(4 a c - b^{2}\right)^{3}}}{80 a c^{3} d^{6} - 20 b^{2} c^{2} d^{6}} \right)} + 10 c d^{6} \sqrt{- \left(4 a c - b^{2}\right)^{3}} \log{\left(x + \frac{40 a b c^{2} d^{6} - 10 b^{3} c d^{6} + 10 c d^{6} \sqrt{- \left(4 a c - b^{2}\right)^{3}}}{80 a c^{3} d^{6} - 20 b^{2} c^{2} d^{6}} \right)} + x \left(- 128 a c^{3} d^{6} + 48 b^{2} c^{2} d^{6}\right) + \frac{- 16 a^{2} b c^{2} d^{6} + 8 a b^{3} c d^{6} - b^{5} d^{6} + x \left(- 32 a^{2} c^{3} d^{6} + 16 a b^{2} c^{2} d^{6} - 2 b^{4} c d^{6}\right)}{a + b x + c x^{2}}"," ",0,"32*b*c**3*d**6*x**2 + 64*c**4*d**6*x**3/3 - 10*c*d**6*sqrt(-(4*a*c - b**2)**3)*log(x + (40*a*b*c**2*d**6 - 10*b**3*c*d**6 - 10*c*d**6*sqrt(-(4*a*c - b**2)**3))/(80*a*c**3*d**6 - 20*b**2*c**2*d**6)) + 10*c*d**6*sqrt(-(4*a*c - b**2)**3)*log(x + (40*a*b*c**2*d**6 - 10*b**3*c*d**6 + 10*c*d**6*sqrt(-(4*a*c - b**2)**3))/(80*a*c**3*d**6 - 20*b**2*c**2*d**6)) + x*(-128*a*c**3*d**6 + 48*b**2*c**2*d**6) + (-16*a**2*b*c**2*d**6 + 8*a*b**3*c*d**6 - b**5*d**6 + x*(-32*a**2*c**3*d**6 + 16*a*b**2*c**2*d**6 - 2*b**4*c*d**6))/(a + b*x + c*x**2)","B",0
1169,1,90,0,1.643861," ","integrate((2*c*d*x+b*d)**5/(c*x**2+b*x+a)**2,x)","16 b c^{2} d^{5} x + 16 c^{3} d^{5} x^{2} - 8 c d^{5} \left(4 a c - b^{2}\right) \log{\left(a + b x + c x^{2} \right)} + \frac{- 16 a^{2} c^{2} d^{5} + 8 a b^{2} c d^{5} - b^{4} d^{5}}{a + b x + c x^{2}}"," ",0,"16*b*c**2*d**5*x + 16*c**3*d**5*x**2 - 8*c*d**5*(4*a*c - b**2)*log(a + b*x + c*x**2) + (-16*a**2*c**2*d**5 + 8*a*b**2*c*d**5 - b**4*d**5)/(a + b*x + c*x**2)","A",0
1170,1,173,0,1.087861," ","integrate((2*c*d*x+b*d)**4/(c*x**2+b*x+a)**2,x)","16 c^{2} d^{4} x + c d^{4} \sqrt{- 144 a c + 36 b^{2}} \log{\left(x + \frac{6 b c d^{4} - c d^{4} \sqrt{- 144 a c + 36 b^{2}}}{12 c^{2} d^{4}} \right)} - c d^{4} \sqrt{- 144 a c + 36 b^{2}} \log{\left(x + \frac{6 b c d^{4} + c d^{4} \sqrt{- 144 a c + 36 b^{2}}}{12 c^{2} d^{4}} \right)} + \frac{4 a b c d^{4} - b^{3} d^{4} + x \left(8 a c^{2} d^{4} - 2 b^{2} c d^{4}\right)}{a + b x + c x^{2}}"," ",0,"16*c**2*d**4*x + c*d**4*sqrt(-144*a*c + 36*b**2)*log(x + (6*b*c*d**4 - c*d**4*sqrt(-144*a*c + 36*b**2))/(12*c**2*d**4)) - c*d**4*sqrt(-144*a*c + 36*b**2)*log(x + (6*b*c*d**4 + c*d**4*sqrt(-144*a*c + 36*b**2))/(12*c**2*d**4)) + (4*a*b*c*d**4 - b**3*d**4 + x*(8*a*c**2*d**4 - 2*b**2*c*d**4))/(a + b*x + c*x**2)","B",0
1171,1,42,0,0.888351," ","integrate((2*c*d*x+b*d)**3/(c*x**2+b*x+a)**2,x)","4 c d^{3} \log{\left(a + b x + c x^{2} \right)} + \frac{4 a c d^{3} - b^{2} d^{3}}{a + b x + c x^{2}}"," ",0,"4*c*d**3*log(a + b*x + c*x**2) + (4*a*c*d**3 - b**2*d**3)/(a + b*x + c*x**2)","A",0
1172,1,211,0,0.646958," ","integrate((2*c*d*x+b*d)**2/(c*x**2+b*x+a)**2,x)","- 2 c d^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{- 8 a c^{2} d^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + 2 b^{2} c d^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + 2 b c d^{2}}{4 c^{2} d^{2}} \right)} + 2 c d^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{8 a c^{2} d^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} - 2 b^{2} c d^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + 2 b c d^{2}}{4 c^{2} d^{2}} \right)} + \frac{- b d^{2} - 2 c d^{2} x}{a + b x + c x^{2}}"," ",0,"-2*c*d**2*sqrt(-1/(4*a*c - b**2))*log(x + (-8*a*c**2*d**2*sqrt(-1/(4*a*c - b**2)) + 2*b**2*c*d**2*sqrt(-1/(4*a*c - b**2)) + 2*b*c*d**2)/(4*c**2*d**2)) + 2*c*d**2*sqrt(-1/(4*a*c - b**2))*log(x + (8*a*c**2*d**2*sqrt(-1/(4*a*c - b**2)) - 2*b**2*c*d**2*sqrt(-1/(4*a*c - b**2)) + 2*b*c*d**2)/(4*c**2*d**2)) + (-b*d**2 - 2*c*d**2*x)/(a + b*x + c*x**2)","B",0
1173,1,12,0,0.409041," ","integrate((2*c*d*x+b*d)/(c*x**2+b*x+a)**2,x)","- \frac{d}{a + b x + c x^{2}}"," ",0,"-d/(a + b*x + c*x**2)","A",0
1174,1,102,0,1.632765," ","integrate(1/(2*c*d*x+b*d)/(c*x**2+b*x+a)**2,x)","\frac{8 c \log{\left(\frac{b}{2 c} + x \right)}}{d \left(4 a c - b^{2}\right)^{2}} - \frac{4 c \log{\left(\frac{a}{c} + \frac{b x}{c} + x^{2} \right)}}{d \left(4 a c - b^{2}\right)^{2}} + \frac{1}{4 a^{2} c d - a b^{2} d + x^{2} \left(4 a c^{2} d - b^{2} c d\right) + x \left(4 a b c d - b^{3} d\right)}"," ",0,"8*c*log(b/(2*c) + x)/(d*(4*a*c - b**2)**2) - 4*c*log(a/c + b*x/c + x**2)/(d*(4*a*c - b**2)**2) + 1/(4*a**2*c*d - a*b**2*d + x**2*(4*a*c**2*d - b**2*c*d) + x*(4*a*b*c*d - b**3*d))","A",0
1175,1,459,0,1.888619," ","integrate(1/(2*c*d*x+b*d)**2/(c*x**2+b*x+a)**2,x)","\frac{6 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{- 384 a^{3} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 288 a^{2} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 72 a b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 b c}{12 c^{2}} \right)}}{d^{2}} - \frac{6 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{384 a^{3} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 288 a^{2} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 72 a b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 6 b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 b c}{12 c^{2}} \right)}}{d^{2}} + \frac{- 8 a c - b^{2} - 12 b c x - 12 c^{2} x^{2}}{16 a^{3} b c^{2} d^{2} - 8 a^{2} b^{3} c d^{2} + a b^{5} d^{2} + x^{3} \left(32 a^{2} c^{4} d^{2} - 16 a b^{2} c^{3} d^{2} + 2 b^{4} c^{2} d^{2}\right) + x^{2} \left(48 a^{2} b c^{3} d^{2} - 24 a b^{3} c^{2} d^{2} + 3 b^{5} c d^{2}\right) + x \left(32 a^{3} c^{3} d^{2} - 6 a b^{4} c d^{2} + b^{6} d^{2}\right)}"," ",0,"6*c*sqrt(-1/(4*a*c - b**2)**5)*log(x + (-384*a**3*c**4*sqrt(-1/(4*a*c - b**2)**5) + 288*a**2*b**2*c**3*sqrt(-1/(4*a*c - b**2)**5) - 72*a*b**4*c**2*sqrt(-1/(4*a*c - b**2)**5) + 6*b**6*c*sqrt(-1/(4*a*c - b**2)**5) + 6*b*c)/(12*c**2))/d**2 - 6*c*sqrt(-1/(4*a*c - b**2)**5)*log(x + (384*a**3*c**4*sqrt(-1/(4*a*c - b**2)**5) - 288*a**2*b**2*c**3*sqrt(-1/(4*a*c - b**2)**5) + 72*a*b**4*c**2*sqrt(-1/(4*a*c - b**2)**5) - 6*b**6*c*sqrt(-1/(4*a*c - b**2)**5) + 6*b*c)/(12*c**2))/d**2 + (-8*a*c - b**2 - 12*b*c*x - 12*c**2*x**2)/(16*a**3*b*c**2*d**2 - 8*a**2*b**3*c*d**2 + a*b**5*d**2 + x**3*(32*a**2*c**4*d**2 - 16*a*b**2*c**3*d**2 + 2*b**4*c**2*d**2) + x**2*(48*a**2*b*c**3*d**2 - 24*a*b**3*c**2*d**2 + 3*b**5*c*d**2) + x*(32*a**3*c**3*d**2 - 6*a*b**4*c*d**2 + b**6*d**2))","B",0
1176,1,304,0,3.179768," ","integrate(1/(2*c*d*x+b*d)**3/(c*x**2+b*x+a)**2,x)","- \frac{16 c \log{\left(\frac{b}{2 c} + x \right)}}{d^{3} \left(4 a c - b^{2}\right)^{3}} + \frac{8 c \log{\left(\frac{a}{c} + \frac{b x}{c} + x^{2} \right)}}{d^{3} \left(4 a c - b^{2}\right)^{3}} + \frac{- 4 a c - b^{2} - 8 b c x - 8 c^{2} x^{2}}{16 a^{3} b^{2} c^{2} d^{3} - 8 a^{2} b^{4} c d^{3} + a b^{6} d^{3} + x^{4} \left(64 a^{2} c^{5} d^{3} - 32 a b^{2} c^{4} d^{3} + 4 b^{4} c^{3} d^{3}\right) + x^{3} \left(128 a^{2} b c^{4} d^{3} - 64 a b^{3} c^{3} d^{3} + 8 b^{5} c^{2} d^{3}\right) + x^{2} \left(64 a^{3} c^{4} d^{3} + 48 a^{2} b^{2} c^{3} d^{3} - 36 a b^{4} c^{2} d^{3} + 5 b^{6} c d^{3}\right) + x \left(64 a^{3} b c^{3} d^{3} - 16 a^{2} b^{3} c^{2} d^{3} - 4 a b^{5} c d^{3} + b^{7} d^{3}\right)}"," ",0,"-16*c*log(b/(2*c) + x)/(d**3*(4*a*c - b**2)**3) + 8*c*log(a/c + b*x/c + x**2)/(d**3*(4*a*c - b**2)**3) + (-4*a*c - b**2 - 8*b*c*x - 8*c**2*x**2)/(16*a**3*b**2*c**2*d**3 - 8*a**2*b**4*c*d**3 + a*b**6*d**3 + x**4*(64*a**2*c**5*d**3 - 32*a*b**2*c**4*d**3 + 4*b**4*c**3*d**3) + x**3*(128*a**2*b*c**4*d**3 - 64*a*b**3*c**3*d**3 + 8*b**5*c**2*d**3) + x**2*(64*a**3*c**4*d**3 + 48*a**2*b**2*c**3*d**3 - 36*a*b**4*c**2*d**3 + 5*b**6*c*d**3) + x*(64*a**3*b*c**3*d**3 - 16*a**2*b**3*c**2*d**3 - 4*a*b**5*c*d**3 + b**7*d**3))","B",0
1177,1,660,0,8.181239," ","integrate((2*c*d*x+b*d)**10/(c*x**2+b*x+a)**3,x)","512 b c^{6} d^{10} x^{4} + \frac{1024 c^{7} d^{10} x^{5}}{5} + 126 c^{2} d^{10} \sqrt{- \left(4 a c - b^{2}\right)^{5}} \log{\left(x + \frac{2016 a^{2} b c^{4} d^{10} - 1008 a b^{3} c^{3} d^{10} + 126 b^{5} c^{2} d^{10} - 126 c^{2} d^{10} \sqrt{- \left(4 a c - b^{2}\right)^{5}}}{4032 a^{2} c^{5} d^{10} - 2016 a b^{2} c^{4} d^{10} + 252 b^{4} c^{3} d^{10}} \right)} - 126 c^{2} d^{10} \sqrt{- \left(4 a c - b^{2}\right)^{5}} \log{\left(x + \frac{2016 a^{2} b c^{4} d^{10} - 1008 a b^{3} c^{3} d^{10} + 126 b^{5} c^{2} d^{10} + 126 c^{2} d^{10} \sqrt{- \left(4 a c - b^{2}\right)^{5}}}{4032 a^{2} c^{5} d^{10} - 2016 a b^{2} c^{4} d^{10} + 252 b^{4} c^{3} d^{10}} \right)} + x^{3} \left(- 1024 a c^{6} d^{10} + 768 b^{2} c^{5} d^{10}\right) + x^{2} \left(- 1536 a b c^{5} d^{10} + 640 b^{3} c^{4} d^{10}\right) + x \left(6144 a^{2} c^{5} d^{10} - 3840 a b^{2} c^{4} d^{10} + 640 b^{4} c^{3} d^{10}\right) + \frac{1920 a^{4} b c^{4} d^{10} - 1376 a^{3} b^{3} c^{3} d^{10} + 312 a^{2} b^{5} c^{2} d^{10} - 18 a b^{7} c d^{10} - b^{9} d^{10} + x^{3} \left(4352 a^{3} c^{6} d^{10} - 3264 a^{2} b^{2} c^{5} d^{10} + 816 a b^{4} c^{4} d^{10} - 68 b^{6} c^{3} d^{10}\right) + x^{2} \left(6528 a^{3} b c^{5} d^{10} - 4896 a^{2} b^{3} c^{4} d^{10} + 1224 a b^{5} c^{3} d^{10} - 102 b^{7} c^{2} d^{10}\right) + x \left(3840 a^{4} c^{5} d^{10} - 576 a^{3} b^{2} c^{4} d^{10} - 1008 a^{2} b^{4} c^{3} d^{10} + 372 a b^{6} c^{2} d^{10} - 36 b^{8} c d^{10}\right)}{2 a^{2} + 4 a b x + 4 b c x^{3} + 2 c^{2} x^{4} + x^{2} \left(4 a c + 2 b^{2}\right)}"," ",0,"512*b*c**6*d**10*x**4 + 1024*c**7*d**10*x**5/5 + 126*c**2*d**10*sqrt(-(4*a*c - b**2)**5)*log(x + (2016*a**2*b*c**4*d**10 - 1008*a*b**3*c**3*d**10 + 126*b**5*c**2*d**10 - 126*c**2*d**10*sqrt(-(4*a*c - b**2)**5))/(4032*a**2*c**5*d**10 - 2016*a*b**2*c**4*d**10 + 252*b**4*c**3*d**10)) - 126*c**2*d**10*sqrt(-(4*a*c - b**2)**5)*log(x + (2016*a**2*b*c**4*d**10 - 1008*a*b**3*c**3*d**10 + 126*b**5*c**2*d**10 + 126*c**2*d**10*sqrt(-(4*a*c - b**2)**5))/(4032*a**2*c**5*d**10 - 2016*a*b**2*c**4*d**10 + 252*b**4*c**3*d**10)) + x**3*(-1024*a*c**6*d**10 + 768*b**2*c**5*d**10) + x**2*(-1536*a*b*c**5*d**10 + 640*b**3*c**4*d**10) + x*(6144*a**2*c**5*d**10 - 3840*a*b**2*c**4*d**10 + 640*b**4*c**3*d**10) + (1920*a**4*b*c**4*d**10 - 1376*a**3*b**3*c**3*d**10 + 312*a**2*b**5*c**2*d**10 - 18*a*b**7*c*d**10 - b**9*d**10 + x**3*(4352*a**3*c**6*d**10 - 3264*a**2*b**2*c**5*d**10 + 816*a*b**4*c**4*d**10 - 68*b**6*c**3*d**10) + x**2*(6528*a**3*b*c**5*d**10 - 4896*a**2*b**3*c**4*d**10 + 1224*a*b**5*c**3*d**10 - 102*b**7*c**2*d**10) + x*(3840*a**4*c**5*d**10 - 576*a**3*b**2*c**4*d**10 - 1008*a**2*b**4*c**3*d**10 + 372*a*b**6*c**2*d**10 - 36*b**8*c*d**10))/(2*a**2 + 4*a*b*x + 4*b*c*x**3 + 2*c**2*x**4 + x**2*(4*a*c + 2*b**2))","B",0
1178,1,320,0,10.978155," ","integrate((2*c*d*x+b*d)**9/(c*x**2+b*x+a)**3,x)","256 b c^{5} d^{9} x^{3} + 128 c^{6} d^{9} x^{4} + 96 c^{2} d^{9} \left(4 a c - b^{2}\right)^{2} \log{\left(a + b x + c x^{2} \right)} + x^{2} \left(- 768 a c^{5} d^{9} + 384 b^{2} c^{4} d^{9}\right) + x \left(- 768 a b c^{4} d^{9} + 256 b^{3} c^{3} d^{9}\right) + \frac{1792 a^{4} c^{4} d^{9} - 1280 a^{3} b^{2} c^{3} d^{9} + 288 a^{2} b^{4} c^{2} d^{9} - 16 a b^{6} c d^{9} - b^{8} d^{9} + x^{2} \left(2048 a^{3} c^{5} d^{9} - 1536 a^{2} b^{2} c^{4} d^{9} + 384 a b^{4} c^{3} d^{9} - 32 b^{6} c^{2} d^{9}\right) + x \left(2048 a^{3} b c^{4} d^{9} - 1536 a^{2} b^{3} c^{3} d^{9} + 384 a b^{5} c^{2} d^{9} - 32 b^{7} c d^{9}\right)}{2 a^{2} + 4 a b x + 4 b c x^{3} + 2 c^{2} x^{4} + x^{2} \left(4 a c + 2 b^{2}\right)}"," ",0,"256*b*c**5*d**9*x**3 + 128*c**6*d**9*x**4 + 96*c**2*d**9*(4*a*c - b**2)**2*log(a + b*x + c*x**2) + x**2*(-768*a*c**5*d**9 + 384*b**2*c**4*d**9) + x*(-768*a*b*c**4*d**9 + 256*b**3*c**3*d**9) + (1792*a**4*c**4*d**9 - 1280*a**3*b**2*c**3*d**9 + 288*a**2*b**4*c**2*d**9 - 16*a*b**6*c*d**9 - b**8*d**9 + x**2*(2048*a**3*c**5*d**9 - 1536*a**2*b**2*c**4*d**9 + 384*a*b**4*c**3*d**9 - 32*b**6*c**2*d**9) + x*(2048*a**3*b*c**4*d**9 - 1536*a**2*b**3*c**3*d**9 + 384*a*b**5*c**2*d**9 - 32*b**7*c*d**9))/(2*a**2 + 4*a*b*x + 4*b*c*x**3 + 2*c**2*x**4 + x**2*(4*a*c + 2*b**2))","B",0
1179,1,469,0,5.433752," ","integrate((2*c*d*x+b*d)**8/(c*x**2+b*x+a)**3,x)","128 b c^{4} d^{8} x^{2} + \frac{256 c^{5} d^{8} x^{3}}{3} - 70 c^{2} d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{3}} \log{\left(x + \frac{280 a b c^{3} d^{8} - 70 b^{3} c^{2} d^{8} - 70 c^{2} d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{3}}}{560 a c^{4} d^{8} - 140 b^{2} c^{3} d^{8}} \right)} + 70 c^{2} d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{3}} \log{\left(x + \frac{280 a b c^{3} d^{8} - 70 b^{3} c^{2} d^{8} + 70 c^{2} d^{8} \sqrt{- \left(4 a c - b^{2}\right)^{3}}}{560 a c^{4} d^{8} - 140 b^{2} c^{3} d^{8}} \right)} + x \left(- 768 a c^{4} d^{8} + 256 b^{2} c^{3} d^{8}\right) + \frac{- 352 a^{3} b c^{3} d^{8} + 160 a^{2} b^{3} c^{2} d^{8} - 14 a b^{5} c d^{8} - b^{7} d^{8} + x^{3} \left(- 832 a^{2} c^{5} d^{8} + 416 a b^{2} c^{4} d^{8} - 52 b^{4} c^{3} d^{8}\right) + x^{2} \left(- 1248 a^{2} b c^{4} d^{8} + 624 a b^{3} c^{3} d^{8} - 78 b^{5} c^{2} d^{8}\right) + x \left(- 704 a^{3} c^{4} d^{8} - 96 a^{2} b^{2} c^{3} d^{8} + 180 a b^{4} c^{2} d^{8} - 28 b^{6} c d^{8}\right)}{2 a^{2} + 4 a b x + 4 b c x^{3} + 2 c^{2} x^{4} + x^{2} \left(4 a c + 2 b^{2}\right)}"," ",0,"128*b*c**4*d**8*x**2 + 256*c**5*d**8*x**3/3 - 70*c**2*d**8*sqrt(-(4*a*c - b**2)**3)*log(x + (280*a*b*c**3*d**8 - 70*b**3*c**2*d**8 - 70*c**2*d**8*sqrt(-(4*a*c - b**2)**3))/(560*a*c**4*d**8 - 140*b**2*c**3*d**8)) + 70*c**2*d**8*sqrt(-(4*a*c - b**2)**3)*log(x + (280*a*b*c**3*d**8 - 70*b**3*c**2*d**8 + 70*c**2*d**8*sqrt(-(4*a*c - b**2)**3))/(560*a*c**4*d**8 - 140*b**2*c**3*d**8)) + x*(-768*a*c**4*d**8 + 256*b**2*c**3*d**8) + (-352*a**3*b*c**3*d**8 + 160*a**2*b**3*c**2*d**8 - 14*a*b**5*c*d**8 - b**7*d**8 + x**3*(-832*a**2*c**5*d**8 + 416*a*b**2*c**4*d**8 - 52*b**4*c**3*d**8) + x**2*(-1248*a**2*b*c**4*d**8 + 624*a*b**3*c**3*d**8 - 78*b**5*c**2*d**8) + x*(-704*a**3*c**4*d**8 - 96*a**2*b**2*c**3*d**8 + 180*a*b**4*c**2*d**8 - 28*b**6*c*d**8))/(2*a**2 + 4*a*b*x + 4*b*c*x**3 + 2*c**2*x**4 + x**2*(4*a*c + 2*b**2))","B",0
1180,1,219,0,6.993800," ","integrate((2*c*d*x+b*d)**7/(c*x**2+b*x+a)**3,x)","64 b c^{3} d^{7} x + 64 c^{4} d^{7} x^{2} - 48 c^{2} d^{7} \left(4 a c - b^{2}\right) \log{\left(a + b x + c x^{2} \right)} + \frac{- 320 a^{3} c^{3} d^{7} + 144 a^{2} b^{2} c^{2} d^{7} - 12 a b^{4} c d^{7} - b^{6} d^{7} + x^{2} \left(- 384 a^{2} c^{4} d^{7} + 192 a b^{2} c^{3} d^{7} - 24 b^{4} c^{2} d^{7}\right) + x \left(- 384 a^{2} b c^{3} d^{7} + 192 a b^{3} c^{2} d^{7} - 24 b^{5} c d^{7}\right)}{2 a^{2} + 4 a b x + 4 b c x^{3} + 2 c^{2} x^{4} + x^{2} \left(4 a c + 2 b^{2}\right)}"," ",0,"64*b*c**3*d**7*x + 64*c**4*d**7*x**2 - 48*c**2*d**7*(4*a*c - b**2)*log(a + b*x + c*x**2) + (-320*a**3*c**3*d**7 + 144*a**2*b**2*c**2*d**7 - 12*a*b**4*c*d**7 - b**6*d**7 + x**2*(-384*a**2*c**4*d**7 + 192*a*b**2*c**3*d**7 - 24*b**4*c**2*d**7) + x*(-384*a**2*b*c**3*d**7 + 192*a*b**3*c**2*d**7 - 24*b**5*c*d**7))/(2*a**2 + 4*a*b*x + 4*b*c*x**3 + 2*c**2*x**4 + x**2*(4*a*c + 2*b**2))","B",0
1181,1,299,0,3.908478," ","integrate((2*c*d*x+b*d)**6/(c*x**2+b*x+a)**3,x)","64 c^{3} d^{6} x + c^{2} d^{6} \sqrt{- 3600 a c + 900 b^{2}} \log{\left(x + \frac{30 b c^{2} d^{6} - c^{2} d^{6} \sqrt{- 3600 a c + 900 b^{2}}}{60 c^{3} d^{6}} \right)} - c^{2} d^{6} \sqrt{- 3600 a c + 900 b^{2}} \log{\left(x + \frac{30 b c^{2} d^{6} + c^{2} d^{6} \sqrt{- 3600 a c + 900 b^{2}}}{60 c^{3} d^{6}} \right)} + \frac{56 a^{2} b c^{2} d^{6} - 10 a b^{3} c d^{6} - b^{5} d^{6} + x^{3} \left(144 a c^{4} d^{6} - 36 b^{2} c^{3} d^{6}\right) + x^{2} \left(216 a b c^{3} d^{6} - 54 b^{3} c^{2} d^{6}\right) + x \left(112 a^{2} c^{3} d^{6} + 52 a b^{2} c^{2} d^{6} - 20 b^{4} c d^{6}\right)}{2 a^{2} + 4 a b x + 4 b c x^{3} + 2 c^{2} x^{4} + x^{2} \left(4 a c + 2 b^{2}\right)}"," ",0,"64*c**3*d**6*x + c**2*d**6*sqrt(-3600*a*c + 900*b**2)*log(x + (30*b*c**2*d**6 - c**2*d**6*sqrt(-3600*a*c + 900*b**2))/(60*c**3*d**6)) - c**2*d**6*sqrt(-3600*a*c + 900*b**2)*log(x + (30*b*c**2*d**6 + c**2*d**6*sqrt(-3600*a*c + 900*b**2))/(60*c**3*d**6)) + (56*a**2*b*c**2*d**6 - 10*a*b**3*c*d**6 - b**5*d**6 + x**3*(144*a*c**4*d**6 - 36*b**2*c**3*d**6) + x**2*(216*a*b*c**3*d**6 - 54*b**3*c**2*d**6) + x*(112*a**2*c**3*d**6 + 52*a*b**2*c**2*d**6 - 20*b**4*c*d**6))/(2*a**2 + 4*a*b*x + 4*b*c*x**3 + 2*c**2*x**4 + x**2*(4*a*c + 2*b**2))","B",0
1182,1,141,0,3.781159," ","integrate((2*c*d*x+b*d)**5/(c*x**2+b*x+a)**3,x)","16 c^{2} d^{5} \log{\left(a + b x + c x^{2} \right)} + \frac{48 a^{2} c^{2} d^{5} - 8 a b^{2} c d^{5} - b^{4} d^{5} + x^{2} \left(64 a c^{3} d^{5} - 16 b^{2} c^{2} d^{5}\right) + x \left(64 a b c^{2} d^{5} - 16 b^{3} c d^{5}\right)}{2 a^{2} + 4 a b x + 4 b c x^{3} + 2 c^{2} x^{4} + x^{2} \left(4 a c + 2 b^{2}\right)}"," ",0,"16*c**2*d**5*log(a + b*x + c*x**2) + (48*a**2*c**2*d**5 - 8*a*b**2*c*d**5 - b**4*d**5 + x**2*(64*a*c**3*d**5 - 16*b**2*c**2*d**5) + x*(64*a*b*c**2*d**5 - 16*b**3*c*d**5))/(2*a**2 + 4*a*b*x + 4*b*c*x**3 + 2*c**2*x**4 + x**2*(4*a*c + 2*b**2))","B",0
1183,1,304,0,2.057051," ","integrate((2*c*d*x+b*d)**4/(c*x**2+b*x+a)**3,x)","- 6 c^{2} d^{4} \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{- 24 a c^{3} d^{4} \sqrt{- \frac{1}{4 a c - b^{2}}} + 6 b^{2} c^{2} d^{4} \sqrt{- \frac{1}{4 a c - b^{2}}} + 6 b c^{2} d^{4}}{12 c^{3} d^{4}} \right)} + 6 c^{2} d^{4} \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{24 a c^{3} d^{4} \sqrt{- \frac{1}{4 a c - b^{2}}} - 6 b^{2} c^{2} d^{4} \sqrt{- \frac{1}{4 a c - b^{2}}} + 6 b c^{2} d^{4}}{12 c^{3} d^{4}} \right)} + \frac{- 6 a b c d^{4} - b^{3} d^{4} - 30 b c^{2} d^{4} x^{2} - 20 c^{3} d^{4} x^{3} + x \left(- 12 a c^{2} d^{4} - 12 b^{2} c d^{4}\right)}{2 a^{2} + 4 a b x + 4 b c x^{3} + 2 c^{2} x^{4} + x^{2} \left(4 a c + 2 b^{2}\right)}"," ",0,"-6*c**2*d**4*sqrt(-1/(4*a*c - b**2))*log(x + (-24*a*c**3*d**4*sqrt(-1/(4*a*c - b**2)) + 6*b**2*c**2*d**4*sqrt(-1/(4*a*c - b**2)) + 6*b*c**2*d**4)/(12*c**3*d**4)) + 6*c**2*d**4*sqrt(-1/(4*a*c - b**2))*log(x + (24*a*c**3*d**4*sqrt(-1/(4*a*c - b**2)) - 6*b**2*c**2*d**4*sqrt(-1/(4*a*c - b**2)) + 6*b*c**2*d**4)/(12*c**3*d**4)) + (-6*a*b*c*d**4 - b**3*d**4 - 30*b*c**2*d**4*x**2 - 20*c**3*d**4*x**3 + x*(-12*a*c**2*d**4 - 12*b**2*c*d**4))/(2*a**2 + 4*a*b*x + 4*b*c*x**3 + 2*c**2*x**4 + x**2*(4*a*c + 2*b**2))","B",0
1184,1,80,0,1.648015," ","integrate((2*c*d*x+b*d)**3/(c*x**2+b*x+a)**3,x)","\frac{- 4 a c d^{3} - b^{2} d^{3} - 8 b c d^{3} x - 8 c^{2} d^{3} x^{2}}{2 a^{2} + 4 a b x + 4 b c x^{3} + 2 c^{2} x^{4} + x^{2} \left(4 a c + 2 b^{2}\right)}"," ",0,"(-4*a*c*d**3 - b**2*d**3 - 8*b*c*d**3*x - 8*c**2*d**3*x**2)/(2*a**2 + 4*a*b*x + 4*b*c*x**3 + 2*c**2*x**4 + x**2*(4*a*c + 2*b**2))","B",0
1185,1,430,0,1.515486," ","integrate((2*c*d*x+b*d)**2/(c*x**2+b*x+a)**3,x)","- 2 c^{2} d^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{- 32 a^{2} c^{4} d^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 16 a b^{2} c^{3} d^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 2 b^{4} c^{2} d^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 b c^{2} d^{2}}{4 c^{3} d^{2}} \right)} + 2 c^{2} d^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{32 a^{2} c^{4} d^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 16 a b^{2} c^{3} d^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 b^{4} c^{2} d^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 b c^{2} d^{2}}{4 c^{3} d^{2}} \right)} + \frac{- 2 a b c d^{2} + b^{3} d^{2} + 6 b c^{2} d^{2} x^{2} + 4 c^{3} d^{2} x^{3} + x \left(- 4 a c^{2} d^{2} + 4 b^{2} c d^{2}\right)}{8 a^{3} c - 2 a^{2} b^{2} + x^{4} \left(8 a c^{3} - 2 b^{2} c^{2}\right) + x^{3} \left(16 a b c^{2} - 4 b^{3} c\right) + x^{2} \left(16 a^{2} c^{2} + 4 a b^{2} c - 2 b^{4}\right) + x \left(16 a^{2} b c - 4 a b^{3}\right)}"," ",0,"-2*c**2*d**2*sqrt(-1/(4*a*c - b**2)**3)*log(x + (-32*a**2*c**4*d**2*sqrt(-1/(4*a*c - b**2)**3) + 16*a*b**2*c**3*d**2*sqrt(-1/(4*a*c - b**2)**3) - 2*b**4*c**2*d**2*sqrt(-1/(4*a*c - b**2)**3) + 2*b*c**2*d**2)/(4*c**3*d**2)) + 2*c**2*d**2*sqrt(-1/(4*a*c - b**2)**3)*log(x + (32*a**2*c**4*d**2*sqrt(-1/(4*a*c - b**2)**3) - 16*a*b**2*c**3*d**2*sqrt(-1/(4*a*c - b**2)**3) + 2*b**4*c**2*d**2*sqrt(-1/(4*a*c - b**2)**3) + 2*b*c**2*d**2)/(4*c**3*d**2)) + (-2*a*b*c*d**2 + b**3*d**2 + 6*b*c**2*d**2*x**2 + 4*c**3*d**2*x**3 + x*(-4*a*c**2*d**2 + 4*b**2*c*d**2))/(8*a**3*c - 2*a**2*b**2 + x**4*(8*a*c**3 - 2*b**2*c**2) + x**3*(16*a*b*c**2 - 4*b**3*c) + x**2*(16*a**2*c**2 + 4*a*b**2*c - 2*b**4) + x*(16*a**2*b*c - 4*a*b**3))","B",0
1186,1,44,0,1.001165," ","integrate((2*c*d*x+b*d)/(c*x**2+b*x+a)**3,x)","- \frac{d}{2 a^{2} + 4 a b x + 4 b c x^{3} + 2 c^{2} x^{4} + x^{2} \left(4 a c + 2 b^{2}\right)}"," ",0,"-d/(2*a**2 + 4*a*b*x + 4*b*c*x**3 + 2*c**2*x**4 + x**2*(4*a*c + 2*b**2))","B",0
1187,1,246,0,3.173682," ","integrate(1/(2*c*d*x+b*d)/(c*x**2+b*x+a)**3,x)","\frac{32 c^{2} \log{\left(\frac{b}{2 c} + x \right)}}{d \left(4 a c - b^{2}\right)^{3}} - \frac{16 c^{2} \log{\left(\frac{a}{c} + \frac{b x}{c} + x^{2} \right)}}{d \left(4 a c - b^{2}\right)^{3}} + \frac{12 a c - b^{2} + 8 b c x + 8 c^{2} x^{2}}{32 a^{4} c^{2} d - 16 a^{3} b^{2} c d + 2 a^{2} b^{4} d + x^{4} \left(32 a^{2} c^{4} d - 16 a b^{2} c^{3} d + 2 b^{4} c^{2} d\right) + x^{3} \left(64 a^{2} b c^{3} d - 32 a b^{3} c^{2} d + 4 b^{5} c d\right) + x^{2} \left(64 a^{3} c^{3} d - 12 a b^{4} c d + 2 b^{6} d\right) + x \left(64 a^{3} b c^{2} d - 32 a^{2} b^{3} c d + 4 a b^{5} d\right)}"," ",0,"32*c**2*log(b/(2*c) + x)/(d*(4*a*c - b**2)**3) - 16*c**2*log(a/c + b*x/c + x**2)/(d*(4*a*c - b**2)**3) + (12*a*c - b**2 + 8*b*c*x + 8*c**2*x**2)/(32*a**4*c**2*d - 16*a**3*b**2*c*d + 2*a**2*b**4*d + x**4*(32*a**2*c**4*d - 16*a*b**2*c**3*d + 2*b**4*c**2*d) + x**3*(64*a**2*b*c**3*d - 32*a*b**3*c**2*d + 4*b**5*c*d) + x**2*(64*a**3*c**3*d - 12*a*b**4*c*d + 2*b**6*d) + x*(64*a**3*b*c**2*d - 32*a**2*b**3*c*d + 4*a*b**5*d))","B",0
1188,1,804,0,3.737335," ","integrate(1/(2*c*d*x+b*d)**2/(c*x**2+b*x+a)**3,x)","\frac{30 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \log{\left(x + \frac{- 7680 a^{4} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 7680 a^{3} b^{2} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 2880 a^{2} b^{4} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 480 a b^{6} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 30 b^{8} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 30 b c^{2}}{60 c^{3}} \right)}}{d^{2}} - \frac{30 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \log{\left(x + \frac{7680 a^{4} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 7680 a^{3} b^{2} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 2880 a^{2} b^{4} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 480 a b^{6} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 30 b^{8} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 30 b c^{2}}{60 c^{3}} \right)}}{d^{2}} + \frac{- 64 a^{2} c^{2} - 18 a b^{2} c + b^{4} - 240 b c^{3} x^{3} - 120 c^{4} x^{4} + x^{2} \left(- 200 a c^{3} - 130 b^{2} c^{2}\right) + x \left(- 200 a b c^{2} - 10 b^{3} c\right)}{128 a^{5} b c^{3} d^{2} - 96 a^{4} b^{3} c^{2} d^{2} + 24 a^{3} b^{5} c d^{2} - 2 a^{2} b^{7} d^{2} + x^{5} \left(256 a^{3} c^{6} d^{2} - 192 a^{2} b^{2} c^{5} d^{2} + 48 a b^{4} c^{4} d^{2} - 4 b^{6} c^{3} d^{2}\right) + x^{4} \left(640 a^{3} b c^{5} d^{2} - 480 a^{2} b^{3} c^{4} d^{2} + 120 a b^{5} c^{3} d^{2} - 10 b^{7} c^{2} d^{2}\right) + x^{3} \left(512 a^{4} c^{5} d^{2} + 128 a^{3} b^{2} c^{4} d^{2} - 288 a^{2} b^{4} c^{3} d^{2} + 88 a b^{6} c^{2} d^{2} - 8 b^{8} c d^{2}\right) + x^{2} \left(768 a^{4} b c^{4} d^{2} - 448 a^{3} b^{3} c^{3} d^{2} + 48 a^{2} b^{5} c^{2} d^{2} + 12 a b^{7} c d^{2} - 2 b^{9} d^{2}\right) + x \left(256 a^{5} c^{4} d^{2} + 64 a^{4} b^{2} c^{3} d^{2} - 144 a^{3} b^{4} c^{2} d^{2} + 44 a^{2} b^{6} c d^{2} - 4 a b^{8} d^{2}\right)}"," ",0,"30*c**2*sqrt(-1/(4*a*c - b**2)**7)*log(x + (-7680*a**4*c**6*sqrt(-1/(4*a*c - b**2)**7) + 7680*a**3*b**2*c**5*sqrt(-1/(4*a*c - b**2)**7) - 2880*a**2*b**4*c**4*sqrt(-1/(4*a*c - b**2)**7) + 480*a*b**6*c**3*sqrt(-1/(4*a*c - b**2)**7) - 30*b**8*c**2*sqrt(-1/(4*a*c - b**2)**7) + 30*b*c**2)/(60*c**3))/d**2 - 30*c**2*sqrt(-1/(4*a*c - b**2)**7)*log(x + (7680*a**4*c**6*sqrt(-1/(4*a*c - b**2)**7) - 7680*a**3*b**2*c**5*sqrt(-1/(4*a*c - b**2)**7) + 2880*a**2*b**4*c**4*sqrt(-1/(4*a*c - b**2)**7) - 480*a*b**6*c**3*sqrt(-1/(4*a*c - b**2)**7) + 30*b**8*c**2*sqrt(-1/(4*a*c - b**2)**7) + 30*b*c**2)/(60*c**3))/d**2 + (-64*a**2*c**2 - 18*a*b**2*c + b**4 - 240*b*c**3*x**3 - 120*c**4*x**4 + x**2*(-200*a*c**3 - 130*b**2*c**2) + x*(-200*a*b*c**2 - 10*b**3*c))/(128*a**5*b*c**3*d**2 - 96*a**4*b**3*c**2*d**2 + 24*a**3*b**5*c*d**2 - 2*a**2*b**7*d**2 + x**5*(256*a**3*c**6*d**2 - 192*a**2*b**2*c**5*d**2 + 48*a*b**4*c**4*d**2 - 4*b**6*c**3*d**2) + x**4*(640*a**3*b*c**5*d**2 - 480*a**2*b**3*c**4*d**2 + 120*a*b**5*c**3*d**2 - 10*b**7*c**2*d**2) + x**3*(512*a**4*c**5*d**2 + 128*a**3*b**2*c**4*d**2 - 288*a**2*b**4*c**3*d**2 + 88*a*b**6*c**2*d**2 - 8*b**8*c*d**2) + x**2*(768*a**4*b*c**4*d**2 - 448*a**3*b**3*c**3*d**2 + 48*a**2*b**5*c**2*d**2 + 12*a*b**7*c*d**2 - 2*b**9*d**2) + x*(256*a**5*c**4*d**2 + 64*a**4*b**2*c**3*d**2 - 144*a**3*b**4*c**2*d**2 + 44*a**2*b**6*c*d**2 - 4*a*b**8*d**2))","B",0
1189,1,600,0,6.467588," ","integrate(1/(2*c*d*x+b*d)**3/(c*x**2+b*x+a)**3,x)","- \frac{96 c^{2} \log{\left(\frac{b}{2 c} + x \right)}}{d^{3} \left(4 a c - b^{2}\right)^{4}} + \frac{48 c^{2} \log{\left(\frac{a}{c} + \frac{b x}{c} + x^{2} \right)}}{d^{3} \left(4 a c - b^{2}\right)^{4}} + \frac{- 32 a^{2} c^{2} - 20 a b^{2} c + b^{4} - 192 b c^{3} x^{3} - 96 c^{4} x^{4} + x^{2} \left(- 144 a c^{3} - 108 b^{2} c^{2}\right) + x \left(- 144 a b c^{2} - 12 b^{3} c\right)}{128 a^{5} b^{2} c^{3} d^{3} - 96 a^{4} b^{4} c^{2} d^{3} + 24 a^{3} b^{6} c d^{3} - 2 a^{2} b^{8} d^{3} + x^{6} \left(512 a^{3} c^{7} d^{3} - 384 a^{2} b^{2} c^{6} d^{3} + 96 a b^{4} c^{5} d^{3} - 8 b^{6} c^{4} d^{3}\right) + x^{5} \left(1536 a^{3} b c^{6} d^{3} - 1152 a^{2} b^{3} c^{5} d^{3} + 288 a b^{5} c^{4} d^{3} - 24 b^{7} c^{3} d^{3}\right) + x^{4} \left(1024 a^{4} c^{6} d^{3} + 896 a^{3} b^{2} c^{5} d^{3} - 1056 a^{2} b^{4} c^{4} d^{3} + 296 a b^{6} c^{3} d^{3} - 26 b^{8} c^{2} d^{3}\right) + x^{3} \left(2048 a^{4} b c^{5} d^{3} - 768 a^{3} b^{3} c^{4} d^{3} - 192 a^{2} b^{5} c^{3} d^{3} + 112 a b^{7} c^{2} d^{3} - 12 b^{9} c d^{3}\right) + x^{2} \left(512 a^{5} c^{5} d^{3} + 896 a^{4} b^{2} c^{4} d^{3} - 736 a^{3} b^{4} c^{3} d^{3} + 136 a^{2} b^{6} c^{2} d^{3} + 4 a b^{8} c d^{3} - 2 b^{10} d^{3}\right) + x \left(512 a^{5} b c^{4} d^{3} - 128 a^{4} b^{3} c^{3} d^{3} - 96 a^{3} b^{5} c^{2} d^{3} + 40 a^{2} b^{7} c d^{3} - 4 a b^{9} d^{3}\right)}"," ",0,"-96*c**2*log(b/(2*c) + x)/(d**3*(4*a*c - b**2)**4) + 48*c**2*log(a/c + b*x/c + x**2)/(d**3*(4*a*c - b**2)**4) + (-32*a**2*c**2 - 20*a*b**2*c + b**4 - 192*b*c**3*x**3 - 96*c**4*x**4 + x**2*(-144*a*c**3 - 108*b**2*c**2) + x*(-144*a*b*c**2 - 12*b**3*c))/(128*a**5*b**2*c**3*d**3 - 96*a**4*b**4*c**2*d**3 + 24*a**3*b**6*c*d**3 - 2*a**2*b**8*d**3 + x**6*(512*a**3*c**7*d**3 - 384*a**2*b**2*c**6*d**3 + 96*a*b**4*c**5*d**3 - 8*b**6*c**4*d**3) + x**5*(1536*a**3*b*c**6*d**3 - 1152*a**2*b**3*c**5*d**3 + 288*a*b**5*c**4*d**3 - 24*b**7*c**3*d**3) + x**4*(1024*a**4*c**6*d**3 + 896*a**3*b**2*c**5*d**3 - 1056*a**2*b**4*c**4*d**3 + 296*a*b**6*c**3*d**3 - 26*b**8*c**2*d**3) + x**3*(2048*a**4*b*c**5*d**3 - 768*a**3*b**3*c**4*d**3 - 192*a**2*b**5*c**3*d**3 + 112*a*b**7*c**2*d**3 - 12*b**9*c*d**3) + x**2*(512*a**5*c**5*d**3 + 896*a**4*b**2*c**4*d**3 - 736*a**3*b**4*c**3*d**3 + 136*a**2*b**6*c**2*d**3 + 4*a*b**8*c*d**3 - 2*b**10*d**3) + x*(512*a**5*b*c**4*d**3 - 128*a**4*b**3*c**3*d**3 - 96*a**3*b**5*c**2*d**3 + 40*a**2*b**7*c*d**3 - 4*a*b**9*d**3))","B",0
1190,1,1238,0,6.632313," ","integrate(1/(2*c*d*x+b*d)**4/(c*x**2+b*x+a)**3,x)","- \frac{70 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \log{\left(x + \frac{- 71680 a^{5} c^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 89600 a^{4} b^{2} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} - 44800 a^{3} b^{4} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 11200 a^{2} b^{6} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} - 1400 a b^{8} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 70 b^{10} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 70 b c^{2}}{140 c^{3}} \right)}}{d^{4}} + \frac{70 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \log{\left(x + \frac{71680 a^{5} c^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} - 89600 a^{4} b^{2} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 44800 a^{3} b^{4} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} - 11200 a^{2} b^{6} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 1400 a b^{8} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} - 70 b^{10} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 70 b c^{2}}{140 c^{3}} \right)}}{d^{4}} + \frac{- 256 a^{3} c^{3} + 640 a^{2} b^{2} c^{2} + 78 a b^{4} c - 3 b^{6} + 10080 b c^{5} x^{5} + 3360 c^{6} x^{6} + x^{4} \left(5600 a c^{5} + 11200 b^{2} c^{4}\right) + x^{3} \left(11200 a b c^{4} + 5600 b^{3} c^{3}\right) + x^{2} \left(1792 a^{2} c^{4} + 7504 a b^{2} c^{3} + 1162 b^{4} c^{2}\right) + x \left(1792 a^{2} b c^{3} + 1904 a b^{3} c^{2} + 42 b^{5} c\right)}{1536 a^{6} b^{3} c^{4} d^{4} - 1536 a^{5} b^{5} c^{3} d^{4} + 576 a^{4} b^{7} c^{2} d^{4} - 96 a^{3} b^{9} c d^{4} + 6 a^{2} b^{11} d^{4} + x^{7} \left(12288 a^{4} c^{9} d^{4} - 12288 a^{3} b^{2} c^{8} d^{4} + 4608 a^{2} b^{4} c^{7} d^{4} - 768 a b^{6} c^{6} d^{4} + 48 b^{8} c^{5} d^{4}\right) + x^{6} \left(43008 a^{4} b c^{8} d^{4} - 43008 a^{3} b^{3} c^{7} d^{4} + 16128 a^{2} b^{5} c^{6} d^{4} - 2688 a b^{7} c^{5} d^{4} + 168 b^{9} c^{4} d^{4}\right) + x^{5} \left(24576 a^{5} c^{8} d^{4} + 33792 a^{4} b^{2} c^{7} d^{4} - 49152 a^{3} b^{4} c^{6} d^{4} + 20352 a^{2} b^{6} c^{5} d^{4} - 3552 a b^{8} c^{4} d^{4} + 228 b^{10} c^{3} d^{4}\right) + x^{4} \left(61440 a^{5} b c^{7} d^{4} - 23040 a^{4} b^{3} c^{6} d^{4} - 15360 a^{3} b^{5} c^{5} d^{4} + 10560 a^{2} b^{7} c^{4} d^{4} - 2160 a b^{9} c^{3} d^{4} + 150 b^{11} c^{2} d^{4}\right) + x^{3} \left(12288 a^{6} c^{7} d^{4} + 43008 a^{5} b^{2} c^{6} d^{4} - 38400 a^{4} b^{4} c^{5} d^{4} + 7680 a^{3} b^{6} c^{4} d^{4} + 1200 a^{2} b^{8} c^{3} d^{4} - 552 a b^{10} c^{2} d^{4} + 48 b^{12} c d^{4}\right) + x^{2} \left(18432 a^{6} b c^{6} d^{4} + 3072 a^{5} b^{3} c^{5} d^{4} - 13056 a^{4} b^{5} c^{4} d^{4} + 5376 a^{3} b^{7} c^{3} d^{4} - 696 a^{2} b^{9} c^{2} d^{4} - 12 a b^{11} c d^{4} + 6 b^{13} d^{4}\right) + x \left(9216 a^{6} b^{2} c^{5} d^{4} - 6144 a^{5} b^{4} c^{4} d^{4} + 384 a^{4} b^{6} c^{3} d^{4} + 576 a^{3} b^{8} c^{2} d^{4} - 156 a^{2} b^{10} c d^{4} + 12 a b^{12} d^{4}\right)}"," ",0,"-70*c**2*sqrt(-1/(4*a*c - b**2)**9)*log(x + (-71680*a**5*c**7*sqrt(-1/(4*a*c - b**2)**9) + 89600*a**4*b**2*c**6*sqrt(-1/(4*a*c - b**2)**9) - 44800*a**3*b**4*c**5*sqrt(-1/(4*a*c - b**2)**9) + 11200*a**2*b**6*c**4*sqrt(-1/(4*a*c - b**2)**9) - 1400*a*b**8*c**3*sqrt(-1/(4*a*c - b**2)**9) + 70*b**10*c**2*sqrt(-1/(4*a*c - b**2)**9) + 70*b*c**2)/(140*c**3))/d**4 + 70*c**2*sqrt(-1/(4*a*c - b**2)**9)*log(x + (71680*a**5*c**7*sqrt(-1/(4*a*c - b**2)**9) - 89600*a**4*b**2*c**6*sqrt(-1/(4*a*c - b**2)**9) + 44800*a**3*b**4*c**5*sqrt(-1/(4*a*c - b**2)**9) - 11200*a**2*b**6*c**4*sqrt(-1/(4*a*c - b**2)**9) + 1400*a*b**8*c**3*sqrt(-1/(4*a*c - b**2)**9) - 70*b**10*c**2*sqrt(-1/(4*a*c - b**2)**9) + 70*b*c**2)/(140*c**3))/d**4 + (-256*a**3*c**3 + 640*a**2*b**2*c**2 + 78*a*b**4*c - 3*b**6 + 10080*b*c**5*x**5 + 3360*c**6*x**6 + x**4*(5600*a*c**5 + 11200*b**2*c**4) + x**3*(11200*a*b*c**4 + 5600*b**3*c**3) + x**2*(1792*a**2*c**4 + 7504*a*b**2*c**3 + 1162*b**4*c**2) + x*(1792*a**2*b*c**3 + 1904*a*b**3*c**2 + 42*b**5*c))/(1536*a**6*b**3*c**4*d**4 - 1536*a**5*b**5*c**3*d**4 + 576*a**4*b**7*c**2*d**4 - 96*a**3*b**9*c*d**4 + 6*a**2*b**11*d**4 + x**7*(12288*a**4*c**9*d**4 - 12288*a**3*b**2*c**8*d**4 + 4608*a**2*b**4*c**7*d**4 - 768*a*b**6*c**6*d**4 + 48*b**8*c**5*d**4) + x**6*(43008*a**4*b*c**8*d**4 - 43008*a**3*b**3*c**7*d**4 + 16128*a**2*b**5*c**6*d**4 - 2688*a*b**7*c**5*d**4 + 168*b**9*c**4*d**4) + x**5*(24576*a**5*c**8*d**4 + 33792*a**4*b**2*c**7*d**4 - 49152*a**3*b**4*c**6*d**4 + 20352*a**2*b**6*c**5*d**4 - 3552*a*b**8*c**4*d**4 + 228*b**10*c**3*d**4) + x**4*(61440*a**5*b*c**7*d**4 - 23040*a**4*b**3*c**6*d**4 - 15360*a**3*b**5*c**5*d**4 + 10560*a**2*b**7*c**4*d**4 - 2160*a*b**9*c**3*d**4 + 150*b**11*c**2*d**4) + x**3*(12288*a**6*c**7*d**4 + 43008*a**5*b**2*c**6*d**4 - 38400*a**4*b**4*c**5*d**4 + 7680*a**3*b**6*c**4*d**4 + 1200*a**2*b**8*c**3*d**4 - 552*a*b**10*c**2*d**4 + 48*b**12*c*d**4) + x**2*(18432*a**6*b*c**6*d**4 + 3072*a**5*b**3*c**5*d**4 - 13056*a**4*b**5*c**4*d**4 + 5376*a**3*b**7*c**3*d**4 - 696*a**2*b**9*c**2*d**4 - 12*a*b**11*c*d**4 + 6*b**13*d**4) + x*(9216*a**6*b**2*c**5*d**4 - 6144*a**5*b**4*c**4*d**4 + 384*a**4*b**6*c**3*d**4 + 576*a**3*b**8*c**2*d**4 - 156*a**2*b**10*c*d**4 + 12*a*b**12*d**4))","B",0
1191,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**4*(c*x**2+b*x+a)**(1/2),x)","d^{4} \left(\int b^{4} \sqrt{a + b x + c x^{2}}\, dx + \int 16 c^{4} x^{4} \sqrt{a + b x + c x^{2}}\, dx + \int 32 b c^{3} x^{3} \sqrt{a + b x + c x^{2}}\, dx + \int 24 b^{2} c^{2} x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 8 b^{3} c x \sqrt{a + b x + c x^{2}}\, dx\right)"," ",0,"d**4*(Integral(b**4*sqrt(a + b*x + c*x**2), x) + Integral(16*c**4*x**4*sqrt(a + b*x + c*x**2), x) + Integral(32*b*c**3*x**3*sqrt(a + b*x + c*x**2), x) + Integral(24*b**2*c**2*x**2*sqrt(a + b*x + c*x**2), x) + Integral(8*b**3*c*x*sqrt(a + b*x + c*x**2), x))","F",0
1192,1,216,0,0.403493," ","integrate((2*c*d*x+b*d)**3*(c*x**2+b*x+a)**(1/2),x)","- \frac{16 a^{2} c d^{3} \sqrt{a + b x + c x^{2}}}{15} + \frac{2 a b^{2} d^{3} \sqrt{a + b x + c x^{2}}}{3} + \frac{8 a b c d^{3} x \sqrt{a + b x + c x^{2}}}{15} + \frac{8 a c^{2} d^{3} x^{2} \sqrt{a + b x + c x^{2}}}{15} + \frac{2 b^{3} d^{3} x \sqrt{a + b x + c x^{2}}}{3} + \frac{34 b^{2} c d^{3} x^{2} \sqrt{a + b x + c x^{2}}}{15} + \frac{16 b c^{2} d^{3} x^{3} \sqrt{a + b x + c x^{2}}}{5} + \frac{8 c^{3} d^{3} x^{4} \sqrt{a + b x + c x^{2}}}{5}"," ",0,"-16*a**2*c*d**3*sqrt(a + b*x + c*x**2)/15 + 2*a*b**2*d**3*sqrt(a + b*x + c*x**2)/3 + 8*a*b*c*d**3*x*sqrt(a + b*x + c*x**2)/15 + 8*a*c**2*d**3*x**2*sqrt(a + b*x + c*x**2)/15 + 2*b**3*d**3*x*sqrt(a + b*x + c*x**2)/3 + 34*b**2*c*d**3*x**2*sqrt(a + b*x + c*x**2)/15 + 16*b*c**2*d**3*x**3*sqrt(a + b*x + c*x**2)/5 + 8*c**3*d**3*x**4*sqrt(a + b*x + c*x**2)/5","B",0
1193,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**2*(c*x**2+b*x+a)**(1/2),x)","d^{2} \left(\int b^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 4 c^{2} x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 4 b c x \sqrt{a + b x + c x^{2}}\, dx\right)"," ",0,"d**2*(Integral(b**2*sqrt(a + b*x + c*x**2), x) + Integral(4*c**2*x**2*sqrt(a + b*x + c*x**2), x) + Integral(4*b*c*x*sqrt(a + b*x + c*x**2), x))","F",0
1194,1,65,0,0.188338," ","integrate((2*c*d*x+b*d)*(c*x**2+b*x+a)**(1/2),x)","\frac{2 a d \sqrt{a + b x + c x^{2}}}{3} + \frac{2 b d x \sqrt{a + b x + c x^{2}}}{3} + \frac{2 c d x^{2} \sqrt{a + b x + c x^{2}}}{3}"," ",0,"2*a*d*sqrt(a + b*x + c*x**2)/3 + 2*b*d*x*sqrt(a + b*x + c*x**2)/3 + 2*c*d*x**2*sqrt(a + b*x + c*x**2)/3","B",0
1195,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d),x)","\frac{\int \frac{\sqrt{a + b x + c x^{2}}}{b + 2 c x}\, dx}{d}"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(b + 2*c*x), x)/d","F",0
1196,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**2,x)","\frac{\int \frac{\sqrt{a + b x + c x^{2}}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx}{d^{2}}"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(b**2 + 4*b*c*x + 4*c**2*x**2), x)/d**2","F",0
1197,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**3,x)","\frac{\int \frac{\sqrt{a + b x + c x^{2}}}{b^{3} + 6 b^{2} c x + 12 b c^{2} x^{2} + 8 c^{3} x^{3}}\, dx}{d^{3}}"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(b**3 + 6*b**2*c*x + 12*b*c**2*x**2 + 8*c**3*x**3), x)/d**3","F",0
1198,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**4,x)","\frac{\int \frac{\sqrt{a + b x + c x^{2}}}{b^{4} + 8 b^{3} c x + 24 b^{2} c^{2} x^{2} + 32 b c^{3} x^{3} + 16 c^{4} x^{4}}\, dx}{d^{4}}"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(b**4 + 8*b**3*c*x + 24*b**2*c**2*x**2 + 32*b*c**3*x**3 + 16*c**4*x**4), x)/d**4","F",0
1199,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**5,x)","\frac{\int \frac{\sqrt{a + b x + c x^{2}}}{b^{5} + 10 b^{4} c x + 40 b^{3} c^{2} x^{2} + 80 b^{2} c^{3} x^{3} + 80 b c^{4} x^{4} + 32 c^{5} x^{5}}\, dx}{d^{5}}"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(b**5 + 10*b**4*c*x + 40*b**3*c**2*x**2 + 80*b**2*c**3*x**3 + 80*b*c**4*x**4 + 32*c**5*x**5), x)/d**5","F",0
1200,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**6,x)","\frac{\int \frac{\sqrt{a + b x + c x^{2}}}{b^{6} + 12 b^{5} c x + 60 b^{4} c^{2} x^{2} + 160 b^{3} c^{3} x^{3} + 240 b^{2} c^{4} x^{4} + 192 b c^{5} x^{5} + 64 c^{6} x^{6}}\, dx}{d^{6}}"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(b**6 + 12*b**5*c*x + 60*b**4*c**2*x**2 + 160*b**3*c**3*x**3 + 240*b**2*c**4*x**4 + 192*b*c**5*x**5 + 64*c**6*x**6), x)/d**6","F",0
1201,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**7,x)","\frac{\int \frac{\sqrt{a + b x + c x^{2}}}{b^{7} + 14 b^{6} c x + 84 b^{5} c^{2} x^{2} + 280 b^{4} c^{3} x^{3} + 560 b^{3} c^{4} x^{4} + 672 b^{2} c^{5} x^{5} + 448 b c^{6} x^{6} + 128 c^{7} x^{7}}\, dx}{d^{7}}"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(b**7 + 14*b**6*c*x + 84*b**5*c**2*x**2 + 280*b**4*c**3*x**3 + 560*b**3*c**4*x**4 + 672*b**2*c**5*x**5 + 448*b*c**6*x**6 + 128*c**7*x**7), x)/d**7","F",0
1202,1,656,0,3.491041," ","integrate((2*c*d*x+b*d)**5*(c*x**2+b*x+a)**(3/2),x)","\frac{256 a^{4} c^{2} d^{5} \sqrt{a + b x + c x^{2}}}{315} - \frac{32 a^{3} b^{2} c d^{5} \sqrt{a + b x + c x^{2}}}{35} - \frac{128 a^{3} b c^{2} d^{5} x \sqrt{a + b x + c x^{2}}}{315} - \frac{128 a^{3} c^{3} d^{5} x^{2} \sqrt{a + b x + c x^{2}}}{315} + \frac{2 a^{2} b^{4} d^{5} \sqrt{a + b x + c x^{2}}}{5} + \frac{16 a^{2} b^{3} c d^{5} x \sqrt{a + b x + c x^{2}}}{35} + \frac{16 a^{2} b^{2} c^{2} d^{5} x^{2} \sqrt{a + b x + c x^{2}}}{21} + \frac{64 a^{2} b c^{3} d^{5} x^{3} \sqrt{a + b x + c x^{2}}}{105} + \frac{32 a^{2} c^{4} d^{5} x^{4} \sqrt{a + b x + c x^{2}}}{105} + \frac{4 a b^{5} d^{5} x \sqrt{a + b x + c x^{2}}}{5} + \frac{156 a b^{4} c d^{5} x^{2} \sqrt{a + b x + c x^{2}}}{35} + \frac{3904 a b^{3} c^{2} d^{5} x^{3} \sqrt{a + b x + c x^{2}}}{315} + \frac{1984 a b^{2} c^{3} d^{5} x^{4} \sqrt{a + b x + c x^{2}}}{105} + \frac{320 a b c^{4} d^{5} x^{5} \sqrt{a + b x + c x^{2}}}{21} + \frac{320 a c^{5} d^{5} x^{6} \sqrt{a + b x + c x^{2}}}{63} + \frac{2 b^{6} d^{5} x^{2} \sqrt{a + b x + c x^{2}}}{5} + \frac{108 b^{5} c d^{5} x^{3} \sqrt{a + b x + c x^{2}}}{35} + \frac{3406 b^{4} c^{2} d^{5} x^{4} \sqrt{a + b x + c x^{2}}}{315} + \frac{1328 b^{3} c^{3} d^{5} x^{5} \sqrt{a + b x + c x^{2}}}{63} + \frac{496 b^{2} c^{4} d^{5} x^{6} \sqrt{a + b x + c x^{2}}}{21} + \frac{128 b c^{5} d^{5} x^{7} \sqrt{a + b x + c x^{2}}}{9} + \frac{32 c^{6} d^{5} x^{8} \sqrt{a + b x + c x^{2}}}{9}"," ",0,"256*a**4*c**2*d**5*sqrt(a + b*x + c*x**2)/315 - 32*a**3*b**2*c*d**5*sqrt(a + b*x + c*x**2)/35 - 128*a**3*b*c**2*d**5*x*sqrt(a + b*x + c*x**2)/315 - 128*a**3*c**3*d**5*x**2*sqrt(a + b*x + c*x**2)/315 + 2*a**2*b**4*d**5*sqrt(a + b*x + c*x**2)/5 + 16*a**2*b**3*c*d**5*x*sqrt(a + b*x + c*x**2)/35 + 16*a**2*b**2*c**2*d**5*x**2*sqrt(a + b*x + c*x**2)/21 + 64*a**2*b*c**3*d**5*x**3*sqrt(a + b*x + c*x**2)/105 + 32*a**2*c**4*d**5*x**4*sqrt(a + b*x + c*x**2)/105 + 4*a*b**5*d**5*x*sqrt(a + b*x + c*x**2)/5 + 156*a*b**4*c*d**5*x**2*sqrt(a + b*x + c*x**2)/35 + 3904*a*b**3*c**2*d**5*x**3*sqrt(a + b*x + c*x**2)/315 + 1984*a*b**2*c**3*d**5*x**4*sqrt(a + b*x + c*x**2)/105 + 320*a*b*c**4*d**5*x**5*sqrt(a + b*x + c*x**2)/21 + 320*a*c**5*d**5*x**6*sqrt(a + b*x + c*x**2)/63 + 2*b**6*d**5*x**2*sqrt(a + b*x + c*x**2)/5 + 108*b**5*c*d**5*x**3*sqrt(a + b*x + c*x**2)/35 + 3406*b**4*c**2*d**5*x**4*sqrt(a + b*x + c*x**2)/315 + 1328*b**3*c**3*d**5*x**5*sqrt(a + b*x + c*x**2)/63 + 496*b**2*c**4*d**5*x**6*sqrt(a + b*x + c*x**2)/21 + 128*b*c**5*d**5*x**7*sqrt(a + b*x + c*x**2)/9 + 32*c**6*d**5*x**8*sqrt(a + b*x + c*x**2)/9","B",0
1203,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**4*(c*x**2+b*x+a)**(3/2),x)","d^{4} \left(\int a b^{4} \sqrt{a + b x + c x^{2}}\, dx + \int b^{5} x \sqrt{a + b x + c x^{2}}\, dx + \int 16 c^{5} x^{6} \sqrt{a + b x + c x^{2}}\, dx + \int 16 a c^{4} x^{4} \sqrt{a + b x + c x^{2}}\, dx + \int 48 b c^{4} x^{5} \sqrt{a + b x + c x^{2}}\, dx + \int 56 b^{2} c^{3} x^{4} \sqrt{a + b x + c x^{2}}\, dx + \int 32 b^{3} c^{2} x^{3} \sqrt{a + b x + c x^{2}}\, dx + \int 9 b^{4} c x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 32 a b c^{3} x^{3} \sqrt{a + b x + c x^{2}}\, dx + \int 24 a b^{2} c^{2} x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 8 a b^{3} c x \sqrt{a + b x + c x^{2}}\, dx\right)"," ",0,"d**4*(Integral(a*b**4*sqrt(a + b*x + c*x**2), x) + Integral(b**5*x*sqrt(a + b*x + c*x**2), x) + Integral(16*c**5*x**6*sqrt(a + b*x + c*x**2), x) + Integral(16*a*c**4*x**4*sqrt(a + b*x + c*x**2), x) + Integral(48*b*c**4*x**5*sqrt(a + b*x + c*x**2), x) + Integral(56*b**2*c**3*x**4*sqrt(a + b*x + c*x**2), x) + Integral(32*b**3*c**2*x**3*sqrt(a + b*x + c*x**2), x) + Integral(9*b**4*c*x**2*sqrt(a + b*x + c*x**2), x) + Integral(32*a*b*c**3*x**3*sqrt(a + b*x + c*x**2), x) + Integral(24*a*b**2*c**2*x**2*sqrt(a + b*x + c*x**2), x) + Integral(8*a*b**3*c*x*sqrt(a + b*x + c*x**2), x))","F",0
1204,1,371,0,1.520472," ","integrate((2*c*d*x+b*d)**3*(c*x**2+b*x+a)**(3/2),x)","- \frac{16 a^{3} c d^{3} \sqrt{a + b x + c x^{2}}}{35} + \frac{2 a^{2} b^{2} d^{3} \sqrt{a + b x + c x^{2}}}{5} + \frac{8 a^{2} b c d^{3} x \sqrt{a + b x + c x^{2}}}{35} + \frac{8 a^{2} c^{2} d^{3} x^{2} \sqrt{a + b x + c x^{2}}}{35} + \frac{4 a b^{3} d^{3} x \sqrt{a + b x + c x^{2}}}{5} + \frac{92 a b^{2} c d^{3} x^{2} \sqrt{a + b x + c x^{2}}}{35} + \frac{128 a b c^{2} d^{3} x^{3} \sqrt{a + b x + c x^{2}}}{35} + \frac{64 a c^{3} d^{3} x^{4} \sqrt{a + b x + c x^{2}}}{35} + \frac{2 b^{4} d^{3} x^{2} \sqrt{a + b x + c x^{2}}}{5} + \frac{68 b^{3} c d^{3} x^{3} \sqrt{a + b x + c x^{2}}}{35} + \frac{134 b^{2} c^{2} d^{3} x^{4} \sqrt{a + b x + c x^{2}}}{35} + \frac{24 b c^{3} d^{3} x^{5} \sqrt{a + b x + c x^{2}}}{7} + \frac{8 c^{4} d^{3} x^{6} \sqrt{a + b x + c x^{2}}}{7}"," ",0,"-16*a**3*c*d**3*sqrt(a + b*x + c*x**2)/35 + 2*a**2*b**2*d**3*sqrt(a + b*x + c*x**2)/5 + 8*a**2*b*c*d**3*x*sqrt(a + b*x + c*x**2)/35 + 8*a**2*c**2*d**3*x**2*sqrt(a + b*x + c*x**2)/35 + 4*a*b**3*d**3*x*sqrt(a + b*x + c*x**2)/5 + 92*a*b**2*c*d**3*x**2*sqrt(a + b*x + c*x**2)/35 + 128*a*b*c**2*d**3*x**3*sqrt(a + b*x + c*x**2)/35 + 64*a*c**3*d**3*x**4*sqrt(a + b*x + c*x**2)/35 + 2*b**4*d**3*x**2*sqrt(a + b*x + c*x**2)/5 + 68*b**3*c*d**3*x**3*sqrt(a + b*x + c*x**2)/35 + 134*b**2*c**2*d**3*x**4*sqrt(a + b*x + c*x**2)/35 + 24*b*c**3*d**3*x**5*sqrt(a + b*x + c*x**2)/7 + 8*c**4*d**3*x**6*sqrt(a + b*x + c*x**2)/7","B",0
1205,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**2*(c*x**2+b*x+a)**(3/2),x)","d^{2} \left(\int a b^{2} \sqrt{a + b x + c x^{2}}\, dx + \int b^{3} x \sqrt{a + b x + c x^{2}}\, dx + \int 4 c^{3} x^{4} \sqrt{a + b x + c x^{2}}\, dx + \int 4 a c^{2} x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 8 b c^{2} x^{3} \sqrt{a + b x + c x^{2}}\, dx + \int 5 b^{2} c x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 4 a b c x \sqrt{a + b x + c x^{2}}\, dx\right)"," ",0,"d**2*(Integral(a*b**2*sqrt(a + b*x + c*x**2), x) + Integral(b**3*x*sqrt(a + b*x + c*x**2), x) + Integral(4*c**3*x**4*sqrt(a + b*x + c*x**2), x) + Integral(4*a*c**2*x**2*sqrt(a + b*x + c*x**2), x) + Integral(8*b*c**2*x**3*sqrt(a + b*x + c*x**2), x) + Integral(5*b**2*c*x**2*sqrt(a + b*x + c*x**2), x) + Integral(4*a*b*c*x*sqrt(a + b*x + c*x**2), x))","F",0
1206,1,146,0,0.712549," ","integrate((2*c*d*x+b*d)*(c*x**2+b*x+a)**(3/2),x)","\frac{2 a^{2} d \sqrt{a + b x + c x^{2}}}{5} + \frac{4 a b d x \sqrt{a + b x + c x^{2}}}{5} + \frac{4 a c d x^{2} \sqrt{a + b x + c x^{2}}}{5} + \frac{2 b^{2} d x^{2} \sqrt{a + b x + c x^{2}}}{5} + \frac{4 b c d x^{3} \sqrt{a + b x + c x^{2}}}{5} + \frac{2 c^{2} d x^{4} \sqrt{a + b x + c x^{2}}}{5}"," ",0,"2*a**2*d*sqrt(a + b*x + c*x**2)/5 + 4*a*b*d*x*sqrt(a + b*x + c*x**2)/5 + 4*a*c*d*x**2*sqrt(a + b*x + c*x**2)/5 + 2*b**2*d*x**2*sqrt(a + b*x + c*x**2)/5 + 4*b*c*d*x**3*sqrt(a + b*x + c*x**2)/5 + 2*c**2*d*x**4*sqrt(a + b*x + c*x**2)/5","B",0
1207,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d),x)","\frac{\int \frac{a \sqrt{a + b x + c x^{2}}}{b + 2 c x}\, dx + \int \frac{b x \sqrt{a + b x + c x^{2}}}{b + 2 c x}\, dx + \int \frac{c x^{2} \sqrt{a + b x + c x^{2}}}{b + 2 c x}\, dx}{d}"," ",0,"(Integral(a*sqrt(a + b*x + c*x**2)/(b + 2*c*x), x) + Integral(b*x*sqrt(a + b*x + c*x**2)/(b + 2*c*x), x) + Integral(c*x**2*sqrt(a + b*x + c*x**2)/(b + 2*c*x), x))/d","F",0
1208,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**2,x)","\frac{\int \frac{a \sqrt{a + b x + c x^{2}}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx + \int \frac{b x \sqrt{a + b x + c x^{2}}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx + \int \frac{c x^{2} \sqrt{a + b x + c x^{2}}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx}{d^{2}}"," ",0,"(Integral(a*sqrt(a + b*x + c*x**2)/(b**2 + 4*b*c*x + 4*c**2*x**2), x) + Integral(b*x*sqrt(a + b*x + c*x**2)/(b**2 + 4*b*c*x + 4*c**2*x**2), x) + Integral(c*x**2*sqrt(a + b*x + c*x**2)/(b**2 + 4*b*c*x + 4*c**2*x**2), x))/d**2","F",0
1209,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**3,x)","\frac{\int \frac{a \sqrt{a + b x + c x^{2}}}{b^{3} + 6 b^{2} c x + 12 b c^{2} x^{2} + 8 c^{3} x^{3}}\, dx + \int \frac{b x \sqrt{a + b x + c x^{2}}}{b^{3} + 6 b^{2} c x + 12 b c^{2} x^{2} + 8 c^{3} x^{3}}\, dx + \int \frac{c x^{2} \sqrt{a + b x + c x^{2}}}{b^{3} + 6 b^{2} c x + 12 b c^{2} x^{2} + 8 c^{3} x^{3}}\, dx}{d^{3}}"," ",0,"(Integral(a*sqrt(a + b*x + c*x**2)/(b**3 + 6*b**2*c*x + 12*b*c**2*x**2 + 8*c**3*x**3), x) + Integral(b*x*sqrt(a + b*x + c*x**2)/(b**3 + 6*b**2*c*x + 12*b*c**2*x**2 + 8*c**3*x**3), x) + Integral(c*x**2*sqrt(a + b*x + c*x**2)/(b**3 + 6*b**2*c*x + 12*b*c**2*x**2 + 8*c**3*x**3), x))/d**3","F",0
1210,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**4,x)","\frac{\int \frac{a \sqrt{a + b x + c x^{2}}}{b^{4} + 8 b^{3} c x + 24 b^{2} c^{2} x^{2} + 32 b c^{3} x^{3} + 16 c^{4} x^{4}}\, dx + \int \frac{b x \sqrt{a + b x + c x^{2}}}{b^{4} + 8 b^{3} c x + 24 b^{2} c^{2} x^{2} + 32 b c^{3} x^{3} + 16 c^{4} x^{4}}\, dx + \int \frac{c x^{2} \sqrt{a + b x + c x^{2}}}{b^{4} + 8 b^{3} c x + 24 b^{2} c^{2} x^{2} + 32 b c^{3} x^{3} + 16 c^{4} x^{4}}\, dx}{d^{4}}"," ",0,"(Integral(a*sqrt(a + b*x + c*x**2)/(b**4 + 8*b**3*c*x + 24*b**2*c**2*x**2 + 32*b*c**3*x**3 + 16*c**4*x**4), x) + Integral(b*x*sqrt(a + b*x + c*x**2)/(b**4 + 8*b**3*c*x + 24*b**2*c**2*x**2 + 32*b*c**3*x**3 + 16*c**4*x**4), x) + Integral(c*x**2*sqrt(a + b*x + c*x**2)/(b**4 + 8*b**3*c*x + 24*b**2*c**2*x**2 + 32*b*c**3*x**3 + 16*c**4*x**4), x))/d**4","F",0
1211,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**5,x)","\frac{\int \frac{a \sqrt{a + b x + c x^{2}}}{b^{5} + 10 b^{4} c x + 40 b^{3} c^{2} x^{2} + 80 b^{2} c^{3} x^{3} + 80 b c^{4} x^{4} + 32 c^{5} x^{5}}\, dx + \int \frac{b x \sqrt{a + b x + c x^{2}}}{b^{5} + 10 b^{4} c x + 40 b^{3} c^{2} x^{2} + 80 b^{2} c^{3} x^{3} + 80 b c^{4} x^{4} + 32 c^{5} x^{5}}\, dx + \int \frac{c x^{2} \sqrt{a + b x + c x^{2}}}{b^{5} + 10 b^{4} c x + 40 b^{3} c^{2} x^{2} + 80 b^{2} c^{3} x^{3} + 80 b c^{4} x^{4} + 32 c^{5} x^{5}}\, dx}{d^{5}}"," ",0,"(Integral(a*sqrt(a + b*x + c*x**2)/(b**5 + 10*b**4*c*x + 40*b**3*c**2*x**2 + 80*b**2*c**3*x**3 + 80*b*c**4*x**4 + 32*c**5*x**5), x) + Integral(b*x*sqrt(a + b*x + c*x**2)/(b**5 + 10*b**4*c*x + 40*b**3*c**2*x**2 + 80*b**2*c**3*x**3 + 80*b*c**4*x**4 + 32*c**5*x**5), x) + Integral(c*x**2*sqrt(a + b*x + c*x**2)/(b**5 + 10*b**4*c*x + 40*b**3*c**2*x**2 + 80*b**2*c**3*x**3 + 80*b*c**4*x**4 + 32*c**5*x**5), x))/d**5","F",0
1212,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**6,x)","\frac{\int \frac{a \sqrt{a + b x + c x^{2}}}{b^{6} + 12 b^{5} c x + 60 b^{4} c^{2} x^{2} + 160 b^{3} c^{3} x^{3} + 240 b^{2} c^{4} x^{4} + 192 b c^{5} x^{5} + 64 c^{6} x^{6}}\, dx + \int \frac{b x \sqrt{a + b x + c x^{2}}}{b^{6} + 12 b^{5} c x + 60 b^{4} c^{2} x^{2} + 160 b^{3} c^{3} x^{3} + 240 b^{2} c^{4} x^{4} + 192 b c^{5} x^{5} + 64 c^{6} x^{6}}\, dx + \int \frac{c x^{2} \sqrt{a + b x + c x^{2}}}{b^{6} + 12 b^{5} c x + 60 b^{4} c^{2} x^{2} + 160 b^{3} c^{3} x^{3} + 240 b^{2} c^{4} x^{4} + 192 b c^{5} x^{5} + 64 c^{6} x^{6}}\, dx}{d^{6}}"," ",0,"(Integral(a*sqrt(a + b*x + c*x**2)/(b**6 + 12*b**5*c*x + 60*b**4*c**2*x**2 + 160*b**3*c**3*x**3 + 240*b**2*c**4*x**4 + 192*b*c**5*x**5 + 64*c**6*x**6), x) + Integral(b*x*sqrt(a + b*x + c*x**2)/(b**6 + 12*b**5*c*x + 60*b**4*c**2*x**2 + 160*b**3*c**3*x**3 + 240*b**2*c**4*x**4 + 192*b*c**5*x**5 + 64*c**6*x**6), x) + Integral(c*x**2*sqrt(a + b*x + c*x**2)/(b**6 + 12*b**5*c*x + 60*b**4*c**2*x**2 + 160*b**3*c**3*x**3 + 240*b**2*c**4*x**4 + 192*b*c**5*x**5 + 64*c**6*x**6), x))/d**6","F",0
1213,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**7,x)","\frac{\int \frac{a \sqrt{a + b x + c x^{2}}}{b^{7} + 14 b^{6} c x + 84 b^{5} c^{2} x^{2} + 280 b^{4} c^{3} x^{3} + 560 b^{3} c^{4} x^{4} + 672 b^{2} c^{5} x^{5} + 448 b c^{6} x^{6} + 128 c^{7} x^{7}}\, dx + \int \frac{b x \sqrt{a + b x + c x^{2}}}{b^{7} + 14 b^{6} c x + 84 b^{5} c^{2} x^{2} + 280 b^{4} c^{3} x^{3} + 560 b^{3} c^{4} x^{4} + 672 b^{2} c^{5} x^{5} + 448 b c^{6} x^{6} + 128 c^{7} x^{7}}\, dx + \int \frac{c x^{2} \sqrt{a + b x + c x^{2}}}{b^{7} + 14 b^{6} c x + 84 b^{5} c^{2} x^{2} + 280 b^{4} c^{3} x^{3} + 560 b^{3} c^{4} x^{4} + 672 b^{2} c^{5} x^{5} + 448 b c^{6} x^{6} + 128 c^{7} x^{7}}\, dx}{d^{7}}"," ",0,"(Integral(a*sqrt(a + b*x + c*x**2)/(b**7 + 14*b**6*c*x + 84*b**5*c**2*x**2 + 280*b**4*c**3*x**3 + 560*b**3*c**4*x**4 + 672*b**2*c**5*x**5 + 448*b*c**6*x**6 + 128*c**7*x**7), x) + Integral(b*x*sqrt(a + b*x + c*x**2)/(b**7 + 14*b**6*c*x + 84*b**5*c**2*x**2 + 280*b**4*c**3*x**3 + 560*b**3*c**4*x**4 + 672*b**2*c**5*x**5 + 448*b*c**6*x**6 + 128*c**7*x**7), x) + Integral(c*x**2*sqrt(a + b*x + c*x**2)/(b**7 + 14*b**6*c*x + 84*b**5*c**2*x**2 + 280*b**4*c**3*x**3 + 560*b**3*c**4*x**4 + 672*b**2*c**5*x**5 + 448*b*c**6*x**6 + 128*c**7*x**7), x))/d**7","F",0
1214,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**8,x)","\frac{\int \frac{a \sqrt{a + b x + c x^{2}}}{b^{8} + 16 b^{7} c x + 112 b^{6} c^{2} x^{2} + 448 b^{5} c^{3} x^{3} + 1120 b^{4} c^{4} x^{4} + 1792 b^{3} c^{5} x^{5} + 1792 b^{2} c^{6} x^{6} + 1024 b c^{7} x^{7} + 256 c^{8} x^{8}}\, dx + \int \frac{b x \sqrt{a + b x + c x^{2}}}{b^{8} + 16 b^{7} c x + 112 b^{6} c^{2} x^{2} + 448 b^{5} c^{3} x^{3} + 1120 b^{4} c^{4} x^{4} + 1792 b^{3} c^{5} x^{5} + 1792 b^{2} c^{6} x^{6} + 1024 b c^{7} x^{7} + 256 c^{8} x^{8}}\, dx + \int \frac{c x^{2} \sqrt{a + b x + c x^{2}}}{b^{8} + 16 b^{7} c x + 112 b^{6} c^{2} x^{2} + 448 b^{5} c^{3} x^{3} + 1120 b^{4} c^{4} x^{4} + 1792 b^{3} c^{5} x^{5} + 1792 b^{2} c^{6} x^{6} + 1024 b c^{7} x^{7} + 256 c^{8} x^{8}}\, dx}{d^{8}}"," ",0,"(Integral(a*sqrt(a + b*x + c*x**2)/(b**8 + 16*b**7*c*x + 112*b**6*c**2*x**2 + 448*b**5*c**3*x**3 + 1120*b**4*c**4*x**4 + 1792*b**3*c**5*x**5 + 1792*b**2*c**6*x**6 + 1024*b*c**7*x**7 + 256*c**8*x**8), x) + Integral(b*x*sqrt(a + b*x + c*x**2)/(b**8 + 16*b**7*c*x + 112*b**6*c**2*x**2 + 448*b**5*c**3*x**3 + 1120*b**4*c**4*x**4 + 1792*b**3*c**5*x**5 + 1792*b**2*c**6*x**6 + 1024*b*c**7*x**7 + 256*c**8*x**8), x) + Integral(c*x**2*sqrt(a + b*x + c*x**2)/(b**8 + 16*b**7*c*x + 112*b**6*c**2*x**2 + 448*b**5*c**3*x**3 + 1120*b**4*c**4*x**4 + 1792*b**3*c**5*x**5 + 1792*b**2*c**6*x**6 + 1024*b*c**7*x**7 + 256*c**8*x**8), x))/d**8","F",0
1215,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**9,x)","\frac{\int \frac{a \sqrt{a + b x + c x^{2}}}{b^{9} + 18 b^{8} c x + 144 b^{7} c^{2} x^{2} + 672 b^{6} c^{3} x^{3} + 2016 b^{5} c^{4} x^{4} + 4032 b^{4} c^{5} x^{5} + 5376 b^{3} c^{6} x^{6} + 4608 b^{2} c^{7} x^{7} + 2304 b c^{8} x^{8} + 512 c^{9} x^{9}}\, dx + \int \frac{b x \sqrt{a + b x + c x^{2}}}{b^{9} + 18 b^{8} c x + 144 b^{7} c^{2} x^{2} + 672 b^{6} c^{3} x^{3} + 2016 b^{5} c^{4} x^{4} + 4032 b^{4} c^{5} x^{5} + 5376 b^{3} c^{6} x^{6} + 4608 b^{2} c^{7} x^{7} + 2304 b c^{8} x^{8} + 512 c^{9} x^{9}}\, dx + \int \frac{c x^{2} \sqrt{a + b x + c x^{2}}}{b^{9} + 18 b^{8} c x + 144 b^{7} c^{2} x^{2} + 672 b^{6} c^{3} x^{3} + 2016 b^{5} c^{4} x^{4} + 4032 b^{4} c^{5} x^{5} + 5376 b^{3} c^{6} x^{6} + 4608 b^{2} c^{7} x^{7} + 2304 b c^{8} x^{8} + 512 c^{9} x^{9}}\, dx}{d^{9}}"," ",0,"(Integral(a*sqrt(a + b*x + c*x**2)/(b**9 + 18*b**8*c*x + 144*b**7*c**2*x**2 + 672*b**6*c**3*x**3 + 2016*b**5*c**4*x**4 + 4032*b**4*c**5*x**5 + 5376*b**3*c**6*x**6 + 4608*b**2*c**7*x**7 + 2304*b*c**8*x**8 + 512*c**9*x**9), x) + Integral(b*x*sqrt(a + b*x + c*x**2)/(b**9 + 18*b**8*c*x + 144*b**7*c**2*x**2 + 672*b**6*c**3*x**3 + 2016*b**5*c**4*x**4 + 4032*b**4*c**5*x**5 + 5376*b**3*c**6*x**6 + 4608*b**2*c**7*x**7 + 2304*b*c**8*x**8 + 512*c**9*x**9), x) + Integral(c*x**2*sqrt(a + b*x + c*x**2)/(b**9 + 18*b**8*c*x + 144*b**7*c**2*x**2 + 672*b**6*c**3*x**3 + 2016*b**5*c**4*x**4 + 4032*b**4*c**5*x**5 + 5376*b**3*c**6*x**6 + 4608*b**2*c**7*x**7 + 2304*b*c**8*x**8 + 512*c**9*x**9), x))/d**9","F",0
1216,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**10,x)","\frac{\int \frac{a \sqrt{a + b x + c x^{2}}}{b^{10} + 20 b^{9} c x + 180 b^{8} c^{2} x^{2} + 960 b^{7} c^{3} x^{3} + 3360 b^{6} c^{4} x^{4} + 8064 b^{5} c^{5} x^{5} + 13440 b^{4} c^{6} x^{6} + 15360 b^{3} c^{7} x^{7} + 11520 b^{2} c^{8} x^{8} + 5120 b c^{9} x^{9} + 1024 c^{10} x^{10}}\, dx + \int \frac{b x \sqrt{a + b x + c x^{2}}}{b^{10} + 20 b^{9} c x + 180 b^{8} c^{2} x^{2} + 960 b^{7} c^{3} x^{3} + 3360 b^{6} c^{4} x^{4} + 8064 b^{5} c^{5} x^{5} + 13440 b^{4} c^{6} x^{6} + 15360 b^{3} c^{7} x^{7} + 11520 b^{2} c^{8} x^{8} + 5120 b c^{9} x^{9} + 1024 c^{10} x^{10}}\, dx + \int \frac{c x^{2} \sqrt{a + b x + c x^{2}}}{b^{10} + 20 b^{9} c x + 180 b^{8} c^{2} x^{2} + 960 b^{7} c^{3} x^{3} + 3360 b^{6} c^{4} x^{4} + 8064 b^{5} c^{5} x^{5} + 13440 b^{4} c^{6} x^{6} + 15360 b^{3} c^{7} x^{7} + 11520 b^{2} c^{8} x^{8} + 5120 b c^{9} x^{9} + 1024 c^{10} x^{10}}\, dx}{d^{10}}"," ",0,"(Integral(a*sqrt(a + b*x + c*x**2)/(b**10 + 20*b**9*c*x + 180*b**8*c**2*x**2 + 960*b**7*c**3*x**3 + 3360*b**6*c**4*x**4 + 8064*b**5*c**5*x**5 + 13440*b**4*c**6*x**6 + 15360*b**3*c**7*x**7 + 11520*b**2*c**8*x**8 + 5120*b*c**9*x**9 + 1024*c**10*x**10), x) + Integral(b*x*sqrt(a + b*x + c*x**2)/(b**10 + 20*b**9*c*x + 180*b**8*c**2*x**2 + 960*b**7*c**3*x**3 + 3360*b**6*c**4*x**4 + 8064*b**5*c**5*x**5 + 13440*b**4*c**6*x**6 + 15360*b**3*c**7*x**7 + 11520*b**2*c**8*x**8 + 5120*b*c**9*x**9 + 1024*c**10*x**10), x) + Integral(c*x**2*sqrt(a + b*x + c*x**2)/(b**10 + 20*b**9*c*x + 180*b**8*c**2*x**2 + 960*b**7*c**3*x**3 + 3360*b**6*c**4*x**4 + 8064*b**5*c**5*x**5 + 13440*b**4*c**6*x**6 + 15360*b**3*c**7*x**7 + 11520*b**2*c**8*x**8 + 5120*b*c**9*x**9 + 1024*c**10*x**10), x))/d**10","F",0
1217,1,913,0,10.077475," ","integrate((2*c*d*x+b*d)**5*(c*x**2+b*x+a)**(5/2),x)","\frac{256 a^{5} c^{2} d^{5} \sqrt{a + b x + c x^{2}}}{693} - \frac{32 a^{4} b^{2} c d^{5} \sqrt{a + b x + c x^{2}}}{63} - \frac{128 a^{4} b c^{2} d^{5} x \sqrt{a + b x + c x^{2}}}{693} - \frac{128 a^{4} c^{3} d^{5} x^{2} \sqrt{a + b x + c x^{2}}}{693} + \frac{2 a^{3} b^{4} d^{5} \sqrt{a + b x + c x^{2}}}{7} + \frac{16 a^{3} b^{3} c d^{5} x \sqrt{a + b x + c x^{2}}}{63} + \frac{272 a^{3} b^{2} c^{2} d^{5} x^{2} \sqrt{a + b x + c x^{2}}}{693} + \frac{64 a^{3} b c^{3} d^{5} x^{3} \sqrt{a + b x + c x^{2}}}{231} + \frac{32 a^{3} c^{4} d^{5} x^{4} \sqrt{a + b x + c x^{2}}}{231} + \frac{6 a^{2} b^{5} d^{5} x \sqrt{a + b x + c x^{2}}}{7} + \frac{14 a^{2} b^{4} c d^{5} x^{2} \sqrt{a + b x + c x^{2}}}{3} + \frac{8896 a^{2} b^{3} c^{2} d^{5} x^{3} \sqrt{a + b x + c x^{2}}}{693} + \frac{4496 a^{2} b^{2} c^{3} d^{5} x^{4} \sqrt{a + b x + c x^{2}}}{231} + \frac{3616 a^{2} b c^{4} d^{5} x^{5} \sqrt{a + b x + c x^{2}}}{231} + \frac{3616 a^{2} c^{5} d^{5} x^{6} \sqrt{a + b x + c x^{2}}}{693} + \frac{6 a b^{6} d^{5} x^{2} \sqrt{a + b x + c x^{2}}}{7} + \frac{412 a b^{5} c d^{5} x^{3} \sqrt{a + b x + c x^{2}}}{63} + \frac{2254 a b^{4} c^{2} d^{5} x^{4} \sqrt{a + b x + c x^{2}}}{99} + \frac{30640 a b^{3} c^{3} d^{5} x^{5} \sqrt{a + b x + c x^{2}}}{693} + \frac{34256 a b^{2} c^{4} d^{5} x^{6} \sqrt{a + b x + c x^{2}}}{693} + \frac{2944 a b c^{5} d^{5} x^{7} \sqrt{a + b x + c x^{2}}}{99} + \frac{736 a c^{6} d^{5} x^{8} \sqrt{a + b x + c x^{2}}}{99} + \frac{2 b^{7} d^{5} x^{3} \sqrt{a + b x + c x^{2}}}{7} + \frac{166 b^{6} c d^{5} x^{4} \sqrt{a + b x + c x^{2}}}{63} + \frac{7538 b^{5} c^{2} d^{5} x^{5} \sqrt{a + b x + c x^{2}}}{693} + \frac{5890 b^{4} c^{3} d^{5} x^{6} \sqrt{a + b x + c x^{2}}}{231} + \frac{3584 b^{3} c^{4} d^{5} x^{7} \sqrt{a + b x + c x^{2}}}{99} + \frac{3056 b^{2} c^{5} d^{5} x^{8} \sqrt{a + b x + c x^{2}}}{99} + \frac{160 b c^{6} d^{5} x^{9} \sqrt{a + b x + c x^{2}}}{11} + \frac{32 c^{7} d^{5} x^{10} \sqrt{a + b x + c x^{2}}}{11}"," ",0,"256*a**5*c**2*d**5*sqrt(a + b*x + c*x**2)/693 - 32*a**4*b**2*c*d**5*sqrt(a + b*x + c*x**2)/63 - 128*a**4*b*c**2*d**5*x*sqrt(a + b*x + c*x**2)/693 - 128*a**4*c**3*d**5*x**2*sqrt(a + b*x + c*x**2)/693 + 2*a**3*b**4*d**5*sqrt(a + b*x + c*x**2)/7 + 16*a**3*b**3*c*d**5*x*sqrt(a + b*x + c*x**2)/63 + 272*a**3*b**2*c**2*d**5*x**2*sqrt(a + b*x + c*x**2)/693 + 64*a**3*b*c**3*d**5*x**3*sqrt(a + b*x + c*x**2)/231 + 32*a**3*c**4*d**5*x**4*sqrt(a + b*x + c*x**2)/231 + 6*a**2*b**5*d**5*x*sqrt(a + b*x + c*x**2)/7 + 14*a**2*b**4*c*d**5*x**2*sqrt(a + b*x + c*x**2)/3 + 8896*a**2*b**3*c**2*d**5*x**3*sqrt(a + b*x + c*x**2)/693 + 4496*a**2*b**2*c**3*d**5*x**4*sqrt(a + b*x + c*x**2)/231 + 3616*a**2*b*c**4*d**5*x**5*sqrt(a + b*x + c*x**2)/231 + 3616*a**2*c**5*d**5*x**6*sqrt(a + b*x + c*x**2)/693 + 6*a*b**6*d**5*x**2*sqrt(a + b*x + c*x**2)/7 + 412*a*b**5*c*d**5*x**3*sqrt(a + b*x + c*x**2)/63 + 2254*a*b**4*c**2*d**5*x**4*sqrt(a + b*x + c*x**2)/99 + 30640*a*b**3*c**3*d**5*x**5*sqrt(a + b*x + c*x**2)/693 + 34256*a*b**2*c**4*d**5*x**6*sqrt(a + b*x + c*x**2)/693 + 2944*a*b*c**5*d**5*x**7*sqrt(a + b*x + c*x**2)/99 + 736*a*c**6*d**5*x**8*sqrt(a + b*x + c*x**2)/99 + 2*b**7*d**5*x**3*sqrt(a + b*x + c*x**2)/7 + 166*b**6*c*d**5*x**4*sqrt(a + b*x + c*x**2)/63 + 7538*b**5*c**2*d**5*x**5*sqrt(a + b*x + c*x**2)/693 + 5890*b**4*c**3*d**5*x**6*sqrt(a + b*x + c*x**2)/231 + 3584*b**3*c**4*d**5*x**7*sqrt(a + b*x + c*x**2)/99 + 3056*b**2*c**5*d**5*x**8*sqrt(a + b*x + c*x**2)/99 + 160*b*c**6*d**5*x**9*sqrt(a + b*x + c*x**2)/11 + 32*c**7*d**5*x**10*sqrt(a + b*x + c*x**2)/11","B",0
1218,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**4*(c*x**2+b*x+a)**(5/2),x)","d^{4} \left(\int a^{2} b^{4} \sqrt{a + b x + c x^{2}}\, dx + \int b^{6} x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 16 c^{6} x^{8} \sqrt{a + b x + c x^{2}}\, dx + \int 2 a b^{5} x \sqrt{a + b x + c x^{2}}\, dx + \int 32 a c^{5} x^{6} \sqrt{a + b x + c x^{2}}\, dx + \int 16 a^{2} c^{4} x^{4} \sqrt{a + b x + c x^{2}}\, dx + \int 64 b c^{5} x^{7} \sqrt{a + b x + c x^{2}}\, dx + \int 104 b^{2} c^{4} x^{6} \sqrt{a + b x + c x^{2}}\, dx + \int 88 b^{3} c^{3} x^{5} \sqrt{a + b x + c x^{2}}\, dx + \int 41 b^{4} c^{2} x^{4} \sqrt{a + b x + c x^{2}}\, dx + \int 10 b^{5} c x^{3} \sqrt{a + b x + c x^{2}}\, dx + \int 96 a b c^{4} x^{5} \sqrt{a + b x + c x^{2}}\, dx + \int 112 a b^{2} c^{3} x^{4} \sqrt{a + b x + c x^{2}}\, dx + \int 64 a b^{3} c^{2} x^{3} \sqrt{a + b x + c x^{2}}\, dx + \int 18 a b^{4} c x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 32 a^{2} b c^{3} x^{3} \sqrt{a + b x + c x^{2}}\, dx + \int 24 a^{2} b^{2} c^{2} x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 8 a^{2} b^{3} c x \sqrt{a + b x + c x^{2}}\, dx\right)"," ",0,"d**4*(Integral(a**2*b**4*sqrt(a + b*x + c*x**2), x) + Integral(b**6*x**2*sqrt(a + b*x + c*x**2), x) + Integral(16*c**6*x**8*sqrt(a + b*x + c*x**2), x) + Integral(2*a*b**5*x*sqrt(a + b*x + c*x**2), x) + Integral(32*a*c**5*x**6*sqrt(a + b*x + c*x**2), x) + Integral(16*a**2*c**4*x**4*sqrt(a + b*x + c*x**2), x) + Integral(64*b*c**5*x**7*sqrt(a + b*x + c*x**2), x) + Integral(104*b**2*c**4*x**6*sqrt(a + b*x + c*x**2), x) + Integral(88*b**3*c**3*x**5*sqrt(a + b*x + c*x**2), x) + Integral(41*b**4*c**2*x**4*sqrt(a + b*x + c*x**2), x) + Integral(10*b**5*c*x**3*sqrt(a + b*x + c*x**2), x) + Integral(96*a*b*c**4*x**5*sqrt(a + b*x + c*x**2), x) + Integral(112*a*b**2*c**3*x**4*sqrt(a + b*x + c*x**2), x) + Integral(64*a*b**3*c**2*x**3*sqrt(a + b*x + c*x**2), x) + Integral(18*a*b**4*c*x**2*sqrt(a + b*x + c*x**2), x) + Integral(32*a**2*b*c**3*x**3*sqrt(a + b*x + c*x**2), x) + Integral(24*a**2*b**2*c**2*x**2*sqrt(a + b*x + c*x**2), x) + Integral(8*a**2*b**3*c*x*sqrt(a + b*x + c*x**2), x))","F",0
1219,1,559,0,5.998051," ","integrate((2*c*d*x+b*d)**3*(c*x**2+b*x+a)**(5/2),x)","- \frac{16 a^{4} c d^{3} \sqrt{a + b x + c x^{2}}}{63} + \frac{2 a^{3} b^{2} d^{3} \sqrt{a + b x + c x^{2}}}{7} + \frac{8 a^{3} b c d^{3} x \sqrt{a + b x + c x^{2}}}{63} + \frac{8 a^{3} c^{2} d^{3} x^{2} \sqrt{a + b x + c x^{2}}}{63} + \frac{6 a^{2} b^{3} d^{3} x \sqrt{a + b x + c x^{2}}}{7} + \frac{58 a^{2} b^{2} c d^{3} x^{2} \sqrt{a + b x + c x^{2}}}{21} + \frac{80 a^{2} b c^{2} d^{3} x^{3} \sqrt{a + b x + c x^{2}}}{21} + \frac{40 a^{2} c^{3} d^{3} x^{4} \sqrt{a + b x + c x^{2}}}{21} + \frac{6 a b^{4} d^{3} x^{2} \sqrt{a + b x + c x^{2}}}{7} + \frac{260 a b^{3} c d^{3} x^{3} \sqrt{a + b x + c x^{2}}}{63} + \frac{170 a b^{2} c^{2} d^{3} x^{4} \sqrt{a + b x + c x^{2}}}{21} + \frac{152 a b c^{3} d^{3} x^{5} \sqrt{a + b x + c x^{2}}}{21} + \frac{152 a c^{4} d^{3} x^{6} \sqrt{a + b x + c x^{2}}}{63} + \frac{2 b^{5} d^{3} x^{3} \sqrt{a + b x + c x^{2}}}{7} + \frac{110 b^{4} c d^{3} x^{4} \sqrt{a + b x + c x^{2}}}{63} + \frac{278 b^{3} c^{2} d^{3} x^{5} \sqrt{a + b x + c x^{2}}}{63} + \frac{118 b^{2} c^{3} d^{3} x^{6} \sqrt{a + b x + c x^{2}}}{21} + \frac{32 b c^{4} d^{3} x^{7} \sqrt{a + b x + c x^{2}}}{9} + \frac{8 c^{5} d^{3} x^{8} \sqrt{a + b x + c x^{2}}}{9}"," ",0,"-16*a**4*c*d**3*sqrt(a + b*x + c*x**2)/63 + 2*a**3*b**2*d**3*sqrt(a + b*x + c*x**2)/7 + 8*a**3*b*c*d**3*x*sqrt(a + b*x + c*x**2)/63 + 8*a**3*c**2*d**3*x**2*sqrt(a + b*x + c*x**2)/63 + 6*a**2*b**3*d**3*x*sqrt(a + b*x + c*x**2)/7 + 58*a**2*b**2*c*d**3*x**2*sqrt(a + b*x + c*x**2)/21 + 80*a**2*b*c**2*d**3*x**3*sqrt(a + b*x + c*x**2)/21 + 40*a**2*c**3*d**3*x**4*sqrt(a + b*x + c*x**2)/21 + 6*a*b**4*d**3*x**2*sqrt(a + b*x + c*x**2)/7 + 260*a*b**3*c*d**3*x**3*sqrt(a + b*x + c*x**2)/63 + 170*a*b**2*c**2*d**3*x**4*sqrt(a + b*x + c*x**2)/21 + 152*a*b*c**3*d**3*x**5*sqrt(a + b*x + c*x**2)/21 + 152*a*c**4*d**3*x**6*sqrt(a + b*x + c*x**2)/63 + 2*b**5*d**3*x**3*sqrt(a + b*x + c*x**2)/7 + 110*b**4*c*d**3*x**4*sqrt(a + b*x + c*x**2)/63 + 278*b**3*c**2*d**3*x**5*sqrt(a + b*x + c*x**2)/63 + 118*b**2*c**3*d**3*x**6*sqrt(a + b*x + c*x**2)/21 + 32*b*c**4*d**3*x**7*sqrt(a + b*x + c*x**2)/9 + 8*c**5*d**3*x**8*sqrt(a + b*x + c*x**2)/9","B",0
1220,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**2*(c*x**2+b*x+a)**(5/2),x)","d^{2} \left(\int a^{2} b^{2} \sqrt{a + b x + c x^{2}}\, dx + \int b^{4} x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 4 c^{4} x^{6} \sqrt{a + b x + c x^{2}}\, dx + \int 2 a b^{3} x \sqrt{a + b x + c x^{2}}\, dx + \int 8 a c^{3} x^{4} \sqrt{a + b x + c x^{2}}\, dx + \int 4 a^{2} c^{2} x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 12 b c^{3} x^{5} \sqrt{a + b x + c x^{2}}\, dx + \int 13 b^{2} c^{2} x^{4} \sqrt{a + b x + c x^{2}}\, dx + \int 6 b^{3} c x^{3} \sqrt{a + b x + c x^{2}}\, dx + \int 16 a b c^{2} x^{3} \sqrt{a + b x + c x^{2}}\, dx + \int 10 a b^{2} c x^{2} \sqrt{a + b x + c x^{2}}\, dx + \int 4 a^{2} b c x \sqrt{a + b x + c x^{2}}\, dx\right)"," ",0,"d**2*(Integral(a**2*b**2*sqrt(a + b*x + c*x**2), x) + Integral(b**4*x**2*sqrt(a + b*x + c*x**2), x) + Integral(4*c**4*x**6*sqrt(a + b*x + c*x**2), x) + Integral(2*a*b**3*x*sqrt(a + b*x + c*x**2), x) + Integral(8*a*c**3*x**4*sqrt(a + b*x + c*x**2), x) + Integral(4*a**2*c**2*x**2*sqrt(a + b*x + c*x**2), x) + Integral(12*b*c**3*x**5*sqrt(a + b*x + c*x**2), x) + Integral(13*b**2*c**2*x**4*sqrt(a + b*x + c*x**2), x) + Integral(6*b**3*c*x**3*sqrt(a + b*x + c*x**2), x) + Integral(16*a*b*c**2*x**3*sqrt(a + b*x + c*x**2), x) + Integral(10*a*b**2*c*x**2*sqrt(a + b*x + c*x**2), x) + Integral(4*a**2*b*c*x*sqrt(a + b*x + c*x**2), x))","F",0
1221,1,260,0,2.841754," ","integrate((2*c*d*x+b*d)*(c*x**2+b*x+a)**(5/2),x)","\frac{2 a^{3} d \sqrt{a + b x + c x^{2}}}{7} + \frac{6 a^{2} b d x \sqrt{a + b x + c x^{2}}}{7} + \frac{6 a^{2} c d x^{2} \sqrt{a + b x + c x^{2}}}{7} + \frac{6 a b^{2} d x^{2} \sqrt{a + b x + c x^{2}}}{7} + \frac{12 a b c d x^{3} \sqrt{a + b x + c x^{2}}}{7} + \frac{6 a c^{2} d x^{4} \sqrt{a + b x + c x^{2}}}{7} + \frac{2 b^{3} d x^{3} \sqrt{a + b x + c x^{2}}}{7} + \frac{6 b^{2} c d x^{4} \sqrt{a + b x + c x^{2}}}{7} + \frac{6 b c^{2} d x^{5} \sqrt{a + b x + c x^{2}}}{7} + \frac{2 c^{3} d x^{6} \sqrt{a + b x + c x^{2}}}{7}"," ",0,"2*a**3*d*sqrt(a + b*x + c*x**2)/7 + 6*a**2*b*d*x*sqrt(a + b*x + c*x**2)/7 + 6*a**2*c*d*x**2*sqrt(a + b*x + c*x**2)/7 + 6*a*b**2*d*x**2*sqrt(a + b*x + c*x**2)/7 + 12*a*b*c*d*x**3*sqrt(a + b*x + c*x**2)/7 + 6*a*c**2*d*x**4*sqrt(a + b*x + c*x**2)/7 + 2*b**3*d*x**3*sqrt(a + b*x + c*x**2)/7 + 6*b**2*c*d*x**4*sqrt(a + b*x + c*x**2)/7 + 6*b*c**2*d*x**5*sqrt(a + b*x + c*x**2)/7 + 2*c**3*d*x**6*sqrt(a + b*x + c*x**2)/7","B",0
1222,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d),x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b + 2 c x}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b + 2 c x}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b + 2 c x}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b + 2 c x}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b + 2 c x}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b + 2 c x}\, dx}{d}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b + 2*c*x), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b + 2*c*x), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b + 2*c*x), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b + 2*c*x), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b + 2*c*x), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b + 2*c*x), x))/d","F",0
1223,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**2,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx}{d^{2}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**2 + 4*b*c*x + 4*c**2*x**2), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**2 + 4*b*c*x + 4*c**2*x**2), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**2 + 4*b*c*x + 4*c**2*x**2), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**2 + 4*b*c*x + 4*c**2*x**2), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**2 + 4*b*c*x + 4*c**2*x**2), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**2 + 4*b*c*x + 4*c**2*x**2), x))/d**2","F",0
1224,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**3,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{3} + 6 b^{2} c x + 12 b c^{2} x^{2} + 8 c^{3} x^{3}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{3} + 6 b^{2} c x + 12 b c^{2} x^{2} + 8 c^{3} x^{3}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{3} + 6 b^{2} c x + 12 b c^{2} x^{2} + 8 c^{3} x^{3}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{3} + 6 b^{2} c x + 12 b c^{2} x^{2} + 8 c^{3} x^{3}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{3} + 6 b^{2} c x + 12 b c^{2} x^{2} + 8 c^{3} x^{3}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{3} + 6 b^{2} c x + 12 b c^{2} x^{2} + 8 c^{3} x^{3}}\, dx}{d^{3}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**3 + 6*b**2*c*x + 12*b*c**2*x**2 + 8*c**3*x**3), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**3 + 6*b**2*c*x + 12*b*c**2*x**2 + 8*c**3*x**3), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**3 + 6*b**2*c*x + 12*b*c**2*x**2 + 8*c**3*x**3), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**3 + 6*b**2*c*x + 12*b*c**2*x**2 + 8*c**3*x**3), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**3 + 6*b**2*c*x + 12*b*c**2*x**2 + 8*c**3*x**3), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**3 + 6*b**2*c*x + 12*b*c**2*x**2 + 8*c**3*x**3), x))/d**3","F",0
1225,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**4,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{4} + 8 b^{3} c x + 24 b^{2} c^{2} x^{2} + 32 b c^{3} x^{3} + 16 c^{4} x^{4}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{4} + 8 b^{3} c x + 24 b^{2} c^{2} x^{2} + 32 b c^{3} x^{3} + 16 c^{4} x^{4}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{4} + 8 b^{3} c x + 24 b^{2} c^{2} x^{2} + 32 b c^{3} x^{3} + 16 c^{4} x^{4}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{4} + 8 b^{3} c x + 24 b^{2} c^{2} x^{2} + 32 b c^{3} x^{3} + 16 c^{4} x^{4}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{4} + 8 b^{3} c x + 24 b^{2} c^{2} x^{2} + 32 b c^{3} x^{3} + 16 c^{4} x^{4}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{4} + 8 b^{3} c x + 24 b^{2} c^{2} x^{2} + 32 b c^{3} x^{3} + 16 c^{4} x^{4}}\, dx}{d^{4}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**4 + 8*b**3*c*x + 24*b**2*c**2*x**2 + 32*b*c**3*x**3 + 16*c**4*x**4), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**4 + 8*b**3*c*x + 24*b**2*c**2*x**2 + 32*b*c**3*x**3 + 16*c**4*x**4), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**4 + 8*b**3*c*x + 24*b**2*c**2*x**2 + 32*b*c**3*x**3 + 16*c**4*x**4), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**4 + 8*b**3*c*x + 24*b**2*c**2*x**2 + 32*b*c**3*x**3 + 16*c**4*x**4), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**4 + 8*b**3*c*x + 24*b**2*c**2*x**2 + 32*b*c**3*x**3 + 16*c**4*x**4), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**4 + 8*b**3*c*x + 24*b**2*c**2*x**2 + 32*b*c**3*x**3 + 16*c**4*x**4), x))/d**4","F",0
1226,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**5,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{5} + 10 b^{4} c x + 40 b^{3} c^{2} x^{2} + 80 b^{2} c^{3} x^{3} + 80 b c^{4} x^{4} + 32 c^{5} x^{5}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{5} + 10 b^{4} c x + 40 b^{3} c^{2} x^{2} + 80 b^{2} c^{3} x^{3} + 80 b c^{4} x^{4} + 32 c^{5} x^{5}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{5} + 10 b^{4} c x + 40 b^{3} c^{2} x^{2} + 80 b^{2} c^{3} x^{3} + 80 b c^{4} x^{4} + 32 c^{5} x^{5}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{5} + 10 b^{4} c x + 40 b^{3} c^{2} x^{2} + 80 b^{2} c^{3} x^{3} + 80 b c^{4} x^{4} + 32 c^{5} x^{5}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{5} + 10 b^{4} c x + 40 b^{3} c^{2} x^{2} + 80 b^{2} c^{3} x^{3} + 80 b c^{4} x^{4} + 32 c^{5} x^{5}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{5} + 10 b^{4} c x + 40 b^{3} c^{2} x^{2} + 80 b^{2} c^{3} x^{3} + 80 b c^{4} x^{4} + 32 c^{5} x^{5}}\, dx}{d^{5}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**5 + 10*b**4*c*x + 40*b**3*c**2*x**2 + 80*b**2*c**3*x**3 + 80*b*c**4*x**4 + 32*c**5*x**5), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**5 + 10*b**4*c*x + 40*b**3*c**2*x**2 + 80*b**2*c**3*x**3 + 80*b*c**4*x**4 + 32*c**5*x**5), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**5 + 10*b**4*c*x + 40*b**3*c**2*x**2 + 80*b**2*c**3*x**3 + 80*b*c**4*x**4 + 32*c**5*x**5), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**5 + 10*b**4*c*x + 40*b**3*c**2*x**2 + 80*b**2*c**3*x**3 + 80*b*c**4*x**4 + 32*c**5*x**5), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**5 + 10*b**4*c*x + 40*b**3*c**2*x**2 + 80*b**2*c**3*x**3 + 80*b*c**4*x**4 + 32*c**5*x**5), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**5 + 10*b**4*c*x + 40*b**3*c**2*x**2 + 80*b**2*c**3*x**3 + 80*b*c**4*x**4 + 32*c**5*x**5), x))/d**5","F",0
1227,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**6,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{6} + 12 b^{5} c x + 60 b^{4} c^{2} x^{2} + 160 b^{3} c^{3} x^{3} + 240 b^{2} c^{4} x^{4} + 192 b c^{5} x^{5} + 64 c^{6} x^{6}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{6} + 12 b^{5} c x + 60 b^{4} c^{2} x^{2} + 160 b^{3} c^{3} x^{3} + 240 b^{2} c^{4} x^{4} + 192 b c^{5} x^{5} + 64 c^{6} x^{6}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{6} + 12 b^{5} c x + 60 b^{4} c^{2} x^{2} + 160 b^{3} c^{3} x^{3} + 240 b^{2} c^{4} x^{4} + 192 b c^{5} x^{5} + 64 c^{6} x^{6}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{6} + 12 b^{5} c x + 60 b^{4} c^{2} x^{2} + 160 b^{3} c^{3} x^{3} + 240 b^{2} c^{4} x^{4} + 192 b c^{5} x^{5} + 64 c^{6} x^{6}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{6} + 12 b^{5} c x + 60 b^{4} c^{2} x^{2} + 160 b^{3} c^{3} x^{3} + 240 b^{2} c^{4} x^{4} + 192 b c^{5} x^{5} + 64 c^{6} x^{6}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{6} + 12 b^{5} c x + 60 b^{4} c^{2} x^{2} + 160 b^{3} c^{3} x^{3} + 240 b^{2} c^{4} x^{4} + 192 b c^{5} x^{5} + 64 c^{6} x^{6}}\, dx}{d^{6}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**6 + 12*b**5*c*x + 60*b**4*c**2*x**2 + 160*b**3*c**3*x**3 + 240*b**2*c**4*x**4 + 192*b*c**5*x**5 + 64*c**6*x**6), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**6 + 12*b**5*c*x + 60*b**4*c**2*x**2 + 160*b**3*c**3*x**3 + 240*b**2*c**4*x**4 + 192*b*c**5*x**5 + 64*c**6*x**6), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**6 + 12*b**5*c*x + 60*b**4*c**2*x**2 + 160*b**3*c**3*x**3 + 240*b**2*c**4*x**4 + 192*b*c**5*x**5 + 64*c**6*x**6), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**6 + 12*b**5*c*x + 60*b**4*c**2*x**2 + 160*b**3*c**3*x**3 + 240*b**2*c**4*x**4 + 192*b*c**5*x**5 + 64*c**6*x**6), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**6 + 12*b**5*c*x + 60*b**4*c**2*x**2 + 160*b**3*c**3*x**3 + 240*b**2*c**4*x**4 + 192*b*c**5*x**5 + 64*c**6*x**6), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**6 + 12*b**5*c*x + 60*b**4*c**2*x**2 + 160*b**3*c**3*x**3 + 240*b**2*c**4*x**4 + 192*b*c**5*x**5 + 64*c**6*x**6), x))/d**6","F",0
1228,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**7,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{7} + 14 b^{6} c x + 84 b^{5} c^{2} x^{2} + 280 b^{4} c^{3} x^{3} + 560 b^{3} c^{4} x^{4} + 672 b^{2} c^{5} x^{5} + 448 b c^{6} x^{6} + 128 c^{7} x^{7}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{7} + 14 b^{6} c x + 84 b^{5} c^{2} x^{2} + 280 b^{4} c^{3} x^{3} + 560 b^{3} c^{4} x^{4} + 672 b^{2} c^{5} x^{5} + 448 b c^{6} x^{6} + 128 c^{7} x^{7}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{7} + 14 b^{6} c x + 84 b^{5} c^{2} x^{2} + 280 b^{4} c^{3} x^{3} + 560 b^{3} c^{4} x^{4} + 672 b^{2} c^{5} x^{5} + 448 b c^{6} x^{6} + 128 c^{7} x^{7}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{7} + 14 b^{6} c x + 84 b^{5} c^{2} x^{2} + 280 b^{4} c^{3} x^{3} + 560 b^{3} c^{4} x^{4} + 672 b^{2} c^{5} x^{5} + 448 b c^{6} x^{6} + 128 c^{7} x^{7}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{7} + 14 b^{6} c x + 84 b^{5} c^{2} x^{2} + 280 b^{4} c^{3} x^{3} + 560 b^{3} c^{4} x^{4} + 672 b^{2} c^{5} x^{5} + 448 b c^{6} x^{6} + 128 c^{7} x^{7}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{7} + 14 b^{6} c x + 84 b^{5} c^{2} x^{2} + 280 b^{4} c^{3} x^{3} + 560 b^{3} c^{4} x^{4} + 672 b^{2} c^{5} x^{5} + 448 b c^{6} x^{6} + 128 c^{7} x^{7}}\, dx}{d^{7}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**7 + 14*b**6*c*x + 84*b**5*c**2*x**2 + 280*b**4*c**3*x**3 + 560*b**3*c**4*x**4 + 672*b**2*c**5*x**5 + 448*b*c**6*x**6 + 128*c**7*x**7), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**7 + 14*b**6*c*x + 84*b**5*c**2*x**2 + 280*b**4*c**3*x**3 + 560*b**3*c**4*x**4 + 672*b**2*c**5*x**5 + 448*b*c**6*x**6 + 128*c**7*x**7), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**7 + 14*b**6*c*x + 84*b**5*c**2*x**2 + 280*b**4*c**3*x**3 + 560*b**3*c**4*x**4 + 672*b**2*c**5*x**5 + 448*b*c**6*x**6 + 128*c**7*x**7), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**7 + 14*b**6*c*x + 84*b**5*c**2*x**2 + 280*b**4*c**3*x**3 + 560*b**3*c**4*x**4 + 672*b**2*c**5*x**5 + 448*b*c**6*x**6 + 128*c**7*x**7), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**7 + 14*b**6*c*x + 84*b**5*c**2*x**2 + 280*b**4*c**3*x**3 + 560*b**3*c**4*x**4 + 672*b**2*c**5*x**5 + 448*b*c**6*x**6 + 128*c**7*x**7), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**7 + 14*b**6*c*x + 84*b**5*c**2*x**2 + 280*b**4*c**3*x**3 + 560*b**3*c**4*x**4 + 672*b**2*c**5*x**5 + 448*b*c**6*x**6 + 128*c**7*x**7), x))/d**7","F",0
1229,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**8,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{8} + 16 b^{7} c x + 112 b^{6} c^{2} x^{2} + 448 b^{5} c^{3} x^{3} + 1120 b^{4} c^{4} x^{4} + 1792 b^{3} c^{5} x^{5} + 1792 b^{2} c^{6} x^{6} + 1024 b c^{7} x^{7} + 256 c^{8} x^{8}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{8} + 16 b^{7} c x + 112 b^{6} c^{2} x^{2} + 448 b^{5} c^{3} x^{3} + 1120 b^{4} c^{4} x^{4} + 1792 b^{3} c^{5} x^{5} + 1792 b^{2} c^{6} x^{6} + 1024 b c^{7} x^{7} + 256 c^{8} x^{8}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{8} + 16 b^{7} c x + 112 b^{6} c^{2} x^{2} + 448 b^{5} c^{3} x^{3} + 1120 b^{4} c^{4} x^{4} + 1792 b^{3} c^{5} x^{5} + 1792 b^{2} c^{6} x^{6} + 1024 b c^{7} x^{7} + 256 c^{8} x^{8}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{8} + 16 b^{7} c x + 112 b^{6} c^{2} x^{2} + 448 b^{5} c^{3} x^{3} + 1120 b^{4} c^{4} x^{4} + 1792 b^{3} c^{5} x^{5} + 1792 b^{2} c^{6} x^{6} + 1024 b c^{7} x^{7} + 256 c^{8} x^{8}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{8} + 16 b^{7} c x + 112 b^{6} c^{2} x^{2} + 448 b^{5} c^{3} x^{3} + 1120 b^{4} c^{4} x^{4} + 1792 b^{3} c^{5} x^{5} + 1792 b^{2} c^{6} x^{6} + 1024 b c^{7} x^{7} + 256 c^{8} x^{8}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{8} + 16 b^{7} c x + 112 b^{6} c^{2} x^{2} + 448 b^{5} c^{3} x^{3} + 1120 b^{4} c^{4} x^{4} + 1792 b^{3} c^{5} x^{5} + 1792 b^{2} c^{6} x^{6} + 1024 b c^{7} x^{7} + 256 c^{8} x^{8}}\, dx}{d^{8}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**8 + 16*b**7*c*x + 112*b**6*c**2*x**2 + 448*b**5*c**3*x**3 + 1120*b**4*c**4*x**4 + 1792*b**3*c**5*x**5 + 1792*b**2*c**6*x**6 + 1024*b*c**7*x**7 + 256*c**8*x**8), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**8 + 16*b**7*c*x + 112*b**6*c**2*x**2 + 448*b**5*c**3*x**3 + 1120*b**4*c**4*x**4 + 1792*b**3*c**5*x**5 + 1792*b**2*c**6*x**6 + 1024*b*c**7*x**7 + 256*c**8*x**8), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**8 + 16*b**7*c*x + 112*b**6*c**2*x**2 + 448*b**5*c**3*x**3 + 1120*b**4*c**4*x**4 + 1792*b**3*c**5*x**5 + 1792*b**2*c**6*x**6 + 1024*b*c**7*x**7 + 256*c**8*x**8), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**8 + 16*b**7*c*x + 112*b**6*c**2*x**2 + 448*b**5*c**3*x**3 + 1120*b**4*c**4*x**4 + 1792*b**3*c**5*x**5 + 1792*b**2*c**6*x**6 + 1024*b*c**7*x**7 + 256*c**8*x**8), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**8 + 16*b**7*c*x + 112*b**6*c**2*x**2 + 448*b**5*c**3*x**3 + 1120*b**4*c**4*x**4 + 1792*b**3*c**5*x**5 + 1792*b**2*c**6*x**6 + 1024*b*c**7*x**7 + 256*c**8*x**8), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**8 + 16*b**7*c*x + 112*b**6*c**2*x**2 + 448*b**5*c**3*x**3 + 1120*b**4*c**4*x**4 + 1792*b**3*c**5*x**5 + 1792*b**2*c**6*x**6 + 1024*b*c**7*x**7 + 256*c**8*x**8), x))/d**8","F",0
1230,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**9,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{9} + 18 b^{8} c x + 144 b^{7} c^{2} x^{2} + 672 b^{6} c^{3} x^{3} + 2016 b^{5} c^{4} x^{4} + 4032 b^{4} c^{5} x^{5} + 5376 b^{3} c^{6} x^{6} + 4608 b^{2} c^{7} x^{7} + 2304 b c^{8} x^{8} + 512 c^{9} x^{9}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{9} + 18 b^{8} c x + 144 b^{7} c^{2} x^{2} + 672 b^{6} c^{3} x^{3} + 2016 b^{5} c^{4} x^{4} + 4032 b^{4} c^{5} x^{5} + 5376 b^{3} c^{6} x^{6} + 4608 b^{2} c^{7} x^{7} + 2304 b c^{8} x^{8} + 512 c^{9} x^{9}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{9} + 18 b^{8} c x + 144 b^{7} c^{2} x^{2} + 672 b^{6} c^{3} x^{3} + 2016 b^{5} c^{4} x^{4} + 4032 b^{4} c^{5} x^{5} + 5376 b^{3} c^{6} x^{6} + 4608 b^{2} c^{7} x^{7} + 2304 b c^{8} x^{8} + 512 c^{9} x^{9}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{9} + 18 b^{8} c x + 144 b^{7} c^{2} x^{2} + 672 b^{6} c^{3} x^{3} + 2016 b^{5} c^{4} x^{4} + 4032 b^{4} c^{5} x^{5} + 5376 b^{3} c^{6} x^{6} + 4608 b^{2} c^{7} x^{7} + 2304 b c^{8} x^{8} + 512 c^{9} x^{9}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{9} + 18 b^{8} c x + 144 b^{7} c^{2} x^{2} + 672 b^{6} c^{3} x^{3} + 2016 b^{5} c^{4} x^{4} + 4032 b^{4} c^{5} x^{5} + 5376 b^{3} c^{6} x^{6} + 4608 b^{2} c^{7} x^{7} + 2304 b c^{8} x^{8} + 512 c^{9} x^{9}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{9} + 18 b^{8} c x + 144 b^{7} c^{2} x^{2} + 672 b^{6} c^{3} x^{3} + 2016 b^{5} c^{4} x^{4} + 4032 b^{4} c^{5} x^{5} + 5376 b^{3} c^{6} x^{6} + 4608 b^{2} c^{7} x^{7} + 2304 b c^{8} x^{8} + 512 c^{9} x^{9}}\, dx}{d^{9}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**9 + 18*b**8*c*x + 144*b**7*c**2*x**2 + 672*b**6*c**3*x**3 + 2016*b**5*c**4*x**4 + 4032*b**4*c**5*x**5 + 5376*b**3*c**6*x**6 + 4608*b**2*c**7*x**7 + 2304*b*c**8*x**8 + 512*c**9*x**9), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**9 + 18*b**8*c*x + 144*b**7*c**2*x**2 + 672*b**6*c**3*x**3 + 2016*b**5*c**4*x**4 + 4032*b**4*c**5*x**5 + 5376*b**3*c**6*x**6 + 4608*b**2*c**7*x**7 + 2304*b*c**8*x**8 + 512*c**9*x**9), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**9 + 18*b**8*c*x + 144*b**7*c**2*x**2 + 672*b**6*c**3*x**3 + 2016*b**5*c**4*x**4 + 4032*b**4*c**5*x**5 + 5376*b**3*c**6*x**6 + 4608*b**2*c**7*x**7 + 2304*b*c**8*x**8 + 512*c**9*x**9), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**9 + 18*b**8*c*x + 144*b**7*c**2*x**2 + 672*b**6*c**3*x**3 + 2016*b**5*c**4*x**4 + 4032*b**4*c**5*x**5 + 5376*b**3*c**6*x**6 + 4608*b**2*c**7*x**7 + 2304*b*c**8*x**8 + 512*c**9*x**9), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**9 + 18*b**8*c*x + 144*b**7*c**2*x**2 + 672*b**6*c**3*x**3 + 2016*b**5*c**4*x**4 + 4032*b**4*c**5*x**5 + 5376*b**3*c**6*x**6 + 4608*b**2*c**7*x**7 + 2304*b*c**8*x**8 + 512*c**9*x**9), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**9 + 18*b**8*c*x + 144*b**7*c**2*x**2 + 672*b**6*c**3*x**3 + 2016*b**5*c**4*x**4 + 4032*b**4*c**5*x**5 + 5376*b**3*c**6*x**6 + 4608*b**2*c**7*x**7 + 2304*b*c**8*x**8 + 512*c**9*x**9), x))/d**9","F",0
1231,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**10,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{10} + 20 b^{9} c x + 180 b^{8} c^{2} x^{2} + 960 b^{7} c^{3} x^{3} + 3360 b^{6} c^{4} x^{4} + 8064 b^{5} c^{5} x^{5} + 13440 b^{4} c^{6} x^{6} + 15360 b^{3} c^{7} x^{7} + 11520 b^{2} c^{8} x^{8} + 5120 b c^{9} x^{9} + 1024 c^{10} x^{10}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{10} + 20 b^{9} c x + 180 b^{8} c^{2} x^{2} + 960 b^{7} c^{3} x^{3} + 3360 b^{6} c^{4} x^{4} + 8064 b^{5} c^{5} x^{5} + 13440 b^{4} c^{6} x^{6} + 15360 b^{3} c^{7} x^{7} + 11520 b^{2} c^{8} x^{8} + 5120 b c^{9} x^{9} + 1024 c^{10} x^{10}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{10} + 20 b^{9} c x + 180 b^{8} c^{2} x^{2} + 960 b^{7} c^{3} x^{3} + 3360 b^{6} c^{4} x^{4} + 8064 b^{5} c^{5} x^{5} + 13440 b^{4} c^{6} x^{6} + 15360 b^{3} c^{7} x^{7} + 11520 b^{2} c^{8} x^{8} + 5120 b c^{9} x^{9} + 1024 c^{10} x^{10}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{10} + 20 b^{9} c x + 180 b^{8} c^{2} x^{2} + 960 b^{7} c^{3} x^{3} + 3360 b^{6} c^{4} x^{4} + 8064 b^{5} c^{5} x^{5} + 13440 b^{4} c^{6} x^{6} + 15360 b^{3} c^{7} x^{7} + 11520 b^{2} c^{8} x^{8} + 5120 b c^{9} x^{9} + 1024 c^{10} x^{10}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{10} + 20 b^{9} c x + 180 b^{8} c^{2} x^{2} + 960 b^{7} c^{3} x^{3} + 3360 b^{6} c^{4} x^{4} + 8064 b^{5} c^{5} x^{5} + 13440 b^{4} c^{6} x^{6} + 15360 b^{3} c^{7} x^{7} + 11520 b^{2} c^{8} x^{8} + 5120 b c^{9} x^{9} + 1024 c^{10} x^{10}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{10} + 20 b^{9} c x + 180 b^{8} c^{2} x^{2} + 960 b^{7} c^{3} x^{3} + 3360 b^{6} c^{4} x^{4} + 8064 b^{5} c^{5} x^{5} + 13440 b^{4} c^{6} x^{6} + 15360 b^{3} c^{7} x^{7} + 11520 b^{2} c^{8} x^{8} + 5120 b c^{9} x^{9} + 1024 c^{10} x^{10}}\, dx}{d^{10}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**10 + 20*b**9*c*x + 180*b**8*c**2*x**2 + 960*b**7*c**3*x**3 + 3360*b**6*c**4*x**4 + 8064*b**5*c**5*x**5 + 13440*b**4*c**6*x**6 + 15360*b**3*c**7*x**7 + 11520*b**2*c**8*x**8 + 5120*b*c**9*x**9 + 1024*c**10*x**10), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**10 + 20*b**9*c*x + 180*b**8*c**2*x**2 + 960*b**7*c**3*x**3 + 3360*b**6*c**4*x**4 + 8064*b**5*c**5*x**5 + 13440*b**4*c**6*x**6 + 15360*b**3*c**7*x**7 + 11520*b**2*c**8*x**8 + 5120*b*c**9*x**9 + 1024*c**10*x**10), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**10 + 20*b**9*c*x + 180*b**8*c**2*x**2 + 960*b**7*c**3*x**3 + 3360*b**6*c**4*x**4 + 8064*b**5*c**5*x**5 + 13440*b**4*c**6*x**6 + 15360*b**3*c**7*x**7 + 11520*b**2*c**8*x**8 + 5120*b*c**9*x**9 + 1024*c**10*x**10), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**10 + 20*b**9*c*x + 180*b**8*c**2*x**2 + 960*b**7*c**3*x**3 + 3360*b**6*c**4*x**4 + 8064*b**5*c**5*x**5 + 13440*b**4*c**6*x**6 + 15360*b**3*c**7*x**7 + 11520*b**2*c**8*x**8 + 5120*b*c**9*x**9 + 1024*c**10*x**10), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**10 + 20*b**9*c*x + 180*b**8*c**2*x**2 + 960*b**7*c**3*x**3 + 3360*b**6*c**4*x**4 + 8064*b**5*c**5*x**5 + 13440*b**4*c**6*x**6 + 15360*b**3*c**7*x**7 + 11520*b**2*c**8*x**8 + 5120*b*c**9*x**9 + 1024*c**10*x**10), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**10 + 20*b**9*c*x + 180*b**8*c**2*x**2 + 960*b**7*c**3*x**3 + 3360*b**6*c**4*x**4 + 8064*b**5*c**5*x**5 + 13440*b**4*c**6*x**6 + 15360*b**3*c**7*x**7 + 11520*b**2*c**8*x**8 + 5120*b*c**9*x**9 + 1024*c**10*x**10), x))/d**10","F",0
1232,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**11,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{11} + 22 b^{10} c x + 220 b^{9} c^{2} x^{2} + 1320 b^{8} c^{3} x^{3} + 5280 b^{7} c^{4} x^{4} + 14784 b^{6} c^{5} x^{5} + 29568 b^{5} c^{6} x^{6} + 42240 b^{4} c^{7} x^{7} + 42240 b^{3} c^{8} x^{8} + 28160 b^{2} c^{9} x^{9} + 11264 b c^{10} x^{10} + 2048 c^{11} x^{11}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{11} + 22 b^{10} c x + 220 b^{9} c^{2} x^{2} + 1320 b^{8} c^{3} x^{3} + 5280 b^{7} c^{4} x^{4} + 14784 b^{6} c^{5} x^{5} + 29568 b^{5} c^{6} x^{6} + 42240 b^{4} c^{7} x^{7} + 42240 b^{3} c^{8} x^{8} + 28160 b^{2} c^{9} x^{9} + 11264 b c^{10} x^{10} + 2048 c^{11} x^{11}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{11} + 22 b^{10} c x + 220 b^{9} c^{2} x^{2} + 1320 b^{8} c^{3} x^{3} + 5280 b^{7} c^{4} x^{4} + 14784 b^{6} c^{5} x^{5} + 29568 b^{5} c^{6} x^{6} + 42240 b^{4} c^{7} x^{7} + 42240 b^{3} c^{8} x^{8} + 28160 b^{2} c^{9} x^{9} + 11264 b c^{10} x^{10} + 2048 c^{11} x^{11}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{11} + 22 b^{10} c x + 220 b^{9} c^{2} x^{2} + 1320 b^{8} c^{3} x^{3} + 5280 b^{7} c^{4} x^{4} + 14784 b^{6} c^{5} x^{5} + 29568 b^{5} c^{6} x^{6} + 42240 b^{4} c^{7} x^{7} + 42240 b^{3} c^{8} x^{8} + 28160 b^{2} c^{9} x^{9} + 11264 b c^{10} x^{10} + 2048 c^{11} x^{11}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{11} + 22 b^{10} c x + 220 b^{9} c^{2} x^{2} + 1320 b^{8} c^{3} x^{3} + 5280 b^{7} c^{4} x^{4} + 14784 b^{6} c^{5} x^{5} + 29568 b^{5} c^{6} x^{6} + 42240 b^{4} c^{7} x^{7} + 42240 b^{3} c^{8} x^{8} + 28160 b^{2} c^{9} x^{9} + 11264 b c^{10} x^{10} + 2048 c^{11} x^{11}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{11} + 22 b^{10} c x + 220 b^{9} c^{2} x^{2} + 1320 b^{8} c^{3} x^{3} + 5280 b^{7} c^{4} x^{4} + 14784 b^{6} c^{5} x^{5} + 29568 b^{5} c^{6} x^{6} + 42240 b^{4} c^{7} x^{7} + 42240 b^{3} c^{8} x^{8} + 28160 b^{2} c^{9} x^{9} + 11264 b c^{10} x^{10} + 2048 c^{11} x^{11}}\, dx}{d^{11}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**11 + 22*b**10*c*x + 220*b**9*c**2*x**2 + 1320*b**8*c**3*x**3 + 5280*b**7*c**4*x**4 + 14784*b**6*c**5*x**5 + 29568*b**5*c**6*x**6 + 42240*b**4*c**7*x**7 + 42240*b**3*c**8*x**8 + 28160*b**2*c**9*x**9 + 11264*b*c**10*x**10 + 2048*c**11*x**11), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**11 + 22*b**10*c*x + 220*b**9*c**2*x**2 + 1320*b**8*c**3*x**3 + 5280*b**7*c**4*x**4 + 14784*b**6*c**5*x**5 + 29568*b**5*c**6*x**6 + 42240*b**4*c**7*x**7 + 42240*b**3*c**8*x**8 + 28160*b**2*c**9*x**9 + 11264*b*c**10*x**10 + 2048*c**11*x**11), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**11 + 22*b**10*c*x + 220*b**9*c**2*x**2 + 1320*b**8*c**3*x**3 + 5280*b**7*c**4*x**4 + 14784*b**6*c**5*x**5 + 29568*b**5*c**6*x**6 + 42240*b**4*c**7*x**7 + 42240*b**3*c**8*x**8 + 28160*b**2*c**9*x**9 + 11264*b*c**10*x**10 + 2048*c**11*x**11), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**11 + 22*b**10*c*x + 220*b**9*c**2*x**2 + 1320*b**8*c**3*x**3 + 5280*b**7*c**4*x**4 + 14784*b**6*c**5*x**5 + 29568*b**5*c**6*x**6 + 42240*b**4*c**7*x**7 + 42240*b**3*c**8*x**8 + 28160*b**2*c**9*x**9 + 11264*b*c**10*x**10 + 2048*c**11*x**11), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**11 + 22*b**10*c*x + 220*b**9*c**2*x**2 + 1320*b**8*c**3*x**3 + 5280*b**7*c**4*x**4 + 14784*b**6*c**5*x**5 + 29568*b**5*c**6*x**6 + 42240*b**4*c**7*x**7 + 42240*b**3*c**8*x**8 + 28160*b**2*c**9*x**9 + 11264*b*c**10*x**10 + 2048*c**11*x**11), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**11 + 22*b**10*c*x + 220*b**9*c**2*x**2 + 1320*b**8*c**3*x**3 + 5280*b**7*c**4*x**4 + 14784*b**6*c**5*x**5 + 29568*b**5*c**6*x**6 + 42240*b**4*c**7*x**7 + 42240*b**3*c**8*x**8 + 28160*b**2*c**9*x**9 + 11264*b*c**10*x**10 + 2048*c**11*x**11), x))/d**11","F",0
1233,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**12,x)","\frac{\int \frac{a^{2} \sqrt{a + b x + c x^{2}}}{b^{12} + 24 b^{11} c x + 264 b^{10} c^{2} x^{2} + 1760 b^{9} c^{3} x^{3} + 7920 b^{8} c^{4} x^{4} + 25344 b^{7} c^{5} x^{5} + 59136 b^{6} c^{6} x^{6} + 101376 b^{5} c^{7} x^{7} + 126720 b^{4} c^{8} x^{8} + 112640 b^{3} c^{9} x^{9} + 67584 b^{2} c^{10} x^{10} + 24576 b c^{11} x^{11} + 4096 c^{12} x^{12}}\, dx + \int \frac{b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{b^{12} + 24 b^{11} c x + 264 b^{10} c^{2} x^{2} + 1760 b^{9} c^{3} x^{3} + 7920 b^{8} c^{4} x^{4} + 25344 b^{7} c^{5} x^{5} + 59136 b^{6} c^{6} x^{6} + 101376 b^{5} c^{7} x^{7} + 126720 b^{4} c^{8} x^{8} + 112640 b^{3} c^{9} x^{9} + 67584 b^{2} c^{10} x^{10} + 24576 b c^{11} x^{11} + 4096 c^{12} x^{12}}\, dx + \int \frac{c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{b^{12} + 24 b^{11} c x + 264 b^{10} c^{2} x^{2} + 1760 b^{9} c^{3} x^{3} + 7920 b^{8} c^{4} x^{4} + 25344 b^{7} c^{5} x^{5} + 59136 b^{6} c^{6} x^{6} + 101376 b^{5} c^{7} x^{7} + 126720 b^{4} c^{8} x^{8} + 112640 b^{3} c^{9} x^{9} + 67584 b^{2} c^{10} x^{10} + 24576 b c^{11} x^{11} + 4096 c^{12} x^{12}}\, dx + \int \frac{2 a b x \sqrt{a + b x + c x^{2}}}{b^{12} + 24 b^{11} c x + 264 b^{10} c^{2} x^{2} + 1760 b^{9} c^{3} x^{3} + 7920 b^{8} c^{4} x^{4} + 25344 b^{7} c^{5} x^{5} + 59136 b^{6} c^{6} x^{6} + 101376 b^{5} c^{7} x^{7} + 126720 b^{4} c^{8} x^{8} + 112640 b^{3} c^{9} x^{9} + 67584 b^{2} c^{10} x^{10} + 24576 b c^{11} x^{11} + 4096 c^{12} x^{12}}\, dx + \int \frac{2 a c x^{2} \sqrt{a + b x + c x^{2}}}{b^{12} + 24 b^{11} c x + 264 b^{10} c^{2} x^{2} + 1760 b^{9} c^{3} x^{3} + 7920 b^{8} c^{4} x^{4} + 25344 b^{7} c^{5} x^{5} + 59136 b^{6} c^{6} x^{6} + 101376 b^{5} c^{7} x^{7} + 126720 b^{4} c^{8} x^{8} + 112640 b^{3} c^{9} x^{9} + 67584 b^{2} c^{10} x^{10} + 24576 b c^{11} x^{11} + 4096 c^{12} x^{12}}\, dx + \int \frac{2 b c x^{3} \sqrt{a + b x + c x^{2}}}{b^{12} + 24 b^{11} c x + 264 b^{10} c^{2} x^{2} + 1760 b^{9} c^{3} x^{3} + 7920 b^{8} c^{4} x^{4} + 25344 b^{7} c^{5} x^{5} + 59136 b^{6} c^{6} x^{6} + 101376 b^{5} c^{7} x^{7} + 126720 b^{4} c^{8} x^{8} + 112640 b^{3} c^{9} x^{9} + 67584 b^{2} c^{10} x^{10} + 24576 b c^{11} x^{11} + 4096 c^{12} x^{12}}\, dx}{d^{12}}"," ",0,"(Integral(a**2*sqrt(a + b*x + c*x**2)/(b**12 + 24*b**11*c*x + 264*b**10*c**2*x**2 + 1760*b**9*c**3*x**3 + 7920*b**8*c**4*x**4 + 25344*b**7*c**5*x**5 + 59136*b**6*c**6*x**6 + 101376*b**5*c**7*x**7 + 126720*b**4*c**8*x**8 + 112640*b**3*c**9*x**9 + 67584*b**2*c**10*x**10 + 24576*b*c**11*x**11 + 4096*c**12*x**12), x) + Integral(b**2*x**2*sqrt(a + b*x + c*x**2)/(b**12 + 24*b**11*c*x + 264*b**10*c**2*x**2 + 1760*b**9*c**3*x**3 + 7920*b**8*c**4*x**4 + 25344*b**7*c**5*x**5 + 59136*b**6*c**6*x**6 + 101376*b**5*c**7*x**7 + 126720*b**4*c**8*x**8 + 112640*b**3*c**9*x**9 + 67584*b**2*c**10*x**10 + 24576*b*c**11*x**11 + 4096*c**12*x**12), x) + Integral(c**2*x**4*sqrt(a + b*x + c*x**2)/(b**12 + 24*b**11*c*x + 264*b**10*c**2*x**2 + 1760*b**9*c**3*x**3 + 7920*b**8*c**4*x**4 + 25344*b**7*c**5*x**5 + 59136*b**6*c**6*x**6 + 101376*b**5*c**7*x**7 + 126720*b**4*c**8*x**8 + 112640*b**3*c**9*x**9 + 67584*b**2*c**10*x**10 + 24576*b*c**11*x**11 + 4096*c**12*x**12), x) + Integral(2*a*b*x*sqrt(a + b*x + c*x**2)/(b**12 + 24*b**11*c*x + 264*b**10*c**2*x**2 + 1760*b**9*c**3*x**3 + 7920*b**8*c**4*x**4 + 25344*b**7*c**5*x**5 + 59136*b**6*c**6*x**6 + 101376*b**5*c**7*x**7 + 126720*b**4*c**8*x**8 + 112640*b**3*c**9*x**9 + 67584*b**2*c**10*x**10 + 24576*b*c**11*x**11 + 4096*c**12*x**12), x) + Integral(2*a*c*x**2*sqrt(a + b*x + c*x**2)/(b**12 + 24*b**11*c*x + 264*b**10*c**2*x**2 + 1760*b**9*c**3*x**3 + 7920*b**8*c**4*x**4 + 25344*b**7*c**5*x**5 + 59136*b**6*c**6*x**6 + 101376*b**5*c**7*x**7 + 126720*b**4*c**8*x**8 + 112640*b**3*c**9*x**9 + 67584*b**2*c**10*x**10 + 24576*b*c**11*x**11 + 4096*c**12*x**12), x) + Integral(2*b*c*x**3*sqrt(a + b*x + c*x**2)/(b**12 + 24*b**11*c*x + 264*b**10*c**2*x**2 + 1760*b**9*c**3*x**3 + 7920*b**8*c**4*x**4 + 25344*b**7*c**5*x**5 + 59136*b**6*c**6*x**6 + 101376*b**5*c**7*x**7 + 126720*b**4*c**8*x**8 + 112640*b**3*c**9*x**9 + 67584*b**2*c**10*x**10 + 24576*b*c**11*x**11 + 4096*c**12*x**12), x))/d**12","F",0
1234,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**4/(c*x**2+b*x+a)**(1/2),x)","d^{4} \left(\int \frac{b^{4}}{\sqrt{a + b x + c x^{2}}}\, dx + \int \frac{16 c^{4} x^{4}}{\sqrt{a + b x + c x^{2}}}\, dx + \int \frac{32 b c^{3} x^{3}}{\sqrt{a + b x + c x^{2}}}\, dx + \int \frac{24 b^{2} c^{2} x^{2}}{\sqrt{a + b x + c x^{2}}}\, dx + \int \frac{8 b^{3} c x}{\sqrt{a + b x + c x^{2}}}\, dx\right)"," ",0,"d**4*(Integral(b**4/sqrt(a + b*x + c*x**2), x) + Integral(16*c**4*x**4/sqrt(a + b*x + c*x**2), x) + Integral(32*b*c**3*x**3/sqrt(a + b*x + c*x**2), x) + Integral(24*b**2*c**2*x**2/sqrt(a + b*x + c*x**2), x) + Integral(8*b**3*c*x/sqrt(a + b*x + c*x**2), x))","F",0
1235,1,97,0,0.370297," ","integrate((2*c*d*x+b*d)**3/(c*x**2+b*x+a)**(1/2),x)","- \frac{16 a c d^{3} \sqrt{a + b x + c x^{2}}}{3} + 2 b^{2} d^{3} \sqrt{a + b x + c x^{2}} + \frac{8 b c d^{3} x \sqrt{a + b x + c x^{2}}}{3} + \frac{8 c^{2} d^{3} x^{2} \sqrt{a + b x + c x^{2}}}{3}"," ",0,"-16*a*c*d**3*sqrt(a + b*x + c*x**2)/3 + 2*b**2*d**3*sqrt(a + b*x + c*x**2) + 8*b*c*d**3*x*sqrt(a + b*x + c*x**2)/3 + 8*c**2*d**3*x**2*sqrt(a + b*x + c*x**2)/3","A",0
1236,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**2/(c*x**2+b*x+a)**(1/2),x)","d^{2} \left(\int \frac{b^{2}}{\sqrt{a + b x + c x^{2}}}\, dx + \int \frac{4 c^{2} x^{2}}{\sqrt{a + b x + c x^{2}}}\, dx + \int \frac{4 b c x}{\sqrt{a + b x + c x^{2}}}\, dx\right)"," ",0,"d**2*(Integral(b**2/sqrt(a + b*x + c*x**2), x) + Integral(4*c**2*x**2/sqrt(a + b*x + c*x**2), x) + Integral(4*b*c*x/sqrt(a + b*x + c*x**2), x))","F",0
1237,1,15,0,0.179851," ","integrate((2*c*d*x+b*d)/(c*x**2+b*x+a)**(1/2),x)","2 d \sqrt{a + b x + c x^{2}}"," ",0,"2*d*sqrt(a + b*x + c*x**2)","A",0
1238,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)/(c*x**2+b*x+a)**(1/2),x)","\frac{\int \frac{1}{b \sqrt{a + b x + c x^{2}} + 2 c x \sqrt{a + b x + c x^{2}}}\, dx}{d}"," ",0,"Integral(1/(b*sqrt(a + b*x + c*x**2) + 2*c*x*sqrt(a + b*x + c*x**2)), x)/d","F",0
1239,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**2/(c*x**2+b*x+a)**(1/2),x)","\frac{\int \frac{1}{b^{2} \sqrt{a + b x + c x^{2}} + 4 b c x \sqrt{a + b x + c x^{2}} + 4 c^{2} x^{2} \sqrt{a + b x + c x^{2}}}\, dx}{d^{2}}"," ",0,"Integral(1/(b**2*sqrt(a + b*x + c*x**2) + 4*b*c*x*sqrt(a + b*x + c*x**2) + 4*c**2*x**2*sqrt(a + b*x + c*x**2)), x)/d**2","F",0
1240,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**3/(c*x**2+b*x+a)**(1/2),x)","\frac{\int \frac{1}{b^{3} \sqrt{a + b x + c x^{2}} + 6 b^{2} c x \sqrt{a + b x + c x^{2}} + 12 b c^{2} x^{2} \sqrt{a + b x + c x^{2}} + 8 c^{3} x^{3} \sqrt{a + b x + c x^{2}}}\, dx}{d^{3}}"," ",0,"Integral(1/(b**3*sqrt(a + b*x + c*x**2) + 6*b**2*c*x*sqrt(a + b*x + c*x**2) + 12*b*c**2*x**2*sqrt(a + b*x + c*x**2) + 8*c**3*x**3*sqrt(a + b*x + c*x**2)), x)/d**3","F",0
1241,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**4/(c*x**2+b*x+a)**(1/2),x)","\frac{\int \frac{1}{b^{4} \sqrt{a + b x + c x^{2}} + 8 b^{3} c x \sqrt{a + b x + c x^{2}} + 24 b^{2} c^{2} x^{2} \sqrt{a + b x + c x^{2}} + 32 b c^{3} x^{3} \sqrt{a + b x + c x^{2}} + 16 c^{4} x^{4} \sqrt{a + b x + c x^{2}}}\, dx}{d^{4}}"," ",0,"Integral(1/(b**4*sqrt(a + b*x + c*x**2) + 8*b**3*c*x*sqrt(a + b*x + c*x**2) + 24*b**2*c**2*x**2*sqrt(a + b*x + c*x**2) + 32*b*c**3*x**3*sqrt(a + b*x + c*x**2) + 16*c**4*x**4*sqrt(a + b*x + c*x**2)), x)/d**4","F",0
1242,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**4/(c*x**2+b*x+a)**(3/2),x)","d^{4} \left(\int \frac{b^{4}}{a \sqrt{a + b x + c x^{2}} + b x \sqrt{a + b x + c x^{2}} + c x^{2} \sqrt{a + b x + c x^{2}}}\, dx + \int \frac{16 c^{4} x^{4}}{a \sqrt{a + b x + c x^{2}} + b x \sqrt{a + b x + c x^{2}} + c x^{2} \sqrt{a + b x + c x^{2}}}\, dx + \int \frac{32 b c^{3} x^{3}}{a \sqrt{a + b x + c x^{2}} + b x \sqrt{a + b x + c x^{2}} + c x^{2} \sqrt{a + b x + c x^{2}}}\, dx + \int \frac{24 b^{2} c^{2} x^{2}}{a \sqrt{a + b x + c x^{2}} + b x \sqrt{a + b x + c x^{2}} + c x^{2} \sqrt{a + b x + c x^{2}}}\, dx + \int \frac{8 b^{3} c x}{a \sqrt{a + b x + c x^{2}} + b x \sqrt{a + b x + c x^{2}} + c x^{2} \sqrt{a + b x + c x^{2}}}\, dx\right)"," ",0,"d**4*(Integral(b**4/(a*sqrt(a + b*x + c*x**2) + b*x*sqrt(a + b*x + c*x**2) + c*x**2*sqrt(a + b*x + c*x**2)), x) + Integral(16*c**4*x**4/(a*sqrt(a + b*x + c*x**2) + b*x*sqrt(a + b*x + c*x**2) + c*x**2*sqrt(a + b*x + c*x**2)), x) + Integral(32*b*c**3*x**3/(a*sqrt(a + b*x + c*x**2) + b*x*sqrt(a + b*x + c*x**2) + c*x**2*sqrt(a + b*x + c*x**2)), x) + Integral(24*b**2*c**2*x**2/(a*sqrt(a + b*x + c*x**2) + b*x*sqrt(a + b*x + c*x**2) + c*x**2*sqrt(a + b*x + c*x**2)), x) + Integral(8*b**3*c*x/(a*sqrt(a + b*x + c*x**2) + b*x*sqrt(a + b*x + c*x**2) + c*x**2*sqrt(a + b*x + c*x**2)), x))","F",0
1243,1,92,0,1.242899," ","integrate((2*c*d*x+b*d)**3/(c*x**2+b*x+a)**(3/2),x)","\frac{16 a c d^{3}}{\sqrt{a + b x + c x^{2}}} - \frac{2 b^{2} d^{3}}{\sqrt{a + b x + c x^{2}}} + \frac{8 b c d^{3} x}{\sqrt{a + b x + c x^{2}}} + \frac{8 c^{2} d^{3} x^{2}}{\sqrt{a + b x + c x^{2}}}"," ",0,"16*a*c*d**3/sqrt(a + b*x + c*x**2) - 2*b**2*d**3/sqrt(a + b*x + c*x**2) + 8*b*c*d**3*x/sqrt(a + b*x + c*x**2) + 8*c**2*d**3*x**2/sqrt(a + b*x + c*x**2)","A",0
1244,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**2/(c*x**2+b*x+a)**(3/2),x)","d^{2} \left(\int \frac{b^{2}}{a \sqrt{a + b x + c x^{2}} + b x \sqrt{a + b x + c x^{2}} + c x^{2} \sqrt{a + b x + c x^{2}}}\, dx + \int \frac{4 c^{2} x^{2}}{a \sqrt{a + b x + c x^{2}} + b x \sqrt{a + b x + c x^{2}} + c x^{2} \sqrt{a + b x + c x^{2}}}\, dx + \int \frac{4 b c x}{a \sqrt{a + b x + c x^{2}} + b x \sqrt{a + b x + c x^{2}} + c x^{2} \sqrt{a + b x + c x^{2}}}\, dx\right)"," ",0,"d**2*(Integral(b**2/(a*sqrt(a + b*x + c*x**2) + b*x*sqrt(a + b*x + c*x**2) + c*x**2*sqrt(a + b*x + c*x**2)), x) + Integral(4*c**2*x**2/(a*sqrt(a + b*x + c*x**2) + b*x*sqrt(a + b*x + c*x**2) + c*x**2*sqrt(a + b*x + c*x**2)), x) + Integral(4*b*c*x/(a*sqrt(a + b*x + c*x**2) + b*x*sqrt(a + b*x + c*x**2) + c*x**2*sqrt(a + b*x + c*x**2)), x))","F",0
1245,1,17,0,1.196469," ","integrate((2*c*d*x+b*d)/(c*x**2+b*x+a)**(3/2),x)","- \frac{2 d}{\sqrt{a + b x + c x^{2}}}"," ",0,"-2*d/sqrt(a + b*x + c*x**2)","A",0
1246,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)/(c*x**2+b*x+a)**(3/2),x)","\frac{\int \frac{1}{a b \sqrt{a + b x + c x^{2}} + 2 a c x \sqrt{a + b x + c x^{2}} + b^{2} x \sqrt{a + b x + c x^{2}} + 3 b c x^{2} \sqrt{a + b x + c x^{2}} + 2 c^{2} x^{3} \sqrt{a + b x + c x^{2}}}\, dx}{d}"," ",0,"Integral(1/(a*b*sqrt(a + b*x + c*x**2) + 2*a*c*x*sqrt(a + b*x + c*x**2) + b**2*x*sqrt(a + b*x + c*x**2) + 3*b*c*x**2*sqrt(a + b*x + c*x**2) + 2*c**2*x**3*sqrt(a + b*x + c*x**2)), x)/d","F",0
1247,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**2/(c*x**2+b*x+a)**(3/2),x)","\frac{\int \frac{1}{a b^{2} \sqrt{a + b x + c x^{2}} + 4 a b c x \sqrt{a + b x + c x^{2}} + 4 a c^{2} x^{2} \sqrt{a + b x + c x^{2}} + b^{3} x \sqrt{a + b x + c x^{2}} + 5 b^{2} c x^{2} \sqrt{a + b x + c x^{2}} + 8 b c^{2} x^{3} \sqrt{a + b x + c x^{2}} + 4 c^{3} x^{4} \sqrt{a + b x + c x^{2}}}\, dx}{d^{2}}"," ",0,"Integral(1/(a*b**2*sqrt(a + b*x + c*x**2) + 4*a*b*c*x*sqrt(a + b*x + c*x**2) + 4*a*c**2*x**2*sqrt(a + b*x + c*x**2) + b**3*x*sqrt(a + b*x + c*x**2) + 5*b**2*c*x**2*sqrt(a + b*x + c*x**2) + 8*b*c**2*x**3*sqrt(a + b*x + c*x**2) + 4*c**3*x**4*sqrt(a + b*x + c*x**2)), x)/d**2","F",0
1248,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**3/(c*x**2+b*x+a)**(3/2),x)","\frac{\int \frac{1}{a b^{3} \sqrt{a + b x + c x^{2}} + 6 a b^{2} c x \sqrt{a + b x + c x^{2}} + 12 a b c^{2} x^{2} \sqrt{a + b x + c x^{2}} + 8 a c^{3} x^{3} \sqrt{a + b x + c x^{2}} + b^{4} x \sqrt{a + b x + c x^{2}} + 7 b^{3} c x^{2} \sqrt{a + b x + c x^{2}} + 18 b^{2} c^{2} x^{3} \sqrt{a + b x + c x^{2}} + 20 b c^{3} x^{4} \sqrt{a + b x + c x^{2}} + 8 c^{4} x^{5} \sqrt{a + b x + c x^{2}}}\, dx}{d^{3}}"," ",0,"Integral(1/(a*b**3*sqrt(a + b*x + c*x**2) + 6*a*b**2*c*x*sqrt(a + b*x + c*x**2) + 12*a*b*c**2*x**2*sqrt(a + b*x + c*x**2) + 8*a*c**3*x**3*sqrt(a + b*x + c*x**2) + b**4*x*sqrt(a + b*x + c*x**2) + 7*b**3*c*x**2*sqrt(a + b*x + c*x**2) + 18*b**2*c**2*x**3*sqrt(a + b*x + c*x**2) + 20*b*c**3*x**4*sqrt(a + b*x + c*x**2) + 8*c**4*x**5*sqrt(a + b*x + c*x**2)), x)/d**3","F",0
1249,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**4/(c*x**2+b*x+a)**(3/2),x)","\frac{\int \frac{1}{a b^{4} \sqrt{a + b x + c x^{2}} + 8 a b^{3} c x \sqrt{a + b x + c x^{2}} + 24 a b^{2} c^{2} x^{2} \sqrt{a + b x + c x^{2}} + 32 a b c^{3} x^{3} \sqrt{a + b x + c x^{2}} + 16 a c^{4} x^{4} \sqrt{a + b x + c x^{2}} + b^{5} x \sqrt{a + b x + c x^{2}} + 9 b^{4} c x^{2} \sqrt{a + b x + c x^{2}} + 32 b^{3} c^{2} x^{3} \sqrt{a + b x + c x^{2}} + 56 b^{2} c^{3} x^{4} \sqrt{a + b x + c x^{2}} + 48 b c^{4} x^{5} \sqrt{a + b x + c x^{2}} + 16 c^{5} x^{6} \sqrt{a + b x + c x^{2}}}\, dx}{d^{4}}"," ",0,"Integral(1/(a*b**4*sqrt(a + b*x + c*x**2) + 8*a*b**3*c*x*sqrt(a + b*x + c*x**2) + 24*a*b**2*c**2*x**2*sqrt(a + b*x + c*x**2) + 32*a*b*c**3*x**3*sqrt(a + b*x + c*x**2) + 16*a*c**4*x**4*sqrt(a + b*x + c*x**2) + b**5*x*sqrt(a + b*x + c*x**2) + 9*b**4*c*x**2*sqrt(a + b*x + c*x**2) + 32*b**3*c**2*x**3*sqrt(a + b*x + c*x**2) + 56*b**2*c**3*x**4*sqrt(a + b*x + c*x**2) + 48*b*c**4*x**5*sqrt(a + b*x + c*x**2) + 16*c**5*x**6*sqrt(a + b*x + c*x**2)), x)/d**4","F",0
1250,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**6/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1251,1,615,0,1.970140," ","integrate((2*c*d*x+b*d)**5/(c*x**2+b*x+a)**(5/2),x)","\frac{256 a^{2} c^{2} d^{5}}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} - \frac{32 a b^{2} c d^{5}}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} + \frac{384 a b c^{2} d^{5} x}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} + \frac{384 a c^{3} d^{5} x^{2}}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} - \frac{2 b^{4} d^{5}}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} - \frac{48 b^{3} c d^{5} x}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} + \frac{48 b^{2} c^{2} d^{5} x^{2}}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} + \frac{192 b c^{3} d^{5} x^{3}}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} + \frac{96 c^{4} d^{5} x^{4}}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}}"," ",0,"256*a**2*c**2*d**5/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) - 32*a*b**2*c*d**5/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) + 384*a*b*c**2*d**5*x/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) + 384*a*c**3*d**5*x**2/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) - 2*b**4*d**5/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) - 48*b**3*c*d**5*x/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) + 48*b**2*c**2*d**5*x**2/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) + 192*b*c**3*d**5*x**3/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) + 96*c**4*d**5*x**4/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2))","B",0
1252,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**4/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1253,1,264,0,1.747629," ","integrate((2*c*d*x+b*d)**3/(c*x**2+b*x+a)**(5/2),x)","- \frac{16 a c d^{3}}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} - \frac{2 b^{2} d^{3}}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} - \frac{24 b c d^{3} x}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}} - \frac{24 c^{2} d^{3} x^{2}}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}}"," ",0,"-16*a*c*d**3/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) - 2*b**2*d**3/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) - 24*b*c*d**3*x/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2)) - 24*c**2*d**3*x**2/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2))","B",0
1254,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**2/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1255,1,60,0,1.676727," ","integrate((2*c*d*x+b*d)/(c*x**2+b*x+a)**(5/2),x)","- \frac{2 d}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}}"," ",0,"-2*d/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2))","B",0
1256,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)/(c*x**2+b*x+a)**(5/2),x)","\frac{\int \frac{1}{a^{2} b \sqrt{a + b x + c x^{2}} + 2 a^{2} c x \sqrt{a + b x + c x^{2}} + 2 a b^{2} x \sqrt{a + b x + c x^{2}} + 6 a b c x^{2} \sqrt{a + b x + c x^{2}} + 4 a c^{2} x^{3} \sqrt{a + b x + c x^{2}} + b^{3} x^{2} \sqrt{a + b x + c x^{2}} + 4 b^{2} c x^{3} \sqrt{a + b x + c x^{2}} + 5 b c^{2} x^{4} \sqrt{a + b x + c x^{2}} + 2 c^{3} x^{5} \sqrt{a + b x + c x^{2}}}\, dx}{d}"," ",0,"Integral(1/(a**2*b*sqrt(a + b*x + c*x**2) + 2*a**2*c*x*sqrt(a + b*x + c*x**2) + 2*a*b**2*x*sqrt(a + b*x + c*x**2) + 6*a*b*c*x**2*sqrt(a + b*x + c*x**2) + 4*a*c**2*x**3*sqrt(a + b*x + c*x**2) + b**3*x**2*sqrt(a + b*x + c*x**2) + 4*b**2*c*x**3*sqrt(a + b*x + c*x**2) + 5*b*c**2*x**4*sqrt(a + b*x + c*x**2) + 2*c**3*x**5*sqrt(a + b*x + c*x**2)), x)/d","F",0
1257,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**2/(c*x**2+b*x+a)**(5/2),x)","\frac{\int \frac{1}{a^{2} b^{2} \sqrt{a + b x + c x^{2}} + 4 a^{2} b c x \sqrt{a + b x + c x^{2}} + 4 a^{2} c^{2} x^{2} \sqrt{a + b x + c x^{2}} + 2 a b^{3} x \sqrt{a + b x + c x^{2}} + 10 a b^{2} c x^{2} \sqrt{a + b x + c x^{2}} + 16 a b c^{2} x^{3} \sqrt{a + b x + c x^{2}} + 8 a c^{3} x^{4} \sqrt{a + b x + c x^{2}} + b^{4} x^{2} \sqrt{a + b x + c x^{2}} + 6 b^{3} c x^{3} \sqrt{a + b x + c x^{2}} + 13 b^{2} c^{2} x^{4} \sqrt{a + b x + c x^{2}} + 12 b c^{3} x^{5} \sqrt{a + b x + c x^{2}} + 4 c^{4} x^{6} \sqrt{a + b x + c x^{2}}}\, dx}{d^{2}}"," ",0,"Integral(1/(a**2*b**2*sqrt(a + b*x + c*x**2) + 4*a**2*b*c*x*sqrt(a + b*x + c*x**2) + 4*a**2*c**2*x**2*sqrt(a + b*x + c*x**2) + 2*a*b**3*x*sqrt(a + b*x + c*x**2) + 10*a*b**2*c*x**2*sqrt(a + b*x + c*x**2) + 16*a*b*c**2*x**3*sqrt(a + b*x + c*x**2) + 8*a*c**3*x**4*sqrt(a + b*x + c*x**2) + b**4*x**2*sqrt(a + b*x + c*x**2) + 6*b**3*c*x**3*sqrt(a + b*x + c*x**2) + 13*b**2*c**2*x**4*sqrt(a + b*x + c*x**2) + 12*b*c**3*x**5*sqrt(a + b*x + c*x**2) + 4*c**4*x**6*sqrt(a + b*x + c*x**2)), x)/d**2","F",0
1258,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**3/(c*x**2+b*x+a)**(5/2),x)","\frac{\int \frac{1}{a^{2} b^{3} \sqrt{a + b x + c x^{2}} + 6 a^{2} b^{2} c x \sqrt{a + b x + c x^{2}} + 12 a^{2} b c^{2} x^{2} \sqrt{a + b x + c x^{2}} + 8 a^{2} c^{3} x^{3} \sqrt{a + b x + c x^{2}} + 2 a b^{4} x \sqrt{a + b x + c x^{2}} + 14 a b^{3} c x^{2} \sqrt{a + b x + c x^{2}} + 36 a b^{2} c^{2} x^{3} \sqrt{a + b x + c x^{2}} + 40 a b c^{3} x^{4} \sqrt{a + b x + c x^{2}} + 16 a c^{4} x^{5} \sqrt{a + b x + c x^{2}} + b^{5} x^{2} \sqrt{a + b x + c x^{2}} + 8 b^{4} c x^{3} \sqrt{a + b x + c x^{2}} + 25 b^{3} c^{2} x^{4} \sqrt{a + b x + c x^{2}} + 38 b^{2} c^{3} x^{5} \sqrt{a + b x + c x^{2}} + 28 b c^{4} x^{6} \sqrt{a + b x + c x^{2}} + 8 c^{5} x^{7} \sqrt{a + b x + c x^{2}}}\, dx}{d^{3}}"," ",0,"Integral(1/(a**2*b**3*sqrt(a + b*x + c*x**2) + 6*a**2*b**2*c*x*sqrt(a + b*x + c*x**2) + 12*a**2*b*c**2*x**2*sqrt(a + b*x + c*x**2) + 8*a**2*c**3*x**3*sqrt(a + b*x + c*x**2) + 2*a*b**4*x*sqrt(a + b*x + c*x**2) + 14*a*b**3*c*x**2*sqrt(a + b*x + c*x**2) + 36*a*b**2*c**2*x**3*sqrt(a + b*x + c*x**2) + 40*a*b*c**3*x**4*sqrt(a + b*x + c*x**2) + 16*a*c**4*x**5*sqrt(a + b*x + c*x**2) + b**5*x**2*sqrt(a + b*x + c*x**2) + 8*b**4*c*x**3*sqrt(a + b*x + c*x**2) + 25*b**3*c**2*x**4*sqrt(a + b*x + c*x**2) + 38*b**2*c**3*x**5*sqrt(a + b*x + c*x**2) + 28*b*c**4*x**6*sqrt(a + b*x + c*x**2) + 8*c**5*x**7*sqrt(a + b*x + c*x**2)), x)/d**3","F",0
1259,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**4/(c*x**2+b*x+a)**(5/2),x)","\frac{\int \frac{1}{a^{2} b^{4} \sqrt{a + b x + c x^{2}} + 8 a^{2} b^{3} c x \sqrt{a + b x + c x^{2}} + 24 a^{2} b^{2} c^{2} x^{2} \sqrt{a + b x + c x^{2}} + 32 a^{2} b c^{3} x^{3} \sqrt{a + b x + c x^{2}} + 16 a^{2} c^{4} x^{4} \sqrt{a + b x + c x^{2}} + 2 a b^{5} x \sqrt{a + b x + c x^{2}} + 18 a b^{4} c x^{2} \sqrt{a + b x + c x^{2}} + 64 a b^{3} c^{2} x^{3} \sqrt{a + b x + c x^{2}} + 112 a b^{2} c^{3} x^{4} \sqrt{a + b x + c x^{2}} + 96 a b c^{4} x^{5} \sqrt{a + b x + c x^{2}} + 32 a c^{5} x^{6} \sqrt{a + b x + c x^{2}} + b^{6} x^{2} \sqrt{a + b x + c x^{2}} + 10 b^{5} c x^{3} \sqrt{a + b x + c x^{2}} + 41 b^{4} c^{2} x^{4} \sqrt{a + b x + c x^{2}} + 88 b^{3} c^{3} x^{5} \sqrt{a + b x + c x^{2}} + 104 b^{2} c^{4} x^{6} \sqrt{a + b x + c x^{2}} + 64 b c^{5} x^{7} \sqrt{a + b x + c x^{2}} + 16 c^{6} x^{8} \sqrt{a + b x + c x^{2}}}\, dx}{d^{4}}"," ",0,"Integral(1/(a**2*b**4*sqrt(a + b*x + c*x**2) + 8*a**2*b**3*c*x*sqrt(a + b*x + c*x**2) + 24*a**2*b**2*c**2*x**2*sqrt(a + b*x + c*x**2) + 32*a**2*b*c**3*x**3*sqrt(a + b*x + c*x**2) + 16*a**2*c**4*x**4*sqrt(a + b*x + c*x**2) + 2*a*b**5*x*sqrt(a + b*x + c*x**2) + 18*a*b**4*c*x**2*sqrt(a + b*x + c*x**2) + 64*a*b**3*c**2*x**3*sqrt(a + b*x + c*x**2) + 112*a*b**2*c**3*x**4*sqrt(a + b*x + c*x**2) + 96*a*b*c**4*x**5*sqrt(a + b*x + c*x**2) + 32*a*c**5*x**6*sqrt(a + b*x + c*x**2) + b**6*x**2*sqrt(a + b*x + c*x**2) + 10*b**5*c*x**3*sqrt(a + b*x + c*x**2) + 41*b**4*c**2*x**4*sqrt(a + b*x + c*x**2) + 88*b**3*c**3*x**5*sqrt(a + b*x + c*x**2) + 104*b**2*c**4*x**6*sqrt(a + b*x + c*x**2) + 64*b*c**5*x**7*sqrt(a + b*x + c*x**2) + 16*c**6*x**8*sqrt(a + b*x + c*x**2)), x)/d**4","F",0
1260,0,0,0,0.000000," ","integrate(1/(b*x+a)/(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\int \frac{1}{\left(a + b x\right) \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx"," ",0,"Integral(1/((a + b*x)*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x)","F",0
1261,1,289,0,3.854125," ","integrate((2*c*d*x+b*d)**(5/2)*(c*x**2+b*x+a),x)","\begin{cases} \frac{a b^{3} d^{2} \sqrt{b d + 2 c d x}}{7 c} + \frac{6 a b^{2} d^{2} x \sqrt{b d + 2 c d x}}{7} + \frac{12 a b c d^{2} x^{2} \sqrt{b d + 2 c d x}}{7} + \frac{8 a c^{2} d^{2} x^{3} \sqrt{b d + 2 c d x}}{7} - \frac{b^{5} d^{2} \sqrt{b d + 2 c d x}}{77 c^{2}} + \frac{b^{4} d^{2} x \sqrt{b d + 2 c d x}}{77 c} + \frac{37 b^{3} d^{2} x^{2} \sqrt{b d + 2 c d x}}{77} + \frac{118 b^{2} c d^{2} x^{3} \sqrt{b d + 2 c d x}}{77} + \frac{20 b c^{2} d^{2} x^{4} \sqrt{b d + 2 c d x}}{11} + \frac{8 c^{3} d^{2} x^{5} \sqrt{b d + 2 c d x}}{11} & \text{for}\: c \neq 0 \\\left(b d\right)^{\frac{5}{2}} \left(a x + \frac{b x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*b**3*d**2*sqrt(b*d + 2*c*d*x)/(7*c) + 6*a*b**2*d**2*x*sqrt(b*d + 2*c*d*x)/7 + 12*a*b*c*d**2*x**2*sqrt(b*d + 2*c*d*x)/7 + 8*a*c**2*d**2*x**3*sqrt(b*d + 2*c*d*x)/7 - b**5*d**2*sqrt(b*d + 2*c*d*x)/(77*c**2) + b**4*d**2*x*sqrt(b*d + 2*c*d*x)/(77*c) + 37*b**3*d**2*x**2*sqrt(b*d + 2*c*d*x)/77 + 118*b**2*c*d**2*x**3*sqrt(b*d + 2*c*d*x)/77 + 20*b*c**2*d**2*x**4*sqrt(b*d + 2*c*d*x)/11 + 8*c**3*d**2*x**5*sqrt(b*d + 2*c*d*x)/11, Ne(c, 0)), ((b*d)**(5/2)*(a*x + b*x**2/2), True))","A",0
1262,1,274,0,9.758733," ","integrate((2*c*d*x+b*d)**(3/2)*(c*x**2+b*x+a),x)","a b d \left(\begin{cases} x \sqrt{b d} & \text{for}\: c = 0 \\0 & \text{for}\: d = 0 \\\frac{\left(b d + 2 c d x\right)^{\frac{3}{2}}}{3 c d} & \text{otherwise} \end{cases}\right) + \frac{a \left(- \frac{b d \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} + \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{5}\right)}{c d} + \frac{b^{2} \left(- \frac{b d \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} + \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{5}\right)}{2 c^{2} d} + \frac{3 b \left(\frac{b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} - \frac{2 b d \left(b d + 2 c d x\right)^{\frac{5}{2}}}{5} + \frac{\left(b d + 2 c d x\right)^{\frac{7}{2}}}{7}\right)}{4 c^{2} d^{2}} + \frac{- \frac{b^{3} d^{3} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} + \frac{3 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{5}{2}}}{5} - \frac{3 b d \left(b d + 2 c d x\right)^{\frac{7}{2}}}{7} + \frac{\left(b d + 2 c d x\right)^{\frac{9}{2}}}{9}}{4 c^{2} d^{3}}"," ",0,"a*b*d*Piecewise((x*sqrt(b*d), Eq(c, 0)), (0, Eq(d, 0)), ((b*d + 2*c*d*x)**(3/2)/(3*c*d), True)) + a*(-b*d*(b*d + 2*c*d*x)**(3/2)/3 + (b*d + 2*c*d*x)**(5/2)/5)/(c*d) + b**2*(-b*d*(b*d + 2*c*d*x)**(3/2)/3 + (b*d + 2*c*d*x)**(5/2)/5)/(2*c**2*d) + 3*b*(b**2*d**2*(b*d + 2*c*d*x)**(3/2)/3 - 2*b*d*(b*d + 2*c*d*x)**(5/2)/5 + (b*d + 2*c*d*x)**(7/2)/7)/(4*c**2*d**2) + (-b**3*d**3*(b*d + 2*c*d*x)**(3/2)/3 + 3*b**2*d**2*(b*d + 2*c*d*x)**(5/2)/5 - 3*b*d*(b*d + 2*c*d*x)**(7/2)/7 + (b*d + 2*c*d*x)**(9/2)/9)/(4*c**2*d**3)","A",0
1263,1,48,0,2.897484," ","integrate((2*c*d*x+b*d)**(1/2)*(c*x**2+b*x+a),x)","\frac{\frac{\left(4 a c - b^{2}\right) \left(b d + 2 c d x\right)^{\frac{3}{2}}}{12 c} + \frac{\left(b d + 2 c d x\right)^{\frac{7}{2}}}{28 c d^{2}}}{c d}"," ",0,"((4*a*c - b**2)*(b*d + 2*c*d*x)**(3/2)/(12*c) + (b*d + 2*c*d*x)**(7/2)/(28*c*d**2))/(c*d)","A",0
1264,1,258,0,10.535301," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**(1/2),x)","\begin{cases} \frac{- \frac{a b}{\sqrt{b d + 2 c d x}} - \frac{a \left(- \frac{b d}{\sqrt{b d + 2 c d x}} - \sqrt{b d + 2 c d x}\right)}{d} - \frac{b^{2} \left(- \frac{b d}{\sqrt{b d + 2 c d x}} - \sqrt{b d + 2 c d x}\right)}{2 c d} - \frac{3 b \left(\frac{b^{2} d^{2}}{\sqrt{b d + 2 c d x}} + 2 b d \sqrt{b d + 2 c d x} - \frac{\left(b d + 2 c d x\right)^{\frac{3}{2}}}{3}\right)}{4 c d^{2}} - \frac{- \frac{b^{3} d^{3}}{\sqrt{b d + 2 c d x}} - 3 b^{2} d^{2} \sqrt{b d + 2 c d x} + b d \left(b d + 2 c d x\right)^{\frac{3}{2}} - \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{5}}{4 c d^{3}}}{c} & \text{for}\: c \neq 0 \\\frac{a x + \frac{b x^{2}}{2}}{\sqrt{b d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a*b/sqrt(b*d + 2*c*d*x) - a*(-b*d/sqrt(b*d + 2*c*d*x) - sqrt(b*d + 2*c*d*x))/d - b**2*(-b*d/sqrt(b*d + 2*c*d*x) - sqrt(b*d + 2*c*d*x))/(2*c*d) - 3*b*(b**2*d**2/sqrt(b*d + 2*c*d*x) + 2*b*d*sqrt(b*d + 2*c*d*x) - (b*d + 2*c*d*x)**(3/2)/3)/(4*c*d**2) - (-b**3*d**3/sqrt(b*d + 2*c*d*x) - 3*b**2*d**2*sqrt(b*d + 2*c*d*x) + b*d*(b*d + 2*c*d*x)**(3/2) - (b*d + 2*c*d*x)**(5/2)/5)/(4*c*d**3))/c, Ne(c, 0)), ((a*x + b*x**2/2)/sqrt(b*d), True))","A",0
1265,1,49,0,13.081997," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**(3/2),x)","- \frac{4 a c - b^{2}}{4 c^{2} d \sqrt{b d + 2 c d x}} + \frac{\left(b d + 2 c d x\right)^{\frac{3}{2}}}{12 c^{2} d^{3}}"," ",0,"-(4*a*c - b**2)/(4*c**2*d*sqrt(b*d + 2*c*d*x)) + (b*d + 2*c*d*x)**(3/2)/(12*c**2*d**3)","A",0
1266,1,235,0,1.280370," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**(5/2),x)","\begin{cases} - \frac{a c \sqrt{b d + 2 c d x}}{3 b^{2} c^{2} d^{3} + 12 b c^{3} d^{3} x + 12 c^{4} d^{3} x^{2}} + \frac{b^{2} \sqrt{b d + 2 c d x}}{3 b^{2} c^{2} d^{3} + 12 b c^{3} d^{3} x + 12 c^{4} d^{3} x^{2}} + \frac{3 b c x \sqrt{b d + 2 c d x}}{3 b^{2} c^{2} d^{3} + 12 b c^{3} d^{3} x + 12 c^{4} d^{3} x^{2}} + \frac{3 c^{2} x^{2} \sqrt{b d + 2 c d x}}{3 b^{2} c^{2} d^{3} + 12 b c^{3} d^{3} x + 12 c^{4} d^{3} x^{2}} & \text{for}\: c \neq 0 \\\frac{a x + \frac{b x^{2}}{2}}{\left(b d\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c*sqrt(b*d + 2*c*d*x)/(3*b**2*c**2*d**3 + 12*b*c**3*d**3*x + 12*c**4*d**3*x**2) + b**2*sqrt(b*d + 2*c*d*x)/(3*b**2*c**2*d**3 + 12*b*c**3*d**3*x + 12*c**4*d**3*x**2) + 3*b*c*x*sqrt(b*d + 2*c*d*x)/(3*b**2*c**2*d**3 + 12*b*c**3*d**3*x + 12*c**4*d**3*x**2) + 3*c**2*x**2*sqrt(b*d + 2*c*d*x)/(3*b**2*c**2*d**3 + 12*b*c**3*d**3*x + 12*c**4*d**3*x**2), Ne(c, 0)), ((a*x + b*x**2/2)/(b*d)**(5/2), True))","A",0
1267,1,298,0,3.015156," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**(7/2),x)","\begin{cases} - \frac{a c \sqrt{b d + 2 c d x}}{5 b^{3} c^{2} d^{4} + 30 b^{2} c^{3} d^{4} x + 60 b c^{4} d^{4} x^{2} + 40 c^{5} d^{4} x^{3}} - \frac{b^{2} \sqrt{b d + 2 c d x}}{5 b^{3} c^{2} d^{4} + 30 b^{2} c^{3} d^{4} x + 60 b c^{4} d^{4} x^{2} + 40 c^{5} d^{4} x^{3}} - \frac{5 b c x \sqrt{b d + 2 c d x}}{5 b^{3} c^{2} d^{4} + 30 b^{2} c^{3} d^{4} x + 60 b c^{4} d^{4} x^{2} + 40 c^{5} d^{4} x^{3}} - \frac{5 c^{2} x^{2} \sqrt{b d + 2 c d x}}{5 b^{3} c^{2} d^{4} + 30 b^{2} c^{3} d^{4} x + 60 b c^{4} d^{4} x^{2} + 40 c^{5} d^{4} x^{3}} & \text{for}\: c \neq 0 \\\frac{a x + \frac{b x^{2}}{2}}{\left(b d\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c*sqrt(b*d + 2*c*d*x)/(5*b**3*c**2*d**4 + 30*b**2*c**3*d**4*x + 60*b*c**4*d**4*x**2 + 40*c**5*d**4*x**3) - b**2*sqrt(b*d + 2*c*d*x)/(5*b**3*c**2*d**4 + 30*b**2*c**3*d**4*x + 60*b*c**4*d**4*x**2 + 40*c**5*d**4*x**3) - 5*b*c*x*sqrt(b*d + 2*c*d*x)/(5*b**3*c**2*d**4 + 30*b**2*c**3*d**4*x + 60*b*c**4*d**4*x**2 + 40*c**5*d**4*x**3) - 5*c**2*x**2*sqrt(b*d + 2*c*d*x)/(5*b**3*c**2*d**4 + 30*b**2*c**3*d**4*x + 60*b*c**4*d**4*x**2 + 40*c**5*d**4*x**3), Ne(c, 0)), ((a*x + b*x**2/2)/(b*d)**(7/2), True))","A",0
1268,1,360,0,6.221052," ","integrate((c*x**2+b*x+a)/(2*c*d*x+b*d)**(9/2),x)","\begin{cases} - \frac{3 a c \sqrt{b d + 2 c d x}}{21 b^{4} c^{2} d^{5} + 168 b^{3} c^{3} d^{5} x + 504 b^{2} c^{4} d^{5} x^{2} + 672 b c^{5} d^{5} x^{3} + 336 c^{6} d^{5} x^{4}} - \frac{b^{2} \sqrt{b d + 2 c d x}}{21 b^{4} c^{2} d^{5} + 168 b^{3} c^{3} d^{5} x + 504 b^{2} c^{4} d^{5} x^{2} + 672 b c^{5} d^{5} x^{3} + 336 c^{6} d^{5} x^{4}} - \frac{7 b c x \sqrt{b d + 2 c d x}}{21 b^{4} c^{2} d^{5} + 168 b^{3} c^{3} d^{5} x + 504 b^{2} c^{4} d^{5} x^{2} + 672 b c^{5} d^{5} x^{3} + 336 c^{6} d^{5} x^{4}} - \frac{7 c^{2} x^{2} \sqrt{b d + 2 c d x}}{21 b^{4} c^{2} d^{5} + 168 b^{3} c^{3} d^{5} x + 504 b^{2} c^{4} d^{5} x^{2} + 672 b c^{5} d^{5} x^{3} + 336 c^{6} d^{5} x^{4}} & \text{for}\: c \neq 0 \\\frac{a x + \frac{b x^{2}}{2}}{\left(b d\right)^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a*c*sqrt(b*d + 2*c*d*x)/(21*b**4*c**2*d**5 + 168*b**3*c**3*d**5*x + 504*b**2*c**4*d**5*x**2 + 672*b*c**5*d**5*x**3 + 336*c**6*d**5*x**4) - b**2*sqrt(b*d + 2*c*d*x)/(21*b**4*c**2*d**5 + 168*b**3*c**3*d**5*x + 504*b**2*c**4*d**5*x**2 + 672*b*c**5*d**5*x**3 + 336*c**6*d**5*x**4) - 7*b*c*x*sqrt(b*d + 2*c*d*x)/(21*b**4*c**2*d**5 + 168*b**3*c**3*d**5*x + 504*b**2*c**4*d**5*x**2 + 672*b*c**5*d**5*x**3 + 336*c**6*d**5*x**4) - 7*c**2*x**2*sqrt(b*d + 2*c*d*x)/(21*b**4*c**2*d**5 + 168*b**3*c**3*d**5*x + 504*b**2*c**4*d**5*x**2 + 672*b*c**5*d**5*x**3 + 336*c**6*d**5*x**4), Ne(c, 0)), ((a*x + b*x**2/2)/(b*d)**(9/2), True))","A",0
1269,1,695,0,19.758626," ","integrate((2*c*d*x+b*d)**(3/2)*(c*x**2+b*x+a)**2,x)","a^{2} b d \left(\begin{cases} x \sqrt{b d} & \text{for}\: c = 0 \\0 & \text{for}\: d = 0 \\\frac{\left(b d + 2 c d x\right)^{\frac{3}{2}}}{3 c d} & \text{otherwise} \end{cases}\right) + \frac{a^{2} \left(- \frac{b d \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} + \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{5}\right)}{c d} + \frac{a b^{2} \left(- \frac{b d \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} + \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{5}\right)}{c^{2} d} + \frac{3 a b \left(\frac{b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} - \frac{2 b d \left(b d + 2 c d x\right)^{\frac{5}{2}}}{5} + \frac{\left(b d + 2 c d x\right)^{\frac{7}{2}}}{7}\right)}{2 c^{2} d^{2}} + \frac{a \left(- \frac{b^{3} d^{3} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} + \frac{3 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{5}{2}}}{5} - \frac{3 b d \left(b d + 2 c d x\right)^{\frac{7}{2}}}{7} + \frac{\left(b d + 2 c d x\right)^{\frac{9}{2}}}{9}\right)}{2 c^{2} d^{3}} + \frac{b^{3} \left(\frac{b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} - \frac{2 b d \left(b d + 2 c d x\right)^{\frac{5}{2}}}{5} + \frac{\left(b d + 2 c d x\right)^{\frac{7}{2}}}{7}\right)}{4 c^{3} d^{2}} + \frac{b^{2} \left(- \frac{b^{3} d^{3} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} + \frac{3 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{5}{2}}}{5} - \frac{3 b d \left(b d + 2 c d x\right)^{\frac{7}{2}}}{7} + \frac{\left(b d + 2 c d x\right)^{\frac{9}{2}}}{9}\right)}{2 c^{3} d^{3}} + \frac{5 b \left(\frac{b^{4} d^{4} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} - \frac{4 b^{3} d^{3} \left(b d + 2 c d x\right)^{\frac{5}{2}}}{5} + \frac{6 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{7}{2}}}{7} - \frac{4 b d \left(b d + 2 c d x\right)^{\frac{9}{2}}}{9} + \frac{\left(b d + 2 c d x\right)^{\frac{11}{2}}}{11}\right)}{16 c^{3} d^{4}} + \frac{- \frac{b^{5} d^{5} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} + b^{4} d^{4} \left(b d + 2 c d x\right)^{\frac{5}{2}} - \frac{10 b^{3} d^{3} \left(b d + 2 c d x\right)^{\frac{7}{2}}}{7} + \frac{10 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{9}{2}}}{9} - \frac{5 b d \left(b d + 2 c d x\right)^{\frac{11}{2}}}{11} + \frac{\left(b d + 2 c d x\right)^{\frac{13}{2}}}{13}}{16 c^{3} d^{5}}"," ",0,"a**2*b*d*Piecewise((x*sqrt(b*d), Eq(c, 0)), (0, Eq(d, 0)), ((b*d + 2*c*d*x)**(3/2)/(3*c*d), True)) + a**2*(-b*d*(b*d + 2*c*d*x)**(3/2)/3 + (b*d + 2*c*d*x)**(5/2)/5)/(c*d) + a*b**2*(-b*d*(b*d + 2*c*d*x)**(3/2)/3 + (b*d + 2*c*d*x)**(5/2)/5)/(c**2*d) + 3*a*b*(b**2*d**2*(b*d + 2*c*d*x)**(3/2)/3 - 2*b*d*(b*d + 2*c*d*x)**(5/2)/5 + (b*d + 2*c*d*x)**(7/2)/7)/(2*c**2*d**2) + a*(-b**3*d**3*(b*d + 2*c*d*x)**(3/2)/3 + 3*b**2*d**2*(b*d + 2*c*d*x)**(5/2)/5 - 3*b*d*(b*d + 2*c*d*x)**(7/2)/7 + (b*d + 2*c*d*x)**(9/2)/9)/(2*c**2*d**3) + b**3*(b**2*d**2*(b*d + 2*c*d*x)**(3/2)/3 - 2*b*d*(b*d + 2*c*d*x)**(5/2)/5 + (b*d + 2*c*d*x)**(7/2)/7)/(4*c**3*d**2) + b**2*(-b**3*d**3*(b*d + 2*c*d*x)**(3/2)/3 + 3*b**2*d**2*(b*d + 2*c*d*x)**(5/2)/5 - 3*b*d*(b*d + 2*c*d*x)**(7/2)/7 + (b*d + 2*c*d*x)**(9/2)/9)/(2*c**3*d**3) + 5*b*(b**4*d**4*(b*d + 2*c*d*x)**(3/2)/3 - 4*b**3*d**3*(b*d + 2*c*d*x)**(5/2)/5 + 6*b**2*d**2*(b*d + 2*c*d*x)**(7/2)/7 - 4*b*d*(b*d + 2*c*d*x)**(9/2)/9 + (b*d + 2*c*d*x)**(11/2)/11)/(16*c**3*d**4) + (-b**5*d**5*(b*d + 2*c*d*x)**(3/2)/3 + b**4*d**4*(b*d + 2*c*d*x)**(5/2) - 10*b**3*d**3*(b*d + 2*c*d*x)**(7/2)/7 + 10*b**2*d**2*(b*d + 2*c*d*x)**(9/2)/9 - 5*b*d*(b*d + 2*c*d*x)**(11/2)/11 + (b*d + 2*c*d*x)**(13/2)/13)/(16*c**3*d**5)","A",0
1270,1,94,0,3.632647," ","integrate((2*c*d*x+b*d)**(1/2)*(c*x**2+b*x+a)**2,x)","\frac{\frac{\left(b d + 2 c d x\right)^{\frac{3}{2}} \left(16 a^{2} c^{2} - 8 a b^{2} c + b^{4}\right)}{48 c^{2}} + \frac{\left(4 a c - b^{2}\right) \left(b d + 2 c d x\right)^{\frac{7}{2}}}{56 c^{2} d^{2}} + \frac{\left(b d + 2 c d x\right)^{\frac{11}{2}}}{176 c^{2} d^{4}}}{c d}"," ",0,"((b*d + 2*c*d*x)**(3/2)*(16*a**2*c**2 - 8*a*b**2*c + b**4)/(48*c**2) + (4*a*c - b**2)*(b*d + 2*c*d*x)**(7/2)/(56*c**2*d**2) + (b*d + 2*c*d*x)**(11/2)/(176*c**2*d**4))/(c*d)","A",0
1271,1,668,0,61.624270," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**(1/2),x)","\begin{cases} \frac{- \frac{a^{2} b}{\sqrt{b d + 2 c d x}} - \frac{a^{2} \left(- \frac{b d}{\sqrt{b d + 2 c d x}} - \sqrt{b d + 2 c d x}\right)}{d} - \frac{a b^{2} \left(- \frac{b d}{\sqrt{b d + 2 c d x}} - \sqrt{b d + 2 c d x}\right)}{c d} - \frac{3 a b \left(\frac{b^{2} d^{2}}{\sqrt{b d + 2 c d x}} + 2 b d \sqrt{b d + 2 c d x} - \frac{\left(b d + 2 c d x\right)^{\frac{3}{2}}}{3}\right)}{2 c d^{2}} - \frac{a \left(- \frac{b^{3} d^{3}}{\sqrt{b d + 2 c d x}} - 3 b^{2} d^{2} \sqrt{b d + 2 c d x} + b d \left(b d + 2 c d x\right)^{\frac{3}{2}} - \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{5}\right)}{2 c d^{3}} - \frac{b^{3} \left(\frac{b^{2} d^{2}}{\sqrt{b d + 2 c d x}} + 2 b d \sqrt{b d + 2 c d x} - \frac{\left(b d + 2 c d x\right)^{\frac{3}{2}}}{3}\right)}{4 c^{2} d^{2}} - \frac{b^{2} \left(- \frac{b^{3} d^{3}}{\sqrt{b d + 2 c d x}} - 3 b^{2} d^{2} \sqrt{b d + 2 c d x} + b d \left(b d + 2 c d x\right)^{\frac{3}{2}} - \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{5}\right)}{2 c^{2} d^{3}} - \frac{5 b \left(\frac{b^{4} d^{4}}{\sqrt{b d + 2 c d x}} + 4 b^{3} d^{3} \sqrt{b d + 2 c d x} - 2 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{3}{2}} + \frac{4 b d \left(b d + 2 c d x\right)^{\frac{5}{2}}}{5} - \frac{\left(b d + 2 c d x\right)^{\frac{7}{2}}}{7}\right)}{16 c^{2} d^{4}} - \frac{- \frac{b^{5} d^{5}}{\sqrt{b d + 2 c d x}} - 5 b^{4} d^{4} \sqrt{b d + 2 c d x} + \frac{10 b^{3} d^{3} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} - 2 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{5}{2}} + \frac{5 b d \left(b d + 2 c d x\right)^{\frac{7}{2}}}{7} - \frac{\left(b d + 2 c d x\right)^{\frac{9}{2}}}{9}}{16 c^{2} d^{5}}}{c} & \text{for}\: c \neq 0 \\\frac{\begin{cases} a^{2} x & \text{for}\: b = 0 \\\frac{\left(a + b x\right)^{3}}{3 b} & \text{otherwise} \end{cases}}{\sqrt{b d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**2*b/sqrt(b*d + 2*c*d*x) - a**2*(-b*d/sqrt(b*d + 2*c*d*x) - sqrt(b*d + 2*c*d*x))/d - a*b**2*(-b*d/sqrt(b*d + 2*c*d*x) - sqrt(b*d + 2*c*d*x))/(c*d) - 3*a*b*(b**2*d**2/sqrt(b*d + 2*c*d*x) + 2*b*d*sqrt(b*d + 2*c*d*x) - (b*d + 2*c*d*x)**(3/2)/3)/(2*c*d**2) - a*(-b**3*d**3/sqrt(b*d + 2*c*d*x) - 3*b**2*d**2*sqrt(b*d + 2*c*d*x) + b*d*(b*d + 2*c*d*x)**(3/2) - (b*d + 2*c*d*x)**(5/2)/5)/(2*c*d**3) - b**3*(b**2*d**2/sqrt(b*d + 2*c*d*x) + 2*b*d*sqrt(b*d + 2*c*d*x) - (b*d + 2*c*d*x)**(3/2)/3)/(4*c**2*d**2) - b**2*(-b**3*d**3/sqrt(b*d + 2*c*d*x) - 3*b**2*d**2*sqrt(b*d + 2*c*d*x) + b*d*(b*d + 2*c*d*x)**(3/2) - (b*d + 2*c*d*x)**(5/2)/5)/(2*c**2*d**3) - 5*b*(b**4*d**4/sqrt(b*d + 2*c*d*x) + 4*b**3*d**3*sqrt(b*d + 2*c*d*x) - 2*b**2*d**2*(b*d + 2*c*d*x)**(3/2) + 4*b*d*(b*d + 2*c*d*x)**(5/2)/5 - (b*d + 2*c*d*x)**(7/2)/7)/(16*c**2*d**4) - (-b**5*d**5/sqrt(b*d + 2*c*d*x) - 5*b**4*d**4*sqrt(b*d + 2*c*d*x) + 10*b**3*d**3*(b*d + 2*c*d*x)**(3/2)/3 - 2*b**2*d**2*(b*d + 2*c*d*x)**(5/2) + 5*b*d*(b*d + 2*c*d*x)**(7/2)/7 - (b*d + 2*c*d*x)**(9/2)/9)/(16*c**2*d**5))/c, Ne(c, 0)), (Piecewise((a**2*x, Eq(b, 0)), ((a + b*x)**3/(3*b), True))/sqrt(b*d), True))","A",0
1272,1,82,0,30.225690," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**(3/2),x)","- \frac{\left(4 a c - b^{2}\right)^{2}}{16 c^{3} d \sqrt{b d + 2 c d x}} + \frac{\left(4 a c - b^{2}\right) \left(b d + 2 c d x\right)^{\frac{3}{2}}}{24 c^{3} d^{3}} + \frac{\left(b d + 2 c d x\right)^{\frac{7}{2}}}{112 c^{3} d^{5}}"," ",0,"-(4*a*c - b**2)**2/(16*c**3*d*sqrt(b*d + 2*c*d*x)) + (4*a*c - b**2)*(b*d + 2*c*d*x)**(3/2)/(24*c**3*d**3) + (b*d + 2*c*d*x)**(7/2)/(112*c**3*d**5)","A",0
1273,1,82,0,54.218910," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**(5/2),x)","- \frac{\left(4 a c - b^{2}\right)^{2}}{48 c^{3} d \left(b d + 2 c d x\right)^{\frac{3}{2}}} + \frac{\left(4 a c - b^{2}\right) \sqrt{b d + 2 c d x}}{8 c^{3} d^{3}} + \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{80 c^{3} d^{5}}"," ",0,"-(4*a*c - b**2)**2/(48*c**3*d*(b*d + 2*c*d*x)**(3/2)) + (4*a*c - b**2)*sqrt(b*d + 2*c*d*x)/(8*c**3*d**3) + (b*d + 2*c*d*x)**(5/2)/(80*c**3*d**5)","A",0
1274,1,688,0,3.684695," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**(7/2),x)","\begin{cases} - \frac{3 a^{2} c^{2} \sqrt{b d + 2 c d x}}{15 b^{3} c^{3} d^{4} + 90 b^{2} c^{4} d^{4} x + 180 b c^{5} d^{4} x^{2} + 120 c^{6} d^{4} x^{3}} - \frac{6 a b^{2} c \sqrt{b d + 2 c d x}}{15 b^{3} c^{3} d^{4} + 90 b^{2} c^{4} d^{4} x + 180 b c^{5} d^{4} x^{2} + 120 c^{6} d^{4} x^{3}} - \frac{30 a b c^{2} x \sqrt{b d + 2 c d x}}{15 b^{3} c^{3} d^{4} + 90 b^{2} c^{4} d^{4} x + 180 b c^{5} d^{4} x^{2} + 120 c^{6} d^{4} x^{3}} - \frac{30 a c^{3} x^{2} \sqrt{b d + 2 c d x}}{15 b^{3} c^{3} d^{4} + 90 b^{2} c^{4} d^{4} x + 180 b c^{5} d^{4} x^{2} + 120 c^{6} d^{4} x^{3}} + \frac{2 b^{4} \sqrt{b d + 2 c d x}}{15 b^{3} c^{3} d^{4} + 90 b^{2} c^{4} d^{4} x + 180 b c^{5} d^{4} x^{2} + 120 c^{6} d^{4} x^{3}} + \frac{10 b^{3} c x \sqrt{b d + 2 c d x}}{15 b^{3} c^{3} d^{4} + 90 b^{2} c^{4} d^{4} x + 180 b c^{5} d^{4} x^{2} + 120 c^{6} d^{4} x^{3}} + \frac{15 b^{2} c^{2} x^{2} \sqrt{b d + 2 c d x}}{15 b^{3} c^{3} d^{4} + 90 b^{2} c^{4} d^{4} x + 180 b c^{5} d^{4} x^{2} + 120 c^{6} d^{4} x^{3}} + \frac{10 b c^{3} x^{3} \sqrt{b d + 2 c d x}}{15 b^{3} c^{3} d^{4} + 90 b^{2} c^{4} d^{4} x + 180 b c^{5} d^{4} x^{2} + 120 c^{6} d^{4} x^{3}} + \frac{5 c^{4} x^{4} \sqrt{b d + 2 c d x}}{15 b^{3} c^{3} d^{4} + 90 b^{2} c^{4} d^{4} x + 180 b c^{5} d^{4} x^{2} + 120 c^{6} d^{4} x^{3}} & \text{for}\: c \neq 0 \\\frac{a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}}{\left(b d\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a**2*c**2*sqrt(b*d + 2*c*d*x)/(15*b**3*c**3*d**4 + 90*b**2*c**4*d**4*x + 180*b*c**5*d**4*x**2 + 120*c**6*d**4*x**3) - 6*a*b**2*c*sqrt(b*d + 2*c*d*x)/(15*b**3*c**3*d**4 + 90*b**2*c**4*d**4*x + 180*b*c**5*d**4*x**2 + 120*c**6*d**4*x**3) - 30*a*b*c**2*x*sqrt(b*d + 2*c*d*x)/(15*b**3*c**3*d**4 + 90*b**2*c**4*d**4*x + 180*b*c**5*d**4*x**2 + 120*c**6*d**4*x**3) - 30*a*c**3*x**2*sqrt(b*d + 2*c*d*x)/(15*b**3*c**3*d**4 + 90*b**2*c**4*d**4*x + 180*b*c**5*d**4*x**2 + 120*c**6*d**4*x**3) + 2*b**4*sqrt(b*d + 2*c*d*x)/(15*b**3*c**3*d**4 + 90*b**2*c**4*d**4*x + 180*b*c**5*d**4*x**2 + 120*c**6*d**4*x**3) + 10*b**3*c*x*sqrt(b*d + 2*c*d*x)/(15*b**3*c**3*d**4 + 90*b**2*c**4*d**4*x + 180*b*c**5*d**4*x**2 + 120*c**6*d**4*x**3) + 15*b**2*c**2*x**2*sqrt(b*d + 2*c*d*x)/(15*b**3*c**3*d**4 + 90*b**2*c**4*d**4*x + 180*b*c**5*d**4*x**2 + 120*c**6*d**4*x**3) + 10*b*c**3*x**3*sqrt(b*d + 2*c*d*x)/(15*b**3*c**3*d**4 + 90*b**2*c**4*d**4*x + 180*b*c**5*d**4*x**2 + 120*c**6*d**4*x**3) + 5*c**4*x**4*sqrt(b*d + 2*c*d*x)/(15*b**3*c**3*d**4 + 90*b**2*c**4*d**4*x + 180*b*c**5*d**4*x**2 + 120*c**6*d**4*x**3), Ne(c, 0)), ((a**2*x + a*b*x**2 + b**2*x**3/3)/(b*d)**(7/2), True))","A",0
1275,1,826,0,7.586625," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**(9/2),x)","\begin{cases} - \frac{3 a^{2} c^{2} \sqrt{b d + 2 c d x}}{21 b^{4} c^{3} d^{5} + 168 b^{3} c^{4} d^{5} x + 504 b^{2} c^{5} d^{5} x^{2} + 672 b c^{6} d^{5} x^{3} + 336 c^{7} d^{5} x^{4}} - \frac{2 a b^{2} c \sqrt{b d + 2 c d x}}{21 b^{4} c^{3} d^{5} + 168 b^{3} c^{4} d^{5} x + 504 b^{2} c^{5} d^{5} x^{2} + 672 b c^{6} d^{5} x^{3} + 336 c^{7} d^{5} x^{4}} - \frac{14 a b c^{2} x \sqrt{b d + 2 c d x}}{21 b^{4} c^{3} d^{5} + 168 b^{3} c^{4} d^{5} x + 504 b^{2} c^{5} d^{5} x^{2} + 672 b c^{6} d^{5} x^{3} + 336 c^{7} d^{5} x^{4}} - \frac{14 a c^{3} x^{2} \sqrt{b d + 2 c d x}}{21 b^{4} c^{3} d^{5} + 168 b^{3} c^{4} d^{5} x + 504 b^{2} c^{5} d^{5} x^{2} + 672 b c^{6} d^{5} x^{3} + 336 c^{7} d^{5} x^{4}} + \frac{2 b^{4} \sqrt{b d + 2 c d x}}{21 b^{4} c^{3} d^{5} + 168 b^{3} c^{4} d^{5} x + 504 b^{2} c^{5} d^{5} x^{2} + 672 b c^{6} d^{5} x^{3} + 336 c^{7} d^{5} x^{4}} + \frac{14 b^{3} c x \sqrt{b d + 2 c d x}}{21 b^{4} c^{3} d^{5} + 168 b^{3} c^{4} d^{5} x + 504 b^{2} c^{5} d^{5} x^{2} + 672 b c^{6} d^{5} x^{3} + 336 c^{7} d^{5} x^{4}} + \frac{35 b^{2} c^{2} x^{2} \sqrt{b d + 2 c d x}}{21 b^{4} c^{3} d^{5} + 168 b^{3} c^{4} d^{5} x + 504 b^{2} c^{5} d^{5} x^{2} + 672 b c^{6} d^{5} x^{3} + 336 c^{7} d^{5} x^{4}} + \frac{42 b c^{3} x^{3} \sqrt{b d + 2 c d x}}{21 b^{4} c^{3} d^{5} + 168 b^{3} c^{4} d^{5} x + 504 b^{2} c^{5} d^{5} x^{2} + 672 b c^{6} d^{5} x^{3} + 336 c^{7} d^{5} x^{4}} + \frac{21 c^{4} x^{4} \sqrt{b d + 2 c d x}}{21 b^{4} c^{3} d^{5} + 168 b^{3} c^{4} d^{5} x + 504 b^{2} c^{5} d^{5} x^{2} + 672 b c^{6} d^{5} x^{3} + 336 c^{7} d^{5} x^{4}} & \text{for}\: c \neq 0 \\\frac{a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}}{\left(b d\right)^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a**2*c**2*sqrt(b*d + 2*c*d*x)/(21*b**4*c**3*d**5 + 168*b**3*c**4*d**5*x + 504*b**2*c**5*d**5*x**2 + 672*b*c**6*d**5*x**3 + 336*c**7*d**5*x**4) - 2*a*b**2*c*sqrt(b*d + 2*c*d*x)/(21*b**4*c**3*d**5 + 168*b**3*c**4*d**5*x + 504*b**2*c**5*d**5*x**2 + 672*b*c**6*d**5*x**3 + 336*c**7*d**5*x**4) - 14*a*b*c**2*x*sqrt(b*d + 2*c*d*x)/(21*b**4*c**3*d**5 + 168*b**3*c**4*d**5*x + 504*b**2*c**5*d**5*x**2 + 672*b*c**6*d**5*x**3 + 336*c**7*d**5*x**4) - 14*a*c**3*x**2*sqrt(b*d + 2*c*d*x)/(21*b**4*c**3*d**5 + 168*b**3*c**4*d**5*x + 504*b**2*c**5*d**5*x**2 + 672*b*c**6*d**5*x**3 + 336*c**7*d**5*x**4) + 2*b**4*sqrt(b*d + 2*c*d*x)/(21*b**4*c**3*d**5 + 168*b**3*c**4*d**5*x + 504*b**2*c**5*d**5*x**2 + 672*b*c**6*d**5*x**3 + 336*c**7*d**5*x**4) + 14*b**3*c*x*sqrt(b*d + 2*c*d*x)/(21*b**4*c**3*d**5 + 168*b**3*c**4*d**5*x + 504*b**2*c**5*d**5*x**2 + 672*b*c**6*d**5*x**3 + 336*c**7*d**5*x**4) + 35*b**2*c**2*x**2*sqrt(b*d + 2*c*d*x)/(21*b**4*c**3*d**5 + 168*b**3*c**4*d**5*x + 504*b**2*c**5*d**5*x**2 + 672*b*c**6*d**5*x**3 + 336*c**7*d**5*x**4) + 42*b*c**3*x**3*sqrt(b*d + 2*c*d*x)/(21*b**4*c**3*d**5 + 168*b**3*c**4*d**5*x + 504*b**2*c**5*d**5*x**2 + 672*b*c**6*d**5*x**3 + 336*c**7*d**5*x**4) + 21*c**4*x**4*sqrt(b*d + 2*c*d*x)/(21*b**4*c**3*d**5 + 168*b**3*c**4*d**5*x + 504*b**2*c**5*d**5*x**2 + 672*b*c**6*d**5*x**3 + 336*c**7*d**5*x**4), Ne(c, 0)), ((a**2*x + a*b*x**2 + b**2*x**3/3)/(b*d)**(9/2), True))","A",0
1276,1,966,0,14.648898," ","integrate((c*x**2+b*x+a)**2/(2*c*d*x+b*d)**(11/2),x)","\begin{cases} - \frac{5 a^{2} c^{2} \sqrt{b d + 2 c d x}}{45 b^{5} c^{3} d^{6} + 450 b^{4} c^{4} d^{6} x + 1800 b^{3} c^{5} d^{6} x^{2} + 3600 b^{2} c^{6} d^{6} x^{3} + 3600 b c^{7} d^{6} x^{4} + 1440 c^{8} d^{6} x^{5}} - \frac{2 a b^{2} c \sqrt{b d + 2 c d x}}{45 b^{5} c^{3} d^{6} + 450 b^{4} c^{4} d^{6} x + 1800 b^{3} c^{5} d^{6} x^{2} + 3600 b^{2} c^{6} d^{6} x^{3} + 3600 b c^{7} d^{6} x^{4} + 1440 c^{8} d^{6} x^{5}} - \frac{18 a b c^{2} x \sqrt{b d + 2 c d x}}{45 b^{5} c^{3} d^{6} + 450 b^{4} c^{4} d^{6} x + 1800 b^{3} c^{5} d^{6} x^{2} + 3600 b^{2} c^{6} d^{6} x^{3} + 3600 b c^{7} d^{6} x^{4} + 1440 c^{8} d^{6} x^{5}} - \frac{18 a c^{3} x^{2} \sqrt{b d + 2 c d x}}{45 b^{5} c^{3} d^{6} + 450 b^{4} c^{4} d^{6} x + 1800 b^{3} c^{5} d^{6} x^{2} + 3600 b^{2} c^{6} d^{6} x^{3} + 3600 b c^{7} d^{6} x^{4} + 1440 c^{8} d^{6} x^{5}} - \frac{2 b^{4} \sqrt{b d + 2 c d x}}{45 b^{5} c^{3} d^{6} + 450 b^{4} c^{4} d^{6} x + 1800 b^{3} c^{5} d^{6} x^{2} + 3600 b^{2} c^{6} d^{6} x^{3} + 3600 b c^{7} d^{6} x^{4} + 1440 c^{8} d^{6} x^{5}} - \frac{18 b^{3} c x \sqrt{b d + 2 c d x}}{45 b^{5} c^{3} d^{6} + 450 b^{4} c^{4} d^{6} x + 1800 b^{3} c^{5} d^{6} x^{2} + 3600 b^{2} c^{6} d^{6} x^{3} + 3600 b c^{7} d^{6} x^{4} + 1440 c^{8} d^{6} x^{5}} - \frac{63 b^{2} c^{2} x^{2} \sqrt{b d + 2 c d x}}{45 b^{5} c^{3} d^{6} + 450 b^{4} c^{4} d^{6} x + 1800 b^{3} c^{5} d^{6} x^{2} + 3600 b^{2} c^{6} d^{6} x^{3} + 3600 b c^{7} d^{6} x^{4} + 1440 c^{8} d^{6} x^{5}} - \frac{90 b c^{3} x^{3} \sqrt{b d + 2 c d x}}{45 b^{5} c^{3} d^{6} + 450 b^{4} c^{4} d^{6} x + 1800 b^{3} c^{5} d^{6} x^{2} + 3600 b^{2} c^{6} d^{6} x^{3} + 3600 b c^{7} d^{6} x^{4} + 1440 c^{8} d^{6} x^{5}} - \frac{45 c^{4} x^{4} \sqrt{b d + 2 c d x}}{45 b^{5} c^{3} d^{6} + 450 b^{4} c^{4} d^{6} x + 1800 b^{3} c^{5} d^{6} x^{2} + 3600 b^{2} c^{6} d^{6} x^{3} + 3600 b c^{7} d^{6} x^{4} + 1440 c^{8} d^{6} x^{5}} & \text{for}\: c \neq 0 \\\frac{a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}}{\left(b d\right)^{\frac{11}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*a**2*c**2*sqrt(b*d + 2*c*d*x)/(45*b**5*c**3*d**6 + 450*b**4*c**4*d**6*x + 1800*b**3*c**5*d**6*x**2 + 3600*b**2*c**6*d**6*x**3 + 3600*b*c**7*d**6*x**4 + 1440*c**8*d**6*x**5) - 2*a*b**2*c*sqrt(b*d + 2*c*d*x)/(45*b**5*c**3*d**6 + 450*b**4*c**4*d**6*x + 1800*b**3*c**5*d**6*x**2 + 3600*b**2*c**6*d**6*x**3 + 3600*b*c**7*d**6*x**4 + 1440*c**8*d**6*x**5) - 18*a*b*c**2*x*sqrt(b*d + 2*c*d*x)/(45*b**5*c**3*d**6 + 450*b**4*c**4*d**6*x + 1800*b**3*c**5*d**6*x**2 + 3600*b**2*c**6*d**6*x**3 + 3600*b*c**7*d**6*x**4 + 1440*c**8*d**6*x**5) - 18*a*c**3*x**2*sqrt(b*d + 2*c*d*x)/(45*b**5*c**3*d**6 + 450*b**4*c**4*d**6*x + 1800*b**3*c**5*d**6*x**2 + 3600*b**2*c**6*d**6*x**3 + 3600*b*c**7*d**6*x**4 + 1440*c**8*d**6*x**5) - 2*b**4*sqrt(b*d + 2*c*d*x)/(45*b**5*c**3*d**6 + 450*b**4*c**4*d**6*x + 1800*b**3*c**5*d**6*x**2 + 3600*b**2*c**6*d**6*x**3 + 3600*b*c**7*d**6*x**4 + 1440*c**8*d**6*x**5) - 18*b**3*c*x*sqrt(b*d + 2*c*d*x)/(45*b**5*c**3*d**6 + 450*b**4*c**4*d**6*x + 1800*b**3*c**5*d**6*x**2 + 3600*b**2*c**6*d**6*x**3 + 3600*b*c**7*d**6*x**4 + 1440*c**8*d**6*x**5) - 63*b**2*c**2*x**2*sqrt(b*d + 2*c*d*x)/(45*b**5*c**3*d**6 + 450*b**4*c**4*d**6*x + 1800*b**3*c**5*d**6*x**2 + 3600*b**2*c**6*d**6*x**3 + 3600*b*c**7*d**6*x**4 + 1440*c**8*d**6*x**5) - 90*b*c**3*x**3*sqrt(b*d + 2*c*d*x)/(45*b**5*c**3*d**6 + 450*b**4*c**4*d**6*x + 1800*b**3*c**5*d**6*x**2 + 3600*b**2*c**6*d**6*x**3 + 3600*b*c**7*d**6*x**4 + 1440*c**8*d**6*x**5) - 45*c**4*x**4*sqrt(b*d + 2*c*d*x)/(45*b**5*c**3*d**6 + 450*b**4*c**4*d**6*x + 1800*b**3*c**5*d**6*x**2 + 3600*b**2*c**6*d**6*x**3 + 3600*b*c**7*d**6*x**4 + 1440*c**8*d**6*x**5), Ne(c, 0)), ((a**2*x + a*b*x**2 + b**2*x**3/3)/(b*d)**(11/2), True))","A",0
1277,1,151,0,4.519712," ","integrate((2*c*d*x+b*d)**(1/2)*(c*x**2+b*x+a)**3,x)","\frac{\frac{\left(b d + 2 c d x\right)^{\frac{3}{2}} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}{192 c^{3}} + \frac{\left(b d + 2 c d x\right)^{\frac{7}{2}} \left(48 a^{2} c^{2} - 24 a b^{2} c + 3 b^{4}\right)}{448 c^{3} d^{2}} + \frac{\left(12 a c - 3 b^{2}\right) \left(b d + 2 c d x\right)^{\frac{11}{2}}}{704 c^{3} d^{4}} + \frac{\left(b d + 2 c d x\right)^{\frac{15}{2}}}{960 c^{3} d^{6}}}{c d}"," ",0,"((b*d + 2*c*d*x)**(3/2)*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)/(192*c**3) + (b*d + 2*c*d*x)**(7/2)*(48*a**2*c**2 - 24*a*b**2*c + 3*b**4)/(448*c**3*d**2) + (12*a*c - 3*b**2)*(b*d + 2*c*d*x)**(11/2)/(704*c**3*d**4) + (b*d + 2*c*d*x)**(15/2)/(960*c**3*d**6))/(c*d)","A",0
1278,1,1363,0,138.867641," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**(1/2),x)","\begin{cases} \frac{- \frac{a^{3} b}{\sqrt{b d + 2 c d x}} - \frac{a^{3} \left(- \frac{b d}{\sqrt{b d + 2 c d x}} - \sqrt{b d + 2 c d x}\right)}{d} - \frac{3 a^{2} b^{2} \left(- \frac{b d}{\sqrt{b d + 2 c d x}} - \sqrt{b d + 2 c d x}\right)}{2 c d} - \frac{9 a^{2} b \left(\frac{b^{2} d^{2}}{\sqrt{b d + 2 c d x}} + 2 b d \sqrt{b d + 2 c d x} - \frac{\left(b d + 2 c d x\right)^{\frac{3}{2}}}{3}\right)}{4 c d^{2}} - \frac{3 a^{2} \left(- \frac{b^{3} d^{3}}{\sqrt{b d + 2 c d x}} - 3 b^{2} d^{2} \sqrt{b d + 2 c d x} + b d \left(b d + 2 c d x\right)^{\frac{3}{2}} - \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{5}\right)}{4 c d^{3}} - \frac{3 a b^{3} \left(\frac{b^{2} d^{2}}{\sqrt{b d + 2 c d x}} + 2 b d \sqrt{b d + 2 c d x} - \frac{\left(b d + 2 c d x\right)^{\frac{3}{2}}}{3}\right)}{4 c^{2} d^{2}} - \frac{3 a b^{2} \left(- \frac{b^{3} d^{3}}{\sqrt{b d + 2 c d x}} - 3 b^{2} d^{2} \sqrt{b d + 2 c d x} + b d \left(b d + 2 c d x\right)^{\frac{3}{2}} - \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{5}\right)}{2 c^{2} d^{3}} - \frac{15 a b \left(\frac{b^{4} d^{4}}{\sqrt{b d + 2 c d x}} + 4 b^{3} d^{3} \sqrt{b d + 2 c d x} - 2 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{3}{2}} + \frac{4 b d \left(b d + 2 c d x\right)^{\frac{5}{2}}}{5} - \frac{\left(b d + 2 c d x\right)^{\frac{7}{2}}}{7}\right)}{16 c^{2} d^{4}} - \frac{3 a \left(- \frac{b^{5} d^{5}}{\sqrt{b d + 2 c d x}} - 5 b^{4} d^{4} \sqrt{b d + 2 c d x} + \frac{10 b^{3} d^{3} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} - 2 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{5}{2}} + \frac{5 b d \left(b d + 2 c d x\right)^{\frac{7}{2}}}{7} - \frac{\left(b d + 2 c d x\right)^{\frac{9}{2}}}{9}\right)}{16 c^{2} d^{5}} - \frac{b^{4} \left(- \frac{b^{3} d^{3}}{\sqrt{b d + 2 c d x}} - 3 b^{2} d^{2} \sqrt{b d + 2 c d x} + b d \left(b d + 2 c d x\right)^{\frac{3}{2}} - \frac{\left(b d + 2 c d x\right)^{\frac{5}{2}}}{5}\right)}{8 c^{3} d^{3}} - \frac{5 b^{3} \left(\frac{b^{4} d^{4}}{\sqrt{b d + 2 c d x}} + 4 b^{3} d^{3} \sqrt{b d + 2 c d x} - 2 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{3}{2}} + \frac{4 b d \left(b d + 2 c d x\right)^{\frac{5}{2}}}{5} - \frac{\left(b d + 2 c d x\right)^{\frac{7}{2}}}{7}\right)}{16 c^{3} d^{4}} - \frac{9 b^{2} \left(- \frac{b^{5} d^{5}}{\sqrt{b d + 2 c d x}} - 5 b^{4} d^{4} \sqrt{b d + 2 c d x} + \frac{10 b^{3} d^{3} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3} - 2 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{5}{2}} + \frac{5 b d \left(b d + 2 c d x\right)^{\frac{7}{2}}}{7} - \frac{\left(b d + 2 c d x\right)^{\frac{9}{2}}}{9}\right)}{32 c^{3} d^{5}} - \frac{7 b \left(\frac{b^{6} d^{6}}{\sqrt{b d + 2 c d x}} + 6 b^{5} d^{5} \sqrt{b d + 2 c d x} - 5 b^{4} d^{4} \left(b d + 2 c d x\right)^{\frac{3}{2}} + 4 b^{3} d^{3} \left(b d + 2 c d x\right)^{\frac{5}{2}} - \frac{15 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{7}{2}}}{7} + \frac{2 b d \left(b d + 2 c d x\right)^{\frac{9}{2}}}{3} - \frac{\left(b d + 2 c d x\right)^{\frac{11}{2}}}{11}\right)}{64 c^{3} d^{6}} - \frac{- \frac{b^{7} d^{7}}{\sqrt{b d + 2 c d x}} - 7 b^{6} d^{6} \sqrt{b d + 2 c d x} + 7 b^{5} d^{5} \left(b d + 2 c d x\right)^{\frac{3}{2}} - 7 b^{4} d^{4} \left(b d + 2 c d x\right)^{\frac{5}{2}} + 5 b^{3} d^{3} \left(b d + 2 c d x\right)^{\frac{7}{2}} - \frac{7 b^{2} d^{2} \left(b d + 2 c d x\right)^{\frac{9}{2}}}{3} + \frac{7 b d \left(b d + 2 c d x\right)^{\frac{11}{2}}}{11} - \frac{\left(b d + 2 c d x\right)^{\frac{13}{2}}}{13}}{64 c^{3} d^{7}}}{c} & \text{for}\: c \neq 0 \\\frac{\begin{cases} a^{3} x & \text{for}\: b = 0 \\\frac{\left(a + b x\right)^{4}}{4 b} & \text{otherwise} \end{cases}}{\sqrt{b d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**3*b/sqrt(b*d + 2*c*d*x) - a**3*(-b*d/sqrt(b*d + 2*c*d*x) - sqrt(b*d + 2*c*d*x))/d - 3*a**2*b**2*(-b*d/sqrt(b*d + 2*c*d*x) - sqrt(b*d + 2*c*d*x))/(2*c*d) - 9*a**2*b*(b**2*d**2/sqrt(b*d + 2*c*d*x) + 2*b*d*sqrt(b*d + 2*c*d*x) - (b*d + 2*c*d*x)**(3/2)/3)/(4*c*d**2) - 3*a**2*(-b**3*d**3/sqrt(b*d + 2*c*d*x) - 3*b**2*d**2*sqrt(b*d + 2*c*d*x) + b*d*(b*d + 2*c*d*x)**(3/2) - (b*d + 2*c*d*x)**(5/2)/5)/(4*c*d**3) - 3*a*b**3*(b**2*d**2/sqrt(b*d + 2*c*d*x) + 2*b*d*sqrt(b*d + 2*c*d*x) - (b*d + 2*c*d*x)**(3/2)/3)/(4*c**2*d**2) - 3*a*b**2*(-b**3*d**3/sqrt(b*d + 2*c*d*x) - 3*b**2*d**2*sqrt(b*d + 2*c*d*x) + b*d*(b*d + 2*c*d*x)**(3/2) - (b*d + 2*c*d*x)**(5/2)/5)/(2*c**2*d**3) - 15*a*b*(b**4*d**4/sqrt(b*d + 2*c*d*x) + 4*b**3*d**3*sqrt(b*d + 2*c*d*x) - 2*b**2*d**2*(b*d + 2*c*d*x)**(3/2) + 4*b*d*(b*d + 2*c*d*x)**(5/2)/5 - (b*d + 2*c*d*x)**(7/2)/7)/(16*c**2*d**4) - 3*a*(-b**5*d**5/sqrt(b*d + 2*c*d*x) - 5*b**4*d**4*sqrt(b*d + 2*c*d*x) + 10*b**3*d**3*(b*d + 2*c*d*x)**(3/2)/3 - 2*b**2*d**2*(b*d + 2*c*d*x)**(5/2) + 5*b*d*(b*d + 2*c*d*x)**(7/2)/7 - (b*d + 2*c*d*x)**(9/2)/9)/(16*c**2*d**5) - b**4*(-b**3*d**3/sqrt(b*d + 2*c*d*x) - 3*b**2*d**2*sqrt(b*d + 2*c*d*x) + b*d*(b*d + 2*c*d*x)**(3/2) - (b*d + 2*c*d*x)**(5/2)/5)/(8*c**3*d**3) - 5*b**3*(b**4*d**4/sqrt(b*d + 2*c*d*x) + 4*b**3*d**3*sqrt(b*d + 2*c*d*x) - 2*b**2*d**2*(b*d + 2*c*d*x)**(3/2) + 4*b*d*(b*d + 2*c*d*x)**(5/2)/5 - (b*d + 2*c*d*x)**(7/2)/7)/(16*c**3*d**4) - 9*b**2*(-b**5*d**5/sqrt(b*d + 2*c*d*x) - 5*b**4*d**4*sqrt(b*d + 2*c*d*x) + 10*b**3*d**3*(b*d + 2*c*d*x)**(3/2)/3 - 2*b**2*d**2*(b*d + 2*c*d*x)**(5/2) + 5*b*d*(b*d + 2*c*d*x)**(7/2)/7 - (b*d + 2*c*d*x)**(9/2)/9)/(32*c**3*d**5) - 7*b*(b**6*d**6/sqrt(b*d + 2*c*d*x) + 6*b**5*d**5*sqrt(b*d + 2*c*d*x) - 5*b**4*d**4*(b*d + 2*c*d*x)**(3/2) + 4*b**3*d**3*(b*d + 2*c*d*x)**(5/2) - 15*b**2*d**2*(b*d + 2*c*d*x)**(7/2)/7 + 2*b*d*(b*d + 2*c*d*x)**(9/2)/3 - (b*d + 2*c*d*x)**(11/2)/11)/(64*c**3*d**6) - (-b**7*d**7/sqrt(b*d + 2*c*d*x) - 7*b**6*d**6*sqrt(b*d + 2*c*d*x) + 7*b**5*d**5*(b*d + 2*c*d*x)**(3/2) - 7*b**4*d**4*(b*d + 2*c*d*x)**(5/2) + 5*b**3*d**3*(b*d + 2*c*d*x)**(7/2) - 7*b**2*d**2*(b*d + 2*c*d*x)**(9/2)/3 + 7*b*d*(b*d + 2*c*d*x)**(11/2)/11 - (b*d + 2*c*d*x)**(13/2)/13)/(64*c**3*d**7))/c, Ne(c, 0)), (Piecewise((a**3*x, Eq(b, 0)), ((a + b*x)**4/(4*b), True))/sqrt(b*d), True))","A",0
1279,1,128,0,59.831996," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**(3/2),x)","- \frac{\left(4 a c - b^{2}\right)^{3}}{64 c^{4} d \sqrt{b d + 2 c d x}} + \frac{\left(b d + 2 c d x\right)^{\frac{3}{2}} \left(48 a^{2} c^{2} - 24 a b^{2} c + 3 b^{4}\right)}{192 c^{4} d^{3}} + \frac{\left(12 a c - 3 b^{2}\right) \left(b d + 2 c d x\right)^{\frac{7}{2}}}{448 c^{4} d^{5}} + \frac{\left(b d + 2 c d x\right)^{\frac{11}{2}}}{704 c^{4} d^{7}}"," ",0,"-(4*a*c - b**2)**3/(64*c**4*d*sqrt(b*d + 2*c*d*x)) + (b*d + 2*c*d*x)**(3/2)*(48*a**2*c**2 - 24*a*b**2*c + 3*b**4)/(192*c**4*d**3) + (12*a*c - 3*b**2)*(b*d + 2*c*d*x)**(7/2)/(448*c**4*d**5) + (b*d + 2*c*d*x)**(11/2)/(704*c**4*d**7)","A",0
1280,1,128,0,86.396693," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**(5/2),x)","- \frac{\left(4 a c - b^{2}\right)^{3}}{192 c^{4} d \left(b d + 2 c d x\right)^{\frac{3}{2}}} + \frac{\sqrt{b d + 2 c d x} \left(48 a^{2} c^{2} - 24 a b^{2} c + 3 b^{4}\right)}{64 c^{4} d^{3}} + \frac{\left(12 a c - 3 b^{2}\right) \left(b d + 2 c d x\right)^{\frac{5}{2}}}{320 c^{4} d^{5}} + \frac{\left(b d + 2 c d x\right)^{\frac{9}{2}}}{576 c^{4} d^{7}}"," ",0,"-(4*a*c - b**2)**3/(192*c**4*d*(b*d + 2*c*d*x)**(3/2)) + sqrt(b*d + 2*c*d*x)*(48*a**2*c**2 - 24*a*b**2*c + 3*b**4)/(64*c**4*d**3) + (12*a*c - 3*b**2)*(b*d + 2*c*d*x)**(5/2)/(320*c**4*d**5) + (b*d + 2*c*d*x)**(9/2)/(576*c**4*d**7)","A",0
1281,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1282,1,1394,0,11.270014," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**(9/2),x)","\begin{cases} - \frac{5 a^{3} c^{3} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} - \frac{5 a^{2} b^{2} c^{2} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} - \frac{35 a^{2} b c^{3} x \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} - \frac{35 a^{2} c^{4} x^{2} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} + \frac{10 a b^{4} c \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} + \frac{70 a b^{3} c^{2} x \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} + \frac{175 a b^{2} c^{3} x^{2} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} + \frac{210 a b c^{4} x^{3} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} + \frac{105 a c^{5} x^{4} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} - \frac{2 b^{6} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} - \frac{14 b^{5} c x \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} - \frac{35 b^{4} c^{2} x^{2} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} - \frac{35 b^{3} c^{3} x^{3} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} + \frac{21 b c^{5} x^{5} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} + \frac{7 c^{6} x^{6} \sqrt{b d + 2 c d x}}{35 b^{4} c^{4} d^{5} + 280 b^{3} c^{5} d^{5} x + 840 b^{2} c^{6} d^{5} x^{2} + 1120 b c^{7} d^{5} x^{3} + 560 c^{8} d^{5} x^{4}} & \text{for}\: c \neq 0 \\\frac{a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}}{\left(b d\right)^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*a**3*c**3*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) - 5*a**2*b**2*c**2*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) - 35*a**2*b*c**3*x*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) - 35*a**2*c**4*x**2*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) + 10*a*b**4*c*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) + 70*a*b**3*c**2*x*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) + 175*a*b**2*c**3*x**2*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) + 210*a*b*c**4*x**3*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) + 105*a*c**5*x**4*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) - 2*b**6*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) - 14*b**5*c*x*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) - 35*b**4*c**2*x**2*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) - 35*b**3*c**3*x**3*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) + 21*b*c**5*x**5*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4) + 7*c**6*x**6*sqrt(b*d + 2*c*d*x)/(35*b**4*c**4*d**5 + 280*b**3*c**5*d**5*x + 840*b**2*c**6*d**5*x**2 + 1120*b*c**7*d**5*x**3 + 560*c**8*d**5*x**4), Ne(c, 0)), ((a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4)/(b*d)**(9/2), True))","A",0
1283,1,1731,0,19.682808," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**(11/2),x)","\begin{cases} - \frac{5 a^{3} c^{3} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} - \frac{3 a^{2} b^{2} c^{2} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} - \frac{27 a^{2} b c^{3} x \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} - \frac{27 a^{2} c^{4} x^{2} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} - \frac{6 a b^{4} c \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} - \frac{54 a b^{3} c^{2} x \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} - \frac{189 a b^{2} c^{3} x^{2} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} - \frac{270 a b c^{4} x^{3} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} - \frac{135 a c^{5} x^{4} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} + \frac{2 b^{6} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} + \frac{18 b^{5} c x \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} + \frac{63 b^{4} c^{2} x^{2} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} + \frac{105 b^{3} c^{3} x^{3} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} + \frac{90 b^{2} c^{4} x^{4} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} + \frac{45 b c^{5} x^{5} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} + \frac{15 c^{6} x^{6} \sqrt{b d + 2 c d x}}{45 b^{5} c^{4} d^{6} + 450 b^{4} c^{5} d^{6} x + 1800 b^{3} c^{6} d^{6} x^{2} + 3600 b^{2} c^{7} d^{6} x^{3} + 3600 b c^{8} d^{6} x^{4} + 1440 c^{9} d^{6} x^{5}} & \text{for}\: c \neq 0 \\\frac{a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}}{\left(b d\right)^{\frac{11}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*a**3*c**3*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) - 3*a**2*b**2*c**2*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) - 27*a**2*b*c**3*x*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) - 27*a**2*c**4*x**2*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) - 6*a*b**4*c*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) - 54*a*b**3*c**2*x*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) - 189*a*b**2*c**3*x**2*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) - 270*a*b*c**4*x**3*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) - 135*a*c**5*x**4*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) + 2*b**6*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) + 18*b**5*c*x*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) + 63*b**4*c**2*x**2*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) + 105*b**3*c**3*x**3*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) + 90*b**2*c**4*x**4*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) + 45*b*c**5*x**5*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5) + 15*c**6*x**6*sqrt(b*d + 2*c*d*x)/(45*b**5*c**4*d**6 + 450*b**4*c**5*d**6*x + 1800*b**3*c**6*d**6*x**2 + 3600*b**2*c**7*d**6*x**3 + 3600*b*c**8*d**6*x**4 + 1440*c**9*d**6*x**5), Ne(c, 0)), ((a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4)/(b*d)**(11/2), True))","A",0
1284,1,1975,0,33.378766," ","integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**(13/2),x)","\begin{cases} - \frac{7 a^{3} c^{3} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} - \frac{3 a^{2} b^{2} c^{2} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} - \frac{33 a^{2} b c^{3} x \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} - \frac{33 a^{2} c^{4} x^{2} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} - \frac{2 a b^{4} c \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} - \frac{22 a b^{3} c^{2} x \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} - \frac{99 a b^{2} c^{3} x^{2} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} - \frac{154 a b c^{4} x^{3} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} - \frac{77 a c^{5} x^{4} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} + \frac{2 b^{6} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} + \frac{22 b^{5} c x \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} + \frac{99 b^{4} c^{2} x^{2} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} + \frac{231 b^{3} c^{3} x^{3} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} + \frac{308 b^{2} c^{4} x^{4} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} + \frac{231 b c^{5} x^{5} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} + \frac{77 c^{6} x^{6} \sqrt{b d + 2 c d x}}{77 b^{6} c^{4} d^{7} + 924 b^{5} c^{5} d^{7} x + 4620 b^{4} c^{6} d^{7} x^{2} + 12320 b^{3} c^{7} d^{7} x^{3} + 18480 b^{2} c^{8} d^{7} x^{4} + 14784 b c^{9} d^{7} x^{5} + 4928 c^{10} d^{7} x^{6}} & \text{for}\: c \neq 0 \\\frac{a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}}{\left(b d\right)^{\frac{13}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-7*a**3*c**3*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) - 3*a**2*b**2*c**2*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) - 33*a**2*b*c**3*x*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) - 33*a**2*c**4*x**2*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) - 2*a*b**4*c*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) - 22*a*b**3*c**2*x*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) - 99*a*b**2*c**3*x**2*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) - 154*a*b*c**4*x**3*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) - 77*a*c**5*x**4*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) + 2*b**6*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) + 22*b**5*c*x*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) + 99*b**4*c**2*x**2*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) + 231*b**3*c**3*x**3*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) + 308*b**2*c**4*x**4*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) + 231*b*c**5*x**5*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6) + 77*c**6*x**6*sqrt(b*d + 2*c*d*x)/(77*b**6*c**4*d**7 + 924*b**5*c**5*d**7*x + 4620*b**4*c**6*d**7*x**2 + 12320*b**3*c**7*d**7*x**3 + 18480*b**2*c**8*d**7*x**4 + 14784*b*c**9*d**7*x**5 + 4928*c**10*d**7*x**6), Ne(c, 0)), ((a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4)/(b*d)**(13/2), True))","A",0
1285,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(11/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1286,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(9/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1287,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1288,1,700,0,97.721008," ","integrate((2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a),x)","32 a b c d^{4} \operatorname{RootSum} {\left(t^{4} \left(16384 a^{3} c^{3} d^{6} - 12288 a^{2} b^{2} c^{2} d^{6} + 3072 a b^{4} c d^{6} - 256 b^{6} d^{6}\right) + 1, \left( t \mapsto t \log{\left(16 t a c d^{2} - 4 t b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} - 32 a b c d^{4} \operatorname{RootSum} {\left(t^{4} \left(16384 a^{3} c^{3} d^{6} - 12288 a^{2} b^{2} c^{2} d^{6} + 3072 a b^{4} c d^{6} - 256 b^{6} d^{6}\right) + 1, \left( t \mapsto t \log{\left(16 t a c d^{2} - 4 t b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} - 16 a c d^{3} \operatorname{RootSum} {\left(t^{4} \left(1024 a c d^{2} - 256 b^{2} d^{2}\right) + 1, \left( t \mapsto t \log{\left(256 t^{3} a c d^{2} - 64 t^{3} b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} - 8 b^{3} d^{4} \operatorname{RootSum} {\left(t^{4} \left(16384 a^{3} c^{3} d^{6} - 12288 a^{2} b^{2} c^{2} d^{6} + 3072 a b^{4} c d^{6} - 256 b^{6} d^{6}\right) + 1, \left( t \mapsto t \log{\left(16 t a c d^{2} - 4 t b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} + 8 b^{3} d^{4} \operatorname{RootSum} {\left(t^{4} \left(16384 a^{3} c^{3} d^{6} - 12288 a^{2} b^{2} c^{2} d^{6} + 3072 a b^{4} c d^{6} - 256 b^{6} d^{6}\right) + 1, \left( t \mapsto t \log{\left(16 t a c d^{2} - 4 t b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} + 8 b^{2} d^{3} \operatorname{RootSum} {\left(t^{4} \left(1024 a c d^{2} - 256 b^{2} d^{2}\right) + 1, \left( t \mapsto t \log{\left(256 t^{3} a c d^{2} - 64 t^{3} b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} - 8 b^{2} d^{3} \operatorname{RootSum} {\left(t^{4} \left(1024 a c d^{2} - 256 b^{2} d^{2}\right) + 1, \left( t \mapsto t \log{\left(256 t^{3} a c d^{2} - 64 t^{3} b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} + 4 b^{2} d^{3} \operatorname{RootSum} {\left(t^{4} \left(1024 a c d^{2} - 256 b^{2} d^{2}\right) + 1, \left( t \mapsto t \log{\left(256 t^{3} a c d^{2} - 64 t^{3} b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} + \frac{4 d \left(b d + 2 c d x\right)^{\frac{3}{2}}}{3}"," ",0,"32*a*b*c*d**4*RootSum(_t**4*(16384*a**3*c**3*d**6 - 12288*a**2*b**2*c**2*d**6 + 3072*a*b**4*c*d**6 - 256*b**6*d**6) + 1, Lambda(_t, _t*log(16*_t*a*c*d**2 - 4*_t*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) - 32*a*b*c*d**4*RootSum(_t**4*(16384*a**3*c**3*d**6 - 12288*a**2*b**2*c**2*d**6 + 3072*a*b**4*c*d**6 - 256*b**6*d**6) + 1, Lambda(_t, _t*log(16*_t*a*c*d**2 - 4*_t*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) - 16*a*c*d**3*RootSum(_t**4*(1024*a*c*d**2 - 256*b**2*d**2) + 1, Lambda(_t, _t*log(256*_t**3*a*c*d**2 - 64*_t**3*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) - 8*b**3*d**4*RootSum(_t**4*(16384*a**3*c**3*d**6 - 12288*a**2*b**2*c**2*d**6 + 3072*a*b**4*c*d**6 - 256*b**6*d**6) + 1, Lambda(_t, _t*log(16*_t*a*c*d**2 - 4*_t*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) + 8*b**3*d**4*RootSum(_t**4*(16384*a**3*c**3*d**6 - 12288*a**2*b**2*c**2*d**6 + 3072*a*b**4*c*d**6 - 256*b**6*d**6) + 1, Lambda(_t, _t*log(16*_t*a*c*d**2 - 4*_t*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) + 8*b**2*d**3*RootSum(_t**4*(1024*a*c*d**2 - 256*b**2*d**2) + 1, Lambda(_t, _t*log(256*_t**3*a*c*d**2 - 64*_t**3*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) - 8*b**2*d**3*RootSum(_t**4*(1024*a*c*d**2 - 256*b**2*d**2) + 1, Lambda(_t, _t*log(256*_t**3*a*c*d**2 - 64*_t**3*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) + 4*b**2*d**3*RootSum(_t**4*(1024*a*c*d**2 - 256*b**2*d**2) + 1, Lambda(_t, _t*log(256*_t**3*a*c*d**2 - 64*_t**3*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) + 4*d*(b*d + 2*c*d*x)**(3/2)/3","B",0
1289,1,352,0,34.616978," ","integrate((2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a),x)","- 16 a c d^{3} \operatorname{RootSum} {\left(t^{4} \left(16384 a^{3} c^{3} d^{6} - 12288 a^{2} b^{2} c^{2} d^{6} + 3072 a b^{4} c d^{6} - 256 b^{6} d^{6}\right) + 1, \left( t \mapsto t \log{\left(16 t a c d^{2} - 4 t b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} + 4 b^{2} d^{3} \operatorname{RootSum} {\left(t^{4} \left(16384 a^{3} c^{3} d^{6} - 12288 a^{2} b^{2} c^{2} d^{6} + 3072 a b^{4} c d^{6} - 256 b^{6} d^{6}\right) + 1, \left( t \mapsto t \log{\left(16 t a c d^{2} - 4 t b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} - 4 b d^{2} \operatorname{RootSum} {\left(t^{4} \left(1024 a c d^{2} - 256 b^{2} d^{2}\right) + 1, \left( t \mapsto t \log{\left(256 t^{3} a c d^{2} - 64 t^{3} b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} + 4 b d^{2} \operatorname{RootSum} {\left(t^{4} \left(1024 a c d^{2} - 256 b^{2} d^{2}\right) + 1, \left( t \mapsto t \log{\left(256 t^{3} a c d^{2} - 64 t^{3} b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)} + 4 d \sqrt{b d + 2 c d x}"," ",0,"-16*a*c*d**3*RootSum(_t**4*(16384*a**3*c**3*d**6 - 12288*a**2*b**2*c**2*d**6 + 3072*a*b**4*c*d**6 - 256*b**6*d**6) + 1, Lambda(_t, _t*log(16*_t*a*c*d**2 - 4*_t*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) + 4*b**2*d**3*RootSum(_t**4*(16384*a**3*c**3*d**6 - 12288*a**2*b**2*c**2*d**6 + 3072*a*b**4*c*d**6 - 256*b**6*d**6) + 1, Lambda(_t, _t*log(16*_t*a*c*d**2 - 4*_t*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) - 4*b*d**2*RootSum(_t**4*(1024*a*c*d**2 - 256*b**2*d**2) + 1, Lambda(_t, _t*log(256*_t**3*a*c*d**2 - 64*_t**3*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) + 4*b*d**2*RootSum(_t**4*(1024*a*c*d**2 - 256*b**2*d**2) + 1, Lambda(_t, _t*log(256*_t**3*a*c*d**2 - 64*_t**3*b**2*d**2 + sqrt(b*d + 2*c*d*x)))) + 4*d*sqrt(b*d + 2*c*d*x)","B",0
1290,1,65,0,5.288361," ","integrate((2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a),x)","4 d \operatorname{RootSum} {\left(t^{4} \left(1024 a c d^{2} - 256 b^{2} d^{2}\right) + 1, \left( t \mapsto t \log{\left(256 t^{3} a c d^{2} - 64 t^{3} b^{2} d^{2} + \sqrt{b d + 2 c d x} \right)} \right)\right)}"," ",0,"4*d*RootSum(_t**4*(1024*a*c*d**2 - 256*b**2*d**2) + 1, Lambda(_t, _t*log(256*_t**3*a*c*d**2 - 64*_t**3*b**2*d**2 + sqrt(b*d + 2*c*d*x))))","A",0
1291,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a),x)","\int \frac{1}{\sqrt{d \left(b + 2 c x\right)} \left(a + b x + c x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(d*(b + 2*c*x))*(a + b*x + c*x**2)), x)","F",0
1292,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a),x)","\int \frac{1}{\left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}} \left(a + b x + c x^{2}\right)}\, dx"," ",0,"Integral(1/((d*(b + 2*c*x))**(3/2)*(a + b*x + c*x**2)), x)","F",0
1293,-1,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1294,-1,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1295,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(15/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1296,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(13/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1297,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(11/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1298,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(9/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1299,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1300,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1301,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1302,1,279,0,53.138764," ","integrate((2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a)**2,x)","\frac{16 c d^{3} \left(b d + 2 c d x\right)^{\frac{3}{2}}}{64 a^{2} c^{2} d^{4} - 32 a b^{2} c d^{4} + 16 a c d^{2} \left(b d + 2 c d x\right)^{2} + 4 b^{4} d^{4} - 4 b^{2} d^{2} \left(b d + 2 c d x\right)^{2}} + 16 c d^{3} \operatorname{RootSum} {\left(t^{4} \left(67108864 a^{5} c^{5} d^{10} - 83886080 a^{4} b^{2} c^{4} d^{10} + 41943040 a^{3} b^{4} c^{3} d^{10} - 10485760 a^{2} b^{6} c^{2} d^{10} + 1310720 a b^{8} c d^{10} - 65536 b^{10} d^{10}\right) + 1, \left( t \mapsto t \log{\left(1048576 t^{3} a^{4} c^{4} d^{8} - 1048576 t^{3} a^{3} b^{2} c^{3} d^{8} + 393216 t^{3} a^{2} b^{4} c^{2} d^{8} - 65536 t^{3} a b^{6} c d^{8} + 4096 t^{3} b^{8} d^{8} + \sqrt{b d + 2 c d x} \right)} \right)\right)}"," ",0,"16*c*d**3*(b*d + 2*c*d*x)**(3/2)/(64*a**2*c**2*d**4 - 32*a*b**2*c*d**4 + 16*a*c*d**2*(b*d + 2*c*d*x)**2 + 4*b**4*d**4 - 4*b**2*d**2*(b*d + 2*c*d*x)**2) + 16*c*d**3*RootSum(_t**4*(67108864*a**5*c**5*d**10 - 83886080*a**4*b**2*c**4*d**10 + 41943040*a**3*b**4*c**3*d**10 - 10485760*a**2*b**6*c**2*d**10 + 1310720*a*b**8*c*d**10 - 65536*b**10*d**10) + 1, Lambda(_t, _t*log(1048576*_t**3*a**4*c**4*d**8 - 1048576*_t**3*a**3*b**2*c**3*d**8 + 393216*_t**3*a**2*b**4*c**2*d**8 - 65536*_t**3*a*b**6*c*d**8 + 4096*_t**3*b**8*d**8 + sqrt(b*d + 2*c*d*x))))","B",0
1303,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a)**2,x)","\int \frac{1}{\sqrt{d \left(b + 2 c x\right)} \left(a + b x + c x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(d*(b + 2*c*x))*(a + b*x + c*x**2)**2), x)","F",0
1304,-1,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1305,-1,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1306,-1,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1307,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(17/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1308,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(15/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1309,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(13/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1310,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(11/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1311,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(9/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1312,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1313,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1314,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1315,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1316,-1,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1317,-1,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1318,-1,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1319,-1,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1320,1,180,0,37.939955," ","integrate((1+2*x)**(7/2)/(x**2+x+1),x)","\frac{4 \left(2 x + 1\right)^{\frac{5}{2}}}{5} - 12 \sqrt{2 x + 1} - \frac{3 \sqrt{2} \sqrt[4]{3} \log{\left(2 x - \sqrt{2} \sqrt[4]{3} \sqrt{2 x + 1} + 1 + \sqrt{3} \right)}}{2} + \frac{3 \sqrt{2} \sqrt[4]{3} \log{\left(2 x + \sqrt{2} \sqrt[4]{3} \sqrt{2 x + 1} + 1 + \sqrt{3} \right)}}{2} + 3 \sqrt{2} \sqrt[4]{3} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \sqrt{2 x + 1}}{3} - 1 \right)} + 3 \sqrt{2} \sqrt[4]{3} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \sqrt{2 x + 1}}{3} + 1 \right)}"," ",0,"4*(2*x + 1)**(5/2)/5 - 12*sqrt(2*x + 1) - 3*sqrt(2)*3**(1/4)*log(2*x - sqrt(2)*3**(1/4)*sqrt(2*x + 1) + 1 + sqrt(3))/2 + 3*sqrt(2)*3**(1/4)*log(2*x + sqrt(2)*3**(1/4)*sqrt(2*x + 1) + 1 + sqrt(3))/2 + 3*sqrt(2)*3**(1/4)*atan(sqrt(2)*3**(3/4)*sqrt(2*x + 1)/3 - 1) + 3*sqrt(2)*3**(1/4)*atan(sqrt(2)*3**(3/4)*sqrt(2*x + 1)/3 + 1)","A",0
1321,1,163,0,25.149512," ","integrate((1+2*x)**(5/2)/(x**2+x+1),x)","\frac{4 \left(2 x + 1\right)^{\frac{3}{2}}}{3} - \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \log{\left(2 x - \sqrt{2} \sqrt[4]{3} \sqrt{2 x + 1} + 1 + \sqrt{3} \right)}}{2} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \log{\left(2 x + \sqrt{2} \sqrt[4]{3} \sqrt{2 x + 1} + 1 + \sqrt{3} \right)}}{2} - \sqrt{2} \cdot 3^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \sqrt{2 x + 1}}{3} - 1 \right)} - \sqrt{2} \cdot 3^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \sqrt{2 x + 1}}{3} + 1 \right)}"," ",0,"4*(2*x + 1)**(3/2)/3 - sqrt(2)*3**(3/4)*log(2*x - sqrt(2)*3**(1/4)*sqrt(2*x + 1) + 1 + sqrt(3))/2 + sqrt(2)*3**(3/4)*log(2*x + sqrt(2)*3**(1/4)*sqrt(2*x + 1) + 1 + sqrt(3))/2 - sqrt(2)*3**(3/4)*atan(sqrt(2)*3**(3/4)*sqrt(2*x + 1)/3 - 1) - sqrt(2)*3**(3/4)*atan(sqrt(2)*3**(3/4)*sqrt(2*x + 1)/3 + 1)","A",0
1322,1,162,0,15.258267," ","integrate((1+2*x)**(3/2)/(x**2+x+1),x)","4 \sqrt{2 x + 1} + \frac{\sqrt{2} \sqrt[4]{3} \log{\left(2 x - \sqrt{2} \sqrt[4]{3} \sqrt{2 x + 1} + 1 + \sqrt{3} \right)}}{2} - \frac{\sqrt{2} \sqrt[4]{3} \log{\left(2 x + \sqrt{2} \sqrt[4]{3} \sqrt{2 x + 1} + 1 + \sqrt{3} \right)}}{2} - \sqrt{2} \sqrt[4]{3} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \sqrt{2 x + 1}}{3} - 1 \right)} - \sqrt{2} \sqrt[4]{3} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \sqrt{2 x + 1}}{3} + 1 \right)}"," ",0,"4*sqrt(2*x + 1) + sqrt(2)*3**(1/4)*log(2*x - sqrt(2)*3**(1/4)*sqrt(2*x + 1) + 1 + sqrt(3))/2 - sqrt(2)*3**(1/4)*log(2*x + sqrt(2)*3**(1/4)*sqrt(2*x + 1) + 1 + sqrt(3))/2 - sqrt(2)*3**(1/4)*atan(sqrt(2)*3**(3/4)*sqrt(2*x + 1)/3 - 1) - sqrt(2)*3**(1/4)*atan(sqrt(2)*3**(3/4)*sqrt(2*x + 1)/3 + 1)","A",0
1323,1,155,0,2.896740," ","integrate((1+2*x)**(1/2)/(x**2+x+1),x)","\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \log{\left(2 x - \sqrt{2} \sqrt[4]{3} \sqrt{2 x + 1} + 1 + \sqrt{3} \right)}}{6} - \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \log{\left(2 x + \sqrt{2} \sqrt[4]{3} \sqrt{2 x + 1} + 1 + \sqrt{3} \right)}}{6} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \sqrt{2 x + 1}}{3} - 1 \right)}}{3} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \sqrt{2 x + 1}}{3} + 1 \right)}}{3}"," ",0,"sqrt(2)*3**(3/4)*log(2*x - sqrt(2)*3**(1/4)*sqrt(2*x + 1) + 1 + sqrt(3))/6 - sqrt(2)*3**(3/4)*log(2*x + sqrt(2)*3**(1/4)*sqrt(2*x + 1) + 1 + sqrt(3))/6 + sqrt(2)*3**(3/4)*atan(sqrt(2)*3**(3/4)*sqrt(2*x + 1)/3 - 1)/3 + sqrt(2)*3**(3/4)*atan(sqrt(2)*3**(3/4)*sqrt(2*x + 1)/3 + 1)/3","A",0
1324,0,0,0,0.000000," ","integrate(1/(1+2*x)**(1/2)/(x**2+x+1),x)","\int \frac{1}{\sqrt{2 x + 1} \left(x^{2} + x + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(2*x + 1)*(x**2 + x + 1)), x)","F",0
1325,0,0,0,0.000000," ","integrate(1/(1+2*x)**(3/2)/(x**2+x+1),x)","\int \frac{1}{\left(2 x + 1\right)^{\frac{3}{2}} \left(x^{2} + x + 1\right)}\, dx"," ",0,"Integral(1/((2*x + 1)**(3/2)*(x**2 + x + 1)), x)","F",0
1326,0,0,0,0.000000," ","integrate(1/(1+2*x)**(5/2)/(x**2+x+1),x)","\int \frac{1}{\left(2 x + 1\right)^{\frac{5}{2}} \left(x^{2} + x + 1\right)}\, dx"," ",0,"Integral(1/((2*x + 1)**(5/2)*(x**2 + x + 1)), x)","F",0
1327,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(7/2)*(c*x**2+b*x+a)**(1/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{\frac{7}{2}} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(7/2)*sqrt(a + b*x + c*x**2), x)","F",0
1328,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(3/2)*(c*x**2+b*x+a)**(1/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(3/2)*sqrt(a + b*x + c*x**2), x)","F",0
1329,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**(1/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\sqrt{d \left(b + 2 c x\right)}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/sqrt(d*(b + 2*c*x)), x)","F",0
1330,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**(5/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d*(b + 2*c*x))**(5/2), x)","F",0
1331,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**(9/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d*(b + 2*c*x))**(9/2), x)","F",0
1332,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1333,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(5/2)*(c*x**2+b*x+a)**(1/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(5/2)*sqrt(a + b*x + c*x**2), x)","F",0
1334,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(1/2)*(c*x**2+b*x+a)**(1/2),x)","\int \sqrt{d \left(b + 2 c x\right)} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral(sqrt(d*(b + 2*c*x))*sqrt(a + b*x + c*x**2), x)","F",0
1335,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**(3/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d*(b + 2*c*x))**(3/2), x)","F",0
1336,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(2*c*d*x+b*d)**(7/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d*(b + 2*c*x))**(7/2), x)","F",0
1337,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(7/2)*(c*x**2+b*x+a)**(3/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{\frac{7}{2}} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(7/2)*(a + b*x + c*x**2)**(3/2), x)","F",0
1338,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(3/2)*(c*x**2+b*x+a)**(3/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(3/2)*(a + b*x + c*x**2)**(3/2), x)","F",0
1339,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**(1/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\sqrt{d \left(b + 2 c x\right)}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/sqrt(d*(b + 2*c*x)), x)","F",0
1340,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**(5/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d*(b + 2*c*x))**(5/2), x)","F",0
1341,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**(9/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d*(b + 2*c*x))**(9/2), x)","F",0
1342,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1343,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1344,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(5/2)*(c*x**2+b*x+a)**(3/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(5/2)*(a + b*x + c*x**2)**(3/2), x)","F",0
1345,1,264,0,7.905867," ","integrate((2*c*d*x+b*d)**(1/2)*(c*x**2+b*x+a)**(3/2),x)","\frac{a \left(b d + 2 c d x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{\left(b d + 2 c d x\right)^{2} e^{i \pi}}{4 c d^{2} \operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}} \right)} \sqrt{\operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}}{4 c d \Gamma\left(\frac{7}{4}\right)} - \frac{b^{2} \left(b d + 2 c d x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{\left(b d + 2 c d x\right)^{2} e^{i \pi}}{4 c d^{2} \operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}} \right)} \sqrt{\operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}}{16 c^{2} d \Gamma\left(\frac{7}{4}\right)} + \frac{\left(b d + 2 c d x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{\left(b d + 2 c d x\right)^{2} e^{i \pi}}{4 c d^{2} \operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}} \right)} \sqrt{\operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}}{16 c^{2} d^{3} \Gamma\left(\frac{11}{4}\right)}"," ",0,"a*(b*d + 2*c*d*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), (b*d + 2*c*d*x)**2*exp_polar(I*pi)/(4*c*d**2*polar_lift(a - b**2/(4*c))))*sqrt(polar_lift(a - b**2/(4*c)))/(4*c*d*gamma(7/4)) - b**2*(b*d + 2*c*d*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), (b*d + 2*c*d*x)**2*exp_polar(I*pi)/(4*c*d**2*polar_lift(a - b**2/(4*c))))*sqrt(polar_lift(a - b**2/(4*c)))/(16*c**2*d*gamma(7/4)) + (b*d + 2*c*d*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), (b*d + 2*c*d*x)**2*exp_polar(I*pi)/(4*c*d**2*polar_lift(a - b**2/(4*c))))*sqrt(polar_lift(a - b**2/(4*c)))/(16*c**2*d**3*gamma(11/4))","A",0
1346,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**(3/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d*(b + 2*c*x))**(3/2), x)","F",0
1347,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**(7/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d*(b + 2*c*x))**(7/2), x)","F",0
1348,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(2*c*d*x+b*d)**(11/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{11}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d*(b + 2*c*x))**(11/2), x)","F",0
1349,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(7/2)*(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1350,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(3/2)*(c*x**2+b*x+a)**(5/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(3/2)*(a + b*x + c*x**2)**(5/2), x)","F",0
1351,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**(1/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\sqrt{d \left(b + 2 c x\right)}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2)/sqrt(d*(b + 2*c*x)), x)","F",0
1352,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**(5/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2)/(d*(b + 2*c*x))**(5/2), x)","F",0
1353,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**(9/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2)/(d*(b + 2*c*x))**(9/2), x)","F",0
1354,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1355,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1356,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**(21/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1357,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(5/2)*(c*x**2+b*x+a)**(5/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(5/2)*(a + b*x + c*x**2)**(5/2), x)","F",0
1358,1,539,0,18.214756," ","integrate((2*c*d*x+b*d)**(1/2)*(c*x**2+b*x+a)**(5/2),x)","\frac{a^{2} \left(b d + 2 c d x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{\left(b d + 2 c d x\right)^{2} e^{i \pi}}{4 c d^{2} \operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}} \right)} \sqrt{\operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}}{4 c d \Gamma\left(\frac{7}{4}\right)} - \frac{a b^{2} \left(b d + 2 c d x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{\left(b d + 2 c d x\right)^{2} e^{i \pi}}{4 c d^{2} \operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}} \right)} \sqrt{\operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}}{8 c^{2} d \Gamma\left(\frac{7}{4}\right)} + \frac{a \left(b d + 2 c d x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{\left(b d + 2 c d x\right)^{2} e^{i \pi}}{4 c d^{2} \operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}} \right)} \sqrt{\operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}}{8 c^{2} d^{3} \Gamma\left(\frac{11}{4}\right)} + \frac{b^{4} \left(b d + 2 c d x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{\left(b d + 2 c d x\right)^{2} e^{i \pi}}{4 c d^{2} \operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}} \right)} \sqrt{\operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}}{64 c^{3} d \Gamma\left(\frac{7}{4}\right)} - \frac{b^{2} \left(b d + 2 c d x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{\left(b d + 2 c d x\right)^{2} e^{i \pi}}{4 c d^{2} \operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}} \right)} \sqrt{\operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}}{32 c^{3} d^{3} \Gamma\left(\frac{11}{4}\right)} + \frac{\left(b d + 2 c d x\right)^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{\left(b d + 2 c d x\right)^{2} e^{i \pi}}{4 c d^{2} \operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}} \right)} \sqrt{\operatorname{polar\_lift}{\left(a - \frac{b^{2}}{4 c} \right)}}}{64 c^{3} d^{5} \Gamma\left(\frac{15}{4}\right)}"," ",0,"a**2*(b*d + 2*c*d*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), (b*d + 2*c*d*x)**2*exp_polar(I*pi)/(4*c*d**2*polar_lift(a - b**2/(4*c))))*sqrt(polar_lift(a - b**2/(4*c)))/(4*c*d*gamma(7/4)) - a*b**2*(b*d + 2*c*d*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), (b*d + 2*c*d*x)**2*exp_polar(I*pi)/(4*c*d**2*polar_lift(a - b**2/(4*c))))*sqrt(polar_lift(a - b**2/(4*c)))/(8*c**2*d*gamma(7/4)) + a*(b*d + 2*c*d*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), (b*d + 2*c*d*x)**2*exp_polar(I*pi)/(4*c*d**2*polar_lift(a - b**2/(4*c))))*sqrt(polar_lift(a - b**2/(4*c)))/(8*c**2*d**3*gamma(11/4)) + b**4*(b*d + 2*c*d*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), (b*d + 2*c*d*x)**2*exp_polar(I*pi)/(4*c*d**2*polar_lift(a - b**2/(4*c))))*sqrt(polar_lift(a - b**2/(4*c)))/(64*c**3*d*gamma(7/4)) - b**2*(b*d + 2*c*d*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), (b*d + 2*c*d*x)**2*exp_polar(I*pi)/(4*c*d**2*polar_lift(a - b**2/(4*c))))*sqrt(polar_lift(a - b**2/(4*c)))/(32*c**3*d**3*gamma(11/4)) + (b*d + 2*c*d*x)**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), (b*d + 2*c*d*x)**2*exp_polar(I*pi)/(4*c*d**2*polar_lift(a - b**2/(4*c))))*sqrt(polar_lift(a - b**2/(4*c)))/(64*c**3*d**5*gamma(15/4))","A",0
1359,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**(3/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2)/(d*(b + 2*c*x))**(3/2), x)","F",0
1360,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**(7/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2)/(d*(b + 2*c*x))**(7/2), x)","F",0
1361,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1362,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(2*c*d*x+b*d)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1363,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d \left(b + 2 c x\right)\right)^{\frac{7}{2}}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(7/2)/sqrt(a + b*x + c*x**2), x)","F",0
1364,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(3/2)/sqrt(a + b*x + c*x**2), x)","F",0
1365,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\sqrt{d \left(b + 2 c x\right)} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(d*(b + 2*c*x))*sqrt(a + b*x + c*x**2)), x)","F",0
1366,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d*(b + 2*c*x))**(5/2)*sqrt(a + b*x + c*x**2)), x)","F",0
1367,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(9/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d \left(b + 2 c x\right)\right)^{\frac{9}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d*(b + 2*c*x))**(9/2)*sqrt(a + b*x + c*x**2)), x)","F",0
1368,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(9/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d \left(b + 2 c x\right)\right)^{\frac{9}{2}}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(9/2)/sqrt(a + b*x + c*x**2), x)","F",0
1369,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(5/2)/sqrt(a + b*x + c*x**2), x)","F",0
1370,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\sqrt{d \left(b + 2 c x\right)}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(sqrt(d*(b + 2*c*x))/sqrt(a + b*x + c*x**2), x)","F",0
1371,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d*(b + 2*c*x))**(3/2)*sqrt(a + b*x + c*x**2)), x)","F",0
1372,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d \left(b + 2 c x\right)\right)^{\frac{7}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d*(b + 2*c*x))**(7/2)*sqrt(a + b*x + c*x**2)), x)","F",0
1373,1,41,0,10.845316," ","integrate((3-2*x)**(3/2)/(x**2-3*x+1)**(1/2),x)","\frac{\sqrt{5} i \left(3 - 2 x\right)^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{\left(3 - 2 x\right)^{2}}{5}} \right)}}{10 \Gamma\left(\frac{9}{4}\right)}"," ",0,"sqrt(5)*I*(3 - 2*x)**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), (3 - 2*x)**2/5)/(10*gamma(9/4))","A",0
1374,0,0,0,0.000000," ","integrate(1/(3-2*x)**(1/2)/(x**2-3*x+1)**(1/2),x)","\int \frac{1}{\sqrt{3 - 2 x} \sqrt{x^{2} - 3 x + 1}}\, dx"," ",0,"Integral(1/(sqrt(3 - 2*x)*sqrt(x**2 - 3*x + 1)), x)","F",0
1375,0,0,0,0.000000," ","integrate(1/(3-2*x)**(5/2)/(x**2-3*x+1)**(1/2),x)","\int \frac{1}{\left(3 - 2 x\right)^{\frac{5}{2}} \sqrt{x^{2} - 3 x + 1}}\, dx"," ",0,"Integral(1/((3 - 2*x)**(5/2)*sqrt(x**2 - 3*x + 1)), x)","F",0
1376,1,41,0,19.803328," ","integrate((3-2*x)**(5/2)/(x**2-3*x+1)**(1/2),x)","\frac{\sqrt{5} i \left(3 - 2 x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{\left(3 - 2 x\right)^{2}}{5}} \right)}}{10 \Gamma\left(\frac{11}{4}\right)}"," ",0,"sqrt(5)*I*(3 - 2*x)**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), (3 - 2*x)**2/5)/(10*gamma(11/4))","A",0
1377,1,41,0,2.849361," ","integrate((3-2*x)**(1/2)/(x**2-3*x+1)**(1/2),x)","\frac{\sqrt{5} i \left(3 - 2 x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{\left(3 - 2 x\right)^{2}}{5}} \right)}}{10 \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(5)*I*(3 - 2*x)**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), (3 - 2*x)**2/5)/(10*gamma(7/4))","A",0
1378,0,0,0,0.000000," ","integrate(1/(3-2*x)**(3/2)/(x**2-3*x+1)**(1/2),x)","\int \frac{1}{\left(3 - 2 x\right)^{\frac{3}{2}} \sqrt{x^{2} - 3 x + 1}}\, dx"," ",0,"Integral(1/((3 - 2*x)**(3/2)*sqrt(x**2 - 3*x + 1)), x)","F",0
1379,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(11/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1380,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1381,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(3/2)/(a + b*x + c*x**2)**(3/2), x)","F",0
1382,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\sqrt{d \left(b + 2 c x\right)} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(d*(b + 2*c*x))*(a + b*x + c*x**2)**(3/2)), x)","F",0
1383,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d*(b + 2*c*x))**(5/2)*(a + b*x + c*x**2)**(3/2)), x)","F",0
1384,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(9/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1385,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**(5/2)/(a + b*x + c*x**2)**(3/2), x)","F",0
1386,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\sqrt{d \left(b + 2 c x\right)}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d*(b + 2*c*x))/(a + b*x + c*x**2)**(3/2), x)","F",0
1387,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d*(b + 2*c*x))**(3/2)*(a + b*x + c*x**2)**(3/2)), x)","F",0
1388,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d \left(b + 2 c x\right)\right)^{\frac{7}{2}} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d*(b + 2*c*x))**(7/2)*(a + b*x + c*x**2)**(3/2)), x)","F",0
1389,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(15/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1390,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(11/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1391,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(7/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1392,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1393,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a)**(5/2),x)","\int \frac{1}{\sqrt{d \left(b + 2 c x\right)} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(d*(b + 2*c*x))*(a + b*x + c*x**2)**(5/2)), x)","F",0
1394,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a)**(5/2),x)","\int \frac{1}{\left(d \left(b + 2 c x\right)\right)^{\frac{5}{2}} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d*(b + 2*c*x))**(5/2)*(a + b*x + c*x**2)**(5/2)), x)","F",0
1395,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(13/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1396,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(9/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1397,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(5/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1398,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**(1/2)/(c*x**2+b*x+a)**(5/2),x)","\int \frac{\sqrt{d \left(b + 2 c x\right)}}{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(d*(b + 2*c*x))/(a + b*x + c*x**2)**(5/2), x)","F",0
1399,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)**(3/2)/(c*x**2+b*x+a)**(5/2),x)","\int \frac{1}{\left(d \left(b + 2 c x\right)\right)^{\frac{3}{2}} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d*(b + 2*c*x))**(3/2)*(a + b*x + c*x**2)**(5/2)), x)","F",0
1400,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(11/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1401,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(7/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\int \frac{\left(e \left(c + d x\right)\right)^{\frac{7}{2}}}{\sqrt{- \left(c + d x - 1\right) \left(c + d x + 1\right)}}\, dx"," ",0,"Integral((e*(c + d*x))**(7/2)/sqrt(-(c + d*x - 1)*(c + d*x + 1)), x)","F",0
1402,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(3/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\int \frac{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}{\sqrt{- \left(c + d x - 1\right) \left(c + d x + 1\right)}}\, dx"," ",0,"Integral((e*(c + d*x))**(3/2)/sqrt(-(c + d*x - 1)*(c + d*x + 1)), x)","F",0
1403,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)**(1/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\int \frac{1}{\sqrt{e \left(c + d x\right)} \sqrt{- \left(c + d x - 1\right) \left(c + d x + 1\right)}}\, dx"," ",0,"Integral(1/(sqrt(e*(c + d*x))*sqrt(-(c + d*x - 1)*(c + d*x + 1))), x)","F",0
1404,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)**(5/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\int \frac{1}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}} \sqrt{- \left(c + d x - 1\right) \left(c + d x + 1\right)}}\, dx"," ",0,"Integral(1/((e*(c + d*x))**(5/2)*sqrt(-(c + d*x - 1)*(c + d*x + 1))), x)","F",0
1405,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)**(9/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\int \frac{1}{\left(e \left(c + d x\right)\right)^{\frac{9}{2}} \sqrt{- \left(c + d x - 1\right) \left(c + d x + 1\right)}}\, dx"," ",0,"Integral(1/((e*(c + d*x))**(9/2)*sqrt(-(c + d*x - 1)*(c + d*x + 1))), x)","F",0
1406,-1,0,0,0.000000," ","integrate(1/(d*e*x+c*e)**(13/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1407,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(9/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\int \frac{\left(e \left(c + d x\right)\right)^{\frac{9}{2}}}{\sqrt{- \left(c + d x - 1\right) \left(c + d x + 1\right)}}\, dx"," ",0,"Integral((e*(c + d*x))**(9/2)/sqrt(-(c + d*x - 1)*(c + d*x + 1)), x)","F",0
1408,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(5/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\int \frac{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}{\sqrt{- \left(c + d x - 1\right) \left(c + d x + 1\right)}}\, dx"," ",0,"Integral((e*(c + d*x))**(5/2)/sqrt(-(c + d*x - 1)*(c + d*x + 1)), x)","F",0
1409,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(1/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\int \frac{\sqrt{e \left(c + d x\right)}}{\sqrt{- \left(c + d x - 1\right) \left(c + d x + 1\right)}}\, dx"," ",0,"Integral(sqrt(e*(c + d*x))/sqrt(-(c + d*x - 1)*(c + d*x + 1)), x)","F",0
1410,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)**(3/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\int \frac{1}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}} \sqrt{- \left(c + d x - 1\right) \left(c + d x + 1\right)}}\, dx"," ",0,"Integral(1/((e*(c + d*x))**(3/2)*sqrt(-(c + d*x - 1)*(c + d*x + 1))), x)","F",0
1411,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)**(7/2)/(-d**2*x**2-2*c*d*x-c**2+1)**(1/2),x)","\int \frac{1}{\left(e \left(c + d x\right)\right)^{\frac{7}{2}} \sqrt{- \left(c + d x - 1\right) \left(c + d x + 1\right)}}\, dx"," ",0,"Integral(1/((e*(c + d*x))**(7/2)*sqrt(-(c + d*x - 1)*(c + d*x + 1))), x)","F",0
1412,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(11/3),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{4}{3}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{11}{3}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(4/3)/(d*(b + 2*c*x))**(11/3), x)","F",0
1413,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(17/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1414,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(23/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1415,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(29/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1416,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(2/3),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{4}{3}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(4/3)/(d*(b + 2*c*x))**(2/3), x)","F",0
1417,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(8/3),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{4}{3}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{8}{3}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(4/3)/(d*(b + 2*c*x))**(8/3), x)","F",0
1418,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(14/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1419,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(20/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1420,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(4/3),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{4}{3}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(4/3)/(d*(b + 2*c*x))**(4/3), x)","F",0
1421,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(10/3),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{4}{3}}}{\left(d \left(b + 2 c x\right)\right)^{\frac{10}{3}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(4/3)/(d*(b + 2*c*x))**(10/3), x)","F",0
1422,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(2*c*d*x+b*d)**(16/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1423,1,9491,0,10.148286," ","integrate((2*c*d*x+b*d)**m*(c*x**2+b*x+a)**3,x)","\begin{cases} \left(b d\right)^{m} \left(a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}\right) & \text{for}\: c = 0 \\- \frac{128 a^{3} c^{3}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} - \frac{48 a^{2} b^{2} c^{2}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} - \frac{576 a^{2} b c^{3} x}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} - \frac{576 a^{2} c^{4} x^{2}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} - \frac{24 a b^{4} c}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} - \frac{288 a b^{3} c^{2} x}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} - \frac{1440 a b^{2} c^{3} x^{2}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} - \frac{2304 a b c^{4} x^{3}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} - \frac{1152 a c^{5} x^{4}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{12 b^{6} \log{\left(\frac{b}{2 c} + x \right)}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{11 b^{6}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{144 b^{5} c x \log{\left(\frac{b}{2 c} + x \right)}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{108 b^{5} c x}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{720 b^{4} c^{2} x^{2} \log{\left(\frac{b}{2 c} + x \right)}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{396 b^{4} c^{2} x^{2}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{1920 b^{3} c^{3} x^{3} \log{\left(\frac{b}{2 c} + x \right)}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{576 b^{3} c^{3} x^{3}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{2880 b^{2} c^{4} x^{4} \log{\left(\frac{b}{2 c} + x \right)}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{288 b^{2} c^{4} x^{4}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{2304 b c^{5} x^{5} \log{\left(\frac{b}{2 c} + x \right)}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} + \frac{768 c^{6} x^{6} \log{\left(\frac{b}{2 c} + x \right)}}{1536 b^{6} c^{4} d^{7} + 18432 b^{5} c^{5} d^{7} x + 92160 b^{4} c^{6} d^{7} x^{2} + 245760 b^{3} c^{7} d^{7} x^{3} + 368640 b^{2} c^{8} d^{7} x^{4} + 294912 b c^{9} d^{7} x^{5} + 98304 c^{10} d^{7} x^{6}} & \text{for}\: m = -7 \\- \frac{64 a^{3} c^{3}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{48 a^{2} b^{2} c^{2}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{384 a^{2} b c^{3} x}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{384 a^{2} c^{4} x^{2}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{48 a b^{4} c \log{\left(\frac{b}{2 c} + x \right)}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{36 a b^{4} c}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{384 a b^{3} c^{2} x \log{\left(\frac{b}{2 c} + x \right)}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{192 a b^{3} c^{2} x}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{1152 a b^{2} c^{3} x^{2} \log{\left(\frac{b}{2 c} + x \right)}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{192 a b^{2} c^{3} x^{2}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{1536 a b c^{4} x^{3} \log{\left(\frac{b}{2 c} + x \right)}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{768 a c^{5} x^{4} \log{\left(\frac{b}{2 c} + x \right)}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{12 b^{6} \log{\left(\frac{b}{2 c} + x \right)}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{33 b^{6}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{96 b^{5} c x \log{\left(\frac{b}{2 c} + x \right)}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{240 b^{5} c x}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{288 b^{4} c^{2} x^{2} \log{\left(\frac{b}{2 c} + x \right)}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{624 b^{4} c^{2} x^{2}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{384 b^{3} c^{3} x^{3} \log{\left(\frac{b}{2 c} + x \right)}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{640 b^{3} c^{3} x^{3}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} - \frac{192 b^{2} c^{4} x^{4} \log{\left(\frac{b}{2 c} + x \right)}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{384 b c^{5} x^{5}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} + \frac{128 c^{6} x^{6}}{512 b^{4} c^{4} d^{5} + 4096 b^{3} c^{5} d^{5} x + 12288 b^{2} c^{6} d^{5} x^{2} + 16384 b c^{7} d^{5} x^{3} + 8192 c^{8} d^{5} x^{4}} & \text{for}\: m = -5 \\- \frac{64 a^{3} c^{3}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{96 a^{2} b^{2} c^{2} \log{\left(\frac{b}{2 c} + x \right)}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{48 a^{2} b^{2} c^{2}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{384 a^{2} b c^{3} x \log{\left(\frac{b}{2 c} + x \right)}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{384 a^{2} c^{4} x^{2} \log{\left(\frac{b}{2 c} + x \right)}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} - \frac{48 a b^{4} c \log{\left(\frac{b}{2 c} + x \right)}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} - \frac{72 a b^{4} c}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} - \frac{192 a b^{3} c^{2} x \log{\left(\frac{b}{2 c} + x \right)}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} - \frac{192 a b^{3} c^{2} x}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} - \frac{192 a b^{2} c^{3} x^{2} \log{\left(\frac{b}{2 c} + x \right)}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{384 a b c^{4} x^{3}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{192 a c^{5} x^{4}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{6 b^{6} \log{\left(\frac{b}{2 c} + x \right)}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{9 b^{6}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{24 b^{5} c x \log{\left(\frac{b}{2 c} + x \right)}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{24 b^{5} c x}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{24 b^{4} c^{2} x^{2} \log{\left(\frac{b}{2 c} + x \right)}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} - \frac{16 b^{3} c^{3} x^{3}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{72 b^{2} c^{4} x^{4}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{96 b c^{5} x^{5}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} + \frac{32 c^{6} x^{6}}{256 b^{2} c^{4} d^{3} + 1024 b c^{5} d^{3} x + 1024 c^{6} d^{3} x^{2}} & \text{for}\: m = -3 \\\frac{a^{3} \log{\left(\frac{b}{2 c} + x \right)}}{2 c d} - \frac{3 a^{2} b^{2} \log{\left(\frac{b}{2 c} + x \right)}}{8 c^{2} d} + \frac{3 a^{2} b x}{4 c d} + \frac{3 a^{2} x^{2}}{4 d} + \frac{3 a b^{4} \log{\left(\frac{b}{2 c} + x \right)}}{32 c^{3} d} - \frac{3 a b^{3} x}{16 c^{2} d} + \frac{3 a b^{2} x^{2}}{16 c d} + \frac{3 a b x^{3}}{4 d} + \frac{3 a c x^{4}}{8 d} - \frac{b^{6} \log{\left(\frac{b}{2 c} + x \right)}}{128 c^{4} d} + \frac{b^{5} x}{64 c^{3} d} - \frac{b^{4} x^{2}}{64 c^{2} d} + \frac{b^{3} x^{3}}{48 c d} + \frac{7 b^{2} x^{4}}{32 d} + \frac{b c x^{5}}{4 d} + \frac{c^{2} x^{6}}{12 d} & \text{for}\: m = -1 \\\frac{4 a^{3} b c^{3} m^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{60 a^{3} b c^{3} m^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{284 a^{3} b c^{3} m \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{420 a^{3} b c^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{8 a^{3} c^{4} m^{3} x \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{120 a^{3} c^{4} m^{2} x \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{568 a^{3} c^{4} m x \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{840 a^{3} c^{4} x \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} - \frac{6 a^{2} b^{3} c^{2} m^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} - \frac{72 a^{2} b^{3} c^{2} m \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} - \frac{210 a^{2} b^{3} c^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{12 a^{2} b^{2} c^{3} m^{3} x \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{144 a^{2} b^{2} c^{3} m^{2} x \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{420 a^{2} b^{2} c^{3} m x \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{36 a^{2} b c^{4} m^{3} x^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{468 a^{2} b c^{4} m^{2} x^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{1692 a^{2} b c^{4} m x^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{1260 a^{2} b c^{4} x^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{24 a^{2} c^{5} m^{3} x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{312 a^{2} c^{5} m^{2} x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{1128 a^{2} c^{5} m x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{840 a^{2} c^{5} x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{6 a b^{5} c m \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{42 a b^{5} c \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} - \frac{12 a b^{4} c^{2} m^{2} x \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} - \frac{84 a b^{4} c^{2} m x \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{12 a b^{3} c^{3} m^{3} x^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{96 a b^{3} c^{3} m^{2} x^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{84 a b^{3} c^{3} m x^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{48 a b^{2} c^{4} m^{3} x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{504 a b^{2} c^{4} m^{2} x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{1296 a b^{2} c^{4} m x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{840 a b^{2} c^{4} x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{60 a b c^{5} m^{3} x^{4} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{660 a b c^{5} m^{2} x^{4} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{1860 a b c^{5} m x^{4} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{1260 a b c^{5} x^{4} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{24 a c^{6} m^{3} x^{5} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{264 a c^{6} m^{2} x^{5} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{744 a c^{6} m x^{5} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{504 a c^{6} x^{5} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} - \frac{3 b^{7} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{6 b^{6} c m x \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} - \frac{6 b^{5} c^{2} m^{2} x^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} - \frac{6 b^{5} c^{2} m x^{2} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{4 b^{4} c^{3} m^{3} x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{12 b^{4} c^{3} m^{2} x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{8 b^{4} c^{3} m x^{3} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{20 b^{3} c^{4} m^{3} x^{4} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{150 b^{3} c^{4} m^{2} x^{4} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{340 b^{3} c^{4} m x^{4} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{210 b^{3} c^{4} x^{4} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{36 b^{2} c^{5} m^{3} x^{5} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{312 b^{2} c^{5} m^{2} x^{5} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{780 b^{2} c^{5} m x^{5} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{504 b^{2} c^{5} x^{5} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{28 b c^{6} m^{3} x^{6} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{252 b c^{6} m^{2} x^{6} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{644 b c^{6} m x^{6} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{420 b c^{6} x^{6} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{8 c^{7} m^{3} x^{7} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{72 c^{7} m^{2} x^{7} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{184 c^{7} m x^{7} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} + \frac{120 c^{7} x^{7} \left(b d + 2 c d x\right)^{m}}{8 c^{4} m^{4} + 128 c^{4} m^{3} + 688 c^{4} m^{2} + 1408 c^{4} m + 840 c^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((b*d)**m*(a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4), Eq(c, 0)), (-128*a**3*c**3/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) - 48*a**2*b**2*c**2/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) - 576*a**2*b*c**3*x/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) - 576*a**2*c**4*x**2/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) - 24*a*b**4*c/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) - 288*a*b**3*c**2*x/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) - 1440*a*b**2*c**3*x**2/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) - 2304*a*b*c**4*x**3/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) - 1152*a*c**5*x**4/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 12*b**6*log(b/(2*c) + x)/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 11*b**6/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 144*b**5*c*x*log(b/(2*c) + x)/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 108*b**5*c*x/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 720*b**4*c**2*x**2*log(b/(2*c) + x)/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 396*b**4*c**2*x**2/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 1920*b**3*c**3*x**3*log(b/(2*c) + x)/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 576*b**3*c**3*x**3/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 2880*b**2*c**4*x**4*log(b/(2*c) + x)/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 288*b**2*c**4*x**4/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 2304*b*c**5*x**5*log(b/(2*c) + x)/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6) + 768*c**6*x**6*log(b/(2*c) + x)/(1536*b**6*c**4*d**7 + 18432*b**5*c**5*d**7*x + 92160*b**4*c**6*d**7*x**2 + 245760*b**3*c**7*d**7*x**3 + 368640*b**2*c**8*d**7*x**4 + 294912*b*c**9*d**7*x**5 + 98304*c**10*d**7*x**6), Eq(m, -7)), (-64*a**3*c**3/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 48*a**2*b**2*c**2/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 384*a**2*b*c**3*x/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 384*a**2*c**4*x**2/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + 48*a*b**4*c*log(b/(2*c) + x)/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + 36*a*b**4*c/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + 384*a*b**3*c**2*x*log(b/(2*c) + x)/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + 192*a*b**3*c**2*x/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + 1152*a*b**2*c**3*x**2*log(b/(2*c) + x)/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + 192*a*b**2*c**3*x**2/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + 1536*a*b*c**4*x**3*log(b/(2*c) + x)/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + 768*a*c**5*x**4*log(b/(2*c) + x)/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 12*b**6*log(b/(2*c) + x)/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 33*b**6/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 96*b**5*c*x*log(b/(2*c) + x)/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 240*b**5*c*x/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 288*b**4*c**2*x**2*log(b/(2*c) + x)/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 624*b**4*c**2*x**2/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 384*b**3*c**3*x**3*log(b/(2*c) + x)/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 640*b**3*c**3*x**3/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) - 192*b**2*c**4*x**4*log(b/(2*c) + x)/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + 384*b*c**5*x**5/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4) + 128*c**6*x**6/(512*b**4*c**4*d**5 + 4096*b**3*c**5*d**5*x + 12288*b**2*c**6*d**5*x**2 + 16384*b*c**7*d**5*x**3 + 8192*c**8*d**5*x**4), Eq(m, -5)), (-64*a**3*c**3/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 96*a**2*b**2*c**2*log(b/(2*c) + x)/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 48*a**2*b**2*c**2/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 384*a**2*b*c**3*x*log(b/(2*c) + x)/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 384*a**2*c**4*x**2*log(b/(2*c) + x)/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) - 48*a*b**4*c*log(b/(2*c) + x)/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) - 72*a*b**4*c/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) - 192*a*b**3*c**2*x*log(b/(2*c) + x)/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) - 192*a*b**3*c**2*x/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) - 192*a*b**2*c**3*x**2*log(b/(2*c) + x)/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 384*a*b*c**4*x**3/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 192*a*c**5*x**4/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 6*b**6*log(b/(2*c) + x)/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 9*b**6/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 24*b**5*c*x*log(b/(2*c) + x)/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 24*b**5*c*x/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 24*b**4*c**2*x**2*log(b/(2*c) + x)/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) - 16*b**3*c**3*x**3/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 72*b**2*c**4*x**4/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 96*b*c**5*x**5/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2) + 32*c**6*x**6/(256*b**2*c**4*d**3 + 1024*b*c**5*d**3*x + 1024*c**6*d**3*x**2), Eq(m, -3)), (a**3*log(b/(2*c) + x)/(2*c*d) - 3*a**2*b**2*log(b/(2*c) + x)/(8*c**2*d) + 3*a**2*b*x/(4*c*d) + 3*a**2*x**2/(4*d) + 3*a*b**4*log(b/(2*c) + x)/(32*c**3*d) - 3*a*b**3*x/(16*c**2*d) + 3*a*b**2*x**2/(16*c*d) + 3*a*b*x**3/(4*d) + 3*a*c*x**4/(8*d) - b**6*log(b/(2*c) + x)/(128*c**4*d) + b**5*x/(64*c**3*d) - b**4*x**2/(64*c**2*d) + b**3*x**3/(48*c*d) + 7*b**2*x**4/(32*d) + b*c*x**5/(4*d) + c**2*x**6/(12*d), Eq(m, -1)), (4*a**3*b*c**3*m**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 60*a**3*b*c**3*m**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 284*a**3*b*c**3*m*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 420*a**3*b*c**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 8*a**3*c**4*m**3*x*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 120*a**3*c**4*m**2*x*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 568*a**3*c**4*m*x*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 840*a**3*c**4*x*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) - 6*a**2*b**3*c**2*m**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) - 72*a**2*b**3*c**2*m*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) - 210*a**2*b**3*c**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 12*a**2*b**2*c**3*m**3*x*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 144*a**2*b**2*c**3*m**2*x*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 420*a**2*b**2*c**3*m*x*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 36*a**2*b*c**4*m**3*x**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 468*a**2*b*c**4*m**2*x**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 1692*a**2*b*c**4*m*x**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 1260*a**2*b*c**4*x**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 24*a**2*c**5*m**3*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 312*a**2*c**5*m**2*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 1128*a**2*c**5*m*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 840*a**2*c**5*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 6*a*b**5*c*m*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 42*a*b**5*c*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) - 12*a*b**4*c**2*m**2*x*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) - 84*a*b**4*c**2*m*x*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 12*a*b**3*c**3*m**3*x**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 96*a*b**3*c**3*m**2*x**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 84*a*b**3*c**3*m*x**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 48*a*b**2*c**4*m**3*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 504*a*b**2*c**4*m**2*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 1296*a*b**2*c**4*m*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 840*a*b**2*c**4*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 60*a*b*c**5*m**3*x**4*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 660*a*b*c**5*m**2*x**4*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 1860*a*b*c**5*m*x**4*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 1260*a*b*c**5*x**4*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 24*a*c**6*m**3*x**5*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 264*a*c**6*m**2*x**5*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 744*a*c**6*m*x**5*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 504*a*c**6*x**5*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) - 3*b**7*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 6*b**6*c*m*x*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) - 6*b**5*c**2*m**2*x**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) - 6*b**5*c**2*m*x**2*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 4*b**4*c**3*m**3*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 12*b**4*c**3*m**2*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 8*b**4*c**3*m*x**3*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 20*b**3*c**4*m**3*x**4*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 150*b**3*c**4*m**2*x**4*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 340*b**3*c**4*m*x**4*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 210*b**3*c**4*x**4*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 36*b**2*c**5*m**3*x**5*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 312*b**2*c**5*m**2*x**5*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 780*b**2*c**5*m*x**5*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 504*b**2*c**5*x**5*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 28*b*c**6*m**3*x**6*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 252*b*c**6*m**2*x**6*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 644*b*c**6*m*x**6*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 420*b*c**6*x**6*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 8*c**7*m**3*x**7*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 72*c**7*m**2*x**7*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 184*c**7*m*x**7*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4) + 120*c**7*x**7*(b*d + 2*c*d*x)**m/(8*c**4*m**4 + 128*c**4*m**3 + 688*c**4*m**2 + 1408*c**4*m + 840*c**4), True))","A",0
1424,1,3196,0,3.818642," ","integrate((2*c*d*x+b*d)**m*(c*x**2+b*x+a)**2,x)","\begin{cases} \left(b d\right)^{m} \left(a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}\right) & \text{for}\: c = 0 \\- \frac{16 a^{2} c^{2}}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} - \frac{8 a b^{2} c}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} - \frac{64 a b c^{2} x}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} - \frac{64 a c^{3} x^{2}}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} + \frac{4 b^{4} \log{\left(\frac{b}{2 c} + x \right)}}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} + \frac{3 b^{4}}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} + \frac{32 b^{3} c x \log{\left(\frac{b}{2 c} + x \right)}}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} + \frac{16 b^{3} c x}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} + \frac{96 b^{2} c^{2} x^{2} \log{\left(\frac{b}{2 c} + x \right)}}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} + \frac{16 b^{2} c^{2} x^{2}}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} + \frac{128 b c^{3} x^{3} \log{\left(\frac{b}{2 c} + x \right)}}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} + \frac{64 c^{4} x^{4} \log{\left(\frac{b}{2 c} + x \right)}}{128 b^{4} c^{3} d^{5} + 1024 b^{3} c^{4} d^{5} x + 3072 b^{2} c^{5} d^{5} x^{2} + 4096 b c^{6} d^{5} x^{3} + 2048 c^{7} d^{5} x^{4}} & \text{for}\: m = -5 \\- \frac{8 a^{2} c^{2}}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} + \frac{8 a b^{2} c \log{\left(\frac{b}{2 c} + x \right)}}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} + \frac{4 a b^{2} c}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} + \frac{32 a b c^{2} x \log{\left(\frac{b}{2 c} + x \right)}}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} + \frac{32 a c^{3} x^{2} \log{\left(\frac{b}{2 c} + x \right)}}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} - \frac{2 b^{4} \log{\left(\frac{b}{2 c} + x \right)}}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} - \frac{3 b^{4}}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} - \frac{8 b^{3} c x \log{\left(\frac{b}{2 c} + x \right)}}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} - \frac{8 b^{3} c x}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} - \frac{8 b^{2} c^{2} x^{2} \log{\left(\frac{b}{2 c} + x \right)}}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} + \frac{16 b c^{3} x^{3}}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} + \frac{8 c^{4} x^{4}}{32 b^{2} c^{3} d^{3} + 128 b c^{4} d^{3} x + 128 c^{5} d^{3} x^{2}} & \text{for}\: m = -3 \\\frac{a^{2} \log{\left(\frac{b}{2 c} + x \right)}}{2 c d} - \frac{a b^{2} \log{\left(\frac{b}{2 c} + x \right)}}{4 c^{2} d} + \frac{a b x}{2 c d} + \frac{a x^{2}}{2 d} + \frac{b^{4} \log{\left(\frac{b}{2 c} + x \right)}}{32 c^{3} d} - \frac{b^{3} x}{16 c^{2} d} + \frac{b^{2} x^{2}}{16 c d} + \frac{b x^{3}}{4 d} + \frac{c x^{4}}{8 d} & \text{for}\: m = -1 \\\frac{2 a^{2} b c^{2} m^{2} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{16 a^{2} b c^{2} m \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{30 a^{2} b c^{2} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{4 a^{2} c^{3} m^{2} x \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{32 a^{2} c^{3} m x \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{60 a^{2} c^{3} x \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} - \frac{2 a b^{3} c m \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} - \frac{10 a b^{3} c \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{4 a b^{2} c^{2} m^{2} x \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{20 a b^{2} c^{2} m x \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{12 a b c^{3} m^{2} x^{2} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{72 a b c^{3} m x^{2} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{60 a b c^{3} x^{2} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{8 a c^{4} m^{2} x^{3} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{48 a c^{4} m x^{3} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{40 a c^{4} x^{3} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{b^{5} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} - \frac{2 b^{4} c m x \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{2 b^{3} c^{2} m^{2} x^{2} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{2 b^{3} c^{2} m x^{2} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{8 b^{2} c^{3} m^{2} x^{3} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{28 b^{2} c^{3} m x^{3} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{20 b^{2} c^{3} x^{3} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{10 b c^{4} m^{2} x^{4} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{40 b c^{4} m x^{4} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{30 b c^{4} x^{4} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{4 c^{5} m^{2} x^{5} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{16 c^{5} m x^{5} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} + \frac{12 c^{5} x^{5} \left(b d + 2 c d x\right)^{m}}{4 c^{3} m^{3} + 36 c^{3} m^{2} + 92 c^{3} m + 60 c^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((b*d)**m*(a**2*x + a*b*x**2 + b**2*x**3/3), Eq(c, 0)), (-16*a**2*c**2/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) - 8*a*b**2*c/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) - 64*a*b*c**2*x/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) - 64*a*c**3*x**2/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) + 4*b**4*log(b/(2*c) + x)/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) + 3*b**4/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) + 32*b**3*c*x*log(b/(2*c) + x)/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) + 16*b**3*c*x/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) + 96*b**2*c**2*x**2*log(b/(2*c) + x)/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) + 16*b**2*c**2*x**2/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) + 128*b*c**3*x**3*log(b/(2*c) + x)/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4) + 64*c**4*x**4*log(b/(2*c) + x)/(128*b**4*c**3*d**5 + 1024*b**3*c**4*d**5*x + 3072*b**2*c**5*d**5*x**2 + 4096*b*c**6*d**5*x**3 + 2048*c**7*d**5*x**4), Eq(m, -5)), (-8*a**2*c**2/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) + 8*a*b**2*c*log(b/(2*c) + x)/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) + 4*a*b**2*c/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) + 32*a*b*c**2*x*log(b/(2*c) + x)/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) + 32*a*c**3*x**2*log(b/(2*c) + x)/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) - 2*b**4*log(b/(2*c) + x)/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) - 3*b**4/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) - 8*b**3*c*x*log(b/(2*c) + x)/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) - 8*b**3*c*x/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) - 8*b**2*c**2*x**2*log(b/(2*c) + x)/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) + 16*b*c**3*x**3/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2) + 8*c**4*x**4/(32*b**2*c**3*d**3 + 128*b*c**4*d**3*x + 128*c**5*d**3*x**2), Eq(m, -3)), (a**2*log(b/(2*c) + x)/(2*c*d) - a*b**2*log(b/(2*c) + x)/(4*c**2*d) + a*b*x/(2*c*d) + a*x**2/(2*d) + b**4*log(b/(2*c) + x)/(32*c**3*d) - b**3*x/(16*c**2*d) + b**2*x**2/(16*c*d) + b*x**3/(4*d) + c*x**4/(8*d), Eq(m, -1)), (2*a**2*b*c**2*m**2*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 16*a**2*b*c**2*m*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 30*a**2*b*c**2*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 4*a**2*c**3*m**2*x*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 32*a**2*c**3*m*x*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 60*a**2*c**3*x*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) - 2*a*b**3*c*m*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) - 10*a*b**3*c*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 4*a*b**2*c**2*m**2*x*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 20*a*b**2*c**2*m*x*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 12*a*b*c**3*m**2*x**2*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 72*a*b*c**3*m*x**2*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 60*a*b*c**3*x**2*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 8*a*c**4*m**2*x**3*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 48*a*c**4*m*x**3*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 40*a*c**4*x**3*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + b**5*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) - 2*b**4*c*m*x*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 2*b**3*c**2*m**2*x**2*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 2*b**3*c**2*m*x**2*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 8*b**2*c**3*m**2*x**3*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 28*b**2*c**3*m*x**3*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 20*b**2*c**3*x**3*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 10*b*c**4*m**2*x**4*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 40*b*c**4*m*x**4*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 30*b*c**4*x**4*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 4*c**5*m**2*x**5*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 16*c**5*m*x**5*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3) + 12*c**5*x**5*(b*d + 2*c*d*x)**m/(4*c**3*m**3 + 36*c**3*m**2 + 92*c**3*m + 60*c**3), True))","A",0
1425,1,707,0,1.327056," ","integrate((2*c*d*x+b*d)**m*(c*x**2+b*x+a),x)","\begin{cases} \left(b d\right)^{m} \left(a x + \frac{b x^{2}}{2}\right) & \text{for}\: c = 0 \\- \frac{4 a c}{16 b^{2} c^{2} d^{3} + 64 b c^{3} d^{3} x + 64 c^{4} d^{3} x^{2}} + \frac{2 b^{2} \log{\left(\frac{b}{2 c} + x \right)}}{16 b^{2} c^{2} d^{3} + 64 b c^{3} d^{3} x + 64 c^{4} d^{3} x^{2}} + \frac{b^{2}}{16 b^{2} c^{2} d^{3} + 64 b c^{3} d^{3} x + 64 c^{4} d^{3} x^{2}} + \frac{8 b c x \log{\left(\frac{b}{2 c} + x \right)}}{16 b^{2} c^{2} d^{3} + 64 b c^{3} d^{3} x + 64 c^{4} d^{3} x^{2}} + \frac{8 c^{2} x^{2} \log{\left(\frac{b}{2 c} + x \right)}}{16 b^{2} c^{2} d^{3} + 64 b c^{3} d^{3} x + 64 c^{4} d^{3} x^{2}} & \text{for}\: m = -3 \\\frac{a \log{\left(\frac{b}{2 c} + x \right)}}{2 c d} - \frac{b^{2} \log{\left(\frac{b}{2 c} + x \right)}}{8 c^{2} d} + \frac{b x}{4 c d} + \frac{x^{2}}{4 d} & \text{for}\: m = -1 \\\frac{2 a b c m \left(b d + 2 c d x\right)^{m}}{4 c^{2} m^{2} + 16 c^{2} m + 12 c^{2}} + \frac{6 a b c \left(b d + 2 c d x\right)^{m}}{4 c^{2} m^{2} + 16 c^{2} m + 12 c^{2}} + \frac{4 a c^{2} m x \left(b d + 2 c d x\right)^{m}}{4 c^{2} m^{2} + 16 c^{2} m + 12 c^{2}} + \frac{12 a c^{2} x \left(b d + 2 c d x\right)^{m}}{4 c^{2} m^{2} + 16 c^{2} m + 12 c^{2}} - \frac{b^{3} \left(b d + 2 c d x\right)^{m}}{4 c^{2} m^{2} + 16 c^{2} m + 12 c^{2}} + \frac{2 b^{2} c m x \left(b d + 2 c d x\right)^{m}}{4 c^{2} m^{2} + 16 c^{2} m + 12 c^{2}} + \frac{6 b c^{2} m x^{2} \left(b d + 2 c d x\right)^{m}}{4 c^{2} m^{2} + 16 c^{2} m + 12 c^{2}} + \frac{6 b c^{2} x^{2} \left(b d + 2 c d x\right)^{m}}{4 c^{2} m^{2} + 16 c^{2} m + 12 c^{2}} + \frac{4 c^{3} m x^{3} \left(b d + 2 c d x\right)^{m}}{4 c^{2} m^{2} + 16 c^{2} m + 12 c^{2}} + \frac{4 c^{3} x^{3} \left(b d + 2 c d x\right)^{m}}{4 c^{2} m^{2} + 16 c^{2} m + 12 c^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((b*d)**m*(a*x + b*x**2/2), Eq(c, 0)), (-4*a*c/(16*b**2*c**2*d**3 + 64*b*c**3*d**3*x + 64*c**4*d**3*x**2) + 2*b**2*log(b/(2*c) + x)/(16*b**2*c**2*d**3 + 64*b*c**3*d**3*x + 64*c**4*d**3*x**2) + b**2/(16*b**2*c**2*d**3 + 64*b*c**3*d**3*x + 64*c**4*d**3*x**2) + 8*b*c*x*log(b/(2*c) + x)/(16*b**2*c**2*d**3 + 64*b*c**3*d**3*x + 64*c**4*d**3*x**2) + 8*c**2*x**2*log(b/(2*c) + x)/(16*b**2*c**2*d**3 + 64*b*c**3*d**3*x + 64*c**4*d**3*x**2), Eq(m, -3)), (a*log(b/(2*c) + x)/(2*c*d) - b**2*log(b/(2*c) + x)/(8*c**2*d) + b*x/(4*c*d) + x**2/(4*d), Eq(m, -1)), (2*a*b*c*m*(b*d + 2*c*d*x)**m/(4*c**2*m**2 + 16*c**2*m + 12*c**2) + 6*a*b*c*(b*d + 2*c*d*x)**m/(4*c**2*m**2 + 16*c**2*m + 12*c**2) + 4*a*c**2*m*x*(b*d + 2*c*d*x)**m/(4*c**2*m**2 + 16*c**2*m + 12*c**2) + 12*a*c**2*x*(b*d + 2*c*d*x)**m/(4*c**2*m**2 + 16*c**2*m + 12*c**2) - b**3*(b*d + 2*c*d*x)**m/(4*c**2*m**2 + 16*c**2*m + 12*c**2) + 2*b**2*c*m*x*(b*d + 2*c*d*x)**m/(4*c**2*m**2 + 16*c**2*m + 12*c**2) + 6*b*c**2*m*x**2*(b*d + 2*c*d*x)**m/(4*c**2*m**2 + 16*c**2*m + 12*c**2) + 6*b*c**2*x**2*(b*d + 2*c*d*x)**m/(4*c**2*m**2 + 16*c**2*m + 12*c**2) + 4*c**3*m*x**3*(b*d + 2*c*d*x)**m/(4*c**2*m**2 + 16*c**2*m + 12*c**2) + 4*c**3*x**3*(b*d + 2*c*d*x)**m/(4*c**2*m**2 + 16*c**2*m + 12*c**2), True))","A",0
1426,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**m/(c*x**2+b*x+a),x)","\int \frac{\left(d \left(b + 2 c x\right)\right)^{m}}{a + b x + c x^{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**m/(a + b*x + c*x**2), x)","F",0
1427,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**m/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1428,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**m/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1429,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**m*(c*x**2+b*x+a)**(5/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{m} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**m*(a + b*x + c*x**2)**(5/2), x)","F",0
1430,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**m*(c*x**2+b*x+a)**(3/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{m} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**m*(a + b*x + c*x**2)**(3/2), x)","F",0
1431,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**m*(c*x**2+b*x+a)**(1/2),x)","\int \left(d \left(b + 2 c x\right)\right)^{m} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**m*sqrt(a + b*x + c*x**2), x)","F",0
1432,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**m/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d \left(b + 2 c x\right)\right)^{m}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**m/sqrt(a + b*x + c*x**2), x)","F",0
1433,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**m/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(d \left(b + 2 c x\right)\right)^{m}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**m/(a + b*x + c*x**2)**(3/2), x)","F",0
1434,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**m/(c*x**2+b*x+a)**(5/2),x)","\int \frac{\left(d \left(b + 2 c x\right)\right)^{m}}{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d*(b + 2*c*x))**m/(a + b*x + c*x**2)**(5/2), x)","F",0
1435,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**m*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1436,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**5*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1437,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**4*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1438,-1,0,0,0.000000," ","integrate((2*c*d*x+b*d)**3*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1439,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)**2*(c*x**2+b*x+a)**p,x)","d^{2} \left(\int b^{2} \left(a + b x + c x^{2}\right)^{p}\, dx + \int 4 c^{2} x^{2} \left(a + b x + c x^{2}\right)^{p}\, dx + \int 4 b c x \left(a + b x + c x^{2}\right)^{p}\, dx\right)"," ",0,"d**2*(Integral(b**2*(a + b*x + c*x**2)**p, x) + Integral(4*c**2*x**2*(a + b*x + c*x**2)**p, x) + Integral(4*b*c*x*(a + b*x + c*x**2)**p, x))","F",0
1440,1,112,0,58.410342," ","integrate((2*c*d*x+b*d)*(c*x**2+b*x+a)**p,x)","\begin{cases} \frac{a d \left(a + b x + c x^{2}\right)^{p}}{p + 1} + \frac{b d x \left(a + b x + c x^{2}\right)^{p}}{p + 1} + \frac{c d x^{2} \left(a + b x + c x^{2}\right)^{p}}{p + 1} & \text{for}\: p \neq -1 \\d \log{\left(\frac{b}{2 c} + x - \frac{\sqrt{- 4 a c + b^{2}}}{2 c} \right)} + d \log{\left(\frac{b}{2 c} + x + \frac{\sqrt{- 4 a c + b^{2}}}{2 c} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*(a + b*x + c*x**2)**p/(p + 1) + b*d*x*(a + b*x + c*x**2)**p/(p + 1) + c*d*x**2*(a + b*x + c*x**2)**p/(p + 1), Ne(p, -1)), (d*log(b/(2*c) + x - sqrt(-4*a*c + b**2)/(2*c)) + d*log(b/(2*c) + x + sqrt(-4*a*c + b**2)/(2*c)), True))","B",0
1441,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(2*c*d*x+b*d),x)","\frac{\int \frac{\left(a + b x + c x^{2}\right)^{p}}{b + 2 c x}\, dx}{d}"," ",0,"Integral((a + b*x + c*x**2)**p/(b + 2*c*x), x)/d","F",0
1442,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(2*c*d*x+b*d)**2,x)","\frac{\int \frac{\left(a + b x + c x^{2}\right)^{p}}{b^{2} + 4 b c x + 4 c^{2} x^{2}}\, dx}{d^{2}}"," ",0,"Integral((a + b*x + c*x**2)**p/(b**2 + 4*b*c*x + 4*c**2*x**2), x)/d**2","F",0
1443,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(2*c*d*x+b*d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1444,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(2*c*d*x+b*d)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1445,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(2*c*d*x+b*d)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1446,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(2*c*d*x+b*d)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1447,1,14,0,0.171559," ","integrate((1+x)/(x**2+2*x-3)**(2/3),x)","\frac{3 \sqrt[3]{x^{2} + 2 x - 3}}{2}"," ",0,"3*(x**2 + 2*x - 3)**(1/3)/2","A",0
1448,1,17,0,0.331556," ","integrate((c*x+b)/(c*x**2+2*b*x+a)**(3/7),x)","\frac{7 \left(a + 2 b x + c x^{2}\right)^{\frac{4}{7}}}{8}"," ",0,"7*(a + 2*b*x + c*x**2)**(4/7)/8","A",0
1449,0,0,0,0.000000," ","integrate((1+x)**m*(x**2+2*x+1)**n,x)","\begin{cases} \frac{x \left(x + 1\right)^{m} \left(x^{2} + 2 x + 1\right)^{n}}{m + 2 n + 1} + \frac{\left(x + 1\right)^{m} \left(x^{2} + 2 x + 1\right)^{n}}{m + 2 n + 1} & \text{for}\: m \neq - 2 n - 1 \\\int \left(x + 1\right)^{- 2 n - 1} \left(\left(x + 1\right)^{2}\right)^{n}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(x + 1)**m*(x**2 + 2*x + 1)**n/(m + 2*n + 1) + (x + 1)**m*(x**2 + 2*x + 1)**n/(m + 2*n + 1), Ne(m, -2*n - 1)), (Integral((x + 1)**(-2*n - 1)*((x + 1)**2)**n, x), True))","F",0
1450,0,0,0,0.000000," ","integrate((1/2*b*e/c+e*x)**m*(1/4/c*b**2+b*x+c*x**2)**n,x)","\begin{cases} \frac{b \left(\frac{b e}{2 c} + e x\right)^{m} \left(\frac{b^{2}}{4 c} + b x + c x^{2}\right)^{n}}{2 c m + 4 c n + 2 c} + \frac{2 c x \left(\frac{b e}{2 c} + e x\right)^{m} \left(\frac{b^{2}}{4 c} + b x + c x^{2}\right)^{n}}{2 c m + 4 c n + 2 c} & \text{for}\: m \neq - 2 n - 1 \\2^{2 n + 1} \cdot 4^{- n} \int \frac{\left(\frac{b^{2}}{c} + 4 b x + 4 c x^{2}\right)^{n}}{\frac{b e \left(\frac{b e}{c} + 2 e x\right)^{2 n}}{c} + 2 e x \left(\frac{b e}{c} + 2 e x\right)^{2 n}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((b*(b*e/(2*c) + e*x)**m*(b**2/(4*c) + b*x + c*x**2)**n/(2*c*m + 4*c*n + 2*c) + 2*c*x*(b*e/(2*c) + e*x)**m*(b**2/(4*c) + b*x + c*x**2)**n/(2*c*m + 4*c*n + 2*c), Ne(m, -2*n - 1)), (2**(2*n + 1)*4**(-n)*Integral((b**2/c + 4*b*x + 4*c*x**2)**n/(b*e*(b*e/c + 2*e*x)**(2*n)/c + 2*e*x*(b*e/c + 2*e*x)**(2*n)), x), True))","F",0
1451,1,168,0,0.097477," ","integrate((e*x+d)**4*(b**2*x**2+2*a*b*x+a**2),x)","a^{2} d^{4} x + \frac{b^{2} e^{4} x^{7}}{7} + x^{6} \left(\frac{a b e^{4}}{3} + \frac{2 b^{2} d e^{3}}{3}\right) + x^{5} \left(\frac{a^{2} e^{4}}{5} + \frac{8 a b d e^{3}}{5} + \frac{6 b^{2} d^{2} e^{2}}{5}\right) + x^{4} \left(a^{2} d e^{3} + 3 a b d^{2} e^{2} + b^{2} d^{3} e\right) + x^{3} \left(2 a^{2} d^{2} e^{2} + \frac{8 a b d^{3} e}{3} + \frac{b^{2} d^{4}}{3}\right) + x^{2} \left(2 a^{2} d^{3} e + a b d^{4}\right)"," ",0,"a**2*d**4*x + b**2*e**4*x**7/7 + x**6*(a*b*e**4/3 + 2*b**2*d*e**3/3) + x**5*(a**2*e**4/5 + 8*a*b*d*e**3/5 + 6*b**2*d**2*e**2/5) + x**4*(a**2*d*e**3 + 3*a*b*d**2*e**2 + b**2*d**3*e) + x**3*(2*a**2*d**2*e**2 + 8*a*b*d**3*e/3 + b**2*d**4/3) + x**2*(2*a**2*d**3*e + a*b*d**4)","B",0
1452,1,133,0,0.088525," ","integrate((e*x+d)**3*(b**2*x**2+2*a*b*x+a**2),x)","a^{2} d^{3} x + \frac{b^{2} e^{3} x^{6}}{6} + x^{5} \left(\frac{2 a b e^{3}}{5} + \frac{3 b^{2} d e^{2}}{5}\right) + x^{4} \left(\frac{a^{2} e^{3}}{4} + \frac{3 a b d e^{2}}{2} + \frac{3 b^{2} d^{2} e}{4}\right) + x^{3} \left(a^{2} d e^{2} + 2 a b d^{2} e + \frac{b^{2} d^{3}}{3}\right) + x^{2} \left(\frac{3 a^{2} d^{2} e}{2} + a b d^{3}\right)"," ",0,"a**2*d**3*x + b**2*e**3*x**6/6 + x**5*(2*a*b*e**3/5 + 3*b**2*d*e**2/5) + x**4*(a**2*e**3/4 + 3*a*b*d*e**2/2 + 3*b**2*d**2*e/4) + x**3*(a**2*d*e**2 + 2*a*b*d**2*e + b**2*d**3/3) + x**2*(3*a**2*d**2*e/2 + a*b*d**3)","B",0
1453,1,87,0,0.080609," ","integrate((e*x+d)**2*(b**2*x**2+2*a*b*x+a**2),x)","a^{2} d^{2} x + \frac{b^{2} e^{2} x^{5}}{5} + x^{4} \left(\frac{a b e^{2}}{2} + \frac{b^{2} d e}{2}\right) + x^{3} \left(\frac{a^{2} e^{2}}{3} + \frac{4 a b d e}{3} + \frac{b^{2} d^{2}}{3}\right) + x^{2} \left(a^{2} d e + a b d^{2}\right)"," ",0,"a**2*d**2*x + b**2*e**2*x**5/5 + x**4*(a*b*e**2/2 + b**2*d*e/2) + x**3*(a**2*e**2/3 + 4*a*b*d*e/3 + b**2*d**2/3) + x**2*(a**2*d*e + a*b*d**2)","A",0
1454,1,49,0,0.069536," ","integrate((e*x+d)*(b**2*x**2+2*a*b*x+a**2),x)","a^{2} d x + \frac{b^{2} e x^{4}}{4} + x^{3} \left(\frac{2 a b e}{3} + \frac{b^{2} d}{3}\right) + x^{2} \left(\frac{a^{2} e}{2} + a b d\right)"," ",0,"a**2*d*x + b**2*e*x**4/4 + x**3*(2*a*b*e/3 + b**2*d/3) + x**2*(a**2*e/2 + a*b*d)","A",0
1455,1,19,0,0.062275," ","integrate(b**2*x**2+2*a*b*x+a**2,x)","a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}"," ",0,"a**2*x + a*b*x**2 + b**2*x**3/3","A",0
1456,1,44,0,0.219469," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d),x)","\frac{b^{2} x^{2}}{2 e} + x \left(\frac{2 a b}{e} - \frac{b^{2} d}{e^{2}}\right) + \frac{\left(a e - b d\right)^{2} \log{\left(d + e x \right)}}{e^{3}}"," ",0,"b**2*x**2/(2*e) + x*(2*a*b/e - b**2*d/e**2) + (a*e - b*d)**2*log(d + e*x)/e**3","A",0
1457,1,60,0,0.336947," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d)**2,x)","\frac{b^{2} x}{e^{2}} + \frac{2 b \left(a e - b d\right) \log{\left(d + e x \right)}}{e^{3}} + \frac{- a^{2} e^{2} + 2 a b d e - b^{2} d^{2}}{d e^{3} + e^{4} x}"," ",0,"b**2*x/e**2 + 2*b*(a*e - b*d)*log(d + e*x)/e**3 + (-a**2*e**2 + 2*a*b*d*e - b**2*d**2)/(d*e**3 + e**4*x)","A",0
1458,1,80,0,0.460640," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d)**3,x)","\frac{b^{2} \log{\left(d + e x \right)}}{e^{3}} + \frac{- a^{2} e^{2} - 2 a b d e + 3 b^{2} d^{2} + x \left(- 4 a b e^{2} + 4 b^{2} d e\right)}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}}"," ",0,"b**2*log(d + e*x)/e**3 + (-a**2*e**2 - 2*a*b*d*e + 3*b**2*d**2 + x*(-4*a*b*e**2 + 4*b**2*d*e))/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2)","A",0
1459,1,88,0,0.606873," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d)**4,x)","\frac{- a^{2} e^{2} - a b d e - b^{2} d^{2} - 3 b^{2} e^{2} x^{2} + x \left(- 3 a b e^{2} - 3 b^{2} d e\right)}{3 d^{3} e^{3} + 9 d^{2} e^{4} x + 9 d e^{5} x^{2} + 3 e^{6} x^{3}}"," ",0,"(-a**2*e**2 - a*b*d*e - b**2*d**2 - 3*b**2*e**2*x**2 + x*(-3*a*b*e**2 - 3*b**2*d*e))/(3*d**3*e**3 + 9*d**2*e**4*x + 9*d*e**5*x**2 + 3*e**6*x**3)","B",0
1460,1,104,0,0.766378," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d)**5,x)","\frac{- 3 a^{2} e^{2} - 2 a b d e - b^{2} d^{2} - 6 b^{2} e^{2} x^{2} + x \left(- 8 a b e^{2} - 4 b^{2} d e\right)}{12 d^{4} e^{3} + 48 d^{3} e^{4} x + 72 d^{2} e^{5} x^{2} + 48 d e^{6} x^{3} + 12 e^{7} x^{4}}"," ",0,"(-3*a**2*e**2 - 2*a*b*d*e - b**2*d**2 - 6*b**2*e**2*x**2 + x*(-8*a*b*e**2 - 4*b**2*d*e))/(12*d**4*e**3 + 48*d**3*e**4*x + 72*d**2*e**5*x**2 + 48*d*e**6*x**3 + 12*e**7*x**4)","A",0
1461,1,116,0,0.989981," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d)**6,x)","\frac{- 6 a^{2} e^{2} - 3 a b d e - b^{2} d^{2} - 10 b^{2} e^{2} x^{2} + x \left(- 15 a b e^{2} - 5 b^{2} d e\right)}{30 d^{5} e^{3} + 150 d^{4} e^{4} x + 300 d^{3} e^{5} x^{2} + 300 d^{2} e^{6} x^{3} + 150 d e^{7} x^{4} + 30 e^{8} x^{5}}"," ",0,"(-6*a**2*e**2 - 3*a*b*d*e - b**2*d**2 - 10*b**2*e**2*x**2 + x*(-15*a*b*e**2 - 5*b**2*d*e))/(30*d**5*e**3 + 150*d**4*e**4*x + 300*d**3*e**5*x**2 + 300*d**2*e**6*x**3 + 150*d*e**7*x**4 + 30*e**8*x**5)","B",0
1462,1,128,0,1.180446," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d)**7,x)","\frac{- 10 a^{2} e^{2} - 4 a b d e - b^{2} d^{2} - 15 b^{2} e^{2} x^{2} + x \left(- 24 a b e^{2} - 6 b^{2} d e\right)}{60 d^{6} e^{3} + 360 d^{5} e^{4} x + 900 d^{4} e^{5} x^{2} + 1200 d^{3} e^{6} x^{3} + 900 d^{2} e^{7} x^{4} + 360 d e^{8} x^{5} + 60 e^{9} x^{6}}"," ",0,"(-10*a**2*e**2 - 4*a*b*d*e - b**2*d**2 - 15*b**2*e**2*x**2 + x*(-24*a*b*e**2 - 6*b**2*d*e))/(60*d**6*e**3 + 360*d**5*e**4*x + 900*d**4*e**5*x**2 + 1200*d**3*e**6*x**3 + 900*d**2*e**7*x**4 + 360*d*e**8*x**5 + 60*e**9*x**6)","B",0
1463,1,462,0,0.142812," ","integrate((e*x+d)**6*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{4} d^{6} x + \frac{b^{4} e^{6} x^{11}}{11} + x^{10} \left(\frac{2 a b^{3} e^{6}}{5} + \frac{3 b^{4} d e^{5}}{5}\right) + x^{9} \left(\frac{2 a^{2} b^{2} e^{6}}{3} + \frac{8 a b^{3} d e^{5}}{3} + \frac{5 b^{4} d^{2} e^{4}}{3}\right) + x^{8} \left(\frac{a^{3} b e^{6}}{2} + \frac{9 a^{2} b^{2} d e^{5}}{2} + \frac{15 a b^{3} d^{2} e^{4}}{2} + \frac{5 b^{4} d^{3} e^{3}}{2}\right) + x^{7} \left(\frac{a^{4} e^{6}}{7} + \frac{24 a^{3} b d e^{5}}{7} + \frac{90 a^{2} b^{2} d^{2} e^{4}}{7} + \frac{80 a b^{3} d^{3} e^{3}}{7} + \frac{15 b^{4} d^{4} e^{2}}{7}\right) + x^{6} \left(a^{4} d e^{5} + 10 a^{3} b d^{2} e^{4} + 20 a^{2} b^{2} d^{3} e^{3} + 10 a b^{3} d^{4} e^{2} + b^{4} d^{5} e\right) + x^{5} \left(3 a^{4} d^{2} e^{4} + 16 a^{3} b d^{3} e^{3} + 18 a^{2} b^{2} d^{4} e^{2} + \frac{24 a b^{3} d^{5} e}{5} + \frac{b^{4} d^{6}}{5}\right) + x^{4} \left(5 a^{4} d^{3} e^{3} + 15 a^{3} b d^{4} e^{2} + 9 a^{2} b^{2} d^{5} e + a b^{3} d^{6}\right) + x^{3} \left(5 a^{4} d^{4} e^{2} + 8 a^{3} b d^{5} e + 2 a^{2} b^{2} d^{6}\right) + x^{2} \left(3 a^{4} d^{5} e + 2 a^{3} b d^{6}\right)"," ",0,"a**4*d**6*x + b**4*e**6*x**11/11 + x**10*(2*a*b**3*e**6/5 + 3*b**4*d*e**5/5) + x**9*(2*a**2*b**2*e**6/3 + 8*a*b**3*d*e**5/3 + 5*b**4*d**2*e**4/3) + x**8*(a**3*b*e**6/2 + 9*a**2*b**2*d*e**5/2 + 15*a*b**3*d**2*e**4/2 + 5*b**4*d**3*e**3/2) + x**7*(a**4*e**6/7 + 24*a**3*b*d*e**5/7 + 90*a**2*b**2*d**2*e**4/7 + 80*a*b**3*d**3*e**3/7 + 15*b**4*d**4*e**2/7) + x**6*(a**4*d*e**5 + 10*a**3*b*d**2*e**4 + 20*a**2*b**2*d**3*e**3 + 10*a*b**3*d**4*e**2 + b**4*d**5*e) + x**5*(3*a**4*d**2*e**4 + 16*a**3*b*d**3*e**3 + 18*a**2*b**2*d**4*e**2 + 24*a*b**3*d**5*e/5 + b**4*d**6/5) + x**4*(5*a**4*d**3*e**3 + 15*a**3*b*d**4*e**2 + 9*a**2*b**2*d**5*e + a*b**3*d**6) + x**3*(5*a**4*d**4*e**2 + 8*a**3*b*d**5*e + 2*a**2*b**2*d**6) + x**2*(3*a**4*d**5*e + 2*a**3*b*d**6)","B",0
1464,1,401,0,0.131380," ","integrate((e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{4} d^{5} x + \frac{b^{4} e^{5} x^{10}}{10} + x^{9} \left(\frac{4 a b^{3} e^{5}}{9} + \frac{5 b^{4} d e^{4}}{9}\right) + x^{8} \left(\frac{3 a^{2} b^{2} e^{5}}{4} + \frac{5 a b^{3} d e^{4}}{2} + \frac{5 b^{4} d^{2} e^{3}}{4}\right) + x^{7} \left(\frac{4 a^{3} b e^{5}}{7} + \frac{30 a^{2} b^{2} d e^{4}}{7} + \frac{40 a b^{3} d^{2} e^{3}}{7} + \frac{10 b^{4} d^{3} e^{2}}{7}\right) + x^{6} \left(\frac{a^{4} e^{5}}{6} + \frac{10 a^{3} b d e^{4}}{3} + 10 a^{2} b^{2} d^{2} e^{3} + \frac{20 a b^{3} d^{3} e^{2}}{3} + \frac{5 b^{4} d^{4} e}{6}\right) + x^{5} \left(a^{4} d e^{4} + 8 a^{3} b d^{2} e^{3} + 12 a^{2} b^{2} d^{3} e^{2} + 4 a b^{3} d^{4} e + \frac{b^{4} d^{5}}{5}\right) + x^{4} \left(\frac{5 a^{4} d^{2} e^{3}}{2} + 10 a^{3} b d^{3} e^{2} + \frac{15 a^{2} b^{2} d^{4} e}{2} + a b^{3} d^{5}\right) + x^{3} \left(\frac{10 a^{4} d^{3} e^{2}}{3} + \frac{20 a^{3} b d^{4} e}{3} + 2 a^{2} b^{2} d^{5}\right) + x^{2} \left(\frac{5 a^{4} d^{4} e}{2} + 2 a^{3} b d^{5}\right)"," ",0,"a**4*d**5*x + b**4*e**5*x**10/10 + x**9*(4*a*b**3*e**5/9 + 5*b**4*d*e**4/9) + x**8*(3*a**2*b**2*e**5/4 + 5*a*b**3*d*e**4/2 + 5*b**4*d**2*e**3/4) + x**7*(4*a**3*b*e**5/7 + 30*a**2*b**2*d*e**4/7 + 40*a*b**3*d**2*e**3/7 + 10*b**4*d**3*e**2/7) + x**6*(a**4*e**5/6 + 10*a**3*b*d*e**4/3 + 10*a**2*b**2*d**2*e**3 + 20*a*b**3*d**3*e**2/3 + 5*b**4*d**4*e/6) + x**5*(a**4*d*e**4 + 8*a**3*b*d**2*e**3 + 12*a**2*b**2*d**3*e**2 + 4*a*b**3*d**4*e + b**4*d**5/5) + x**4*(5*a**4*d**2*e**3/2 + 10*a**3*b*d**3*e**2 + 15*a**2*b**2*d**4*e/2 + a*b**3*d**5) + x**3*(10*a**4*d**3*e**2/3 + 20*a**3*b*d**4*e/3 + 2*a**2*b**2*d**5) + x**2*(5*a**4*d**4*e/2 + 2*a**3*b*d**5)","B",0
1465,1,318,0,0.119671," ","integrate((e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{4} d^{4} x + \frac{b^{4} e^{4} x^{9}}{9} + x^{8} \left(\frac{a b^{3} e^{4}}{2} + \frac{b^{4} d e^{3}}{2}\right) + x^{7} \left(\frac{6 a^{2} b^{2} e^{4}}{7} + \frac{16 a b^{3} d e^{3}}{7} + \frac{6 b^{4} d^{2} e^{2}}{7}\right) + x^{6} \left(\frac{2 a^{3} b e^{4}}{3} + 4 a^{2} b^{2} d e^{3} + 4 a b^{3} d^{2} e^{2} + \frac{2 b^{4} d^{3} e}{3}\right) + x^{5} \left(\frac{a^{4} e^{4}}{5} + \frac{16 a^{3} b d e^{3}}{5} + \frac{36 a^{2} b^{2} d^{2} e^{2}}{5} + \frac{16 a b^{3} d^{3} e}{5} + \frac{b^{4} d^{4}}{5}\right) + x^{4} \left(a^{4} d e^{3} + 6 a^{3} b d^{2} e^{2} + 6 a^{2} b^{2} d^{3} e + a b^{3} d^{4}\right) + x^{3} \left(2 a^{4} d^{2} e^{2} + \frac{16 a^{3} b d^{3} e}{3} + 2 a^{2} b^{2} d^{4}\right) + x^{2} \left(2 a^{4} d^{3} e + 2 a^{3} b d^{4}\right)"," ",0,"a**4*d**4*x + b**4*e**4*x**9/9 + x**8*(a*b**3*e**4/2 + b**4*d*e**3/2) + x**7*(6*a**2*b**2*e**4/7 + 16*a*b**3*d*e**3/7 + 6*b**4*d**2*e**2/7) + x**6*(2*a**3*b*e**4/3 + 4*a**2*b**2*d*e**3 + 4*a*b**3*d**2*e**2 + 2*b**4*d**3*e/3) + x**5*(a**4*e**4/5 + 16*a**3*b*d*e**3/5 + 36*a**2*b**2*d**2*e**2/5 + 16*a*b**3*d**3*e/5 + b**4*d**4/5) + x**4*(a**4*d*e**3 + 6*a**3*b*d**2*e**2 + 6*a**2*b**2*d**3*e + a*b**3*d**4) + x**3*(2*a**4*d**2*e**2 + 16*a**3*b*d**3*e/3 + 2*a**2*b**2*d**4) + x**2*(2*a**4*d**3*e + 2*a**3*b*d**4)","B",0
1466,1,243,0,0.108854," ","integrate((e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{4} d^{3} x + \frac{b^{4} e^{3} x^{8}}{8} + x^{7} \left(\frac{4 a b^{3} e^{3}}{7} + \frac{3 b^{4} d e^{2}}{7}\right) + x^{6} \left(a^{2} b^{2} e^{3} + 2 a b^{3} d e^{2} + \frac{b^{4} d^{2} e}{2}\right) + x^{5} \left(\frac{4 a^{3} b e^{3}}{5} + \frac{18 a^{2} b^{2} d e^{2}}{5} + \frac{12 a b^{3} d^{2} e}{5} + \frac{b^{4} d^{3}}{5}\right) + x^{4} \left(\frac{a^{4} e^{3}}{4} + 3 a^{3} b d e^{2} + \frac{9 a^{2} b^{2} d^{2} e}{2} + a b^{3} d^{3}\right) + x^{3} \left(a^{4} d e^{2} + 4 a^{3} b d^{2} e + 2 a^{2} b^{2} d^{3}\right) + x^{2} \left(\frac{3 a^{4} d^{2} e}{2} + 2 a^{3} b d^{3}\right)"," ",0,"a**4*d**3*x + b**4*e**3*x**8/8 + x**7*(4*a*b**3*e**3/7 + 3*b**4*d*e**2/7) + x**6*(a**2*b**2*e**3 + 2*a*b**3*d*e**2 + b**4*d**2*e/2) + x**5*(4*a**3*b*e**3/5 + 18*a**2*b**2*d*e**2/5 + 12*a*b**3*d**2*e/5 + b**4*d**3/5) + x**4*(a**4*e**3/4 + 3*a**3*b*d*e**2 + 9*a**2*b**2*d**2*e/2 + a*b**3*d**3) + x**3*(a**4*d*e**2 + 4*a**3*b*d**2*e + 2*a**2*b**2*d**3) + x**2*(3*a**4*d**2*e/2 + 2*a**3*b*d**3)","B",0
1467,1,168,0,0.098463," ","integrate((e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{4} d^{2} x + \frac{b^{4} e^{2} x^{7}}{7} + x^{6} \left(\frac{2 a b^{3} e^{2}}{3} + \frac{b^{4} d e}{3}\right) + x^{5} \left(\frac{6 a^{2} b^{2} e^{2}}{5} + \frac{8 a b^{3} d e}{5} + \frac{b^{4} d^{2}}{5}\right) + x^{4} \left(a^{3} b e^{2} + 3 a^{2} b^{2} d e + a b^{3} d^{2}\right) + x^{3} \left(\frac{a^{4} e^{2}}{3} + \frac{8 a^{3} b d e}{3} + 2 a^{2} b^{2} d^{2}\right) + x^{2} \left(a^{4} d e + 2 a^{3} b d^{2}\right)"," ",0,"a**4*d**2*x + b**4*e**2*x**7/7 + x**6*(2*a*b**3*e**2/3 + b**4*d*e/3) + x**5*(6*a**2*b**2*e**2/5 + 8*a*b**3*d*e/5 + b**4*d**2/5) + x**4*(a**3*b*e**2 + 3*a**2*b**2*d*e + a*b**3*d**2) + x**3*(a**4*e**2/3 + 8*a**3*b*d*e/3 + 2*a**2*b**2*d**2) + x**2*(a**4*d*e + 2*a**3*b*d**2)","B",0
1468,1,100,0,0.085036," ","integrate((e*x+d)*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{4} d x + \frac{b^{4} e x^{6}}{6} + x^{5} \left(\frac{4 a b^{3} e}{5} + \frac{b^{4} d}{5}\right) + x^{4} \left(\frac{3 a^{2} b^{2} e}{2} + a b^{3} d\right) + x^{3} \left(\frac{4 a^{3} b e}{3} + 2 a^{2} b^{2} d\right) + x^{2} \left(\frac{a^{4} e}{2} + 2 a^{3} b d\right)"," ",0,"a**4*d*x + b**4*e*x**6/6 + x**5*(4*a*b**3*e/5 + b**4*d/5) + x**4*(3*a**2*b**2*e/2 + a*b**3*d) + x**3*(4*a**3*b*e/3 + 2*a**2*b**2*d) + x**2*(a**4*e/2 + 2*a**3*b*d)","B",0
1469,1,42,0,0.070284," ","integrate((b**2*x**2+2*a*b*x+a**2)**2,x)","a^{4} x + 2 a^{3} b x^{2} + 2 a^{2} b^{2} x^{3} + a b^{3} x^{4} + \frac{b^{4} x^{5}}{5}"," ",0,"a**4*x + 2*a**3*b*x**2 + 2*a**2*b**2*x**3 + a*b**3*x**4 + b**4*x**5/5","B",0
1470,1,136,0,0.403761," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d),x)","\frac{b^{4} x^{4}}{4 e} + x^{3} \left(\frac{4 a b^{3}}{3 e} - \frac{b^{4} d}{3 e^{2}}\right) + x^{2} \left(\frac{3 a^{2} b^{2}}{e} - \frac{2 a b^{3} d}{e^{2}} + \frac{b^{4} d^{2}}{2 e^{3}}\right) + x \left(\frac{4 a^{3} b}{e} - \frac{6 a^{2} b^{2} d}{e^{2}} + \frac{4 a b^{3} d^{2}}{e^{3}} - \frac{b^{4} d^{3}}{e^{4}}\right) + \frac{\left(a e - b d\right)^{4} \log{\left(d + e x \right)}}{e^{5}}"," ",0,"b**4*x**4/(4*e) + x**3*(4*a*b**3/(3*e) - b**4*d/(3*e**2)) + x**2*(3*a**2*b**2/e - 2*a*b**3*d/e**2 + b**4*d**2/(2*e**3)) + x*(4*a**3*b/e - 6*a**2*b**2*d/e**2 + 4*a*b**3*d**2/e**3 - b**4*d**3/e**4) + (a*e - b*d)**4*log(d + e*x)/e**5","A",0
1471,1,155,0,0.711586," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**2,x)","\frac{b^{4} x^{3}}{3 e^{2}} + \frac{4 b \left(a e - b d\right)^{3} \log{\left(d + e x \right)}}{e^{5}} + x^{2} \left(\frac{2 a b^{3}}{e^{2}} - \frac{b^{4} d}{e^{3}}\right) + x \left(\frac{6 a^{2} b^{2}}{e^{2}} - \frac{8 a b^{3} d}{e^{3}} + \frac{3 b^{4} d^{2}}{e^{4}}\right) + \frac{- a^{4} e^{4} + 4 a^{3} b d e^{3} - 6 a^{2} b^{2} d^{2} e^{2} + 4 a b^{3} d^{3} e - b^{4} d^{4}}{d e^{5} + e^{6} x}"," ",0,"b**4*x**3/(3*e**2) + 4*b*(a*e - b*d)**3*log(d + e*x)/e**5 + x**2*(2*a*b**3/e**2 - b**4*d/e**3) + x*(6*a**2*b**2/e**2 - 8*a*b**3*d/e**3 + 3*b**4*d**2/e**4) + (-a**4*e**4 + 4*a**3*b*d*e**3 - 6*a**2*b**2*d**2*e**2 + 4*a*b**3*d**3*e - b**4*d**4)/(d*e**5 + e**6*x)","A",0
1472,1,185,0,1.237578," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**3,x)","\frac{b^{4} x^{2}}{2 e^{3}} + \frac{6 b^{2} \left(a e - b d\right)^{2} \log{\left(d + e x \right)}}{e^{5}} + x \left(\frac{4 a b^{3}}{e^{3}} - \frac{3 b^{4} d}{e^{4}}\right) + \frac{- a^{4} e^{4} - 4 a^{3} b d e^{3} + 18 a^{2} b^{2} d^{2} e^{2} - 20 a b^{3} d^{3} e + 7 b^{4} d^{4} + x \left(- 8 a^{3} b e^{4} + 24 a^{2} b^{2} d e^{3} - 24 a b^{3} d^{2} e^{2} + 8 b^{4} d^{3} e\right)}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}}"," ",0,"b**4*x**2/(2*e**3) + 6*b**2*(a*e - b*d)**2*log(d + e*x)/e**5 + x*(4*a*b**3/e**3 - 3*b**4*d/e**4) + (-a**4*e**4 - 4*a**3*b*d*e**3 + 18*a**2*b**2*d**2*e**2 - 20*a*b**3*d**3*e + 7*b**4*d**4 + x*(-8*a**3*b*e**4 + 24*a**2*b**2*d*e**3 - 24*a*b**3*d**2*e**2 + 8*b**4*d**3*e))/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2)","A",0
1473,1,209,0,1.984116," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**4,x)","\frac{b^{4} x}{e^{4}} + \frac{4 b^{3} \left(a e - b d\right) \log{\left(d + e x \right)}}{e^{5}} + \frac{- a^{4} e^{4} - 2 a^{3} b d e^{3} - 6 a^{2} b^{2} d^{2} e^{2} + 22 a b^{3} d^{3} e - 13 b^{4} d^{4} + x^{2} \left(- 18 a^{2} b^{2} e^{4} + 36 a b^{3} d e^{3} - 18 b^{4} d^{2} e^{2}\right) + x \left(- 6 a^{3} b e^{4} - 18 a^{2} b^{2} d e^{3} + 54 a b^{3} d^{2} e^{2} - 30 b^{4} d^{3} e\right)}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}}"," ",0,"b**4*x/e**4 + 4*b**3*(a*e - b*d)*log(d + e*x)/e**5 + (-a**4*e**4 - 2*a**3*b*d*e**3 - 6*a**2*b**2*d**2*e**2 + 22*a*b**3*d**3*e - 13*b**4*d**4 + x**2*(-18*a**2*b**2*e**4 + 36*a*b**3*d*e**3 - 18*b**4*d**2*e**2) + x*(-6*a**3*b*e**4 - 18*a**2*b**2*d*e**3 + 54*a*b**3*d**2*e**2 - 30*b**4*d**3*e))/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3)","B",0
1474,1,230,0,2.888258," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**5,x)","\frac{b^{4} \log{\left(d + e x \right)}}{e^{5}} + \frac{- 3 a^{4} e^{4} - 4 a^{3} b d e^{3} - 6 a^{2} b^{2} d^{2} e^{2} - 12 a b^{3} d^{3} e + 25 b^{4} d^{4} + x^{3} \left(- 48 a b^{3} e^{4} + 48 b^{4} d e^{3}\right) + x^{2} \left(- 36 a^{2} b^{2} e^{4} - 72 a b^{3} d e^{3} + 108 b^{4} d^{2} e^{2}\right) + x \left(- 16 a^{3} b e^{4} - 24 a^{2} b^{2} d e^{3} - 48 a b^{3} d^{2} e^{2} + 88 b^{4} d^{3} e\right)}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}}"," ",0,"b**4*log(d + e*x)/e**5 + (-3*a**4*e**4 - 4*a**3*b*d*e**3 - 6*a**2*b**2*d**2*e**2 - 12*a*b**3*d**3*e + 25*b**4*d**4 + x**3*(-48*a*b**3*e**4 + 48*b**4*d*e**3) + x**2*(-36*a**2*b**2*e**4 - 72*a*b**3*d*e**3 + 108*b**4*d**2*e**2) + x*(-16*a**3*b*e**4 - 24*a**2*b**2*d*e**3 - 48*a*b**3*d**2*e**2 + 88*b**4*d**3*e))/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4)","B",0
1475,1,236,0,4.126738," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**6,x)","\frac{- a^{4} e^{4} - a^{3} b d e^{3} - a^{2} b^{2} d^{2} e^{2} - a b^{3} d^{3} e - b^{4} d^{4} - 5 b^{4} e^{4} x^{4} + x^{3} \left(- 10 a b^{3} e^{4} - 10 b^{4} d e^{3}\right) + x^{2} \left(- 10 a^{2} b^{2} e^{4} - 10 a b^{3} d e^{3} - 10 b^{4} d^{2} e^{2}\right) + x \left(- 5 a^{3} b e^{4} - 5 a^{2} b^{2} d e^{3} - 5 a b^{3} d^{2} e^{2} - 5 b^{4} d^{3} e\right)}{5 d^{5} e^{5} + 25 d^{4} e^{6} x + 50 d^{3} e^{7} x^{2} + 50 d^{2} e^{8} x^{3} + 25 d e^{9} x^{4} + 5 e^{10} x^{5}}"," ",0,"(-a**4*e**4 - a**3*b*d*e**3 - a**2*b**2*d**2*e**2 - a*b**3*d**3*e - b**4*d**4 - 5*b**4*e**4*x**4 + x**3*(-10*a*b**3*e**4 - 10*b**4*d*e**3) + x**2*(-10*a**2*b**2*e**4 - 10*a*b**3*d*e**3 - 10*b**4*d**2*e**2) + x*(-5*a**3*b*e**4 - 5*a**2*b**2*d*e**3 - 5*a*b**3*d**2*e**2 - 5*b**4*d**3*e))/(5*d**5*e**5 + 25*d**4*e**6*x + 50*d**3*e**7*x**2 + 50*d**2*e**8*x**3 + 25*d*e**9*x**4 + 5*e**10*x**5)","B",0
1476,1,255,0,5.916683," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**7,x)","\frac{- 5 a^{4} e^{4} - 4 a^{3} b d e^{3} - 3 a^{2} b^{2} d^{2} e^{2} - 2 a b^{3} d^{3} e - b^{4} d^{4} - 15 b^{4} e^{4} x^{4} + x^{3} \left(- 40 a b^{3} e^{4} - 20 b^{4} d e^{3}\right) + x^{2} \left(- 45 a^{2} b^{2} e^{4} - 30 a b^{3} d e^{3} - 15 b^{4} d^{2} e^{2}\right) + x \left(- 24 a^{3} b e^{4} - 18 a^{2} b^{2} d e^{3} - 12 a b^{3} d^{2} e^{2} - 6 b^{4} d^{3} e\right)}{30 d^{6} e^{5} + 180 d^{5} e^{6} x + 450 d^{4} e^{7} x^{2} + 600 d^{3} e^{8} x^{3} + 450 d^{2} e^{9} x^{4} + 180 d e^{10} x^{5} + 30 e^{11} x^{6}}"," ",0,"(-5*a**4*e**4 - 4*a**3*b*d*e**3 - 3*a**2*b**2*d**2*e**2 - 2*a*b**3*d**3*e - b**4*d**4 - 15*b**4*e**4*x**4 + x**3*(-40*a*b**3*e**4 - 20*b**4*d*e**3) + x**2*(-45*a**2*b**2*e**4 - 30*a*b**3*d*e**3 - 15*b**4*d**2*e**2) + x*(-24*a**3*b*e**4 - 18*a**2*b**2*d*e**3 - 12*a*b**3*d**2*e**2 - 6*b**4*d**3*e))/(30*d**6*e**5 + 180*d**5*e**6*x + 450*d**4*e**7*x**2 + 600*d**3*e**8*x**3 + 450*d**2*e**9*x**4 + 180*d*e**10*x**5 + 30*e**11*x**6)","B",0
1477,1,267,0,9.884614," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**8,x)","\frac{- 15 a^{4} e^{4} - 10 a^{3} b d e^{3} - 6 a^{2} b^{2} d^{2} e^{2} - 3 a b^{3} d^{3} e - b^{4} d^{4} - 35 b^{4} e^{4} x^{4} + x^{3} \left(- 105 a b^{3} e^{4} - 35 b^{4} d e^{3}\right) + x^{2} \left(- 126 a^{2} b^{2} e^{4} - 63 a b^{3} d e^{3} - 21 b^{4} d^{2} e^{2}\right) + x \left(- 70 a^{3} b e^{4} - 42 a^{2} b^{2} d e^{3} - 21 a b^{3} d^{2} e^{2} - 7 b^{4} d^{3} e\right)}{105 d^{7} e^{5} + 735 d^{6} e^{6} x + 2205 d^{5} e^{7} x^{2} + 3675 d^{4} e^{8} x^{3} + 3675 d^{3} e^{9} x^{4} + 2205 d^{2} e^{10} x^{5} + 735 d e^{11} x^{6} + 105 e^{12} x^{7}}"," ",0,"(-15*a**4*e**4 - 10*a**3*b*d*e**3 - 6*a**2*b**2*d**2*e**2 - 3*a*b**3*d**3*e - b**4*d**4 - 35*b**4*e**4*x**4 + x**3*(-105*a*b**3*e**4 - 35*b**4*d*e**3) + x**2*(-126*a**2*b**2*e**4 - 63*a*b**3*d*e**3 - 21*b**4*d**2*e**2) + x*(-70*a**3*b*e**4 - 42*a**2*b**2*d*e**3 - 21*a*b**3*d**2*e**2 - 7*b**4*d**3*e))/(105*d**7*e**5 + 735*d**6*e**6*x + 2205*d**5*e**7*x**2 + 3675*d**4*e**8*x**3 + 3675*d**3*e**9*x**4 + 2205*d**2*e**10*x**5 + 735*d*e**11*x**6 + 105*e**12*x**7)","B",0
1478,1,279,0,17.050744," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**9,x)","\frac{- 35 a^{4} e^{4} - 20 a^{3} b d e^{3} - 10 a^{2} b^{2} d^{2} e^{2} - 4 a b^{3} d^{3} e - b^{4} d^{4} - 70 b^{4} e^{4} x^{4} + x^{3} \left(- 224 a b^{3} e^{4} - 56 b^{4} d e^{3}\right) + x^{2} \left(- 280 a^{2} b^{2} e^{4} - 112 a b^{3} d e^{3} - 28 b^{4} d^{2} e^{2}\right) + x \left(- 160 a^{3} b e^{4} - 80 a^{2} b^{2} d e^{3} - 32 a b^{3} d^{2} e^{2} - 8 b^{4} d^{3} e\right)}{280 d^{8} e^{5} + 2240 d^{7} e^{6} x + 7840 d^{6} e^{7} x^{2} + 15680 d^{5} e^{8} x^{3} + 19600 d^{4} e^{9} x^{4} + 15680 d^{3} e^{10} x^{5} + 7840 d^{2} e^{11} x^{6} + 2240 d e^{12} x^{7} + 280 e^{13} x^{8}}"," ",0,"(-35*a**4*e**4 - 20*a**3*b*d*e**3 - 10*a**2*b**2*d**2*e**2 - 4*a*b**3*d**3*e - b**4*d**4 - 70*b**4*e**4*x**4 + x**3*(-224*a*b**3*e**4 - 56*b**4*d*e**3) + x**2*(-280*a**2*b**2*e**4 - 112*a*b**3*d*e**3 - 28*b**4*d**2*e**2) + x*(-160*a**3*b*e**4 - 80*a**2*b**2*d*e**3 - 32*a*b**3*d**2*e**2 - 8*b**4*d**3*e))/(280*d**8*e**5 + 2240*d**7*e**6*x + 7840*d**6*e**7*x**2 + 15680*d**5*e**8*x**3 + 19600*d**4*e**9*x**4 + 15680*d**3*e**10*x**5 + 7840*d**2*e**11*x**6 + 2240*d*e**12*x**7 + 280*e**13*x**8)","B",0
1479,1,291,0,31.183531," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**10,x)","\frac{- 70 a^{4} e^{4} - 35 a^{3} b d e^{3} - 15 a^{2} b^{2} d^{2} e^{2} - 5 a b^{3} d^{3} e - b^{4} d^{4} - 126 b^{4} e^{4} x^{4} + x^{3} \left(- 420 a b^{3} e^{4} - 84 b^{4} d e^{3}\right) + x^{2} \left(- 540 a^{2} b^{2} e^{4} - 180 a b^{3} d e^{3} - 36 b^{4} d^{2} e^{2}\right) + x \left(- 315 a^{3} b e^{4} - 135 a^{2} b^{2} d e^{3} - 45 a b^{3} d^{2} e^{2} - 9 b^{4} d^{3} e\right)}{630 d^{9} e^{5} + 5670 d^{8} e^{6} x + 22680 d^{7} e^{7} x^{2} + 52920 d^{6} e^{8} x^{3} + 79380 d^{5} e^{9} x^{4} + 79380 d^{4} e^{10} x^{5} + 52920 d^{3} e^{11} x^{6} + 22680 d^{2} e^{12} x^{7} + 5670 d e^{13} x^{8} + 630 e^{14} x^{9}}"," ",0,"(-70*a**4*e**4 - 35*a**3*b*d*e**3 - 15*a**2*b**2*d**2*e**2 - 5*a*b**3*d**3*e - b**4*d**4 - 126*b**4*e**4*x**4 + x**3*(-420*a*b**3*e**4 - 84*b**4*d*e**3) + x**2*(-540*a**2*b**2*e**4 - 180*a*b**3*d*e**3 - 36*b**4*d**2*e**2) + x*(-315*a**3*b*e**4 - 135*a**2*b**2*d*e**3 - 45*a*b**3*d**2*e**2 - 9*b**4*d**3*e))/(630*d**9*e**5 + 5670*d**8*e**6*x + 22680*d**7*e**7*x**2 + 52920*d**6*e**8*x**3 + 79380*d**5*e**9*x**4 + 79380*d**4*e**10*x**5 + 52920*d**3*e**11*x**6 + 22680*d**2*e**12*x**7 + 5670*d*e**13*x**8 + 630*e**14*x**9)","B",0
1480,1,303,0,58.375682," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**11,x)","\frac{- 126 a^{4} e^{4} - 56 a^{3} b d e^{3} - 21 a^{2} b^{2} d^{2} e^{2} - 6 a b^{3} d^{3} e - b^{4} d^{4} - 210 b^{4} e^{4} x^{4} + x^{3} \left(- 720 a b^{3} e^{4} - 120 b^{4} d e^{3}\right) + x^{2} \left(- 945 a^{2} b^{2} e^{4} - 270 a b^{3} d e^{3} - 45 b^{4} d^{2} e^{2}\right) + x \left(- 560 a^{3} b e^{4} - 210 a^{2} b^{2} d e^{3} - 60 a b^{3} d^{2} e^{2} - 10 b^{4} d^{3} e\right)}{1260 d^{10} e^{5} + 12600 d^{9} e^{6} x + 56700 d^{8} e^{7} x^{2} + 151200 d^{7} e^{8} x^{3} + 264600 d^{6} e^{9} x^{4} + 317520 d^{5} e^{10} x^{5} + 264600 d^{4} e^{11} x^{6} + 151200 d^{3} e^{12} x^{7} + 56700 d^{2} e^{13} x^{8} + 12600 d e^{14} x^{9} + 1260 e^{15} x^{10}}"," ",0,"(-126*a**4*e**4 - 56*a**3*b*d*e**3 - 21*a**2*b**2*d**2*e**2 - 6*a*b**3*d**3*e - b**4*d**4 - 210*b**4*e**4*x**4 + x**3*(-720*a*b**3*e**4 - 120*b**4*d*e**3) + x**2*(-945*a**2*b**2*e**4 - 270*a*b**3*d*e**3 - 45*b**4*d**2*e**2) + x*(-560*a**3*b*e**4 - 210*a**2*b**2*d*e**3 - 60*a*b**3*d**2*e**2 - 10*b**4*d**3*e))/(1260*d**10*e**5 + 12600*d**9*e**6*x + 56700*d**8*e**7*x**2 + 151200*d**7*e**8*x**3 + 264600*d**6*e**9*x**4 + 317520*d**5*e**10*x**5 + 264600*d**4*e**11*x**6 + 151200*d**3*e**12*x**7 + 56700*d**2*e**13*x**8 + 12600*d*e**14*x**9 + 1260*e**15*x**10)","B",0
1481,1,884,0,0.198874," ","integrate((e*x+d)**8*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d^{8} x + \frac{b^{6} e^{8} x^{15}}{15} + x^{14} \left(\frac{3 a b^{5} e^{8}}{7} + \frac{4 b^{6} d e^{7}}{7}\right) + x^{13} \left(\frac{15 a^{2} b^{4} e^{8}}{13} + \frac{48 a b^{5} d e^{7}}{13} + \frac{28 b^{6} d^{2} e^{6}}{13}\right) + x^{12} \left(\frac{5 a^{3} b^{3} e^{8}}{3} + 10 a^{2} b^{4} d e^{7} + 14 a b^{5} d^{2} e^{6} + \frac{14 b^{6} d^{3} e^{5}}{3}\right) + x^{11} \left(\frac{15 a^{4} b^{2} e^{8}}{11} + \frac{160 a^{3} b^{3} d e^{7}}{11} + \frac{420 a^{2} b^{4} d^{2} e^{6}}{11} + \frac{336 a b^{5} d^{3} e^{5}}{11} + \frac{70 b^{6} d^{4} e^{4}}{11}\right) + x^{10} \left(\frac{3 a^{5} b e^{8}}{5} + 12 a^{4} b^{2} d e^{7} + 56 a^{3} b^{3} d^{2} e^{6} + 84 a^{2} b^{4} d^{3} e^{5} + 42 a b^{5} d^{4} e^{4} + \frac{28 b^{6} d^{5} e^{3}}{5}\right) + x^{9} \left(\frac{a^{6} e^{8}}{9} + \frac{16 a^{5} b d e^{7}}{3} + \frac{140 a^{4} b^{2} d^{2} e^{6}}{3} + \frac{1120 a^{3} b^{3} d^{3} e^{5}}{9} + \frac{350 a^{2} b^{4} d^{4} e^{4}}{3} + \frac{112 a b^{5} d^{5} e^{3}}{3} + \frac{28 b^{6} d^{6} e^{2}}{9}\right) + x^{8} \left(a^{6} d e^{7} + 21 a^{5} b d^{2} e^{6} + 105 a^{4} b^{2} d^{3} e^{5} + 175 a^{3} b^{3} d^{4} e^{4} + 105 a^{2} b^{4} d^{5} e^{3} + 21 a b^{5} d^{6} e^{2} + b^{6} d^{7} e\right) + x^{7} \left(4 a^{6} d^{2} e^{6} + 48 a^{5} b d^{3} e^{5} + 150 a^{4} b^{2} d^{4} e^{4} + 160 a^{3} b^{3} d^{5} e^{3} + 60 a^{2} b^{4} d^{6} e^{2} + \frac{48 a b^{5} d^{7} e}{7} + \frac{b^{6} d^{8}}{7}\right) + x^{6} \left(\frac{28 a^{6} d^{3} e^{5}}{3} + 70 a^{5} b d^{4} e^{4} + 140 a^{4} b^{2} d^{5} e^{3} + \frac{280 a^{3} b^{3} d^{6} e^{2}}{3} + 20 a^{2} b^{4} d^{7} e + a b^{5} d^{8}\right) + x^{5} \left(14 a^{6} d^{4} e^{4} + \frac{336 a^{5} b d^{5} e^{3}}{5} + 84 a^{4} b^{2} d^{6} e^{2} + 32 a^{3} b^{3} d^{7} e + 3 a^{2} b^{4} d^{8}\right) + x^{4} \left(14 a^{6} d^{5} e^{3} + 42 a^{5} b d^{6} e^{2} + 30 a^{4} b^{2} d^{7} e + 5 a^{3} b^{3} d^{8}\right) + x^{3} \left(\frac{28 a^{6} d^{6} e^{2}}{3} + 16 a^{5} b d^{7} e + 5 a^{4} b^{2} d^{8}\right) + x^{2} \left(4 a^{6} d^{7} e + 3 a^{5} b d^{8}\right)"," ",0,"a**6*d**8*x + b**6*e**8*x**15/15 + x**14*(3*a*b**5*e**8/7 + 4*b**6*d*e**7/7) + x**13*(15*a**2*b**4*e**8/13 + 48*a*b**5*d*e**7/13 + 28*b**6*d**2*e**6/13) + x**12*(5*a**3*b**3*e**8/3 + 10*a**2*b**4*d*e**7 + 14*a*b**5*d**2*e**6 + 14*b**6*d**3*e**5/3) + x**11*(15*a**4*b**2*e**8/11 + 160*a**3*b**3*d*e**7/11 + 420*a**2*b**4*d**2*e**6/11 + 336*a*b**5*d**3*e**5/11 + 70*b**6*d**4*e**4/11) + x**10*(3*a**5*b*e**8/5 + 12*a**4*b**2*d*e**7 + 56*a**3*b**3*d**2*e**6 + 84*a**2*b**4*d**3*e**5 + 42*a*b**5*d**4*e**4 + 28*b**6*d**5*e**3/5) + x**9*(a**6*e**8/9 + 16*a**5*b*d*e**7/3 + 140*a**4*b**2*d**2*e**6/3 + 1120*a**3*b**3*d**3*e**5/9 + 350*a**2*b**4*d**4*e**4/3 + 112*a*b**5*d**5*e**3/3 + 28*b**6*d**6*e**2/9) + x**8*(a**6*d*e**7 + 21*a**5*b*d**2*e**6 + 105*a**4*b**2*d**3*e**5 + 175*a**3*b**3*d**4*e**4 + 105*a**2*b**4*d**5*e**3 + 21*a*b**5*d**6*e**2 + b**6*d**7*e) + x**7*(4*a**6*d**2*e**6 + 48*a**5*b*d**3*e**5 + 150*a**4*b**2*d**4*e**4 + 160*a**3*b**3*d**5*e**3 + 60*a**2*b**4*d**6*e**2 + 48*a*b**5*d**7*e/7 + b**6*d**8/7) + x**6*(28*a**6*d**3*e**5/3 + 70*a**5*b*d**4*e**4 + 140*a**4*b**2*d**5*e**3 + 280*a**3*b**3*d**6*e**2/3 + 20*a**2*b**4*d**7*e + a*b**5*d**8) + x**5*(14*a**6*d**4*e**4 + 336*a**5*b*d**5*e**3/5 + 84*a**4*b**2*d**6*e**2 + 32*a**3*b**3*d**7*e + 3*a**2*b**4*d**8) + x**4*(14*a**6*d**5*e**3 + 42*a**5*b*d**6*e**2 + 30*a**4*b**2*d**7*e + 5*a**3*b**3*d**8) + x**3*(28*a**6*d**6*e**2/3 + 16*a**5*b*d**7*e + 5*a**4*b**2*d**8) + x**2*(4*a**6*d**7*e + 3*a**5*b*d**8)","B",0
1482,1,796,0,0.183879," ","integrate((e*x+d)**7*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d^{7} x + \frac{b^{6} e^{7} x^{14}}{14} + x^{13} \left(\frac{6 a b^{5} e^{7}}{13} + \frac{7 b^{6} d e^{6}}{13}\right) + x^{12} \left(\frac{5 a^{2} b^{4} e^{7}}{4} + \frac{7 a b^{5} d e^{6}}{2} + \frac{7 b^{6} d^{2} e^{5}}{4}\right) + x^{11} \left(\frac{20 a^{3} b^{3} e^{7}}{11} + \frac{105 a^{2} b^{4} d e^{6}}{11} + \frac{126 a b^{5} d^{2} e^{5}}{11} + \frac{35 b^{6} d^{3} e^{4}}{11}\right) + x^{10} \left(\frac{3 a^{4} b^{2} e^{7}}{2} + 14 a^{3} b^{3} d e^{6} + \frac{63 a^{2} b^{4} d^{2} e^{5}}{2} + 21 a b^{5} d^{3} e^{4} + \frac{7 b^{6} d^{4} e^{3}}{2}\right) + x^{9} \left(\frac{2 a^{5} b e^{7}}{3} + \frac{35 a^{4} b^{2} d e^{6}}{3} + \frac{140 a^{3} b^{3} d^{2} e^{5}}{3} + \frac{175 a^{2} b^{4} d^{3} e^{4}}{3} + \frac{70 a b^{5} d^{4} e^{3}}{3} + \frac{7 b^{6} d^{5} e^{2}}{3}\right) + x^{8} \left(\frac{a^{6} e^{7}}{8} + \frac{21 a^{5} b d e^{6}}{4} + \frac{315 a^{4} b^{2} d^{2} e^{5}}{8} + \frac{175 a^{3} b^{3} d^{3} e^{4}}{2} + \frac{525 a^{2} b^{4} d^{4} e^{3}}{8} + \frac{63 a b^{5} d^{5} e^{2}}{4} + \frac{7 b^{6} d^{6} e}{8}\right) + x^{7} \left(a^{6} d e^{6} + 18 a^{5} b d^{2} e^{5} + 75 a^{4} b^{2} d^{3} e^{4} + 100 a^{3} b^{3} d^{4} e^{3} + 45 a^{2} b^{4} d^{5} e^{2} + 6 a b^{5} d^{6} e + \frac{b^{6} d^{7}}{7}\right) + x^{6} \left(\frac{7 a^{6} d^{2} e^{5}}{2} + 35 a^{5} b d^{3} e^{4} + \frac{175 a^{4} b^{2} d^{4} e^{3}}{2} + 70 a^{3} b^{3} d^{5} e^{2} + \frac{35 a^{2} b^{4} d^{6} e}{2} + a b^{5} d^{7}\right) + x^{5} \left(7 a^{6} d^{3} e^{4} + 42 a^{5} b d^{4} e^{3} + 63 a^{4} b^{2} d^{5} e^{2} + 28 a^{3} b^{3} d^{6} e + 3 a^{2} b^{4} d^{7}\right) + x^{4} \left(\frac{35 a^{6} d^{4} e^{3}}{4} + \frac{63 a^{5} b d^{5} e^{2}}{2} + \frac{105 a^{4} b^{2} d^{6} e}{4} + 5 a^{3} b^{3} d^{7}\right) + x^{3} \left(7 a^{6} d^{5} e^{2} + 14 a^{5} b d^{6} e + 5 a^{4} b^{2} d^{7}\right) + x^{2} \left(\frac{7 a^{6} d^{6} e}{2} + 3 a^{5} b d^{7}\right)"," ",0,"a**6*d**7*x + b**6*e**7*x**14/14 + x**13*(6*a*b**5*e**7/13 + 7*b**6*d*e**6/13) + x**12*(5*a**2*b**4*e**7/4 + 7*a*b**5*d*e**6/2 + 7*b**6*d**2*e**5/4) + x**11*(20*a**3*b**3*e**7/11 + 105*a**2*b**4*d*e**6/11 + 126*a*b**5*d**2*e**5/11 + 35*b**6*d**3*e**4/11) + x**10*(3*a**4*b**2*e**7/2 + 14*a**3*b**3*d*e**6 + 63*a**2*b**4*d**2*e**5/2 + 21*a*b**5*d**3*e**4 + 7*b**6*d**4*e**3/2) + x**9*(2*a**5*b*e**7/3 + 35*a**4*b**2*d*e**6/3 + 140*a**3*b**3*d**2*e**5/3 + 175*a**2*b**4*d**3*e**4/3 + 70*a*b**5*d**4*e**3/3 + 7*b**6*d**5*e**2/3) + x**8*(a**6*e**7/8 + 21*a**5*b*d*e**6/4 + 315*a**4*b**2*d**2*e**5/8 + 175*a**3*b**3*d**3*e**4/2 + 525*a**2*b**4*d**4*e**3/8 + 63*a*b**5*d**5*e**2/4 + 7*b**6*d**6*e/8) + x**7*(a**6*d*e**6 + 18*a**5*b*d**2*e**5 + 75*a**4*b**2*d**3*e**4 + 100*a**3*b**3*d**4*e**3 + 45*a**2*b**4*d**5*e**2 + 6*a*b**5*d**6*e + b**6*d**7/7) + x**6*(7*a**6*d**2*e**5/2 + 35*a**5*b*d**3*e**4 + 175*a**4*b**2*d**4*e**3/2 + 70*a**3*b**3*d**5*e**2 + 35*a**2*b**4*d**6*e/2 + a*b**5*d**7) + x**5*(7*a**6*d**3*e**4 + 42*a**5*b*d**4*e**3 + 63*a**4*b**2*d**5*e**2 + 28*a**3*b**3*d**6*e + 3*a**2*b**4*d**7) + x**4*(35*a**6*d**4*e**3/4 + 63*a**5*b*d**5*e**2/2 + 105*a**4*b**2*d**6*e/4 + 5*a**3*b**3*d**7) + x**3*(7*a**6*d**5*e**2 + 14*a**5*b*d**6*e + 5*a**4*b**2*d**7) + x**2*(7*a**6*d**6*e/2 + 3*a**5*b*d**7)","B",0
1483,1,677,0,0.170400," ","integrate((e*x+d)**6*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d^{6} x + \frac{b^{6} e^{6} x^{13}}{13} + x^{12} \left(\frac{a b^{5} e^{6}}{2} + \frac{b^{6} d e^{5}}{2}\right) + x^{11} \left(\frac{15 a^{2} b^{4} e^{6}}{11} + \frac{36 a b^{5} d e^{5}}{11} + \frac{15 b^{6} d^{2} e^{4}}{11}\right) + x^{10} \left(2 a^{3} b^{3} e^{6} + 9 a^{2} b^{4} d e^{5} + 9 a b^{5} d^{2} e^{4} + 2 b^{6} d^{3} e^{3}\right) + x^{9} \left(\frac{5 a^{4} b^{2} e^{6}}{3} + \frac{40 a^{3} b^{3} d e^{5}}{3} + 25 a^{2} b^{4} d^{2} e^{4} + \frac{40 a b^{5} d^{3} e^{3}}{3} + \frac{5 b^{6} d^{4} e^{2}}{3}\right) + x^{8} \left(\frac{3 a^{5} b e^{6}}{4} + \frac{45 a^{4} b^{2} d e^{5}}{4} + \frac{75 a^{3} b^{3} d^{2} e^{4}}{2} + \frac{75 a^{2} b^{4} d^{3} e^{3}}{2} + \frac{45 a b^{5} d^{4} e^{2}}{4} + \frac{3 b^{6} d^{5} e}{4}\right) + x^{7} \left(\frac{a^{6} e^{6}}{7} + \frac{36 a^{5} b d e^{5}}{7} + \frac{225 a^{4} b^{2} d^{2} e^{4}}{7} + \frac{400 a^{3} b^{3} d^{3} e^{3}}{7} + \frac{225 a^{2} b^{4} d^{4} e^{2}}{7} + \frac{36 a b^{5} d^{5} e}{7} + \frac{b^{6} d^{6}}{7}\right) + x^{6} \left(a^{6} d e^{5} + 15 a^{5} b d^{2} e^{4} + 50 a^{4} b^{2} d^{3} e^{3} + 50 a^{3} b^{3} d^{4} e^{2} + 15 a^{2} b^{4} d^{5} e + a b^{5} d^{6}\right) + x^{5} \left(3 a^{6} d^{2} e^{4} + 24 a^{5} b d^{3} e^{3} + 45 a^{4} b^{2} d^{4} e^{2} + 24 a^{3} b^{3} d^{5} e + 3 a^{2} b^{4} d^{6}\right) + x^{4} \left(5 a^{6} d^{3} e^{3} + \frac{45 a^{5} b d^{4} e^{2}}{2} + \frac{45 a^{4} b^{2} d^{5} e}{2} + 5 a^{3} b^{3} d^{6}\right) + x^{3} \left(5 a^{6} d^{4} e^{2} + 12 a^{5} b d^{5} e + 5 a^{4} b^{2} d^{6}\right) + x^{2} \left(3 a^{6} d^{5} e + 3 a^{5} b d^{6}\right)"," ",0,"a**6*d**6*x + b**6*e**6*x**13/13 + x**12*(a*b**5*e**6/2 + b**6*d*e**5/2) + x**11*(15*a**2*b**4*e**6/11 + 36*a*b**5*d*e**5/11 + 15*b**6*d**2*e**4/11) + x**10*(2*a**3*b**3*e**6 + 9*a**2*b**4*d*e**5 + 9*a*b**5*d**2*e**4 + 2*b**6*d**3*e**3) + x**9*(5*a**4*b**2*e**6/3 + 40*a**3*b**3*d*e**5/3 + 25*a**2*b**4*d**2*e**4 + 40*a*b**5*d**3*e**3/3 + 5*b**6*d**4*e**2/3) + x**8*(3*a**5*b*e**6/4 + 45*a**4*b**2*d*e**5/4 + 75*a**3*b**3*d**2*e**4/2 + 75*a**2*b**4*d**3*e**3/2 + 45*a*b**5*d**4*e**2/4 + 3*b**6*d**5*e/4) + x**7*(a**6*e**6/7 + 36*a**5*b*d*e**5/7 + 225*a**4*b**2*d**2*e**4/7 + 400*a**3*b**3*d**3*e**3/7 + 225*a**2*b**4*d**4*e**2/7 + 36*a*b**5*d**5*e/7 + b**6*d**6/7) + x**6*(a**6*d*e**5 + 15*a**5*b*d**2*e**4 + 50*a**4*b**2*d**3*e**3 + 50*a**3*b**3*d**4*e**2 + 15*a**2*b**4*d**5*e + a*b**5*d**6) + x**5*(3*a**6*d**2*e**4 + 24*a**5*b*d**3*e**3 + 45*a**4*b**2*d**4*e**2 + 24*a**3*b**3*d**5*e + 3*a**2*b**4*d**6) + x**4*(5*a**6*d**3*e**3 + 45*a**5*b*d**4*e**2/2 + 45*a**4*b**2*d**5*e/2 + 5*a**3*b**3*d**6) + x**3*(5*a**6*d**4*e**2 + 12*a**5*b*d**5*e + 5*a**4*b**2*d**6) + x**2*(3*a**6*d**5*e + 3*a**5*b*d**6)","B",0
1484,1,580,0,0.155669," ","integrate((e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d^{5} x + \frac{b^{6} e^{5} x^{12}}{12} + x^{11} \left(\frac{6 a b^{5} e^{5}}{11} + \frac{5 b^{6} d e^{4}}{11}\right) + x^{10} \left(\frac{3 a^{2} b^{4} e^{5}}{2} + 3 a b^{5} d e^{4} + b^{6} d^{2} e^{3}\right) + x^{9} \left(\frac{20 a^{3} b^{3} e^{5}}{9} + \frac{25 a^{2} b^{4} d e^{4}}{3} + \frac{20 a b^{5} d^{2} e^{3}}{3} + \frac{10 b^{6} d^{3} e^{2}}{9}\right) + x^{8} \left(\frac{15 a^{4} b^{2} e^{5}}{8} + \frac{25 a^{3} b^{3} d e^{4}}{2} + \frac{75 a^{2} b^{4} d^{2} e^{3}}{4} + \frac{15 a b^{5} d^{3} e^{2}}{2} + \frac{5 b^{6} d^{4} e}{8}\right) + x^{7} \left(\frac{6 a^{5} b e^{5}}{7} + \frac{75 a^{4} b^{2} d e^{4}}{7} + \frac{200 a^{3} b^{3} d^{2} e^{3}}{7} + \frac{150 a^{2} b^{4} d^{3} e^{2}}{7} + \frac{30 a b^{5} d^{4} e}{7} + \frac{b^{6} d^{5}}{7}\right) + x^{6} \left(\frac{a^{6} e^{5}}{6} + 5 a^{5} b d e^{4} + 25 a^{4} b^{2} d^{2} e^{3} + \frac{100 a^{3} b^{3} d^{3} e^{2}}{3} + \frac{25 a^{2} b^{4} d^{4} e}{2} + a b^{5} d^{5}\right) + x^{5} \left(a^{6} d e^{4} + 12 a^{5} b d^{2} e^{3} + 30 a^{4} b^{2} d^{3} e^{2} + 20 a^{3} b^{3} d^{4} e + 3 a^{2} b^{4} d^{5}\right) + x^{4} \left(\frac{5 a^{6} d^{2} e^{3}}{2} + 15 a^{5} b d^{3} e^{2} + \frac{75 a^{4} b^{2} d^{4} e}{4} + 5 a^{3} b^{3} d^{5}\right) + x^{3} \left(\frac{10 a^{6} d^{3} e^{2}}{3} + 10 a^{5} b d^{4} e + 5 a^{4} b^{2} d^{5}\right) + x^{2} \left(\frac{5 a^{6} d^{4} e}{2} + 3 a^{5} b d^{5}\right)"," ",0,"a**6*d**5*x + b**6*e**5*x**12/12 + x**11*(6*a*b**5*e**5/11 + 5*b**6*d*e**4/11) + x**10*(3*a**2*b**4*e**5/2 + 3*a*b**5*d*e**4 + b**6*d**2*e**3) + x**9*(20*a**3*b**3*e**5/9 + 25*a**2*b**4*d*e**4/3 + 20*a*b**5*d**2*e**3/3 + 10*b**6*d**3*e**2/9) + x**8*(15*a**4*b**2*e**5/8 + 25*a**3*b**3*d*e**4/2 + 75*a**2*b**4*d**2*e**3/4 + 15*a*b**5*d**3*e**2/2 + 5*b**6*d**4*e/8) + x**7*(6*a**5*b*e**5/7 + 75*a**4*b**2*d*e**4/7 + 200*a**3*b**3*d**2*e**3/7 + 150*a**2*b**4*d**3*e**2/7 + 30*a*b**5*d**4*e/7 + b**6*d**5/7) + x**6*(a**6*e**5/6 + 5*a**5*b*d*e**4 + 25*a**4*b**2*d**2*e**3 + 100*a**3*b**3*d**3*e**2/3 + 25*a**2*b**4*d**4*e/2 + a*b**5*d**5) + x**5*(a**6*d*e**4 + 12*a**5*b*d**2*e**3 + 30*a**4*b**2*d**3*e**2 + 20*a**3*b**3*d**4*e + 3*a**2*b**4*d**5) + x**4*(5*a**6*d**2*e**3/2 + 15*a**5*b*d**3*e**2 + 75*a**4*b**2*d**4*e/4 + 5*a**3*b**3*d**5) + x**3*(10*a**6*d**3*e**2/3 + 10*a**5*b*d**4*e + 5*a**4*b**2*d**5) + x**2*(5*a**6*d**4*e/2 + 3*a**5*b*d**5)","B",0
1485,1,462,0,0.140732," ","integrate((e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d^{4} x + \frac{b^{6} e^{4} x^{11}}{11} + x^{10} \left(\frac{3 a b^{5} e^{4}}{5} + \frac{2 b^{6} d e^{3}}{5}\right) + x^{9} \left(\frac{5 a^{2} b^{4} e^{4}}{3} + \frac{8 a b^{5} d e^{3}}{3} + \frac{2 b^{6} d^{2} e^{2}}{3}\right) + x^{8} \left(\frac{5 a^{3} b^{3} e^{4}}{2} + \frac{15 a^{2} b^{4} d e^{3}}{2} + \frac{9 a b^{5} d^{2} e^{2}}{2} + \frac{b^{6} d^{3} e}{2}\right) + x^{7} \left(\frac{15 a^{4} b^{2} e^{4}}{7} + \frac{80 a^{3} b^{3} d e^{3}}{7} + \frac{90 a^{2} b^{4} d^{2} e^{2}}{7} + \frac{24 a b^{5} d^{3} e}{7} + \frac{b^{6} d^{4}}{7}\right) + x^{6} \left(a^{5} b e^{4} + 10 a^{4} b^{2} d e^{3} + 20 a^{3} b^{3} d^{2} e^{2} + 10 a^{2} b^{4} d^{3} e + a b^{5} d^{4}\right) + x^{5} \left(\frac{a^{6} e^{4}}{5} + \frac{24 a^{5} b d e^{3}}{5} + 18 a^{4} b^{2} d^{2} e^{2} + 16 a^{3} b^{3} d^{3} e + 3 a^{2} b^{4} d^{4}\right) + x^{4} \left(a^{6} d e^{3} + 9 a^{5} b d^{2} e^{2} + 15 a^{4} b^{2} d^{3} e + 5 a^{3} b^{3} d^{4}\right) + x^{3} \left(2 a^{6} d^{2} e^{2} + 8 a^{5} b d^{3} e + 5 a^{4} b^{2} d^{4}\right) + x^{2} \left(2 a^{6} d^{3} e + 3 a^{5} b d^{4}\right)"," ",0,"a**6*d**4*x + b**6*e**4*x**11/11 + x**10*(3*a*b**5*e**4/5 + 2*b**6*d*e**3/5) + x**9*(5*a**2*b**4*e**4/3 + 8*a*b**5*d*e**3/3 + 2*b**6*d**2*e**2/3) + x**8*(5*a**3*b**3*e**4/2 + 15*a**2*b**4*d*e**3/2 + 9*a*b**5*d**2*e**2/2 + b**6*d**3*e/2) + x**7*(15*a**4*b**2*e**4/7 + 80*a**3*b**3*d*e**3/7 + 90*a**2*b**4*d**2*e**2/7 + 24*a*b**5*d**3*e/7 + b**6*d**4/7) + x**6*(a**5*b*e**4 + 10*a**4*b**2*d*e**3 + 20*a**3*b**3*d**2*e**2 + 10*a**2*b**4*d**3*e + a*b**5*d**4) + x**5*(a**6*e**4/5 + 24*a**5*b*d*e**3/5 + 18*a**4*b**2*d**2*e**2 + 16*a**3*b**3*d**3*e + 3*a**2*b**4*d**4) + x**4*(a**6*d*e**3 + 9*a**5*b*d**2*e**2 + 15*a**4*b**2*d**3*e + 5*a**3*b**3*d**4) + x**3*(2*a**6*d**2*e**2 + 8*a**5*b*d**3*e + 5*a**4*b**2*d**4) + x**2*(2*a**6*d**3*e + 3*a**5*b*d**4)","B",0
1486,1,364,0,0.127428," ","integrate((e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d^{3} x + \frac{b^{6} e^{3} x^{10}}{10} + x^{9} \left(\frac{2 a b^{5} e^{3}}{3} + \frac{b^{6} d e^{2}}{3}\right) + x^{8} \left(\frac{15 a^{2} b^{4} e^{3}}{8} + \frac{9 a b^{5} d e^{2}}{4} + \frac{3 b^{6} d^{2} e}{8}\right) + x^{7} \left(\frac{20 a^{3} b^{3} e^{3}}{7} + \frac{45 a^{2} b^{4} d e^{2}}{7} + \frac{18 a b^{5} d^{2} e}{7} + \frac{b^{6} d^{3}}{7}\right) + x^{6} \left(\frac{5 a^{4} b^{2} e^{3}}{2} + 10 a^{3} b^{3} d e^{2} + \frac{15 a^{2} b^{4} d^{2} e}{2} + a b^{5} d^{3}\right) + x^{5} \left(\frac{6 a^{5} b e^{3}}{5} + 9 a^{4} b^{2} d e^{2} + 12 a^{3} b^{3} d^{2} e + 3 a^{2} b^{4} d^{3}\right) + x^{4} \left(\frac{a^{6} e^{3}}{4} + \frac{9 a^{5} b d e^{2}}{2} + \frac{45 a^{4} b^{2} d^{2} e}{4} + 5 a^{3} b^{3} d^{3}\right) + x^{3} \left(a^{6} d e^{2} + 6 a^{5} b d^{2} e + 5 a^{4} b^{2} d^{3}\right) + x^{2} \left(\frac{3 a^{6} d^{2} e}{2} + 3 a^{5} b d^{3}\right)"," ",0,"a**6*d**3*x + b**6*e**3*x**10/10 + x**9*(2*a*b**5*e**3/3 + b**6*d*e**2/3) + x**8*(15*a**2*b**4*e**3/8 + 9*a*b**5*d*e**2/4 + 3*b**6*d**2*e/8) + x**7*(20*a**3*b**3*e**3/7 + 45*a**2*b**4*d*e**2/7 + 18*a*b**5*d**2*e/7 + b**6*d**3/7) + x**6*(5*a**4*b**2*e**3/2 + 10*a**3*b**3*d*e**2 + 15*a**2*b**4*d**2*e/2 + a*b**5*d**3) + x**5*(6*a**5*b*e**3/5 + 9*a**4*b**2*d*e**2 + 12*a**3*b**3*d**2*e + 3*a**2*b**4*d**3) + x**4*(a**6*e**3/4 + 9*a**5*b*d*e**2/2 + 45*a**4*b**2*d**2*e/4 + 5*a**3*b**3*d**3) + x**3*(a**6*d*e**2 + 6*a**5*b*d**2*e + 5*a**4*b**2*d**3) + x**2*(3*a**6*d**2*e/2 + 3*a**5*b*d**3)","B",0
1487,1,252,0,0.113273," ","integrate((e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d^{2} x + \frac{b^{6} e^{2} x^{9}}{9} + x^{8} \left(\frac{3 a b^{5} e^{2}}{4} + \frac{b^{6} d e}{4}\right) + x^{7} \left(\frac{15 a^{2} b^{4} e^{2}}{7} + \frac{12 a b^{5} d e}{7} + \frac{b^{6} d^{2}}{7}\right) + x^{6} \left(\frac{10 a^{3} b^{3} e^{2}}{3} + 5 a^{2} b^{4} d e + a b^{5} d^{2}\right) + x^{5} \left(3 a^{4} b^{2} e^{2} + 8 a^{3} b^{3} d e + 3 a^{2} b^{4} d^{2}\right) + x^{4} \left(\frac{3 a^{5} b e^{2}}{2} + \frac{15 a^{4} b^{2} d e}{2} + 5 a^{3} b^{3} d^{2}\right) + x^{3} \left(\frac{a^{6} e^{2}}{3} + 4 a^{5} b d e + 5 a^{4} b^{2} d^{2}\right) + x^{2} \left(a^{6} d e + 3 a^{5} b d^{2}\right)"," ",0,"a**6*d**2*x + b**6*e**2*x**9/9 + x**8*(3*a*b**5*e**2/4 + b**6*d*e/4) + x**7*(15*a**2*b**4*e**2/7 + 12*a*b**5*d*e/7 + b**6*d**2/7) + x**6*(10*a**3*b**3*e**2/3 + 5*a**2*b**4*d*e + a*b**5*d**2) + x**5*(3*a**4*b**2*e**2 + 8*a**3*b**3*d*e + 3*a**2*b**4*d**2) + x**4*(3*a**5*b*e**2/2 + 15*a**4*b**2*d*e/2 + 5*a**3*b**3*d**2) + x**3*(a**6*e**2/3 + 4*a**5*b*d*e + 5*a**4*b**2*d**2) + x**2*(a**6*d*e + 3*a**5*b*d**2)","B",0
1488,1,148,0,0.097571," ","integrate((e*x+d)*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d x + \frac{b^{6} e x^{8}}{8} + x^{7} \left(\frac{6 a b^{5} e}{7} + \frac{b^{6} d}{7}\right) + x^{6} \left(\frac{5 a^{2} b^{4} e}{2} + a b^{5} d\right) + x^{5} \left(4 a^{3} b^{3} e + 3 a^{2} b^{4} d\right) + x^{4} \left(\frac{15 a^{4} b^{2} e}{4} + 5 a^{3} b^{3} d\right) + x^{3} \left(2 a^{5} b e + 5 a^{4} b^{2} d\right) + x^{2} \left(\frac{a^{6} e}{2} + 3 a^{5} b d\right)"," ",0,"a**6*d*x + b**6*e*x**8/8 + x**7*(6*a*b**5*e/7 + b**6*d/7) + x**6*(5*a**2*b**4*e/2 + a*b**5*d) + x**5*(4*a**3*b**3*e + 3*a**2*b**4*d) + x**4*(15*a**4*b**2*e/4 + 5*a**3*b**3*d) + x**3*(2*a**5*b*e + 5*a**4*b**2*d) + x**2*(a**6*e/2 + 3*a**5*b*d)","B",0
1489,1,66,0,0.076720," ","integrate((b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} x + 3 a^{5} b x^{2} + 5 a^{4} b^{2} x^{3} + 5 a^{3} b^{3} x^{4} + 3 a^{2} b^{4} x^{5} + a b^{5} x^{6} + \frac{b^{6} x^{7}}{7}"," ",0,"a**6*x + 3*a**5*b*x**2 + 5*a**4*b**2*x**3 + 5*a**3*b**3*x**4 + 3*a**2*b**4*x**5 + a*b**5*x**6 + b**6*x**7/7","B",0
1490,1,296,0,0.650429," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d),x)","\frac{b^{6} x^{6}}{6 e} + x^{5} \left(\frac{6 a b^{5}}{5 e} - \frac{b^{6} d}{5 e^{2}}\right) + x^{4} \left(\frac{15 a^{2} b^{4}}{4 e} - \frac{3 a b^{5} d}{2 e^{2}} + \frac{b^{6} d^{2}}{4 e^{3}}\right) + x^{3} \left(\frac{20 a^{3} b^{3}}{3 e} - \frac{5 a^{2} b^{4} d}{e^{2}} + \frac{2 a b^{5} d^{2}}{e^{3}} - \frac{b^{6} d^{3}}{3 e^{4}}\right) + x^{2} \left(\frac{15 a^{4} b^{2}}{2 e} - \frac{10 a^{3} b^{3} d}{e^{2}} + \frac{15 a^{2} b^{4} d^{2}}{2 e^{3}} - \frac{3 a b^{5} d^{3}}{e^{4}} + \frac{b^{6} d^{4}}{2 e^{5}}\right) + x \left(\frac{6 a^{5} b}{e} - \frac{15 a^{4} b^{2} d}{e^{2}} + \frac{20 a^{3} b^{3} d^{2}}{e^{3}} - \frac{15 a^{2} b^{4} d^{3}}{e^{4}} + \frac{6 a b^{5} d^{4}}{e^{5}} - \frac{b^{6} d^{5}}{e^{6}}\right) + \frac{\left(a e - b d\right)^{6} \log{\left(d + e x \right)}}{e^{7}}"," ",0,"b**6*x**6/(6*e) + x**5*(6*a*b**5/(5*e) - b**6*d/(5*e**2)) + x**4*(15*a**2*b**4/(4*e) - 3*a*b**5*d/(2*e**2) + b**6*d**2/(4*e**3)) + x**3*(20*a**3*b**3/(3*e) - 5*a**2*b**4*d/e**2 + 2*a*b**5*d**2/e**3 - b**6*d**3/(3*e**4)) + x**2*(15*a**4*b**2/(2*e) - 10*a**3*b**3*d/e**2 + 15*a**2*b**4*d**2/(2*e**3) - 3*a*b**5*d**3/e**4 + b**6*d**4/(2*e**5)) + x*(6*a**5*b/e - 15*a**4*b**2*d/e**2 + 20*a**3*b**3*d**2/e**3 - 15*a**2*b**4*d**3/e**4 + 6*a*b**5*d**4/e**5 - b**6*d**5/e**6) + (a*e - b*d)**6*log(d + e*x)/e**7","B",0
1491,1,311,0,1.192248," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**2,x)","\frac{b^{6} x^{5}}{5 e^{2}} + \frac{6 b \left(a e - b d\right)^{5} \log{\left(d + e x \right)}}{e^{7}} + x^{4} \left(\frac{3 a b^{5}}{2 e^{2}} - \frac{b^{6} d}{2 e^{3}}\right) + x^{3} \left(\frac{5 a^{2} b^{4}}{e^{2}} - \frac{4 a b^{5} d}{e^{3}} + \frac{b^{6} d^{2}}{e^{4}}\right) + x^{2} \left(\frac{10 a^{3} b^{3}}{e^{2}} - \frac{15 a^{2} b^{4} d}{e^{3}} + \frac{9 a b^{5} d^{2}}{e^{4}} - \frac{2 b^{6} d^{3}}{e^{5}}\right) + x \left(\frac{15 a^{4} b^{2}}{e^{2}} - \frac{40 a^{3} b^{3} d}{e^{3}} + \frac{45 a^{2} b^{4} d^{2}}{e^{4}} - \frac{24 a b^{5} d^{3}}{e^{5}} + \frac{5 b^{6} d^{4}}{e^{6}}\right) + \frac{- a^{6} e^{6} + 6 a^{5} b d e^{5} - 15 a^{4} b^{2} d^{2} e^{4} + 20 a^{3} b^{3} d^{3} e^{3} - 15 a^{2} b^{4} d^{4} e^{2} + 6 a b^{5} d^{5} e - b^{6} d^{6}}{d e^{7} + e^{8} x}"," ",0,"b**6*x**5/(5*e**2) + 6*b*(a*e - b*d)**5*log(d + e*x)/e**7 + x**4*(3*a*b**5/(2*e**2) - b**6*d/(2*e**3)) + x**3*(5*a**2*b**4/e**2 - 4*a*b**5*d/e**3 + b**6*d**2/e**4) + x**2*(10*a**3*b**3/e**2 - 15*a**2*b**4*d/e**3 + 9*a*b**5*d**2/e**4 - 2*b**6*d**3/e**5) + x*(15*a**4*b**2/e**2 - 40*a**3*b**3*d/e**3 + 45*a**2*b**4*d**2/e**4 - 24*a*b**5*d**3/e**5 + 5*b**6*d**4/e**6) + (-a**6*e**6 + 6*a**5*b*d*e**5 - 15*a**4*b**2*d**2*e**4 + 20*a**3*b**3*d**3*e**3 - 15*a**2*b**4*d**4*e**2 + 6*a*b**5*d**5*e - b**6*d**6)/(d*e**7 + e**8*x)","B",0
1492,1,340,0,2.299891," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**3,x)","\frac{b^{6} x^{4}}{4 e^{3}} + \frac{15 b^{2} \left(a e - b d\right)^{4} \log{\left(d + e x \right)}}{e^{7}} + x^{3} \left(\frac{2 a b^{5}}{e^{3}} - \frac{b^{6} d}{e^{4}}\right) + x^{2} \left(\frac{15 a^{2} b^{4}}{2 e^{3}} - \frac{9 a b^{5} d}{e^{4}} + \frac{3 b^{6} d^{2}}{e^{5}}\right) + x \left(\frac{20 a^{3} b^{3}}{e^{3}} - \frac{45 a^{2} b^{4} d}{e^{4}} + \frac{36 a b^{5} d^{2}}{e^{5}} - \frac{10 b^{6} d^{3}}{e^{6}}\right) + \frac{- a^{6} e^{6} - 6 a^{5} b d e^{5} + 45 a^{4} b^{2} d^{2} e^{4} - 100 a^{3} b^{3} d^{3} e^{3} + 105 a^{2} b^{4} d^{4} e^{2} - 54 a b^{5} d^{5} e + 11 b^{6} d^{6} + x \left(- 12 a^{5} b e^{6} + 60 a^{4} b^{2} d e^{5} - 120 a^{3} b^{3} d^{2} e^{4} + 120 a^{2} b^{4} d^{3} e^{3} - 60 a b^{5} d^{4} e^{2} + 12 b^{6} d^{5} e\right)}{2 d^{2} e^{7} + 4 d e^{8} x + 2 e^{9} x^{2}}"," ",0,"b**6*x**4/(4*e**3) + 15*b**2*(a*e - b*d)**4*log(d + e*x)/e**7 + x**3*(2*a*b**5/e**3 - b**6*d/e**4) + x**2*(15*a**2*b**4/(2*e**3) - 9*a*b**5*d/e**4 + 3*b**6*d**2/e**5) + x*(20*a**3*b**3/e**3 - 45*a**2*b**4*d/e**4 + 36*a*b**5*d**2/e**5 - 10*b**6*d**3/e**6) + (-a**6*e**6 - 6*a**5*b*d*e**5 + 45*a**4*b**2*d**2*e**4 - 100*a**3*b**3*d**3*e**3 + 105*a**2*b**4*d**4*e**2 - 54*a*b**5*d**5*e + 11*b**6*d**6 + x*(-12*a**5*b*e**6 + 60*a**4*b**2*d*e**5 - 120*a**3*b**3*d**2*e**4 + 120*a**2*b**4*d**3*e**3 - 60*a*b**5*d**4*e**2 + 12*b**6*d**5*e))/(2*d**2*e**7 + 4*d*e**8*x + 2*e**9*x**2)","B",0
1493,1,367,0,4.349586," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**4,x)","\frac{b^{6} x^{3}}{3 e^{4}} + \frac{20 b^{3} \left(a e - b d\right)^{3} \log{\left(d + e x \right)}}{e^{7}} + x^{2} \left(\frac{3 a b^{5}}{e^{4}} - \frac{2 b^{6} d}{e^{5}}\right) + x \left(\frac{15 a^{2} b^{4}}{e^{4}} - \frac{24 a b^{5} d}{e^{5}} + \frac{10 b^{6} d^{2}}{e^{6}}\right) + \frac{- a^{6} e^{6} - 3 a^{5} b d e^{5} - 15 a^{4} b^{2} d^{2} e^{4} + 110 a^{3} b^{3} d^{3} e^{3} - 195 a^{2} b^{4} d^{4} e^{2} + 141 a b^{5} d^{5} e - 37 b^{6} d^{6} + x^{2} \left(- 45 a^{4} b^{2} e^{6} + 180 a^{3} b^{3} d e^{5} - 270 a^{2} b^{4} d^{2} e^{4} + 180 a b^{5} d^{3} e^{3} - 45 b^{6} d^{4} e^{2}\right) + x \left(- 9 a^{5} b e^{6} - 45 a^{4} b^{2} d e^{5} + 270 a^{3} b^{3} d^{2} e^{4} - 450 a^{2} b^{4} d^{3} e^{3} + 315 a b^{5} d^{4} e^{2} - 81 b^{6} d^{5} e\right)}{3 d^{3} e^{7} + 9 d^{2} e^{8} x + 9 d e^{9} x^{2} + 3 e^{10} x^{3}}"," ",0,"b**6*x**3/(3*e**4) + 20*b**3*(a*e - b*d)**3*log(d + e*x)/e**7 + x**2*(3*a*b**5/e**4 - 2*b**6*d/e**5) + x*(15*a**2*b**4/e**4 - 24*a*b**5*d/e**5 + 10*b**6*d**2/e**6) + (-a**6*e**6 - 3*a**5*b*d*e**5 - 15*a**4*b**2*d**2*e**4 + 110*a**3*b**3*d**3*e**3 - 195*a**2*b**4*d**4*e**2 + 141*a*b**5*d**5*e - 37*b**6*d**6 + x**2*(-45*a**4*b**2*e**6 + 180*a**3*b**3*d*e**5 - 270*a**2*b**4*d**2*e**4 + 180*a*b**5*d**3*e**3 - 45*b**6*d**4*e**2) + x*(-9*a**5*b*e**6 - 45*a**4*b**2*d*e**5 + 270*a**3*b**3*d**2*e**4 - 450*a**2*b**4*d**3*e**3 + 315*a*b**5*d**4*e**2 - 81*b**6*d**5*e))/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3)","B",0
1494,1,394,0,10.020733," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**5,x)","\frac{b^{6} x^{2}}{2 e^{5}} + \frac{15 b^{4} \left(a e - b d\right)^{2} \log{\left(d + e x \right)}}{e^{7}} + x \left(\frac{6 a b^{5}}{e^{5}} - \frac{5 b^{6} d}{e^{6}}\right) + \frac{- a^{6} e^{6} - 2 a^{5} b d e^{5} - 5 a^{4} b^{2} d^{2} e^{4} - 20 a^{3} b^{3} d^{3} e^{3} + 125 a^{2} b^{4} d^{4} e^{2} - 154 a b^{5} d^{5} e + 57 b^{6} d^{6} + x^{3} \left(- 80 a^{3} b^{3} e^{6} + 240 a^{2} b^{4} d e^{5} - 240 a b^{5} d^{2} e^{4} + 80 b^{6} d^{3} e^{3}\right) + x^{2} \left(- 30 a^{4} b^{2} e^{6} - 120 a^{3} b^{3} d e^{5} + 540 a^{2} b^{4} d^{2} e^{4} - 600 a b^{5} d^{3} e^{3} + 210 b^{6} d^{4} e^{2}\right) + x \left(- 8 a^{5} b e^{6} - 20 a^{4} b^{2} d e^{5} - 80 a^{3} b^{3} d^{2} e^{4} + 440 a^{2} b^{4} d^{3} e^{3} - 520 a b^{5} d^{4} e^{2} + 188 b^{6} d^{5} e\right)}{4 d^{4} e^{7} + 16 d^{3} e^{8} x + 24 d^{2} e^{9} x^{2} + 16 d e^{10} x^{3} + 4 e^{11} x^{4}}"," ",0,"b**6*x**2/(2*e**5) + 15*b**4*(a*e - b*d)**2*log(d + e*x)/e**7 + x*(6*a*b**5/e**5 - 5*b**6*d/e**6) + (-a**6*e**6 - 2*a**5*b*d*e**5 - 5*a**4*b**2*d**2*e**4 - 20*a**3*b**3*d**3*e**3 + 125*a**2*b**4*d**4*e**2 - 154*a*b**5*d**5*e + 57*b**6*d**6 + x**3*(-80*a**3*b**3*e**6 + 240*a**2*b**4*d*e**5 - 240*a*b**5*d**2*e**4 + 80*b**6*d**3*e**3) + x**2*(-30*a**4*b**2*e**6 - 120*a**3*b**3*d*e**5 + 540*a**2*b**4*d**2*e**4 - 600*a*b**5*d**3*e**3 + 210*b**6*d**4*e**2) + x*(-8*a**5*b*e**6 - 20*a**4*b**2*d*e**5 - 80*a**3*b**3*d**2*e**4 + 440*a**2*b**4*d**3*e**3 - 520*a*b**5*d**4*e**2 + 188*b**6*d**5*e))/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4)","B",0
1495,1,420,0,30.166113," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**6,x)","\frac{b^{6} x}{e^{6}} + \frac{6 b^{5} \left(a e - b d\right) \log{\left(d + e x \right)}}{e^{7}} + \frac{- 2 a^{6} e^{6} - 3 a^{5} b d e^{5} - 5 a^{4} b^{2} d^{2} e^{4} - 10 a^{3} b^{3} d^{3} e^{3} - 30 a^{2} b^{4} d^{4} e^{2} + 137 a b^{5} d^{5} e - 87 b^{6} d^{6} + x^{4} \left(- 150 a^{2} b^{4} e^{6} + 300 a b^{5} d e^{5} - 150 b^{6} d^{2} e^{4}\right) + x^{3} \left(- 100 a^{3} b^{3} e^{6} - 300 a^{2} b^{4} d e^{5} + 900 a b^{5} d^{2} e^{4} - 500 b^{6} d^{3} e^{3}\right) + x^{2} \left(- 50 a^{4} b^{2} e^{6} - 100 a^{3} b^{3} d e^{5} - 300 a^{2} b^{4} d^{2} e^{4} + 1100 a b^{5} d^{3} e^{3} - 650 b^{6} d^{4} e^{2}\right) + x \left(- 15 a^{5} b e^{6} - 25 a^{4} b^{2} d e^{5} - 50 a^{3} b^{3} d^{2} e^{4} - 150 a^{2} b^{4} d^{3} e^{3} + 625 a b^{5} d^{4} e^{2} - 385 b^{6} d^{5} e\right)}{10 d^{5} e^{7} + 50 d^{4} e^{8} x + 100 d^{3} e^{9} x^{2} + 100 d^{2} e^{10} x^{3} + 50 d e^{11} x^{4} + 10 e^{12} x^{5}}"," ",0,"b**6*x/e**6 + 6*b**5*(a*e - b*d)*log(d + e*x)/e**7 + (-2*a**6*e**6 - 3*a**5*b*d*e**5 - 5*a**4*b**2*d**2*e**4 - 10*a**3*b**3*d**3*e**3 - 30*a**2*b**4*d**4*e**2 + 137*a*b**5*d**5*e - 87*b**6*d**6 + x**4*(-150*a**2*b**4*e**6 + 300*a*b**5*d*e**5 - 150*b**6*d**2*e**4) + x**3*(-100*a**3*b**3*e**6 - 300*a**2*b**4*d*e**5 + 900*a*b**5*d**2*e**4 - 500*b**6*d**3*e**3) + x**2*(-50*a**4*b**2*e**6 - 100*a**3*b**3*d*e**5 - 300*a**2*b**4*d**2*e**4 + 1100*a*b**5*d**3*e**3 - 650*b**6*d**4*e**2) + x*(-15*a**5*b*e**6 - 25*a**4*b**2*d*e**5 - 50*a**3*b**3*d**2*e**4 - 150*a**2*b**4*d**3*e**3 + 625*a*b**5*d**4*e**2 - 385*b**6*d**5*e))/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5)","B",0
1496,1,439,0,99.028342," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**7,x)","\frac{b^{6} \log{\left(d + e x \right)}}{e^{7}} + \frac{- 10 a^{6} e^{6} - 12 a^{5} b d e^{5} - 15 a^{4} b^{2} d^{2} e^{4} - 20 a^{3} b^{3} d^{3} e^{3} - 30 a^{2} b^{4} d^{4} e^{2} - 60 a b^{5} d^{5} e + 147 b^{6} d^{6} + x^{5} \left(- 360 a b^{5} e^{6} + 360 b^{6} d e^{5}\right) + x^{4} \left(- 450 a^{2} b^{4} e^{6} - 900 a b^{5} d e^{5} + 1350 b^{6} d^{2} e^{4}\right) + x^{3} \left(- 400 a^{3} b^{3} e^{6} - 600 a^{2} b^{4} d e^{5} - 1200 a b^{5} d^{2} e^{4} + 2200 b^{6} d^{3} e^{3}\right) + x^{2} \left(- 225 a^{4} b^{2} e^{6} - 300 a^{3} b^{3} d e^{5} - 450 a^{2} b^{4} d^{2} e^{4} - 900 a b^{5} d^{3} e^{3} + 1875 b^{6} d^{4} e^{2}\right) + x \left(- 72 a^{5} b e^{6} - 90 a^{4} b^{2} d e^{5} - 120 a^{3} b^{3} d^{2} e^{4} - 180 a^{2} b^{4} d^{3} e^{3} - 360 a b^{5} d^{4} e^{2} + 822 b^{6} d^{5} e\right)}{60 d^{6} e^{7} + 360 d^{5} e^{8} x + 900 d^{4} e^{9} x^{2} + 1200 d^{3} e^{10} x^{3} + 900 d^{2} e^{11} x^{4} + 360 d e^{12} x^{5} + 60 e^{13} x^{6}}"," ",0,"b**6*log(d + e*x)/e**7 + (-10*a**6*e**6 - 12*a**5*b*d*e**5 - 15*a**4*b**2*d**2*e**4 - 20*a**3*b**3*d**3*e**3 - 30*a**2*b**4*d**4*e**2 - 60*a*b**5*d**5*e + 147*b**6*d**6 + x**5*(-360*a*b**5*e**6 + 360*b**6*d*e**5) + x**4*(-450*a**2*b**4*e**6 - 900*a*b**5*d*e**5 + 1350*b**6*d**2*e**4) + x**3*(-400*a**3*b**3*e**6 - 600*a**2*b**4*d*e**5 - 1200*a*b**5*d**2*e**4 + 2200*b**6*d**3*e**3) + x**2*(-225*a**4*b**2*e**6 - 300*a**3*b**3*d*e**5 - 450*a**2*b**4*d**2*e**4 - 900*a*b**5*d**3*e**3 + 1875*b**6*d**4*e**2) + x*(-72*a**5*b*e**6 - 90*a**4*b**2*d*e**5 - 120*a**3*b**3*d**2*e**4 - 180*a**2*b**4*d**3*e**3 - 360*a*b**5*d**4*e**2 + 822*b**6*d**5*e))/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6)","B",0
1497,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1498,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1499,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1500,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1501,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**12,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1502,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**13,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1503,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**14,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1504,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**15,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1505,1,231,0,0.937357," ","integrate((e*x+d)**5/(b**2*x**2+2*a*b*x+a**2),x)","x^{3} \left(- \frac{2 a e^{5}}{3 b^{3}} + \frac{5 d e^{4}}{3 b^{2}}\right) + x^{2} \left(\frac{3 a^{2} e^{5}}{2 b^{4}} - \frac{5 a d e^{4}}{b^{3}} + \frac{5 d^{2} e^{3}}{b^{2}}\right) + x \left(- \frac{4 a^{3} e^{5}}{b^{5}} + \frac{15 a^{2} d e^{4}}{b^{4}} - \frac{20 a d^{2} e^{3}}{b^{3}} + \frac{10 d^{3} e^{2}}{b^{2}}\right) + \frac{a^{5} e^{5} - 5 a^{4} b d e^{4} + 10 a^{3} b^{2} d^{2} e^{3} - 10 a^{2} b^{3} d^{3} e^{2} + 5 a b^{4} d^{4} e - b^{5} d^{5}}{a b^{6} + b^{7} x} + \frac{e^{5} x^{4}}{4 b^{2}} + \frac{5 e \left(a e - b d\right)^{4} \log{\left(a + b x \right)}}{b^{6}}"," ",0,"x**3*(-2*a*e**5/(3*b**3) + 5*d*e**4/(3*b**2)) + x**2*(3*a**2*e**5/(2*b**4) - 5*a*d*e**4/b**3 + 5*d**2*e**3/b**2) + x*(-4*a**3*e**5/b**5 + 15*a**2*d*e**4/b**4 - 20*a*d**2*e**3/b**3 + 10*d**3*e**2/b**2) + (a**5*e**5 - 5*a**4*b*d*e**4 + 10*a**3*b**2*d**2*e**3 - 10*a**2*b**3*d**3*e**2 + 5*a*b**4*d**4*e - b**5*d**5)/(a*b**6 + b**7*x) + e**5*x**4/(4*b**2) + 5*e*(a*e - b*d)**4*log(a + b*x)/b**6","A",0
1506,1,155,0,0.705939," ","integrate((e*x+d)**4/(b**2*x**2+2*a*b*x+a**2),x)","x^{2} \left(- \frac{a e^{4}}{b^{3}} + \frac{2 d e^{3}}{b^{2}}\right) + x \left(\frac{3 a^{2} e^{4}}{b^{4}} - \frac{8 a d e^{3}}{b^{3}} + \frac{6 d^{2} e^{2}}{b^{2}}\right) + \frac{- a^{4} e^{4} + 4 a^{3} b d e^{3} - 6 a^{2} b^{2} d^{2} e^{2} + 4 a b^{3} d^{3} e - b^{4} d^{4}}{a b^{5} + b^{6} x} + \frac{e^{4} x^{3}}{3 b^{2}} - \frac{4 e \left(a e - b d\right)^{3} \log{\left(a + b x \right)}}{b^{5}}"," ",0,"x**2*(-a*e**4/b**3 + 2*d*e**3/b**2) + x*(3*a**2*e**4/b**4 - 8*a*d*e**3/b**3 + 6*d**2*e**2/b**2) + (-a**4*e**4 + 4*a**3*b*d*e**3 - 6*a**2*b**2*d**2*e**2 + 4*a*b**3*d**3*e - b**4*d**4)/(a*b**5 + b**6*x) + e**4*x**3/(3*b**2) - 4*e*(a*e - b*d)**3*log(a + b*x)/b**5","A",0
1507,1,102,0,0.513012," ","integrate((e*x+d)**3/(b**2*x**2+2*a*b*x+a**2),x)","x \left(- \frac{2 a e^{3}}{b^{3}} + \frac{3 d e^{2}}{b^{2}}\right) + \frac{a^{3} e^{3} - 3 a^{2} b d e^{2} + 3 a b^{2} d^{2} e - b^{3} d^{3}}{a b^{4} + b^{5} x} + \frac{e^{3} x^{2}}{2 b^{2}} + \frac{3 e \left(a e - b d\right)^{2} \log{\left(a + b x \right)}}{b^{4}}"," ",0,"x*(-2*a*e**3/b**3 + 3*d*e**2/b**2) + (a**3*e**3 - 3*a**2*b*d*e**2 + 3*a*b**2*d**2*e - b**3*d**3)/(a*b**4 + b**5*x) + e**3*x**2/(2*b**2) + 3*e*(a*e - b*d)**2*log(a + b*x)/b**4","A",0
1508,1,60,0,0.343154," ","integrate((e*x+d)**2/(b**2*x**2+2*a*b*x+a**2),x)","\frac{- a^{2} e^{2} + 2 a b d e - b^{2} d^{2}}{a b^{3} + b^{4} x} + \frac{e^{2} x}{b^{2}} - \frac{2 e \left(a e - b d\right) \log{\left(a + b x \right)}}{b^{3}}"," ",0,"(-a**2*e**2 + 2*a*b*d*e - b**2*d**2)/(a*b**3 + b**4*x) + e**2*x/b**2 - 2*e*(a*e - b*d)*log(a + b*x)/b**3","A",0
1509,1,27,0,0.184150," ","integrate((e*x+d)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{a e - b d}{a b^{2} + b^{3} x} + \frac{e \log{\left(a + b x \right)}}{b^{2}}"," ",0,"(a*e - b*d)/(a*b**2 + b**3*x) + e*log(a + b*x)/b**2","A",0
1510,1,10,0,0.127932," ","integrate(1/(b**2*x**2+2*a*b*x+a**2),x)","- \frac{1}{a b + b^{2} x}"," ",0,"-1/(a*b + b**2*x)","A",0
1511,1,233,0,0.700279," ","integrate(1/(e*x+d)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{e \log{\left(x + \frac{- \frac{a^{3} e^{4}}{\left(a e - b d\right)^{2}} + \frac{3 a^{2} b d e^{3}}{\left(a e - b d\right)^{2}} - \frac{3 a b^{2} d^{2} e^{2}}{\left(a e - b d\right)^{2}} + a e^{2} + \frac{b^{3} d^{3} e}{\left(a e - b d\right)^{2}} + b d e}{2 b e^{2}} \right)}}{\left(a e - b d\right)^{2}} - \frac{e \log{\left(x + \frac{\frac{a^{3} e^{4}}{\left(a e - b d\right)^{2}} - \frac{3 a^{2} b d e^{3}}{\left(a e - b d\right)^{2}} + \frac{3 a b^{2} d^{2} e^{2}}{\left(a e - b d\right)^{2}} + a e^{2} - \frac{b^{3} d^{3} e}{\left(a e - b d\right)^{2}} + b d e}{2 b e^{2}} \right)}}{\left(a e - b d\right)^{2}} + \frac{1}{a^{2} e - a b d + x \left(a b e - b^{2} d\right)}"," ",0,"e*log(x + (-a**3*e**4/(a*e - b*d)**2 + 3*a**2*b*d*e**3/(a*e - b*d)**2 - 3*a*b**2*d**2*e**2/(a*e - b*d)**2 + a*e**2 + b**3*d**3*e/(a*e - b*d)**2 + b*d*e)/(2*b*e**2))/(a*e - b*d)**2 - e*log(x + (a**3*e**4/(a*e - b*d)**2 - 3*a**2*b*d*e**3/(a*e - b*d)**2 + 3*a*b**2*d**2*e**2/(a*e - b*d)**2 + a*e**2 - b**3*d**3*e/(a*e - b*d)**2 + b*d*e)/(2*b*e**2))/(a*e - b*d)**2 + 1/(a**2*e - a*b*d + x*(a*b*e - b**2*d))","B",0
1512,1,406,0,1.148122," ","integrate(1/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2),x)","- \frac{2 b e \log{\left(x + \frac{- \frac{2 a^{4} b e^{5}}{\left(a e - b d\right)^{3}} + \frac{8 a^{3} b^{2} d e^{4}}{\left(a e - b d\right)^{3}} - \frac{12 a^{2} b^{3} d^{2} e^{3}}{\left(a e - b d\right)^{3}} + \frac{8 a b^{4} d^{3} e^{2}}{\left(a e - b d\right)^{3}} + 2 a b e^{2} - \frac{2 b^{5} d^{4} e}{\left(a e - b d\right)^{3}} + 2 b^{2} d e}{4 b^{2} e^{2}} \right)}}{\left(a e - b d\right)^{3}} + \frac{2 b e \log{\left(x + \frac{\frac{2 a^{4} b e^{5}}{\left(a e - b d\right)^{3}} - \frac{8 a^{3} b^{2} d e^{4}}{\left(a e - b d\right)^{3}} + \frac{12 a^{2} b^{3} d^{2} e^{3}}{\left(a e - b d\right)^{3}} - \frac{8 a b^{4} d^{3} e^{2}}{\left(a e - b d\right)^{3}} + 2 a b e^{2} + \frac{2 b^{5} d^{4} e}{\left(a e - b d\right)^{3}} + 2 b^{2} d e}{4 b^{2} e^{2}} \right)}}{\left(a e - b d\right)^{3}} + \frac{- a e - b d - 2 b e x}{a^{3} d e^{2} - 2 a^{2} b d^{2} e + a b^{2} d^{3} + x^{2} \left(a^{2} b e^{3} - 2 a b^{2} d e^{2} + b^{3} d^{2} e\right) + x \left(a^{3} e^{3} - a^{2} b d e^{2} - a b^{2} d^{2} e + b^{3} d^{3}\right)}"," ",0,"-2*b*e*log(x + (-2*a**4*b*e**5/(a*e - b*d)**3 + 8*a**3*b**2*d*e**4/(a*e - b*d)**3 - 12*a**2*b**3*d**2*e**3/(a*e - b*d)**3 + 8*a*b**4*d**3*e**2/(a*e - b*d)**3 + 2*a*b*e**2 - 2*b**5*d**4*e/(a*e - b*d)**3 + 2*b**2*d*e)/(4*b**2*e**2))/(a*e - b*d)**3 + 2*b*e*log(x + (2*a**4*b*e**5/(a*e - b*d)**3 - 8*a**3*b**2*d*e**4/(a*e - b*d)**3 + 12*a**2*b**3*d**2*e**3/(a*e - b*d)**3 - 8*a*b**4*d**3*e**2/(a*e - b*d)**3 + 2*a*b*e**2 + 2*b**5*d**4*e/(a*e - b*d)**3 + 2*b**2*d*e)/(4*b**2*e**2))/(a*e - b*d)**3 + (-a*e - b*d - 2*b*e*x)/(a**3*d*e**2 - 2*a**2*b*d**2*e + a*b**2*d**3 + x**2*(a**2*b*e**3 - 2*a*b**2*d*e**2 + b**3*d**2*e) + x*(a**3*e**3 - a**2*b*d*e**2 - a*b**2*d**2*e + b**3*d**3))","B",0
1513,1,632,0,1.737880," ","integrate(1/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2),x)","\frac{3 b^{2} e \log{\left(x + \frac{- \frac{3 a^{5} b^{2} e^{6}}{\left(a e - b d\right)^{4}} + \frac{15 a^{4} b^{3} d e^{5}}{\left(a e - b d\right)^{4}} - \frac{30 a^{3} b^{4} d^{2} e^{4}}{\left(a e - b d\right)^{4}} + \frac{30 a^{2} b^{5} d^{3} e^{3}}{\left(a e - b d\right)^{4}} - \frac{15 a b^{6} d^{4} e^{2}}{\left(a e - b d\right)^{4}} + 3 a b^{2} e^{2} + \frac{3 b^{7} d^{5} e}{\left(a e - b d\right)^{4}} + 3 b^{3} d e}{6 b^{3} e^{2}} \right)}}{\left(a e - b d\right)^{4}} - \frac{3 b^{2} e \log{\left(x + \frac{\frac{3 a^{5} b^{2} e^{6}}{\left(a e - b d\right)^{4}} - \frac{15 a^{4} b^{3} d e^{5}}{\left(a e - b d\right)^{4}} + \frac{30 a^{3} b^{4} d^{2} e^{4}}{\left(a e - b d\right)^{4}} - \frac{30 a^{2} b^{5} d^{3} e^{3}}{\left(a e - b d\right)^{4}} + \frac{15 a b^{6} d^{4} e^{2}}{\left(a e - b d\right)^{4}} + 3 a b^{2} e^{2} - \frac{3 b^{7} d^{5} e}{\left(a e - b d\right)^{4}} + 3 b^{3} d e}{6 b^{3} e^{2}} \right)}}{\left(a e - b d\right)^{4}} + \frac{- a^{2} e^{2} + 5 a b d e + 2 b^{2} d^{2} + 6 b^{2} e^{2} x^{2} + x \left(3 a b e^{2} + 9 b^{2} d e\right)}{2 a^{4} d^{2} e^{3} - 6 a^{3} b d^{3} e^{2} + 6 a^{2} b^{2} d^{4} e - 2 a b^{3} d^{5} + x^{3} \left(2 a^{3} b e^{5} - 6 a^{2} b^{2} d e^{4} + 6 a b^{3} d^{2} e^{3} - 2 b^{4} d^{3} e^{2}\right) + x^{2} \left(2 a^{4} e^{5} - 2 a^{3} b d e^{4} - 6 a^{2} b^{2} d^{2} e^{3} + 10 a b^{3} d^{3} e^{2} - 4 b^{4} d^{4} e\right) + x \left(4 a^{4} d e^{4} - 10 a^{3} b d^{2} e^{3} + 6 a^{2} b^{2} d^{3} e^{2} + 2 a b^{3} d^{4} e - 2 b^{4} d^{5}\right)}"," ",0,"3*b**2*e*log(x + (-3*a**5*b**2*e**6/(a*e - b*d)**4 + 15*a**4*b**3*d*e**5/(a*e - b*d)**4 - 30*a**3*b**4*d**2*e**4/(a*e - b*d)**4 + 30*a**2*b**5*d**3*e**3/(a*e - b*d)**4 - 15*a*b**6*d**4*e**2/(a*e - b*d)**4 + 3*a*b**2*e**2 + 3*b**7*d**5*e/(a*e - b*d)**4 + 3*b**3*d*e)/(6*b**3*e**2))/(a*e - b*d)**4 - 3*b**2*e*log(x + (3*a**5*b**2*e**6/(a*e - b*d)**4 - 15*a**4*b**3*d*e**5/(a*e - b*d)**4 + 30*a**3*b**4*d**2*e**4/(a*e - b*d)**4 - 30*a**2*b**5*d**3*e**3/(a*e - b*d)**4 + 15*a*b**6*d**4*e**2/(a*e - b*d)**4 + 3*a*b**2*e**2 - 3*b**7*d**5*e/(a*e - b*d)**4 + 3*b**3*d*e)/(6*b**3*e**2))/(a*e - b*d)**4 + (-a**2*e**2 + 5*a*b*d*e + 2*b**2*d**2 + 6*b**2*e**2*x**2 + x*(3*a*b*e**2 + 9*b**2*d*e))/(2*a**4*d**2*e**3 - 6*a**3*b*d**3*e**2 + 6*a**2*b**2*d**4*e - 2*a*b**3*d**5 + x**3*(2*a**3*b*e**5 - 6*a**2*b**2*d*e**4 + 6*a*b**3*d**2*e**3 - 2*b**4*d**3*e**2) + x**2*(2*a**4*e**5 - 2*a**3*b*d*e**4 - 6*a**2*b**2*d**2*e**3 + 10*a*b**3*d**3*e**2 - 4*b**4*d**4*e) + x*(4*a**4*d*e**4 - 10*a**3*b*d**2*e**3 + 6*a**2*b**2*d**3*e**2 + 2*a*b**3*d**4*e - 2*b**4*d**5))","B",0
1514,1,882,0,2.406189," ","integrate(1/(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2),x)","- \frac{4 b^{3} e \log{\left(x + \frac{- \frac{4 a^{6} b^{3} e^{7}}{\left(a e - b d\right)^{5}} + \frac{24 a^{5} b^{4} d e^{6}}{\left(a e - b d\right)^{5}} - \frac{60 a^{4} b^{5} d^{2} e^{5}}{\left(a e - b d\right)^{5}} + \frac{80 a^{3} b^{6} d^{3} e^{4}}{\left(a e - b d\right)^{5}} - \frac{60 a^{2} b^{7} d^{4} e^{3}}{\left(a e - b d\right)^{5}} + \frac{24 a b^{8} d^{5} e^{2}}{\left(a e - b d\right)^{5}} + 4 a b^{3} e^{2} - \frac{4 b^{9} d^{6} e}{\left(a e - b d\right)^{5}} + 4 b^{4} d e}{8 b^{4} e^{2}} \right)}}{\left(a e - b d\right)^{5}} + \frac{4 b^{3} e \log{\left(x + \frac{\frac{4 a^{6} b^{3} e^{7}}{\left(a e - b d\right)^{5}} - \frac{24 a^{5} b^{4} d e^{6}}{\left(a e - b d\right)^{5}} + \frac{60 a^{4} b^{5} d^{2} e^{5}}{\left(a e - b d\right)^{5}} - \frac{80 a^{3} b^{6} d^{3} e^{4}}{\left(a e - b d\right)^{5}} + \frac{60 a^{2} b^{7} d^{4} e^{3}}{\left(a e - b d\right)^{5}} - \frac{24 a b^{8} d^{5} e^{2}}{\left(a e - b d\right)^{5}} + 4 a b^{3} e^{2} + \frac{4 b^{9} d^{6} e}{\left(a e - b d\right)^{5}} + 4 b^{4} d e}{8 b^{4} e^{2}} \right)}}{\left(a e - b d\right)^{5}} + \frac{- a^{3} e^{3} + 5 a^{2} b d e^{2} - 13 a b^{2} d^{2} e - 3 b^{3} d^{3} - 12 b^{3} e^{3} x^{3} + x^{2} \left(- 6 a b^{2} e^{3} - 30 b^{3} d e^{2}\right) + x \left(2 a^{2} b e^{3} - 16 a b^{2} d e^{2} - 22 b^{3} d^{2} e\right)}{3 a^{5} d^{3} e^{4} - 12 a^{4} b d^{4} e^{3} + 18 a^{3} b^{2} d^{5} e^{2} - 12 a^{2} b^{3} d^{6} e + 3 a b^{4} d^{7} + x^{4} \left(3 a^{4} b e^{7} - 12 a^{3} b^{2} d e^{6} + 18 a^{2} b^{3} d^{2} e^{5} - 12 a b^{4} d^{3} e^{4} + 3 b^{5} d^{4} e^{3}\right) + x^{3} \left(3 a^{5} e^{7} - 3 a^{4} b d e^{6} - 18 a^{3} b^{2} d^{2} e^{5} + 42 a^{2} b^{3} d^{3} e^{4} - 33 a b^{4} d^{4} e^{3} + 9 b^{5} d^{5} e^{2}\right) + x^{2} \left(9 a^{5} d e^{6} - 27 a^{4} b d^{2} e^{5} + 18 a^{3} b^{2} d^{3} e^{4} + 18 a^{2} b^{3} d^{4} e^{3} - 27 a b^{4} d^{5} e^{2} + 9 b^{5} d^{6} e\right) + x \left(9 a^{5} d^{2} e^{5} - 33 a^{4} b d^{3} e^{4} + 42 a^{3} b^{2} d^{4} e^{3} - 18 a^{2} b^{3} d^{5} e^{2} - 3 a b^{4} d^{6} e + 3 b^{5} d^{7}\right)}"," ",0,"-4*b**3*e*log(x + (-4*a**6*b**3*e**7/(a*e - b*d)**5 + 24*a**5*b**4*d*e**6/(a*e - b*d)**5 - 60*a**4*b**5*d**2*e**5/(a*e - b*d)**5 + 80*a**3*b**6*d**3*e**4/(a*e - b*d)**5 - 60*a**2*b**7*d**4*e**3/(a*e - b*d)**5 + 24*a*b**8*d**5*e**2/(a*e - b*d)**5 + 4*a*b**3*e**2 - 4*b**9*d**6*e/(a*e - b*d)**5 + 4*b**4*d*e)/(8*b**4*e**2))/(a*e - b*d)**5 + 4*b**3*e*log(x + (4*a**6*b**3*e**7/(a*e - b*d)**5 - 24*a**5*b**4*d*e**6/(a*e - b*d)**5 + 60*a**4*b**5*d**2*e**5/(a*e - b*d)**5 - 80*a**3*b**6*d**3*e**4/(a*e - b*d)**5 + 60*a**2*b**7*d**4*e**3/(a*e - b*d)**5 - 24*a*b**8*d**5*e**2/(a*e - b*d)**5 + 4*a*b**3*e**2 + 4*b**9*d**6*e/(a*e - b*d)**5 + 4*b**4*d*e)/(8*b**4*e**2))/(a*e - b*d)**5 + (-a**3*e**3 + 5*a**2*b*d*e**2 - 13*a*b**2*d**2*e - 3*b**3*d**3 - 12*b**3*e**3*x**3 + x**2*(-6*a*b**2*e**3 - 30*b**3*d*e**2) + x*(2*a**2*b*e**3 - 16*a*b**2*d*e**2 - 22*b**3*d**2*e))/(3*a**5*d**3*e**4 - 12*a**4*b*d**4*e**3 + 18*a**3*b**2*d**5*e**2 - 12*a**2*b**3*d**6*e + 3*a*b**4*d**7 + x**4*(3*a**4*b*e**7 - 12*a**3*b**2*d*e**6 + 18*a**2*b**3*d**2*e**5 - 12*a*b**4*d**3*e**4 + 3*b**5*d**4*e**3) + x**3*(3*a**5*e**7 - 3*a**4*b*d*e**6 - 18*a**3*b**2*d**2*e**5 + 42*a**2*b**3*d**3*e**4 - 33*a*b**4*d**4*e**3 + 9*b**5*d**5*e**2) + x**2*(9*a**5*d*e**6 - 27*a**4*b*d**2*e**5 + 18*a**3*b**2*d**3*e**4 + 18*a**2*b**3*d**4*e**3 - 27*a*b**4*d**5*e**2 + 9*b**5*d**6*e) + x*(9*a**5*d**2*e**5 - 33*a**4*b*d**3*e**4 + 42*a**3*b**2*d**4*e**3 - 18*a**2*b**3*d**5*e**2 - 3*a*b**4*d**6*e + 3*b**5*d**7))","B",0
1515,1,367,0,4.373899," ","integrate((e*x+d)**6/(b**2*x**2+2*a*b*x+a**2)**2,x)","x^{2} \left(- \frac{2 a e^{6}}{b^{5}} + \frac{3 d e^{5}}{b^{4}}\right) + x \left(\frac{10 a^{2} e^{6}}{b^{6}} - \frac{24 a d e^{5}}{b^{5}} + \frac{15 d^{2} e^{4}}{b^{4}}\right) + \frac{- 37 a^{6} e^{6} + 141 a^{5} b d e^{5} - 195 a^{4} b^{2} d^{2} e^{4} + 110 a^{3} b^{3} d^{3} e^{3} - 15 a^{2} b^{4} d^{4} e^{2} - 3 a b^{5} d^{5} e - b^{6} d^{6} + x^{2} \left(- 45 a^{4} b^{2} e^{6} + 180 a^{3} b^{3} d e^{5} - 270 a^{2} b^{4} d^{2} e^{4} + 180 a b^{5} d^{3} e^{3} - 45 b^{6} d^{4} e^{2}\right) + x \left(- 81 a^{5} b e^{6} + 315 a^{4} b^{2} d e^{5} - 450 a^{3} b^{3} d^{2} e^{4} + 270 a^{2} b^{4} d^{3} e^{3} - 45 a b^{5} d^{4} e^{2} - 9 b^{6} d^{5} e\right)}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{e^{6} x^{3}}{3 b^{4}} - \frac{20 e^{3} \left(a e - b d\right)^{3} \log{\left(a + b x \right)}}{b^{7}}"," ",0,"x**2*(-2*a*e**6/b**5 + 3*d*e**5/b**4) + x*(10*a**2*e**6/b**6 - 24*a*d*e**5/b**5 + 15*d**2*e**4/b**4) + (-37*a**6*e**6 + 141*a**5*b*d*e**5 - 195*a**4*b**2*d**2*e**4 + 110*a**3*b**3*d**3*e**3 - 15*a**2*b**4*d**4*e**2 - 3*a*b**5*d**5*e - b**6*d**6 + x**2*(-45*a**4*b**2*e**6 + 180*a**3*b**3*d*e**5 - 270*a**2*b**4*d**2*e**4 + 180*a*b**5*d**3*e**3 - 45*b**6*d**4*e**2) + x*(-81*a**5*b*e**6 + 315*a**4*b**2*d*e**5 - 450*a**3*b**3*d**2*e**4 + 270*a**2*b**4*d**3*e**3 - 45*a*b**5*d**4*e**2 - 9*b**6*d**5*e))/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + e**6*x**3/(3*b**4) - 20*e**3*(a*e - b*d)**3*log(a + b*x)/b**7","B",0
1516,1,284,0,2.935604," ","integrate((e*x+d)**5/(b**2*x**2+2*a*b*x+a**2)**2,x)","x \left(- \frac{4 a e^{5}}{b^{5}} + \frac{5 d e^{4}}{b^{4}}\right) + \frac{47 a^{5} e^{5} - 130 a^{4} b d e^{4} + 110 a^{3} b^{2} d^{2} e^{3} - 20 a^{2} b^{3} d^{3} e^{2} - 5 a b^{4} d^{4} e - 2 b^{5} d^{5} + x^{2} \left(60 a^{3} b^{2} e^{5} - 180 a^{2} b^{3} d e^{4} + 180 a b^{4} d^{2} e^{3} - 60 b^{5} d^{3} e^{2}\right) + x \left(105 a^{4} b e^{5} - 300 a^{3} b^{2} d e^{4} + 270 a^{2} b^{3} d^{2} e^{3} - 60 a b^{4} d^{3} e^{2} - 15 b^{5} d^{4} e\right)}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{e^{5} x^{2}}{2 b^{4}} + \frac{10 e^{3} \left(a e - b d\right)^{2} \log{\left(a + b x \right)}}{b^{6}}"," ",0,"x*(-4*a*e**5/b**5 + 5*d*e**4/b**4) + (47*a**5*e**5 - 130*a**4*b*d*e**4 + 110*a**3*b**2*d**2*e**3 - 20*a**2*b**3*d**3*e**2 - 5*a*b**4*d**4*e - 2*b**5*d**5 + x**2*(60*a**3*b**2*e**5 - 180*a**2*b**3*d*e**4 + 180*a*b**4*d**2*e**3 - 60*b**5*d**3*e**2) + x*(105*a**4*b*e**5 - 300*a**3*b**2*d*e**4 + 270*a**2*b**3*d**2*e**3 - 60*a*b**4*d**3*e**2 - 15*b**5*d**4*e))/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + e**5*x**2/(2*b**4) + 10*e**3*(a*e - b*d)**2*log(a + b*x)/b**6","B",0
1517,1,209,0,1.939253," ","integrate((e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- 13 a^{4} e^{4} + 22 a^{3} b d e^{3} - 6 a^{2} b^{2} d^{2} e^{2} - 2 a b^{3} d^{3} e - b^{4} d^{4} + x^{2} \left(- 18 a^{2} b^{2} e^{4} + 36 a b^{3} d e^{3} - 18 b^{4} d^{2} e^{2}\right) + x \left(- 30 a^{3} b e^{4} + 54 a^{2} b^{2} d e^{3} - 18 a b^{3} d^{2} e^{2} - 6 b^{4} d^{3} e\right)}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} + \frac{e^{4} x}{b^{4}} - \frac{4 e^{3} \left(a e - b d\right) \log{\left(a + b x \right)}}{b^{5}}"," ",0,"(-13*a**4*e**4 + 22*a**3*b*d*e**3 - 6*a**2*b**2*d**2*e**2 - 2*a*b**3*d**3*e - b**4*d**4 + x**2*(-18*a**2*b**2*e**4 + 36*a*b**3*d*e**3 - 18*b**4*d**2*e**2) + x*(-30*a**3*b*e**4 + 54*a**2*b**2*d*e**3 - 18*a*b**3*d**2*e**2 - 6*b**4*d**3*e))/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) + e**4*x/b**4 - 4*e**3*(a*e - b*d)*log(a + b*x)/b**5","B",0
1518,1,148,0,1.141811," ","integrate((e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{11 a^{3} e^{3} - 6 a^{2} b d e^{2} - 3 a b^{2} d^{2} e - 2 b^{3} d^{3} + x^{2} \left(18 a b^{2} e^{3} - 18 b^{3} d e^{2}\right) + x \left(27 a^{2} b e^{3} - 18 a b^{2} d e^{2} - 9 b^{3} d^{2} e\right)}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{e^{3} \log{\left(a + b x \right)}}{b^{4}}"," ",0,"(11*a**3*e**3 - 6*a**2*b*d*e**2 - 3*a*b**2*d**2*e - 2*b**3*d**3 + x**2*(18*a*b**2*e**3 - 18*b**3*d*e**2) + x*(27*a**2*b*e**3 - 18*a*b**2*d*e**2 - 9*b**3*d**2*e))/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + e**3*log(a + b*x)/b**4","A",0
1519,1,88,0,0.609680," ","integrate((e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- a^{2} e^{2} - a b d e - b^{2} d^{2} - 3 b^{2} e^{2} x^{2} + x \left(- 3 a b e^{2} - 3 b^{2} d e\right)}{3 a^{3} b^{3} + 9 a^{2} b^{4} x + 9 a b^{5} x^{2} + 3 b^{6} x^{3}}"," ",0,"(-a**2*e**2 - a*b*d*e - b**2*d**2 - 3*b**2*e**2*x**2 + x*(-3*a*b*e**2 - 3*b**2*d*e))/(3*a**3*b**3 + 9*a**2*b**4*x + 9*a*b**5*x**2 + 3*b**6*x**3)","B",0
1520,1,53,0,0.354549," ","integrate((e*x+d)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- a e - 2 b d - 3 b e x}{6 a^{3} b^{2} + 18 a^{2} b^{3} x + 18 a b^{4} x^{2} + 6 b^{5} x^{3}}"," ",0,"(-a*e - 2*b*d - 3*b*e*x)/(6*a**3*b**2 + 18*a**2*b**3*x + 18*a*b**4*x**2 + 6*b**5*x**3)","A",0
1521,1,37,0,0.238552," ","integrate(1/(b**2*x**2+2*a*b*x+a**2)**2,x)","- \frac{1}{3 a^{3} b + 9 a^{2} b^{2} x + 9 a b^{3} x^{2} + 3 b^{4} x^{3}}"," ",0,"-1/(3*a**3*b + 9*a**2*b**2*x + 9*a*b**3*x**2 + 3*b**4*x**3)","B",0
1522,1,570,0,1.581339," ","integrate(1/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{e^{3} \log{\left(x + \frac{- \frac{a^{5} e^{8}}{\left(a e - b d\right)^{4}} + \frac{5 a^{4} b d e^{7}}{\left(a e - b d\right)^{4}} - \frac{10 a^{3} b^{2} d^{2} e^{6}}{\left(a e - b d\right)^{4}} + \frac{10 a^{2} b^{3} d^{3} e^{5}}{\left(a e - b d\right)^{4}} - \frac{5 a b^{4} d^{4} e^{4}}{\left(a e - b d\right)^{4}} + a e^{4} + \frac{b^{5} d^{5} e^{3}}{\left(a e - b d\right)^{4}} + b d e^{3}}{2 b e^{4}} \right)}}{\left(a e - b d\right)^{4}} - \frac{e^{3} \log{\left(x + \frac{\frac{a^{5} e^{8}}{\left(a e - b d\right)^{4}} - \frac{5 a^{4} b d e^{7}}{\left(a e - b d\right)^{4}} + \frac{10 a^{3} b^{2} d^{2} e^{6}}{\left(a e - b d\right)^{4}} - \frac{10 a^{2} b^{3} d^{3} e^{5}}{\left(a e - b d\right)^{4}} + \frac{5 a b^{4} d^{4} e^{4}}{\left(a e - b d\right)^{4}} + a e^{4} - \frac{b^{5} d^{5} e^{3}}{\left(a e - b d\right)^{4}} + b d e^{3}}{2 b e^{4}} \right)}}{\left(a e - b d\right)^{4}} + \frac{11 a^{2} e^{2} - 7 a b d e + 2 b^{2} d^{2} + 6 b^{2} e^{2} x^{2} + x \left(15 a b e^{2} - 3 b^{2} d e\right)}{6 a^{6} e^{3} - 18 a^{5} b d e^{2} + 18 a^{4} b^{2} d^{2} e - 6 a^{3} b^{3} d^{3} + x^{3} \left(6 a^{3} b^{3} e^{3} - 18 a^{2} b^{4} d e^{2} + 18 a b^{5} d^{2} e - 6 b^{6} d^{3}\right) + x^{2} \left(18 a^{4} b^{2} e^{3} - 54 a^{3} b^{3} d e^{2} + 54 a^{2} b^{4} d^{2} e - 18 a b^{5} d^{3}\right) + x \left(18 a^{5} b e^{3} - 54 a^{4} b^{2} d e^{2} + 54 a^{3} b^{3} d^{2} e - 18 a^{2} b^{4} d^{3}\right)}"," ",0,"e**3*log(x + (-a**5*e**8/(a*e - b*d)**4 + 5*a**4*b*d*e**7/(a*e - b*d)**4 - 10*a**3*b**2*d**2*e**6/(a*e - b*d)**4 + 10*a**2*b**3*d**3*e**5/(a*e - b*d)**4 - 5*a*b**4*d**4*e**4/(a*e - b*d)**4 + a*e**4 + b**5*d**5*e**3/(a*e - b*d)**4 + b*d*e**3)/(2*b*e**4))/(a*e - b*d)**4 - e**3*log(x + (a**5*e**8/(a*e - b*d)**4 - 5*a**4*b*d*e**7/(a*e - b*d)**4 + 10*a**3*b**2*d**2*e**6/(a*e - b*d)**4 - 10*a**2*b**3*d**3*e**5/(a*e - b*d)**4 + 5*a*b**4*d**4*e**4/(a*e - b*d)**4 + a*e**4 - b**5*d**5*e**3/(a*e - b*d)**4 + b*d*e**3)/(2*b*e**4))/(a*e - b*d)**4 + (11*a**2*e**2 - 7*a*b*d*e + 2*b**2*d**2 + 6*b**2*e**2*x**2 + x*(15*a*b*e**2 - 3*b**2*d*e))/(6*a**6*e**3 - 18*a**5*b*d*e**2 + 18*a**4*b**2*d**2*e - 6*a**3*b**3*d**3 + x**3*(6*a**3*b**3*e**3 - 18*a**2*b**4*d*e**2 + 18*a*b**5*d**2*e - 6*b**6*d**3) + x**2*(18*a**4*b**2*e**3 - 54*a**3*b**3*d*e**2 + 54*a**2*b**4*d**2*e - 18*a*b**5*d**3) + x*(18*a**5*b*e**3 - 54*a**4*b**2*d*e**2 + 54*a**3*b**3*d**2*e - 18*a**2*b**4*d**3))","B",0
1523,1,882,0,2.478110," ","integrate(1/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**2,x)","- \frac{4 b e^{3} \log{\left(x + \frac{- \frac{4 a^{6} b e^{9}}{\left(a e - b d\right)^{5}} + \frac{24 a^{5} b^{2} d e^{8}}{\left(a e - b d\right)^{5}} - \frac{60 a^{4} b^{3} d^{2} e^{7}}{\left(a e - b d\right)^{5}} + \frac{80 a^{3} b^{4} d^{3} e^{6}}{\left(a e - b d\right)^{5}} - \frac{60 a^{2} b^{5} d^{4} e^{5}}{\left(a e - b d\right)^{5}} + \frac{24 a b^{6} d^{5} e^{4}}{\left(a e - b d\right)^{5}} + 4 a b e^{4} - \frac{4 b^{7} d^{6} e^{3}}{\left(a e - b d\right)^{5}} + 4 b^{2} d e^{3}}{8 b^{2} e^{4}} \right)}}{\left(a e - b d\right)^{5}} + \frac{4 b e^{3} \log{\left(x + \frac{\frac{4 a^{6} b e^{9}}{\left(a e - b d\right)^{5}} - \frac{24 a^{5} b^{2} d e^{8}}{\left(a e - b d\right)^{5}} + \frac{60 a^{4} b^{3} d^{2} e^{7}}{\left(a e - b d\right)^{5}} - \frac{80 a^{3} b^{4} d^{3} e^{6}}{\left(a e - b d\right)^{5}} + \frac{60 a^{2} b^{5} d^{4} e^{5}}{\left(a e - b d\right)^{5}} - \frac{24 a b^{6} d^{5} e^{4}}{\left(a e - b d\right)^{5}} + 4 a b e^{4} + \frac{4 b^{7} d^{6} e^{3}}{\left(a e - b d\right)^{5}} + 4 b^{2} d e^{3}}{8 b^{2} e^{4}} \right)}}{\left(a e - b d\right)^{5}} + \frac{- 3 a^{3} e^{3} - 13 a^{2} b d e^{2} + 5 a b^{2} d^{2} e - b^{3} d^{3} - 12 b^{3} e^{3} x^{3} + x^{2} \left(- 30 a b^{2} e^{3} - 6 b^{3} d e^{2}\right) + x \left(- 22 a^{2} b e^{3} - 16 a b^{2} d e^{2} + 2 b^{3} d^{2} e\right)}{3 a^{7} d e^{4} - 12 a^{6} b d^{2} e^{3} + 18 a^{5} b^{2} d^{3} e^{2} - 12 a^{4} b^{3} d^{4} e + 3 a^{3} b^{4} d^{5} + x^{4} \left(3 a^{4} b^{3} e^{5} - 12 a^{3} b^{4} d e^{4} + 18 a^{2} b^{5} d^{2} e^{3} - 12 a b^{6} d^{3} e^{2} + 3 b^{7} d^{4} e\right) + x^{3} \left(9 a^{5} b^{2} e^{5} - 33 a^{4} b^{3} d e^{4} + 42 a^{3} b^{4} d^{2} e^{3} - 18 a^{2} b^{5} d^{3} e^{2} - 3 a b^{6} d^{4} e + 3 b^{7} d^{5}\right) + x^{2} \left(9 a^{6} b e^{5} - 27 a^{5} b^{2} d e^{4} + 18 a^{4} b^{3} d^{2} e^{3} + 18 a^{3} b^{4} d^{3} e^{2} - 27 a^{2} b^{5} d^{4} e + 9 a b^{6} d^{5}\right) + x \left(3 a^{7} e^{5} - 3 a^{6} b d e^{4} - 18 a^{5} b^{2} d^{2} e^{3} + 42 a^{4} b^{3} d^{3} e^{2} - 33 a^{3} b^{4} d^{4} e + 9 a^{2} b^{5} d^{5}\right)}"," ",0,"-4*b*e**3*log(x + (-4*a**6*b*e**9/(a*e - b*d)**5 + 24*a**5*b**2*d*e**8/(a*e - b*d)**5 - 60*a**4*b**3*d**2*e**7/(a*e - b*d)**5 + 80*a**3*b**4*d**3*e**6/(a*e - b*d)**5 - 60*a**2*b**5*d**4*e**5/(a*e - b*d)**5 + 24*a*b**6*d**5*e**4/(a*e - b*d)**5 + 4*a*b*e**4 - 4*b**7*d**6*e**3/(a*e - b*d)**5 + 4*b**2*d*e**3)/(8*b**2*e**4))/(a*e - b*d)**5 + 4*b*e**3*log(x + (4*a**6*b*e**9/(a*e - b*d)**5 - 24*a**5*b**2*d*e**8/(a*e - b*d)**5 + 60*a**4*b**3*d**2*e**7/(a*e - b*d)**5 - 80*a**3*b**4*d**3*e**6/(a*e - b*d)**5 + 60*a**2*b**5*d**4*e**5/(a*e - b*d)**5 - 24*a*b**6*d**5*e**4/(a*e - b*d)**5 + 4*a*b*e**4 + 4*b**7*d**6*e**3/(a*e - b*d)**5 + 4*b**2*d*e**3)/(8*b**2*e**4))/(a*e - b*d)**5 + (-3*a**3*e**3 - 13*a**2*b*d*e**2 + 5*a*b**2*d**2*e - b**3*d**3 - 12*b**3*e**3*x**3 + x**2*(-30*a*b**2*e**3 - 6*b**3*d*e**2) + x*(-22*a**2*b*e**3 - 16*a*b**2*d*e**2 + 2*b**3*d**2*e))/(3*a**7*d*e**4 - 12*a**6*b*d**2*e**3 + 18*a**5*b**2*d**3*e**2 - 12*a**4*b**3*d**4*e + 3*a**3*b**4*d**5 + x**4*(3*a**4*b**3*e**5 - 12*a**3*b**4*d*e**4 + 18*a**2*b**5*d**2*e**3 - 12*a*b**6*d**3*e**2 + 3*b**7*d**4*e) + x**3*(9*a**5*b**2*e**5 - 33*a**4*b**3*d*e**4 + 42*a**3*b**4*d**2*e**3 - 18*a**2*b**5*d**3*e**2 - 3*a*b**6*d**4*e + 3*b**7*d**5) + x**2*(9*a**6*b*e**5 - 27*a**5*b**2*d*e**4 + 18*a**4*b**3*d**2*e**3 + 18*a**3*b**4*d**3*e**2 - 27*a**2*b**5*d**4*e + 9*a*b**6*d**5) + x*(3*a**7*e**5 - 3*a**6*b*d*e**4 - 18*a**5*b**2*d**2*e**3 + 42*a**4*b**3*d**3*e**2 - 33*a**3*b**4*d**4*e + 9*a**2*b**5*d**5))","B",0
1524,1,1217,0,3.530501," ","integrate(1/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{10 b^{2} e^{3} \log{\left(x + \frac{- \frac{10 a^{7} b^{2} e^{10}}{\left(a e - b d\right)^{6}} + \frac{70 a^{6} b^{3} d e^{9}}{\left(a e - b d\right)^{6}} - \frac{210 a^{5} b^{4} d^{2} e^{8}}{\left(a e - b d\right)^{6}} + \frac{350 a^{4} b^{5} d^{3} e^{7}}{\left(a e - b d\right)^{6}} - \frac{350 a^{3} b^{6} d^{4} e^{6}}{\left(a e - b d\right)^{6}} + \frac{210 a^{2} b^{7} d^{5} e^{5}}{\left(a e - b d\right)^{6}} - \frac{70 a b^{8} d^{6} e^{4}}{\left(a e - b d\right)^{6}} + 10 a b^{2} e^{4} + \frac{10 b^{9} d^{7} e^{3}}{\left(a e - b d\right)^{6}} + 10 b^{3} d e^{3}}{20 b^{3} e^{4}} \right)}}{\left(a e - b d\right)^{6}} - \frac{10 b^{2} e^{3} \log{\left(x + \frac{\frac{10 a^{7} b^{2} e^{10}}{\left(a e - b d\right)^{6}} - \frac{70 a^{6} b^{3} d e^{9}}{\left(a e - b d\right)^{6}} + \frac{210 a^{5} b^{4} d^{2} e^{8}}{\left(a e - b d\right)^{6}} - \frac{350 a^{4} b^{5} d^{3} e^{7}}{\left(a e - b d\right)^{6}} + \frac{350 a^{3} b^{6} d^{4} e^{6}}{\left(a e - b d\right)^{6}} - \frac{210 a^{2} b^{7} d^{5} e^{5}}{\left(a e - b d\right)^{6}} + \frac{70 a b^{8} d^{6} e^{4}}{\left(a e - b d\right)^{6}} + 10 a b^{2} e^{4} - \frac{10 b^{9} d^{7} e^{3}}{\left(a e - b d\right)^{6}} + 10 b^{3} d e^{3}}{20 b^{3} e^{4}} \right)}}{\left(a e - b d\right)^{6}} + \frac{- 3 a^{4} e^{4} + 27 a^{3} b d e^{3} + 47 a^{2} b^{2} d^{2} e^{2} - 13 a b^{3} d^{3} e + 2 b^{4} d^{4} + 60 b^{4} e^{4} x^{4} + x^{3} \left(150 a b^{3} e^{4} + 90 b^{4} d e^{3}\right) + x^{2} \left(110 a^{2} b^{2} e^{4} + 230 a b^{3} d e^{3} + 20 b^{4} d^{2} e^{2}\right) + x \left(15 a^{3} b e^{4} + 175 a^{2} b^{2} d e^{3} + 55 a b^{3} d^{2} e^{2} - 5 b^{4} d^{3} e\right)}{6 a^{8} d^{2} e^{5} - 30 a^{7} b d^{3} e^{4} + 60 a^{6} b^{2} d^{4} e^{3} - 60 a^{5} b^{3} d^{5} e^{2} + 30 a^{4} b^{4} d^{6} e - 6 a^{3} b^{5} d^{7} + x^{5} \left(6 a^{5} b^{3} e^{7} - 30 a^{4} b^{4} d e^{6} + 60 a^{3} b^{5} d^{2} e^{5} - 60 a^{2} b^{6} d^{3} e^{4} + 30 a b^{7} d^{4} e^{3} - 6 b^{8} d^{5} e^{2}\right) + x^{4} \left(18 a^{6} b^{2} e^{7} - 78 a^{5} b^{3} d e^{6} + 120 a^{4} b^{4} d^{2} e^{5} - 60 a^{3} b^{5} d^{3} e^{4} - 30 a^{2} b^{6} d^{4} e^{3} + 42 a b^{7} d^{5} e^{2} - 12 b^{8} d^{6} e\right) + x^{3} \left(18 a^{7} b e^{7} - 54 a^{6} b^{2} d e^{6} + 6 a^{5} b^{3} d^{2} e^{5} + 150 a^{4} b^{4} d^{3} e^{4} - 210 a^{3} b^{5} d^{4} e^{3} + 102 a^{2} b^{6} d^{5} e^{2} - 6 a b^{7} d^{6} e - 6 b^{8} d^{7}\right) + x^{2} \left(6 a^{8} e^{7} + 6 a^{7} b d e^{6} - 102 a^{6} b^{2} d^{2} e^{5} + 210 a^{5} b^{3} d^{3} e^{4} - 150 a^{4} b^{4} d^{4} e^{3} - 6 a^{3} b^{5} d^{5} e^{2} + 54 a^{2} b^{6} d^{6} e - 18 a b^{7} d^{7}\right) + x \left(12 a^{8} d e^{6} - 42 a^{7} b d^{2} e^{5} + 30 a^{6} b^{2} d^{3} e^{4} + 60 a^{5} b^{3} d^{4} e^{3} - 120 a^{4} b^{4} d^{5} e^{2} + 78 a^{3} b^{5} d^{6} e - 18 a^{2} b^{6} d^{7}\right)}"," ",0,"10*b**2*e**3*log(x + (-10*a**7*b**2*e**10/(a*e - b*d)**6 + 70*a**6*b**3*d*e**9/(a*e - b*d)**6 - 210*a**5*b**4*d**2*e**8/(a*e - b*d)**6 + 350*a**4*b**5*d**3*e**7/(a*e - b*d)**6 - 350*a**3*b**6*d**4*e**6/(a*e - b*d)**6 + 210*a**2*b**7*d**5*e**5/(a*e - b*d)**6 - 70*a*b**8*d**6*e**4/(a*e - b*d)**6 + 10*a*b**2*e**4 + 10*b**9*d**7*e**3/(a*e - b*d)**6 + 10*b**3*d*e**3)/(20*b**3*e**4))/(a*e - b*d)**6 - 10*b**2*e**3*log(x + (10*a**7*b**2*e**10/(a*e - b*d)**6 - 70*a**6*b**3*d*e**9/(a*e - b*d)**6 + 210*a**5*b**4*d**2*e**8/(a*e - b*d)**6 - 350*a**4*b**5*d**3*e**7/(a*e - b*d)**6 + 350*a**3*b**6*d**4*e**6/(a*e - b*d)**6 - 210*a**2*b**7*d**5*e**5/(a*e - b*d)**6 + 70*a*b**8*d**6*e**4/(a*e - b*d)**6 + 10*a*b**2*e**4 - 10*b**9*d**7*e**3/(a*e - b*d)**6 + 10*b**3*d*e**3)/(20*b**3*e**4))/(a*e - b*d)**6 + (-3*a**4*e**4 + 27*a**3*b*d*e**3 + 47*a**2*b**2*d**2*e**2 - 13*a*b**3*d**3*e + 2*b**4*d**4 + 60*b**4*e**4*x**4 + x**3*(150*a*b**3*e**4 + 90*b**4*d*e**3) + x**2*(110*a**2*b**2*e**4 + 230*a*b**3*d*e**3 + 20*b**4*d**2*e**2) + x*(15*a**3*b*e**4 + 175*a**2*b**2*d*e**3 + 55*a*b**3*d**2*e**2 - 5*b**4*d**3*e))/(6*a**8*d**2*e**5 - 30*a**7*b*d**3*e**4 + 60*a**6*b**2*d**4*e**3 - 60*a**5*b**3*d**5*e**2 + 30*a**4*b**4*d**6*e - 6*a**3*b**5*d**7 + x**5*(6*a**5*b**3*e**7 - 30*a**4*b**4*d*e**6 + 60*a**3*b**5*d**2*e**5 - 60*a**2*b**6*d**3*e**4 + 30*a*b**7*d**4*e**3 - 6*b**8*d**5*e**2) + x**4*(18*a**6*b**2*e**7 - 78*a**5*b**3*d*e**6 + 120*a**4*b**4*d**2*e**5 - 60*a**3*b**5*d**3*e**4 - 30*a**2*b**6*d**4*e**3 + 42*a*b**7*d**5*e**2 - 12*b**8*d**6*e) + x**3*(18*a**7*b*e**7 - 54*a**6*b**2*d*e**6 + 6*a**5*b**3*d**2*e**5 + 150*a**4*b**4*d**3*e**4 - 210*a**3*b**5*d**4*e**3 + 102*a**2*b**6*d**5*e**2 - 6*a*b**7*d**6*e - 6*b**8*d**7) + x**2*(6*a**8*e**7 + 6*a**7*b*d*e**6 - 102*a**6*b**2*d**2*e**5 + 210*a**5*b**3*d**3*e**4 - 150*a**4*b**4*d**4*e**3 - 6*a**3*b**5*d**5*e**2 + 54*a**2*b**6*d**6*e - 18*a*b**7*d**7) + x*(12*a**8*d*e**6 - 42*a**7*b*d**2*e**5 + 30*a**6*b**2*d**3*e**4 + 60*a**5*b**3*d**4*e**3 - 120*a**4*b**4*d**5*e**2 + 78*a**3*b**5*d**6*e - 18*a**2*b**6*d**7))","B",0
1525,-1,0,0,0.000000," ","integrate((e*x+d)**8/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1526,1,524,0,98.972325," ","integrate((e*x+d)**7/(b**2*x**2+2*a*b*x+a**2)**3,x)","x \left(- \frac{6 a e^{7}}{b^{7}} + \frac{7 d e^{6}}{b^{6}}\right) + \frac{459 a^{7} e^{7} - 1218 a^{6} b d e^{6} + 959 a^{5} b^{2} d^{2} e^{5} - 140 a^{4} b^{3} d^{3} e^{4} - 35 a^{3} b^{4} d^{4} e^{3} - 14 a^{2} b^{5} d^{5} e^{2} - 7 a b^{6} d^{6} e - 4 b^{7} d^{7} + x^{4} \left(700 a^{3} b^{4} e^{7} - 2100 a^{2} b^{5} d e^{6} + 2100 a b^{6} d^{2} e^{5} - 700 b^{7} d^{3} e^{4}\right) + x^{3} \left(2450 a^{4} b^{3} e^{7} - 7000 a^{3} b^{4} d e^{6} + 6300 a^{2} b^{5} d^{2} e^{5} - 1400 a b^{6} d^{3} e^{4} - 350 b^{7} d^{4} e^{3}\right) + x^{2} \left(3290 a^{5} b^{2} e^{7} - 9100 a^{4} b^{3} d e^{6} + 7700 a^{3} b^{4} d^{2} e^{5} - 1400 a^{2} b^{5} d^{3} e^{4} - 350 a b^{6} d^{4} e^{3} - 140 b^{7} d^{5} e^{2}\right) + x \left(1995 a^{6} b e^{7} - 5390 a^{5} b^{2} d e^{6} + 4375 a^{4} b^{3} d^{2} e^{5} - 700 a^{3} b^{4} d^{3} e^{4} - 175 a^{2} b^{5} d^{4} e^{3} - 70 a b^{6} d^{5} e^{2} - 35 b^{7} d^{6} e\right)}{20 a^{5} b^{8} + 100 a^{4} b^{9} x + 200 a^{3} b^{10} x^{2} + 200 a^{2} b^{11} x^{3} + 100 a b^{12} x^{4} + 20 b^{13} x^{5}} + \frac{e^{7} x^{2}}{2 b^{6}} + \frac{21 e^{5} \left(a e - b d\right)^{2} \log{\left(a + b x \right)}}{b^{8}}"," ",0,"x*(-6*a*e**7/b**7 + 7*d*e**6/b**6) + (459*a**7*e**7 - 1218*a**6*b*d*e**6 + 959*a**5*b**2*d**2*e**5 - 140*a**4*b**3*d**3*e**4 - 35*a**3*b**4*d**4*e**3 - 14*a**2*b**5*d**5*e**2 - 7*a*b**6*d**6*e - 4*b**7*d**7 + x**4*(700*a**3*b**4*e**7 - 2100*a**2*b**5*d*e**6 + 2100*a*b**6*d**2*e**5 - 700*b**7*d**3*e**4) + x**3*(2450*a**4*b**3*e**7 - 7000*a**3*b**4*d*e**6 + 6300*a**2*b**5*d**2*e**5 - 1400*a*b**6*d**3*e**4 - 350*b**7*d**4*e**3) + x**2*(3290*a**5*b**2*e**7 - 9100*a**4*b**3*d*e**6 + 7700*a**3*b**4*d**2*e**5 - 1400*a**2*b**5*d**3*e**4 - 350*a*b**6*d**4*e**3 - 140*b**7*d**5*e**2) + x*(1995*a**6*b*e**7 - 5390*a**5*b**2*d*e**6 + 4375*a**4*b**3*d**2*e**5 - 700*a**3*b**4*d**3*e**4 - 175*a**2*b**5*d**4*e**3 - 70*a*b**6*d**5*e**2 - 35*b**7*d**6*e))/(20*a**5*b**8 + 100*a**4*b**9*x + 200*a**3*b**10*x**2 + 200*a**2*b**11*x**3 + 100*a*b**12*x**4 + 20*b**13*x**5) + e**7*x**2/(2*b**6) + 21*e**5*(a*e - b*d)**2*log(a + b*x)/b**8","B",0
1527,1,420,0,30.050271," ","integrate((e*x+d)**6/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- 87 a^{6} e^{6} + 137 a^{5} b d e^{5} - 30 a^{4} b^{2} d^{2} e^{4} - 10 a^{3} b^{3} d^{3} e^{3} - 5 a^{2} b^{4} d^{4} e^{2} - 3 a b^{5} d^{5} e - 2 b^{6} d^{6} + x^{4} \left(- 150 a^{2} b^{4} e^{6} + 300 a b^{5} d e^{5} - 150 b^{6} d^{2} e^{4}\right) + x^{3} \left(- 500 a^{3} b^{3} e^{6} + 900 a^{2} b^{4} d e^{5} - 300 a b^{5} d^{2} e^{4} - 100 b^{6} d^{3} e^{3}\right) + x^{2} \left(- 650 a^{4} b^{2} e^{6} + 1100 a^{3} b^{3} d e^{5} - 300 a^{2} b^{4} d^{2} e^{4} - 100 a b^{5} d^{3} e^{3} - 50 b^{6} d^{4} e^{2}\right) + x \left(- 385 a^{5} b e^{6} + 625 a^{4} b^{2} d e^{5} - 150 a^{3} b^{3} d^{2} e^{4} - 50 a^{2} b^{4} d^{3} e^{3} - 25 a b^{5} d^{4} e^{2} - 15 b^{6} d^{5} e\right)}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} + \frac{e^{6} x}{b^{6}} - \frac{6 e^{5} \left(a e - b d\right) \log{\left(a + b x \right)}}{b^{7}}"," ",0,"(-87*a**6*e**6 + 137*a**5*b*d*e**5 - 30*a**4*b**2*d**2*e**4 - 10*a**3*b**3*d**3*e**3 - 5*a**2*b**4*d**4*e**2 - 3*a*b**5*d**5*e - 2*b**6*d**6 + x**4*(-150*a**2*b**4*e**6 + 300*a*b**5*d*e**5 - 150*b**6*d**2*e**4) + x**3*(-500*a**3*b**3*e**6 + 900*a**2*b**4*d*e**5 - 300*a*b**5*d**2*e**4 - 100*b**6*d**3*e**3) + x**2*(-650*a**4*b**2*e**6 + 1100*a**3*b**3*d*e**5 - 300*a**2*b**4*d**2*e**4 - 100*a*b**5*d**3*e**3 - 50*b**6*d**4*e**2) + x*(-385*a**5*b*e**6 + 625*a**4*b**2*d*e**5 - 150*a**3*b**3*d**2*e**4 - 50*a**2*b**4*d**3*e**3 - 25*a*b**5*d**4*e**2 - 15*b**6*d**5*e))/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) + e**6*x/b**6 - 6*e**5*(a*e - b*d)*log(a + b*x)/b**7","B",0
1528,1,326,0,9.864138," ","integrate((e*x+d)**5/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{137 a^{5} e^{5} - 60 a^{4} b d e^{4} - 30 a^{3} b^{2} d^{2} e^{3} - 20 a^{2} b^{3} d^{3} e^{2} - 15 a b^{4} d^{4} e - 12 b^{5} d^{5} + x^{4} \left(300 a b^{4} e^{5} - 300 b^{5} d e^{4}\right) + x^{3} \left(900 a^{2} b^{3} e^{5} - 600 a b^{4} d e^{4} - 300 b^{5} d^{2} e^{3}\right) + x^{2} \left(1100 a^{3} b^{2} e^{5} - 600 a^{2} b^{3} d e^{4} - 300 a b^{4} d^{2} e^{3} - 200 b^{5} d^{3} e^{2}\right) + x \left(625 a^{4} b e^{5} - 300 a^{3} b^{2} d e^{4} - 150 a^{2} b^{3} d^{2} e^{3} - 100 a b^{4} d^{3} e^{2} - 75 b^{5} d^{4} e\right)}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{e^{5} \log{\left(a + b x \right)}}{b^{6}}"," ",0,"(137*a**5*e**5 - 60*a**4*b*d*e**4 - 30*a**3*b**2*d**2*e**3 - 20*a**2*b**3*d**3*e**2 - 15*a*b**4*d**4*e - 12*b**5*d**5 + x**4*(300*a*b**4*e**5 - 300*b**5*d*e**4) + x**3*(900*a**2*b**3*e**5 - 600*a*b**4*d*e**4 - 300*b**5*d**2*e**3) + x**2*(1100*a**3*b**2*e**5 - 600*a**2*b**3*d*e**4 - 300*a*b**4*d**2*e**3 - 200*b**5*d**3*e**2) + x*(625*a**4*b*e**5 - 300*a**3*b**2*d*e**4 - 150*a**2*b**3*d**2*e**3 - 100*a*b**4*d**3*e**2 - 75*b**5*d**4*e))/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + e**5*log(a + b*x)/b**6","B",0
1529,1,236,0,4.090647," ","integrate((e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- a^{4} e^{4} - a^{3} b d e^{3} - a^{2} b^{2} d^{2} e^{2} - a b^{3} d^{3} e - b^{4} d^{4} - 5 b^{4} e^{4} x^{4} + x^{3} \left(- 10 a b^{3} e^{4} - 10 b^{4} d e^{3}\right) + x^{2} \left(- 10 a^{2} b^{2} e^{4} - 10 a b^{3} d e^{3} - 10 b^{4} d^{2} e^{2}\right) + x \left(- 5 a^{3} b e^{4} - 5 a^{2} b^{2} d e^{3} - 5 a b^{3} d^{2} e^{2} - 5 b^{4} d^{3} e\right)}{5 a^{5} b^{5} + 25 a^{4} b^{6} x + 50 a^{3} b^{7} x^{2} + 50 a^{2} b^{8} x^{3} + 25 a b^{9} x^{4} + 5 b^{10} x^{5}}"," ",0,"(-a**4*e**4 - a**3*b*d*e**3 - a**2*b**2*d**2*e**2 - a*b**3*d**3*e - b**4*d**4 - 5*b**4*e**4*x**4 + x**3*(-10*a*b**3*e**4 - 10*b**4*d*e**3) + x**2*(-10*a**2*b**2*e**4 - 10*a*b**3*d*e**3 - 10*b**4*d**2*e**2) + x*(-5*a**3*b*e**4 - 5*a**2*b**2*d*e**3 - 5*a*b**3*d**2*e**2 - 5*b**4*d**3*e))/(5*a**5*b**5 + 25*a**4*b**6*x + 50*a**3*b**7*x**2 + 50*a**2*b**8*x**3 + 25*a*b**9*x**4 + 5*b**10*x**5)","B",0
1530,1,172,0,2.027766," ","integrate((e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- a^{3} e^{3} - 2 a^{2} b d e^{2} - 3 a b^{2} d^{2} e - 4 b^{3} d^{3} - 10 b^{3} e^{3} x^{3} + x^{2} \left(- 10 a b^{2} e^{3} - 20 b^{3} d e^{2}\right) + x \left(- 5 a^{2} b e^{3} - 10 a b^{2} d e^{2} - 15 b^{3} d^{2} e\right)}{20 a^{5} b^{4} + 100 a^{4} b^{5} x + 200 a^{3} b^{6} x^{2} + 200 a^{2} b^{7} x^{3} + 100 a b^{8} x^{4} + 20 b^{9} x^{5}}"," ",0,"(-a**3*e**3 - 2*a**2*b*d*e**2 - 3*a*b**2*d**2*e - 4*b**3*d**3 - 10*b**3*e**3*x**3 + x**2*(-10*a*b**2*e**3 - 20*b**3*d*e**2) + x*(-5*a**2*b*e**3 - 10*a*b**2*d*e**2 - 15*b**3*d**2*e))/(20*a**5*b**4 + 100*a**4*b**5*x + 200*a**3*b**6*x**2 + 200*a**2*b**7*x**3 + 100*a*b**8*x**4 + 20*b**9*x**5)","B",0
1531,1,116,0,0.974009," ","integrate((e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- a^{2} e^{2} - 3 a b d e - 6 b^{2} d^{2} - 10 b^{2} e^{2} x^{2} + x \left(- 5 a b e^{2} - 15 b^{2} d e\right)}{30 a^{5} b^{3} + 150 a^{4} b^{4} x + 300 a^{3} b^{5} x^{2} + 300 a^{2} b^{6} x^{3} + 150 a b^{7} x^{4} + 30 b^{8} x^{5}}"," ",0,"(-a**2*e**2 - 3*a*b*d*e - 6*b**2*d**2 - 10*b**2*e**2*x**2 + x*(-5*a*b*e**2 - 15*b**2*d*e))/(30*a**5*b**3 + 150*a**4*b**4*x + 300*a**3*b**5*x**2 + 300*a**2*b**6*x**3 + 150*a*b**7*x**4 + 30*b**8*x**5)","B",0
1532,1,76,0,0.530359," ","integrate((e*x+d)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- a e - 4 b d - 5 b e x}{20 a^{5} b^{2} + 100 a^{4} b^{3} x + 200 a^{3} b^{4} x^{2} + 200 a^{2} b^{5} x^{3} + 100 a b^{6} x^{4} + 20 b^{7} x^{5}}"," ",0,"(-a*e - 4*b*d - 5*b*e*x)/(20*a**5*b**2 + 100*a**4*b**3*x + 200*a**3*b**4*x**2 + 200*a**2*b**5*x**3 + 100*a*b**6*x**4 + 20*b**7*x**5)","B",0
1533,1,61,0,0.353709," ","integrate(1/(b**2*x**2+2*a*b*x+a**2)**3,x)","- \frac{1}{5 a^{5} b + 25 a^{4} b^{2} x + 50 a^{3} b^{3} x^{2} + 50 a^{2} b^{4} x^{3} + 25 a b^{5} x^{4} + 5 b^{6} x^{5}}"," ",0,"-1/(5*a**5*b + 25*a**4*b**2*x + 50*a**3*b**3*x**2 + 50*a**2*b**4*x**3 + 25*a*b**5*x**4 + 5*b**6*x**5)","B",0
1534,1,1081,0,3.152781," ","integrate(1/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{e^{5} \log{\left(x + \frac{- \frac{a^{7} e^{12}}{\left(a e - b d\right)^{6}} + \frac{7 a^{6} b d e^{11}}{\left(a e - b d\right)^{6}} - \frac{21 a^{5} b^{2} d^{2} e^{10}}{\left(a e - b d\right)^{6}} + \frac{35 a^{4} b^{3} d^{3} e^{9}}{\left(a e - b d\right)^{6}} - \frac{35 a^{3} b^{4} d^{4} e^{8}}{\left(a e - b d\right)^{6}} + \frac{21 a^{2} b^{5} d^{5} e^{7}}{\left(a e - b d\right)^{6}} - \frac{7 a b^{6} d^{6} e^{6}}{\left(a e - b d\right)^{6}} + a e^{6} + \frac{b^{7} d^{7} e^{5}}{\left(a e - b d\right)^{6}} + b d e^{5}}{2 b e^{6}} \right)}}{\left(a e - b d\right)^{6}} - \frac{e^{5} \log{\left(x + \frac{\frac{a^{7} e^{12}}{\left(a e - b d\right)^{6}} - \frac{7 a^{6} b d e^{11}}{\left(a e - b d\right)^{6}} + \frac{21 a^{5} b^{2} d^{2} e^{10}}{\left(a e - b d\right)^{6}} - \frac{35 a^{4} b^{3} d^{3} e^{9}}{\left(a e - b d\right)^{6}} + \frac{35 a^{3} b^{4} d^{4} e^{8}}{\left(a e - b d\right)^{6}} - \frac{21 a^{2} b^{5} d^{5} e^{7}}{\left(a e - b d\right)^{6}} + \frac{7 a b^{6} d^{6} e^{6}}{\left(a e - b d\right)^{6}} + a e^{6} - \frac{b^{7} d^{7} e^{5}}{\left(a e - b d\right)^{6}} + b d e^{5}}{2 b e^{6}} \right)}}{\left(a e - b d\right)^{6}} + \frac{137 a^{4} e^{4} - 163 a^{3} b d e^{3} + 137 a^{2} b^{2} d^{2} e^{2} - 63 a b^{3} d^{3} e + 12 b^{4} d^{4} + 60 b^{4} e^{4} x^{4} + x^{3} \left(270 a b^{3} e^{4} - 30 b^{4} d e^{3}\right) + x^{2} \left(470 a^{2} b^{2} e^{4} - 130 a b^{3} d e^{3} + 20 b^{4} d^{2} e^{2}\right) + x \left(385 a^{3} b e^{4} - 215 a^{2} b^{2} d e^{3} + 85 a b^{3} d^{2} e^{2} - 15 b^{4} d^{3} e\right)}{60 a^{10} e^{5} - 300 a^{9} b d e^{4} + 600 a^{8} b^{2} d^{2} e^{3} - 600 a^{7} b^{3} d^{3} e^{2} + 300 a^{6} b^{4} d^{4} e - 60 a^{5} b^{5} d^{5} + x^{5} \left(60 a^{5} b^{5} e^{5} - 300 a^{4} b^{6} d e^{4} + 600 a^{3} b^{7} d^{2} e^{3} - 600 a^{2} b^{8} d^{3} e^{2} + 300 a b^{9} d^{4} e - 60 b^{10} d^{5}\right) + x^{4} \left(300 a^{6} b^{4} e^{5} - 1500 a^{5} b^{5} d e^{4} + 3000 a^{4} b^{6} d^{2} e^{3} - 3000 a^{3} b^{7} d^{3} e^{2} + 1500 a^{2} b^{8} d^{4} e - 300 a b^{9} d^{5}\right) + x^{3} \left(600 a^{7} b^{3} e^{5} - 3000 a^{6} b^{4} d e^{4} + 6000 a^{5} b^{5} d^{2} e^{3} - 6000 a^{4} b^{6} d^{3} e^{2} + 3000 a^{3} b^{7} d^{4} e - 600 a^{2} b^{8} d^{5}\right) + x^{2} \left(600 a^{8} b^{2} e^{5} - 3000 a^{7} b^{3} d e^{4} + 6000 a^{6} b^{4} d^{2} e^{3} - 6000 a^{5} b^{5} d^{3} e^{2} + 3000 a^{4} b^{6} d^{4} e - 600 a^{3} b^{7} d^{5}\right) + x \left(300 a^{9} b e^{5} - 1500 a^{8} b^{2} d e^{4} + 3000 a^{7} b^{3} d^{2} e^{3} - 3000 a^{6} b^{4} d^{3} e^{2} + 1500 a^{5} b^{5} d^{4} e - 300 a^{4} b^{6} d^{5}\right)}"," ",0,"e**5*log(x + (-a**7*e**12/(a*e - b*d)**6 + 7*a**6*b*d*e**11/(a*e - b*d)**6 - 21*a**5*b**2*d**2*e**10/(a*e - b*d)**6 + 35*a**4*b**3*d**3*e**9/(a*e - b*d)**6 - 35*a**3*b**4*d**4*e**8/(a*e - b*d)**6 + 21*a**2*b**5*d**5*e**7/(a*e - b*d)**6 - 7*a*b**6*d**6*e**6/(a*e - b*d)**6 + a*e**6 + b**7*d**7*e**5/(a*e - b*d)**6 + b*d*e**5)/(2*b*e**6))/(a*e - b*d)**6 - e**5*log(x + (a**7*e**12/(a*e - b*d)**6 - 7*a**6*b*d*e**11/(a*e - b*d)**6 + 21*a**5*b**2*d**2*e**10/(a*e - b*d)**6 - 35*a**4*b**3*d**3*e**9/(a*e - b*d)**6 + 35*a**3*b**4*d**4*e**8/(a*e - b*d)**6 - 21*a**2*b**5*d**5*e**7/(a*e - b*d)**6 + 7*a*b**6*d**6*e**6/(a*e - b*d)**6 + a*e**6 - b**7*d**7*e**5/(a*e - b*d)**6 + b*d*e**5)/(2*b*e**6))/(a*e - b*d)**6 + (137*a**4*e**4 - 163*a**3*b*d*e**3 + 137*a**2*b**2*d**2*e**2 - 63*a*b**3*d**3*e + 12*b**4*d**4 + 60*b**4*e**4*x**4 + x**3*(270*a*b**3*e**4 - 30*b**4*d*e**3) + x**2*(470*a**2*b**2*e**4 - 130*a*b**3*d*e**3 + 20*b**4*d**2*e**2) + x*(385*a**3*b*e**4 - 215*a**2*b**2*d*e**3 + 85*a*b**3*d**2*e**2 - 15*b**4*d**3*e))/(60*a**10*e**5 - 300*a**9*b*d*e**4 + 600*a**8*b**2*d**2*e**3 - 600*a**7*b**3*d**3*e**2 + 300*a**6*b**4*d**4*e - 60*a**5*b**5*d**5 + x**5*(60*a**5*b**5*e**5 - 300*a**4*b**6*d*e**4 + 600*a**3*b**7*d**2*e**3 - 600*a**2*b**8*d**3*e**2 + 300*a*b**9*d**4*e - 60*b**10*d**5) + x**4*(300*a**6*b**4*e**5 - 1500*a**5*b**5*d*e**4 + 3000*a**4*b**6*d**2*e**3 - 3000*a**3*b**7*d**3*e**2 + 1500*a**2*b**8*d**4*e - 300*a*b**9*d**5) + x**3*(600*a**7*b**3*e**5 - 3000*a**6*b**4*d*e**4 + 6000*a**5*b**5*d**2*e**3 - 6000*a**4*b**6*d**3*e**2 + 3000*a**3*b**7*d**4*e - 600*a**2*b**8*d**5) + x**2*(600*a**8*b**2*e**5 - 3000*a**7*b**3*d*e**4 + 6000*a**6*b**4*d**2*e**3 - 6000*a**5*b**5*d**3*e**2 + 3000*a**4*b**6*d**4*e - 600*a**3*b**7*d**5) + x*(300*a**9*b*e**5 - 1500*a**8*b**2*d*e**4 + 3000*a**7*b**3*d**2*e**3 - 3000*a**6*b**4*d**3*e**2 + 1500*a**5*b**5*d**4*e - 300*a**4*b**6*d**5))","B",0
1535,1,1518,0,5.175745," ","integrate(1/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**3,x)","- \frac{6 b e^{5} \log{\left(x + \frac{- \frac{6 a^{8} b e^{13}}{\left(a e - b d\right)^{7}} + \frac{48 a^{7} b^{2} d e^{12}}{\left(a e - b d\right)^{7}} - \frac{168 a^{6} b^{3} d^{2} e^{11}}{\left(a e - b d\right)^{7}} + \frac{336 a^{5} b^{4} d^{3} e^{10}}{\left(a e - b d\right)^{7}} - \frac{420 a^{4} b^{5} d^{4} e^{9}}{\left(a e - b d\right)^{7}} + \frac{336 a^{3} b^{6} d^{5} e^{8}}{\left(a e - b d\right)^{7}} - \frac{168 a^{2} b^{7} d^{6} e^{7}}{\left(a e - b d\right)^{7}} + \frac{48 a b^{8} d^{7} e^{6}}{\left(a e - b d\right)^{7}} + 6 a b e^{6} - \frac{6 b^{9} d^{8} e^{5}}{\left(a e - b d\right)^{7}} + 6 b^{2} d e^{5}}{12 b^{2} e^{6}} \right)}}{\left(a e - b d\right)^{7}} + \frac{6 b e^{5} \log{\left(x + \frac{\frac{6 a^{8} b e^{13}}{\left(a e - b d\right)^{7}} - \frac{48 a^{7} b^{2} d e^{12}}{\left(a e - b d\right)^{7}} + \frac{168 a^{6} b^{3} d^{2} e^{11}}{\left(a e - b d\right)^{7}} - \frac{336 a^{5} b^{4} d^{3} e^{10}}{\left(a e - b d\right)^{7}} + \frac{420 a^{4} b^{5} d^{4} e^{9}}{\left(a e - b d\right)^{7}} - \frac{336 a^{3} b^{6} d^{5} e^{8}}{\left(a e - b d\right)^{7}} + \frac{168 a^{2} b^{7} d^{6} e^{7}}{\left(a e - b d\right)^{7}} - \frac{48 a b^{8} d^{7} e^{6}}{\left(a e - b d\right)^{7}} + 6 a b e^{6} + \frac{6 b^{9} d^{8} e^{5}}{\left(a e - b d\right)^{7}} + 6 b^{2} d e^{5}}{12 b^{2} e^{6}} \right)}}{\left(a e - b d\right)^{7}} + \frac{- 10 a^{5} e^{5} - 87 a^{4} b d e^{4} + 63 a^{3} b^{2} d^{2} e^{3} - 37 a^{2} b^{3} d^{3} e^{2} + 13 a b^{4} d^{4} e - 2 b^{5} d^{5} - 60 b^{5} e^{5} x^{5} + x^{4} \left(- 270 a b^{4} e^{5} - 30 b^{5} d e^{4}\right) + x^{3} \left(- 470 a^{2} b^{3} e^{5} - 140 a b^{4} d e^{4} + 10 b^{5} d^{2} e^{3}\right) + x^{2} \left(- 385 a^{3} b^{2} e^{5} - 255 a^{2} b^{3} d e^{4} + 45 a b^{4} d^{2} e^{3} - 5 b^{5} d^{3} e^{2}\right) + x \left(- 137 a^{4} b e^{5} - 222 a^{3} b^{2} d e^{4} + 78 a^{2} b^{3} d^{2} e^{3} - 22 a b^{4} d^{3} e^{2} + 3 b^{5} d^{4} e\right)}{10 a^{11} d e^{6} - 60 a^{10} b d^{2} e^{5} + 150 a^{9} b^{2} d^{3} e^{4} - 200 a^{8} b^{3} d^{4} e^{3} + 150 a^{7} b^{4} d^{5} e^{2} - 60 a^{6} b^{5} d^{6} e + 10 a^{5} b^{6} d^{7} + x^{6} \left(10 a^{6} b^{5} e^{7} - 60 a^{5} b^{6} d e^{6} + 150 a^{4} b^{7} d^{2} e^{5} - 200 a^{3} b^{8} d^{3} e^{4} + 150 a^{2} b^{9} d^{4} e^{3} - 60 a b^{10} d^{5} e^{2} + 10 b^{11} d^{6} e\right) + x^{5} \left(50 a^{7} b^{4} e^{7} - 290 a^{6} b^{5} d e^{6} + 690 a^{5} b^{6} d^{2} e^{5} - 850 a^{4} b^{7} d^{3} e^{4} + 550 a^{3} b^{8} d^{4} e^{3} - 150 a^{2} b^{9} d^{5} e^{2} - 10 a b^{10} d^{6} e + 10 b^{11} d^{7}\right) + x^{4} \left(100 a^{8} b^{3} e^{7} - 550 a^{7} b^{4} d e^{6} + 1200 a^{6} b^{5} d^{2} e^{5} - 1250 a^{5} b^{6} d^{3} e^{4} + 500 a^{4} b^{7} d^{4} e^{3} + 150 a^{3} b^{8} d^{5} e^{2} - 200 a^{2} b^{9} d^{6} e + 50 a b^{10} d^{7}\right) + x^{3} \left(100 a^{9} b^{2} e^{7} - 500 a^{8} b^{3} d e^{6} + 900 a^{7} b^{4} d^{2} e^{5} - 500 a^{6} b^{5} d^{3} e^{4} - 500 a^{5} b^{6} d^{4} e^{3} + 900 a^{4} b^{7} d^{5} e^{2} - 500 a^{3} b^{8} d^{6} e + 100 a^{2} b^{9} d^{7}\right) + x^{2} \left(50 a^{10} b e^{7} - 200 a^{9} b^{2} d e^{6} + 150 a^{8} b^{3} d^{2} e^{5} + 500 a^{7} b^{4} d^{3} e^{4} - 1250 a^{6} b^{5} d^{4} e^{3} + 1200 a^{5} b^{6} d^{5} e^{2} - 550 a^{4} b^{7} d^{6} e + 100 a^{3} b^{8} d^{7}\right) + x \left(10 a^{11} e^{7} - 10 a^{10} b d e^{6} - 150 a^{9} b^{2} d^{2} e^{5} + 550 a^{8} b^{3} d^{3} e^{4} - 850 a^{7} b^{4} d^{4} e^{3} + 690 a^{6} b^{5} d^{5} e^{2} - 290 a^{5} b^{6} d^{6} e + 50 a^{4} b^{7} d^{7}\right)}"," ",0,"-6*b*e**5*log(x + (-6*a**8*b*e**13/(a*e - b*d)**7 + 48*a**7*b**2*d*e**12/(a*e - b*d)**7 - 168*a**6*b**3*d**2*e**11/(a*e - b*d)**7 + 336*a**5*b**4*d**3*e**10/(a*e - b*d)**7 - 420*a**4*b**5*d**4*e**9/(a*e - b*d)**7 + 336*a**3*b**6*d**5*e**8/(a*e - b*d)**7 - 168*a**2*b**7*d**6*e**7/(a*e - b*d)**7 + 48*a*b**8*d**7*e**6/(a*e - b*d)**7 + 6*a*b*e**6 - 6*b**9*d**8*e**5/(a*e - b*d)**7 + 6*b**2*d*e**5)/(12*b**2*e**6))/(a*e - b*d)**7 + 6*b*e**5*log(x + (6*a**8*b*e**13/(a*e - b*d)**7 - 48*a**7*b**2*d*e**12/(a*e - b*d)**7 + 168*a**6*b**3*d**2*e**11/(a*e - b*d)**7 - 336*a**5*b**4*d**3*e**10/(a*e - b*d)**7 + 420*a**4*b**5*d**4*e**9/(a*e - b*d)**7 - 336*a**3*b**6*d**5*e**8/(a*e - b*d)**7 + 168*a**2*b**7*d**6*e**7/(a*e - b*d)**7 - 48*a*b**8*d**7*e**6/(a*e - b*d)**7 + 6*a*b*e**6 + 6*b**9*d**8*e**5/(a*e - b*d)**7 + 6*b**2*d*e**5)/(12*b**2*e**6))/(a*e - b*d)**7 + (-10*a**5*e**5 - 87*a**4*b*d*e**4 + 63*a**3*b**2*d**2*e**3 - 37*a**2*b**3*d**3*e**2 + 13*a*b**4*d**4*e - 2*b**5*d**5 - 60*b**5*e**5*x**5 + x**4*(-270*a*b**4*e**5 - 30*b**5*d*e**4) + x**3*(-470*a**2*b**3*e**5 - 140*a*b**4*d*e**4 + 10*b**5*d**2*e**3) + x**2*(-385*a**3*b**2*e**5 - 255*a**2*b**3*d*e**4 + 45*a*b**4*d**2*e**3 - 5*b**5*d**3*e**2) + x*(-137*a**4*b*e**5 - 222*a**3*b**2*d*e**4 + 78*a**2*b**3*d**2*e**3 - 22*a*b**4*d**3*e**2 + 3*b**5*d**4*e))/(10*a**11*d*e**6 - 60*a**10*b*d**2*e**5 + 150*a**9*b**2*d**3*e**4 - 200*a**8*b**3*d**4*e**3 + 150*a**7*b**4*d**5*e**2 - 60*a**6*b**5*d**6*e + 10*a**5*b**6*d**7 + x**6*(10*a**6*b**5*e**7 - 60*a**5*b**6*d*e**6 + 150*a**4*b**7*d**2*e**5 - 200*a**3*b**8*d**3*e**4 + 150*a**2*b**9*d**4*e**3 - 60*a*b**10*d**5*e**2 + 10*b**11*d**6*e) + x**5*(50*a**7*b**4*e**7 - 290*a**6*b**5*d*e**6 + 690*a**5*b**6*d**2*e**5 - 850*a**4*b**7*d**3*e**4 + 550*a**3*b**8*d**4*e**3 - 150*a**2*b**9*d**5*e**2 - 10*a*b**10*d**6*e + 10*b**11*d**7) + x**4*(100*a**8*b**3*e**7 - 550*a**7*b**4*d*e**6 + 1200*a**6*b**5*d**2*e**5 - 1250*a**5*b**6*d**3*e**4 + 500*a**4*b**7*d**4*e**3 + 150*a**3*b**8*d**5*e**2 - 200*a**2*b**9*d**6*e + 50*a*b**10*d**7) + x**3*(100*a**9*b**2*e**7 - 500*a**8*b**3*d*e**6 + 900*a**7*b**4*d**2*e**5 - 500*a**6*b**5*d**3*e**4 - 500*a**5*b**6*d**4*e**3 + 900*a**4*b**7*d**5*e**2 - 500*a**3*b**8*d**6*e + 100*a**2*b**9*d**7) + x**2*(50*a**10*b*e**7 - 200*a**9*b**2*d*e**6 + 150*a**8*b**3*d**2*e**5 + 500*a**7*b**4*d**3*e**4 - 1250*a**6*b**5*d**4*e**3 + 1200*a**5*b**6*d**5*e**2 - 550*a**4*b**7*d**6*e + 100*a**3*b**8*d**7) + x*(10*a**11*e**7 - 10*a**10*b*d*e**6 - 150*a**9*b**2*d**2*e**5 + 550*a**8*b**3*d**3*e**4 - 850*a**7*b**4*d**4*e**3 + 690*a**6*b**5*d**5*e**2 - 290*a**5*b**6*d**6*e + 50*a**4*b**7*d**7))","B",0
1536,1,1974,0,8.386948," ","integrate(1/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{21 b^{2} e^{5} \log{\left(x + \frac{- \frac{21 a^{9} b^{2} e^{14}}{\left(a e - b d\right)^{8}} + \frac{189 a^{8} b^{3} d e^{13}}{\left(a e - b d\right)^{8}} - \frac{756 a^{7} b^{4} d^{2} e^{12}}{\left(a e - b d\right)^{8}} + \frac{1764 a^{6} b^{5} d^{3} e^{11}}{\left(a e - b d\right)^{8}} - \frac{2646 a^{5} b^{6} d^{4} e^{10}}{\left(a e - b d\right)^{8}} + \frac{2646 a^{4} b^{7} d^{5} e^{9}}{\left(a e - b d\right)^{8}} - \frac{1764 a^{3} b^{8} d^{6} e^{8}}{\left(a e - b d\right)^{8}} + \frac{756 a^{2} b^{9} d^{7} e^{7}}{\left(a e - b d\right)^{8}} - \frac{189 a b^{10} d^{8} e^{6}}{\left(a e - b d\right)^{8}} + 21 a b^{2} e^{6} + \frac{21 b^{11} d^{9} e^{5}}{\left(a e - b d\right)^{8}} + 21 b^{3} d e^{5}}{42 b^{3} e^{6}} \right)}}{\left(a e - b d\right)^{8}} - \frac{21 b^{2} e^{5} \log{\left(x + \frac{\frac{21 a^{9} b^{2} e^{14}}{\left(a e - b d\right)^{8}} - \frac{189 a^{8} b^{3} d e^{13}}{\left(a e - b d\right)^{8}} + \frac{756 a^{7} b^{4} d^{2} e^{12}}{\left(a e - b d\right)^{8}} - \frac{1764 a^{6} b^{5} d^{3} e^{11}}{\left(a e - b d\right)^{8}} + \frac{2646 a^{5} b^{6} d^{4} e^{10}}{\left(a e - b d\right)^{8}} - \frac{2646 a^{4} b^{7} d^{5} e^{9}}{\left(a e - b d\right)^{8}} + \frac{1764 a^{3} b^{8} d^{6} e^{8}}{\left(a e - b d\right)^{8}} - \frac{756 a^{2} b^{9} d^{7} e^{7}}{\left(a e - b d\right)^{8}} + \frac{189 a b^{10} d^{8} e^{6}}{\left(a e - b d\right)^{8}} + 21 a b^{2} e^{6} - \frac{21 b^{11} d^{9} e^{5}}{\left(a e - b d\right)^{8}} + 21 b^{3} d e^{5}}{42 b^{3} e^{6}} \right)}}{\left(a e - b d\right)^{8}} + \frac{- 10 a^{6} e^{6} + 130 a^{5} b d e^{5} + 459 a^{4} b^{2} d^{2} e^{4} - 241 a^{3} b^{3} d^{3} e^{3} + 109 a^{2} b^{4} d^{4} e^{2} - 31 a b^{5} d^{5} e + 4 b^{6} d^{6} + 420 b^{6} e^{6} x^{6} + x^{5} \left(1890 a b^{5} e^{6} + 630 b^{6} d e^{5}\right) + x^{4} \left(3290 a^{2} b^{4} e^{6} + 2870 a b^{5} d e^{5} + 140 b^{6} d^{2} e^{4}\right) + x^{3} \left(2695 a^{3} b^{3} e^{6} + 5075 a^{2} b^{4} d e^{5} + 665 a b^{5} d^{2} e^{4} - 35 b^{6} d^{3} e^{3}\right) + x^{2} \left(959 a^{4} b^{2} e^{6} + 4249 a^{3} b^{3} d e^{5} + 1239 a^{2} b^{4} d^{2} e^{4} - 161 a b^{5} d^{3} e^{3} + 14 b^{6} d^{4} e^{2}\right) + x \left(70 a^{5} b e^{6} + 1568 a^{4} b^{2} d e^{5} + 1113 a^{3} b^{3} d^{2} e^{4} - 287 a^{2} b^{4} d^{3} e^{3} + 63 a b^{5} d^{4} e^{2} - 7 b^{6} d^{5} e\right)}{20 a^{12} d^{2} e^{7} - 140 a^{11} b d^{3} e^{6} + 420 a^{10} b^{2} d^{4} e^{5} - 700 a^{9} b^{3} d^{5} e^{4} + 700 a^{8} b^{4} d^{6} e^{3} - 420 a^{7} b^{5} d^{7} e^{2} + 140 a^{6} b^{6} d^{8} e - 20 a^{5} b^{7} d^{9} + x^{7} \left(20 a^{7} b^{5} e^{9} - 140 a^{6} b^{6} d e^{8} + 420 a^{5} b^{7} d^{2} e^{7} - 700 a^{4} b^{8} d^{3} e^{6} + 700 a^{3} b^{9} d^{4} e^{5} - 420 a^{2} b^{10} d^{5} e^{4} + 140 a b^{11} d^{6} e^{3} - 20 b^{12} d^{7} e^{2}\right) + x^{6} \left(100 a^{8} b^{4} e^{9} - 660 a^{7} b^{5} d e^{8} + 1820 a^{6} b^{6} d^{2} e^{7} - 2660 a^{5} b^{7} d^{3} e^{6} + 2100 a^{4} b^{8} d^{4} e^{5} - 700 a^{3} b^{9} d^{5} e^{4} - 140 a^{2} b^{10} d^{6} e^{3} + 180 a b^{11} d^{7} e^{2} - 40 b^{12} d^{8} e\right) + x^{5} \left(200 a^{9} b^{3} e^{9} - 1200 a^{8} b^{4} d e^{8} + 2820 a^{7} b^{5} d^{2} e^{7} - 2940 a^{6} b^{6} d^{3} e^{6} + 420 a^{5} b^{7} d^{4} e^{5} + 2100 a^{4} b^{8} d^{5} e^{4} - 2100 a^{3} b^{9} d^{6} e^{3} + 780 a^{2} b^{10} d^{7} e^{2} - 60 a b^{11} d^{8} e - 20 b^{12} d^{9}\right) + x^{4} \left(200 a^{10} b^{2} e^{9} - 1000 a^{9} b^{3} d e^{8} + 1500 a^{8} b^{4} d^{2} e^{7} + 700 a^{7} b^{5} d^{3} e^{6} - 4900 a^{6} b^{6} d^{4} e^{5} + 6300 a^{5} b^{7} d^{5} e^{4} - 3500 a^{4} b^{8} d^{6} e^{3} + 500 a^{3} b^{9} d^{7} e^{2} + 300 a^{2} b^{10} d^{8} e - 100 a b^{11} d^{9}\right) + x^{3} \left(100 a^{11} b e^{9} - 300 a^{10} b^{2} d e^{8} - 500 a^{9} b^{3} d^{2} e^{7} + 3500 a^{8} b^{4} d^{3} e^{6} - 6300 a^{7} b^{5} d^{4} e^{5} + 4900 a^{6} b^{6} d^{5} e^{4} - 700 a^{5} b^{7} d^{6} e^{3} - 1500 a^{4} b^{8} d^{7} e^{2} + 1000 a^{3} b^{9} d^{8} e - 200 a^{2} b^{10} d^{9}\right) + x^{2} \left(20 a^{12} e^{9} + 60 a^{11} b d e^{8} - 780 a^{10} b^{2} d^{2} e^{7} + 2100 a^{9} b^{3} d^{3} e^{6} - 2100 a^{8} b^{4} d^{4} e^{5} - 420 a^{7} b^{5} d^{5} e^{4} + 2940 a^{6} b^{6} d^{6} e^{3} - 2820 a^{5} b^{7} d^{7} e^{2} + 1200 a^{4} b^{8} d^{8} e - 200 a^{3} b^{9} d^{9}\right) + x \left(40 a^{12} d e^{8} - 180 a^{11} b d^{2} e^{7} + 140 a^{10} b^{2} d^{3} e^{6} + 700 a^{9} b^{3} d^{4} e^{5} - 2100 a^{8} b^{4} d^{5} e^{4} + 2660 a^{7} b^{5} d^{6} e^{3} - 1820 a^{6} b^{6} d^{7} e^{2} + 660 a^{5} b^{7} d^{8} e - 100 a^{4} b^{8} d^{9}\right)}"," ",0,"21*b**2*e**5*log(x + (-21*a**9*b**2*e**14/(a*e - b*d)**8 + 189*a**8*b**3*d*e**13/(a*e - b*d)**8 - 756*a**7*b**4*d**2*e**12/(a*e - b*d)**8 + 1764*a**6*b**5*d**3*e**11/(a*e - b*d)**8 - 2646*a**5*b**6*d**4*e**10/(a*e - b*d)**8 + 2646*a**4*b**7*d**5*e**9/(a*e - b*d)**8 - 1764*a**3*b**8*d**6*e**8/(a*e - b*d)**8 + 756*a**2*b**9*d**7*e**7/(a*e - b*d)**8 - 189*a*b**10*d**8*e**6/(a*e - b*d)**8 + 21*a*b**2*e**6 + 21*b**11*d**9*e**5/(a*e - b*d)**8 + 21*b**3*d*e**5)/(42*b**3*e**6))/(a*e - b*d)**8 - 21*b**2*e**5*log(x + (21*a**9*b**2*e**14/(a*e - b*d)**8 - 189*a**8*b**3*d*e**13/(a*e - b*d)**8 + 756*a**7*b**4*d**2*e**12/(a*e - b*d)**8 - 1764*a**6*b**5*d**3*e**11/(a*e - b*d)**8 + 2646*a**5*b**6*d**4*e**10/(a*e - b*d)**8 - 2646*a**4*b**7*d**5*e**9/(a*e - b*d)**8 + 1764*a**3*b**8*d**6*e**8/(a*e - b*d)**8 - 756*a**2*b**9*d**7*e**7/(a*e - b*d)**8 + 189*a*b**10*d**8*e**6/(a*e - b*d)**8 + 21*a*b**2*e**6 - 21*b**11*d**9*e**5/(a*e - b*d)**8 + 21*b**3*d*e**5)/(42*b**3*e**6))/(a*e - b*d)**8 + (-10*a**6*e**6 + 130*a**5*b*d*e**5 + 459*a**4*b**2*d**2*e**4 - 241*a**3*b**3*d**3*e**3 + 109*a**2*b**4*d**4*e**2 - 31*a*b**5*d**5*e + 4*b**6*d**6 + 420*b**6*e**6*x**6 + x**5*(1890*a*b**5*e**6 + 630*b**6*d*e**5) + x**4*(3290*a**2*b**4*e**6 + 2870*a*b**5*d*e**5 + 140*b**6*d**2*e**4) + x**3*(2695*a**3*b**3*e**6 + 5075*a**2*b**4*d*e**5 + 665*a*b**5*d**2*e**4 - 35*b**6*d**3*e**3) + x**2*(959*a**4*b**2*e**6 + 4249*a**3*b**3*d*e**5 + 1239*a**2*b**4*d**2*e**4 - 161*a*b**5*d**3*e**3 + 14*b**6*d**4*e**2) + x*(70*a**5*b*e**6 + 1568*a**4*b**2*d*e**5 + 1113*a**3*b**3*d**2*e**4 - 287*a**2*b**4*d**3*e**3 + 63*a*b**5*d**4*e**2 - 7*b**6*d**5*e))/(20*a**12*d**2*e**7 - 140*a**11*b*d**3*e**6 + 420*a**10*b**2*d**4*e**5 - 700*a**9*b**3*d**5*e**4 + 700*a**8*b**4*d**6*e**3 - 420*a**7*b**5*d**7*e**2 + 140*a**6*b**6*d**8*e - 20*a**5*b**7*d**9 + x**7*(20*a**7*b**5*e**9 - 140*a**6*b**6*d*e**8 + 420*a**5*b**7*d**2*e**7 - 700*a**4*b**8*d**3*e**6 + 700*a**3*b**9*d**4*e**5 - 420*a**2*b**10*d**5*e**4 + 140*a*b**11*d**6*e**3 - 20*b**12*d**7*e**2) + x**6*(100*a**8*b**4*e**9 - 660*a**7*b**5*d*e**8 + 1820*a**6*b**6*d**2*e**7 - 2660*a**5*b**7*d**3*e**6 + 2100*a**4*b**8*d**4*e**5 - 700*a**3*b**9*d**5*e**4 - 140*a**2*b**10*d**6*e**3 + 180*a*b**11*d**7*e**2 - 40*b**12*d**8*e) + x**5*(200*a**9*b**3*e**9 - 1200*a**8*b**4*d*e**8 + 2820*a**7*b**5*d**2*e**7 - 2940*a**6*b**6*d**3*e**6 + 420*a**5*b**7*d**4*e**5 + 2100*a**4*b**8*d**5*e**4 - 2100*a**3*b**9*d**6*e**3 + 780*a**2*b**10*d**7*e**2 - 60*a*b**11*d**8*e - 20*b**12*d**9) + x**4*(200*a**10*b**2*e**9 - 1000*a**9*b**3*d*e**8 + 1500*a**8*b**4*d**2*e**7 + 700*a**7*b**5*d**3*e**6 - 4900*a**6*b**6*d**4*e**5 + 6300*a**5*b**7*d**5*e**4 - 3500*a**4*b**8*d**6*e**3 + 500*a**3*b**9*d**7*e**2 + 300*a**2*b**10*d**8*e - 100*a*b**11*d**9) + x**3*(100*a**11*b*e**9 - 300*a**10*b**2*d*e**8 - 500*a**9*b**3*d**2*e**7 + 3500*a**8*b**4*d**3*e**6 - 6300*a**7*b**5*d**4*e**5 + 4900*a**6*b**6*d**5*e**4 - 700*a**5*b**7*d**6*e**3 - 1500*a**4*b**8*d**7*e**2 + 1000*a**3*b**9*d**8*e - 200*a**2*b**10*d**9) + x**2*(20*a**12*e**9 + 60*a**11*b*d*e**8 - 780*a**10*b**2*d**2*e**7 + 2100*a**9*b**3*d**3*e**6 - 2100*a**8*b**4*d**4*e**5 - 420*a**7*b**5*d**5*e**4 + 2940*a**6*b**6*d**6*e**3 - 2820*a**5*b**7*d**7*e**2 + 1200*a**4*b**8*d**8*e - 200*a**3*b**9*d**9) + x*(40*a**12*d*e**8 - 180*a**11*b*d**2*e**7 + 140*a**10*b**2*d**3*e**6 + 700*a**9*b**3*d**4*e**5 - 2100*a**8*b**4*d**5*e**4 + 2660*a**7*b**5*d**6*e**3 - 1820*a**6*b**6*d**7*e**2 + 660*a**5*b**7*d**8*e - 100*a**4*b**8*d**9))","B",0
1537,1,76,0,0.088132," ","integrate((e*x+d)*(4*x**2+12*x+9)**3,x)","729 d x + 8 e x^{8} + x^{7} \left(\frac{64 d}{7} + \frac{576 e}{7}\right) + x^{6} \left(96 d + 360 e\right) + x^{5} \left(432 d + 864 e\right) + x^{4} \left(1080 d + 1215 e\right) + x^{3} \left(1620 d + 972 e\right) + x^{2} \left(1458 d + \frac{729 e}{2}\right)"," ",0,"729*d*x + 8*e*x**8 + x**7*(64*d/7 + 576*e/7) + x**6*(96*d + 360*e) + x**5*(432*d + 864*e) + x**4*(1080*d + 1215*e) + x**3*(1620*d + 972*e) + x**2*(1458*d + 729*e/2)","B",0
1538,1,58,0,0.079416," ","integrate((e*x+d)*(4*x**2+12*x+9)**2,x)","81 d x + \frac{8 e x^{6}}{3} + x^{5} \left(\frac{16 d}{5} + \frac{96 e}{5}\right) + x^{4} \left(24 d + 54 e\right) + x^{3} \left(72 d + 72 e\right) + x^{2} \left(108 d + \frac{81 e}{2}\right)"," ",0,"81*d*x + 8*e*x**6/3 + x**5*(16*d/5 + 96*e/5) + x**4*(24*d + 54*e) + x**3*(72*d + 72*e) + x**2*(108*d + 81*e/2)","B",0
1539,1,32,0,0.066850," ","integrate((e*x+d)*(4*x**2+12*x+9),x)","9 d x + e x^{4} + x^{3} \left(\frac{4 d}{3} + 4 e\right) + x^{2} \left(6 d + \frac{9 e}{2}\right)"," ",0,"9*d*x + e*x**4 + x**3*(4*d/3 + 4*e) + x**2*(6*d + 9*e/2)","A",0
1540,1,20,0,0.141608," ","integrate((e*x+d)/(4*x**2+12*x+9),x)","\frac{e \log{\left(2 x + 3 \right)}}{4} + \frac{- 2 d + 3 e}{8 x + 12}"," ",0,"e*log(2*x + 3)/4 + (-2*d + 3*e)/(8*x + 12)","A",0
1541,1,27,0,0.219605," ","integrate((e*x+d)/(4*x**2+12*x+9)**2,x)","\frac{- 4 d - 6 e x - 3 e}{192 x^{3} + 864 x^{2} + 1296 x + 648}"," ",0,"(-4*d - 6*e*x - 3*e)/(192*x**3 + 864*x**2 + 1296*x + 648)","A",0
1542,1,37,0,0.326570," ","integrate((e*x+d)/(4*x**2+12*x+9)**3,x)","\frac{- 8 d - 10 e x - 3 e}{2560 x^{5} + 19200 x^{4} + 57600 x^{3} + 86400 x^{2} + 64800 x + 19440}"," ",0,"(-8*d - 10*e*x - 3*e)/(2560*x**5 + 19200*x**4 + 57600*x**3 + 86400*x**2 + 64800*x + 19440)","A",0
1543,1,100,0,0.126309," ","integrate((e*x+d)**4*((b*x+a)**2)**(1/2),x)","a d^{4} x + \frac{b e^{4} x^{6}}{6} + x^{5} \left(\frac{a e^{4}}{5} + \frac{4 b d e^{3}}{5}\right) + x^{4} \left(a d e^{3} + \frac{3 b d^{2} e^{2}}{2}\right) + x^{3} \left(2 a d^{2} e^{2} + \frac{4 b d^{3} e}{3}\right) + x^{2} \left(2 a d^{3} e + \frac{b d^{4}}{2}\right)"," ",0,"a*d**4*x + b*e**4*x**6/6 + x**5*(a*e**4/5 + 4*b*d*e**3/5) + x**4*(a*d*e**3 + 3*b*d**2*e**2/2) + x**3*(2*a*d**2*e**2 + 4*b*d**3*e/3) + x**2*(2*a*d**3*e + b*d**4/2)","A",0
1544,1,73,0,0.117523," ","integrate((e*x+d)**3*((b*x+a)**2)**(1/2),x)","a d^{3} x + \frac{b e^{3} x^{5}}{5} + x^{4} \left(\frac{a e^{3}}{4} + \frac{3 b d e^{2}}{4}\right) + x^{3} \left(a d e^{2} + b d^{2} e\right) + x^{2} \left(\frac{3 a d^{2} e}{2} + \frac{b d^{3}}{2}\right)"," ",0,"a*d**3*x + b*e**3*x**5/5 + x**4*(a*e**3/4 + 3*b*d*e**2/4) + x**3*(a*d*e**2 + b*d**2*e) + x**2*(3*a*d**2*e/2 + b*d**3/2)","A",0
1545,1,49,0,0.107575," ","integrate((e*x+d)**2*((b*x+a)**2)**(1/2),x)","a d^{2} x + \frac{b e^{2} x^{4}}{4} + x^{3} \left(\frac{a e^{2}}{3} + \frac{2 b d e}{3}\right) + x^{2} \left(a d e + \frac{b d^{2}}{2}\right)"," ",0,"a*d**2*x + b*e**2*x**4/4 + x**3*(a*e**2/3 + 2*b*d*e/3) + x**2*(a*d*e + b*d**2/2)","A",0
1546,1,26,0,0.093132," ","integrate((e*x+d)*((b*x+a)**2)**(1/2),x)","a d x + \frac{b e x^{3}}{3} + x^{2} \left(\frac{a e}{2} + \frac{b d}{2}\right)"," ",0,"a*d*x + b*e*x**3/3 + x**2*(a*e/2 + b*d/2)","A",0
1547,1,8,0,0.079391," ","integrate(((b*x+a)**2)**(1/2),x)","a x + \frac{b x^{2}}{2}"," ",0,"a*x + b*x**2/2","A",0
1548,1,20,0,0.168907," ","integrate(((b*x+a)**2)**(1/2)/(e*x+d),x)","\frac{b x}{e} + \frac{\left(a e - b d\right) \log{\left(d + e x \right)}}{e^{2}}"," ",0,"b*x/e + (a*e - b*d)*log(d + e*x)/e**2","A",0
1549,1,27,0,0.208717," ","integrate(((b*x+a)**2)**(1/2)/(e*x+d)**2,x)","\frac{b \log{\left(d + e x \right)}}{e^{2}} + \frac{- a e + b d}{d e^{2} + e^{3} x}"," ",0,"b*log(d + e*x)/e**2 + (-a*e + b*d)/(d*e**2 + e**3*x)","A",0
1550,1,39,0,0.285347," ","integrate(((b*x+a)**2)**(1/2)/(e*x+d)**3,x)","\frac{- a e - b d - 2 b e x}{2 d^{2} e^{2} + 4 d e^{3} x + 2 e^{4} x^{2}}"," ",0,"(-a*e - b*d - 2*b*e*x)/(2*d**2*e**2 + 4*d*e**3*x + 2*e**4*x**2)","A",0
1551,1,53,0,0.366203," ","integrate(((b*x+a)**2)**(1/2)/(e*x+d)**4,x)","\frac{- 2 a e - b d - 3 b e x}{6 d^{3} e^{2} + 18 d^{2} e^{3} x + 18 d e^{4} x^{2} + 6 e^{5} x^{3}}"," ",0,"(-2*a*e - b*d - 3*b*e*x)/(6*d**3*e**2 + 18*d**2*e**3*x + 18*d*e**4*x**2 + 6*e**5*x**3)","A",0
1552,1,65,0,0.464152," ","integrate(((b*x+a)**2)**(1/2)/(e*x+d)**5,x)","\frac{- 3 a e - b d - 4 b e x}{12 d^{4} e^{2} + 48 d^{3} e^{3} x + 72 d^{2} e^{4} x^{2} + 48 d e^{5} x^{3} + 12 e^{6} x^{4}}"," ",0,"(-3*a*e - b*d - 4*b*e*x)/(12*d**4*e**2 + 48*d**3*e**3*x + 72*d**2*e**4*x**2 + 48*d*e**5*x**3 + 12*e**6*x**4)","A",0
1553,1,76,0,0.562634," ","integrate(((b*x+a)**2)**(1/2)/(e*x+d)**6,x)","\frac{- 4 a e - b d - 5 b e x}{20 d^{5} e^{2} + 100 d^{4} e^{3} x + 200 d^{3} e^{4} x^{2} + 200 d^{2} e^{5} x^{3} + 100 d e^{6} x^{4} + 20 e^{7} x^{5}}"," ",0,"(-4*a*e - b*d - 5*b*e*x)/(20*d**5*e**2 + 100*d**4*e**3*x + 200*d**3*e**4*x**2 + 200*d**2*e**5*x**3 + 100*d*e**6*x**4 + 20*e**7*x**5)","A",0
1554,0,0,0,0.000000," ","integrate((e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(d + e x\right)^{5} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)**5*((a + b*x)**2)**(3/2), x)","F",0
1555,0,0,0,0.000000," ","integrate((e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(d + e x\right)^{4} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)**4*((a + b*x)**2)**(3/2), x)","F",0
1556,0,0,0,0.000000," ","integrate((e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(d + e x\right)^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)**3*((a + b*x)**2)**(3/2), x)","F",0
1557,0,0,0,0.000000," ","integrate((e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(d + e x\right)^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)**2*((a + b*x)**2)**(3/2), x)","F",0
1558,0,0,0,0.000000," ","integrate((e*x+d)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)*((a + b*x)**2)**(3/2), x)","F",0
1559,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2)**(3/2), x)","F",0
1560,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d),x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x), x)","F",0
1561,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**2, x)","F",0
1562,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**3,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**3, x)","F",0
1563,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**4,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**4, x)","F",0
1564,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**5,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**5, x)","F",0
1565,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**6,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**6, x)","F",0
1566,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**7,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**7, x)","F",0
1567,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**8,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{8}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**8, x)","F",0
1568,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**9,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{9}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**9, x)","F",0
1569,0,0,0,0.000000," ","integrate((e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(d + e x\right)^{5} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x)**5*((a + b*x)**2)**(5/2), x)","F",0
1570,0,0,0,0.000000," ","integrate((e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(d + e x\right)^{4} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x)**4*((a + b*x)**2)**(5/2), x)","F",0
1571,0,0,0,0.000000," ","integrate((e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(d + e x\right)^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x)**3*((a + b*x)**2)**(5/2), x)","F",0
1572,0,0,0,0.000000," ","integrate((e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(d + e x\right)^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x)**2*((a + b*x)**2)**(5/2), x)","F",0
1573,0,0,0,0.000000," ","integrate((e*x+d)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x)*((a + b*x)**2)**(5/2), x)","F",0
1574,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2)**(5/2), x)","F",0
1575,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d),x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{d + e x}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x), x)","F",0
1576,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**2,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**2, x)","F",0
1577,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**3, x)","F",0
1578,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**4, x)","F",0
1579,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**5,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**5, x)","F",0
1580,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**6,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**6, x)","F",0
1581,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**7,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**7, x)","F",0
1582,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**8,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{8}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**8, x)","F",0
1583,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**9,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{9}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**9, x)","F",0
1584,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**10,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{10}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**10, x)","F",0
1585,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**11,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{11}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**11, x)","F",0
1586,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**12,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{12}}\, dx"," ",0,"Integral(((a + b*x)**2)**(5/2)/(d + e*x)**12, x)","F",0
1587,1,136,0,0.431545," ","integrate((e*x+d)**4/((b*x+a)**2)**(1/2),x)","x^{3} \left(- \frac{a e^{4}}{3 b^{2}} + \frac{4 d e^{3}}{3 b}\right) + x^{2} \left(\frac{a^{2} e^{4}}{2 b^{3}} - \frac{2 a d e^{3}}{b^{2}} + \frac{3 d^{2} e^{2}}{b}\right) + x \left(- \frac{a^{3} e^{4}}{b^{4}} + \frac{4 a^{2} d e^{3}}{b^{3}} - \frac{6 a d^{2} e^{2}}{b^{2}} + \frac{4 d^{3} e}{b}\right) + \frac{e^{4} x^{4}}{4 b} + \frac{\left(a e - b d\right)^{4} \log{\left(a + b x \right)}}{b^{5}}"," ",0,"x**3*(-a*e**4/(3*b**2) + 4*d*e**3/(3*b)) + x**2*(a**2*e**4/(2*b**3) - 2*a*d*e**3/b**2 + 3*d**2*e**2/b) + x*(-a**3*e**4/b**4 + 4*a**2*d*e**3/b**3 - 6*a*d**2*e**2/b**2 + 4*d**3*e/b) + e**4*x**4/(4*b) + (a*e - b*d)**4*log(a + b*x)/b**5","A",0
1588,1,83,0,0.332451," ","integrate((e*x+d)**3/((b*x+a)**2)**(1/2),x)","x^{2} \left(- \frac{a e^{3}}{2 b^{2}} + \frac{3 d e^{2}}{2 b}\right) + x \left(\frac{a^{2} e^{3}}{b^{3}} - \frac{3 a d e^{2}}{b^{2}} + \frac{3 d^{2} e}{b}\right) + \frac{e^{3} x^{3}}{3 b} - \frac{\left(a e - b d\right)^{3} \log{\left(a + b x \right)}}{b^{4}}"," ",0,"x**2*(-a*e**3/(2*b**2) + 3*d*e**2/(2*b)) + x*(a**2*e**3/b**3 - 3*a*d*e**2/b**2 + 3*d**2*e/b) + e**3*x**3/(3*b) - (a*e - b*d)**3*log(a + b*x)/b**4","A",0
1589,1,44,0,0.249301," ","integrate((e*x+d)**2/((b*x+a)**2)**(1/2),x)","x \left(- \frac{a e^{2}}{b^{2}} + \frac{2 d e}{b}\right) + \frac{e^{2} x^{2}}{2 b} + \frac{\left(a e - b d\right)^{2} \log{\left(a + b x \right)}}{b^{3}}"," ",0,"x*(-a*e**2/b**2 + 2*d*e/b) + e**2*x**2/(2*b) + (a*e - b*d)**2*log(a + b*x)/b**3","A",0
1590,1,20,0,0.173340," ","integrate((e*x+d)/((b*x+a)**2)**(1/2),x)","\frac{e x}{b} - \frac{\left(a e - b d\right) \log{\left(a + b x \right)}}{b^{2}}"," ",0,"e*x/b - (a*e - b*d)*log(a + b*x)/b**2","A",0
1591,1,7,0,0.083230," ","integrate(1/((b*x+a)**2)**(1/2),x)","\frac{\log{\left(a + b x \right)}}{b}"," ",0,"log(a + b*x)/b","A",0
1592,1,128,0,0.363608," ","integrate(1/(e*x+d)/((b*x+a)**2)**(1/2),x)","\frac{\log{\left(x + \frac{- \frac{a^{2} e^{2}}{a e - b d} + \frac{2 a b d e}{a e - b d} + a e - \frac{b^{2} d^{2}}{a e - b d} + b d}{2 b e} \right)}}{a e - b d} - \frac{\log{\left(x + \frac{\frac{a^{2} e^{2}}{a e - b d} - \frac{2 a b d e}{a e - b d} + a e + \frac{b^{2} d^{2}}{a e - b d} + b d}{2 b e} \right)}}{a e - b d}"," ",0,"log(x + (-a**2*e**2/(a*e - b*d) + 2*a*b*d*e/(a*e - b*d) + a*e - b**2*d**2/(a*e - b*d) + b*d)/(2*b*e))/(a*e - b*d) - log(x + (a**2*e**2/(a*e - b*d) - 2*a*b*d*e/(a*e - b*d) + a*e + b**2*d**2/(a*e - b*d) + b*d)/(2*b*e))/(a*e - b*d)","B",0
1593,1,233,0,0.714843," ","integrate(1/(e*x+d)**2/((b*x+a)**2)**(1/2),x)","- \frac{b \log{\left(x + \frac{- \frac{a^{3} b e^{3}}{\left(a e - b d\right)^{2}} + \frac{3 a^{2} b^{2} d e^{2}}{\left(a e - b d\right)^{2}} - \frac{3 a b^{3} d^{2} e}{\left(a e - b d\right)^{2}} + a b e + \frac{b^{4} d^{3}}{\left(a e - b d\right)^{2}} + b^{2} d}{2 b^{2} e} \right)}}{\left(a e - b d\right)^{2}} + \frac{b \log{\left(x + \frac{\frac{a^{3} b e^{3}}{\left(a e - b d\right)^{2}} - \frac{3 a^{2} b^{2} d e^{2}}{\left(a e - b d\right)^{2}} + \frac{3 a b^{3} d^{2} e}{\left(a e - b d\right)^{2}} + a b e - \frac{b^{4} d^{3}}{\left(a e - b d\right)^{2}} + b^{2} d}{2 b^{2} e} \right)}}{\left(a e - b d\right)^{2}} - \frac{1}{a d e - b d^{2} + x \left(a e^{2} - b d e\right)}"," ",0,"-b*log(x + (-a**3*b*e**3/(a*e - b*d)**2 + 3*a**2*b**2*d*e**2/(a*e - b*d)**2 - 3*a*b**3*d**2*e/(a*e - b*d)**2 + a*b*e + b**4*d**3/(a*e - b*d)**2 + b**2*d)/(2*b**2*e))/(a*e - b*d)**2 + b*log(x + (a**3*b*e**3/(a*e - b*d)**2 - 3*a**2*b**2*d*e**2/(a*e - b*d)**2 + 3*a*b**3*d**2*e/(a*e - b*d)**2 + a*b*e - b**4*d**3/(a*e - b*d)**2 + b**2*d)/(2*b**2*e))/(a*e - b*d)**2 - 1/(a*d*e - b*d**2 + x*(a*e**2 - b*d*e))","B",0
1594,1,381,0,1.117212," ","integrate(1/(e*x+d)**3/((b*x+a)**2)**(1/2),x)","\frac{b^{2} \log{\left(x + \frac{- \frac{a^{4} b^{2} e^{4}}{\left(a e - b d\right)^{3}} + \frac{4 a^{3} b^{3} d e^{3}}{\left(a e - b d\right)^{3}} - \frac{6 a^{2} b^{4} d^{2} e^{2}}{\left(a e - b d\right)^{3}} + \frac{4 a b^{5} d^{3} e}{\left(a e - b d\right)^{3}} + a b^{2} e - \frac{b^{6} d^{4}}{\left(a e - b d\right)^{3}} + b^{3} d}{2 b^{3} e} \right)}}{\left(a e - b d\right)^{3}} - \frac{b^{2} \log{\left(x + \frac{\frac{a^{4} b^{2} e^{4}}{\left(a e - b d\right)^{3}} - \frac{4 a^{3} b^{3} d e^{3}}{\left(a e - b d\right)^{3}} + \frac{6 a^{2} b^{4} d^{2} e^{2}}{\left(a e - b d\right)^{3}} - \frac{4 a b^{5} d^{3} e}{\left(a e - b d\right)^{3}} + a b^{2} e + \frac{b^{6} d^{4}}{\left(a e - b d\right)^{3}} + b^{3} d}{2 b^{3} e} \right)}}{\left(a e - b d\right)^{3}} + \frac{- a e + 3 b d + 2 b e x}{2 a^{2} d^{2} e^{2} - 4 a b d^{3} e + 2 b^{2} d^{4} + x^{2} \left(2 a^{2} e^{4} - 4 a b d e^{3} + 2 b^{2} d^{2} e^{2}\right) + x \left(4 a^{2} d e^{3} - 8 a b d^{2} e^{2} + 4 b^{2} d^{3} e\right)}"," ",0,"b**2*log(x + (-a**4*b**2*e**4/(a*e - b*d)**3 + 4*a**3*b**3*d*e**3/(a*e - b*d)**3 - 6*a**2*b**4*d**2*e**2/(a*e - b*d)**3 + 4*a*b**5*d**3*e/(a*e - b*d)**3 + a*b**2*e - b**6*d**4/(a*e - b*d)**3 + b**3*d)/(2*b**3*e))/(a*e - b*d)**3 - b**2*log(x + (a**4*b**2*e**4/(a*e - b*d)**3 - 4*a**3*b**3*d*e**3/(a*e - b*d)**3 + 6*a**2*b**4*d**2*e**2/(a*e - b*d)**3 - 4*a*b**5*d**3*e/(a*e - b*d)**3 + a*b**2*e + b**6*d**4/(a*e - b*d)**3 + b**3*d)/(2*b**3*e))/(a*e - b*d)**3 + (-a*e + 3*b*d + 2*b*e*x)/(2*a**2*d**2*e**2 - 4*a*b*d**3*e + 2*b**2*d**4 + x**2*(2*a**2*e**4 - 4*a*b*d*e**3 + 2*b**2*d**2*e**2) + x*(4*a**2*d*e**3 - 8*a*b*d**2*e**2 + 4*b**2*d**3*e))","B",0
1595,1,570,0,1.545079," ","integrate(1/(e*x+d)**4/((b*x+a)**2)**(1/2),x)","- \frac{b^{3} \log{\left(x + \frac{- \frac{a^{5} b^{3} e^{5}}{\left(a e - b d\right)^{4}} + \frac{5 a^{4} b^{4} d e^{4}}{\left(a e - b d\right)^{4}} - \frac{10 a^{3} b^{5} d^{2} e^{3}}{\left(a e - b d\right)^{4}} + \frac{10 a^{2} b^{6} d^{3} e^{2}}{\left(a e - b d\right)^{4}} - \frac{5 a b^{7} d^{4} e}{\left(a e - b d\right)^{4}} + a b^{3} e + \frac{b^{8} d^{5}}{\left(a e - b d\right)^{4}} + b^{4} d}{2 b^{4} e} \right)}}{\left(a e - b d\right)^{4}} + \frac{b^{3} \log{\left(x + \frac{\frac{a^{5} b^{3} e^{5}}{\left(a e - b d\right)^{4}} - \frac{5 a^{4} b^{4} d e^{4}}{\left(a e - b d\right)^{4}} + \frac{10 a^{3} b^{5} d^{2} e^{3}}{\left(a e - b d\right)^{4}} - \frac{10 a^{2} b^{6} d^{3} e^{2}}{\left(a e - b d\right)^{4}} + \frac{5 a b^{7} d^{4} e}{\left(a e - b d\right)^{4}} + a b^{3} e - \frac{b^{8} d^{5}}{\left(a e - b d\right)^{4}} + b^{4} d}{2 b^{4} e} \right)}}{\left(a e - b d\right)^{4}} + \frac{- 2 a^{2} e^{2} + 7 a b d e - 11 b^{2} d^{2} - 6 b^{2} e^{2} x^{2} + x \left(3 a b e^{2} - 15 b^{2} d e\right)}{6 a^{3} d^{3} e^{3} - 18 a^{2} b d^{4} e^{2} + 18 a b^{2} d^{5} e - 6 b^{3} d^{6} + x^{3} \left(6 a^{3} e^{6} - 18 a^{2} b d e^{5} + 18 a b^{2} d^{2} e^{4} - 6 b^{3} d^{3} e^{3}\right) + x^{2} \left(18 a^{3} d e^{5} - 54 a^{2} b d^{2} e^{4} + 54 a b^{2} d^{3} e^{3} - 18 b^{3} d^{4} e^{2}\right) + x \left(18 a^{3} d^{2} e^{4} - 54 a^{2} b d^{3} e^{3} + 54 a b^{2} d^{4} e^{2} - 18 b^{3} d^{5} e\right)}"," ",0,"-b**3*log(x + (-a**5*b**3*e**5/(a*e - b*d)**4 + 5*a**4*b**4*d*e**4/(a*e - b*d)**4 - 10*a**3*b**5*d**2*e**3/(a*e - b*d)**4 + 10*a**2*b**6*d**3*e**2/(a*e - b*d)**4 - 5*a*b**7*d**4*e/(a*e - b*d)**4 + a*b**3*e + b**8*d**5/(a*e - b*d)**4 + b**4*d)/(2*b**4*e))/(a*e - b*d)**4 + b**3*log(x + (a**5*b**3*e**5/(a*e - b*d)**4 - 5*a**4*b**4*d*e**4/(a*e - b*d)**4 + 10*a**3*b**5*d**2*e**3/(a*e - b*d)**4 - 10*a**2*b**6*d**3*e**2/(a*e - b*d)**4 + 5*a*b**7*d**4*e/(a*e - b*d)**4 + a*b**3*e - b**8*d**5/(a*e - b*d)**4 + b**4*d)/(2*b**4*e))/(a*e - b*d)**4 + (-2*a**2*e**2 + 7*a*b*d*e - 11*b**2*d**2 - 6*b**2*e**2*x**2 + x*(3*a*b*e**2 - 15*b**2*d*e))/(6*a**3*d**3*e**3 - 18*a**2*b*d**4*e**2 + 18*a*b**2*d**5*e - 6*b**3*d**6 + x**3*(6*a**3*e**6 - 18*a**2*b*d*e**5 + 18*a*b**2*d**2*e**4 - 6*b**3*d**3*e**3) + x**2*(18*a**3*d*e**5 - 54*a**2*b*d**2*e**4 + 54*a*b**2*d**3*e**3 - 18*b**3*d**4*e**2) + x*(18*a**3*d**2*e**4 - 54*a**2*b*d**3*e**3 + 54*a*b**2*d**4*e**2 - 18*b**3*d**5*e))","B",0
1596,0,0,0,0.000000," ","integrate((e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/((a + b*x)**2)**(3/2), x)","F",0
1597,0,0,0,0.000000," ","integrate((e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/((a + b*x)**2)**(3/2), x)","F",0
1598,0,0,0,0.000000," ","integrate((e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/((a + b*x)**2)**(3/2), x)","F",0
1599,0,0,0,0.000000," ","integrate((e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{d + e x}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)/((a + b*x)**2)**(3/2), x)","F",0
1600,0,0,0,0.000000," ","integrate(1/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{\left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2)**(-3/2), x)","F",0
1601,0,0,0,0.000000," ","integrate(1/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{\left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*((a + b*x)**2)**(3/2)), x)","F",0
1602,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{\left(d + e x\right)^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**2*((a + b*x)**2)**(3/2)), x)","F",0
1603,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{\left(d + e x\right)^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**3*((a + b*x)**2)**(3/2)), x)","F",0
1604,0,0,0,0.000000," ","integrate((e*x+d)**6/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{6}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**6/((a + b*x)**2)**(5/2), x)","F",0
1605,0,0,0,0.000000," ","integrate((e*x+d)**5/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{5}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**5/((a + b*x)**2)**(5/2), x)","F",0
1606,0,0,0,0.000000," ","integrate((e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/((a + b*x)**2)**(5/2), x)","F",0
1607,0,0,0,0.000000," ","integrate((e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/((a + b*x)**2)**(5/2), x)","F",0
1608,0,0,0,0.000000," ","integrate((e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/((a + b*x)**2)**(5/2), x)","F",0
1609,0,0,0,0.000000," ","integrate((e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{d + e x}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)/((a + b*x)**2)**(5/2), x)","F",0
1610,0,0,0,0.000000," ","integrate(1/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{1}{\left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2)**(-5/2), x)","F",0
1611,0,0,0,0.000000," ","integrate(1/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{1}{\left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*((a + b*x)**2)**(5/2)), x)","F",0
1612,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{1}{\left(d + e x\right)^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**2*((a + b*x)**2)**(5/2)), x)","F",0
1613,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{1}{\left(d + e x\right)^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**3*((a + b*x)**2)**(5/2)), x)","F",0
1614,0,0,0,0.000000," ","integrate((e*x+d)*(4*x**2+12*x+9)**(5/2),x)","\int \left(d + e x\right) \left(\left(2 x + 3\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x)*((2*x + 3)**2)**(5/2), x)","F",0
1615,0,0,0,0.000000," ","integrate((e*x+d)*(4*x**2+12*x+9)**(3/2),x)","\int \left(d + e x\right) \left(\left(2 x + 3\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)*((2*x + 3)**2)**(3/2), x)","F",0
1616,0,0,0,0.000000," ","integrate((e*x+d)*(4*x**2+12*x+9)**(1/2),x)","\int \left(d + e x\right) \sqrt{\left(2 x + 3\right)^{2}}\, dx"," ",0,"Integral((d + e*x)*sqrt((2*x + 3)**2), x)","F",0
1617,0,0,0,0.000000," ","integrate((e*x+d)/(4*x**2+12*x+9)**(1/2),x)","\int \frac{d + e x}{\sqrt{\left(2 x + 3\right)^{2}}}\, dx"," ",0,"Integral((d + e*x)/sqrt((2*x + 3)**2), x)","F",0
1618,0,0,0,0.000000," ","integrate((e*x+d)/(4*x**2+12*x+9)**(3/2),x)","\int \frac{d + e x}{\left(\left(2 x + 3\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)/((2*x + 3)**2)**(3/2), x)","F",0
1619,0,0,0,0.000000," ","integrate((e*x+d)/(4*x**2+12*x+9)**(5/2),x)","\int \frac{d + e x}{\left(\left(2 x + 3\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)/((2*x + 3)**2)**(5/2), x)","F",0
1620,0,0,0,0.000000," ","integrate((e*x+d)/(4*x**2+12*x+9)**(7/2),x)","\int \frac{d + e x}{\left(\left(2 x + 3\right)^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)/((2*x + 3)**2)**(7/2), x)","F",0
1621,1,432,0,8.345594," ","integrate((e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \frac{2 a^{2} d^{4} \sqrt{d + e x}}{9 e} + \frac{8 a^{2} d^{3} x \sqrt{d + e x}}{9} + \frac{4 a^{2} d^{2} e x^{2} \sqrt{d + e x}}{3} + \frac{8 a^{2} d e^{2} x^{3} \sqrt{d + e x}}{9} + \frac{2 a^{2} e^{3} x^{4} \sqrt{d + e x}}{9} - \frac{8 a b d^{5} \sqrt{d + e x}}{99 e^{2}} + \frac{4 a b d^{4} x \sqrt{d + e x}}{99 e} + \frac{32 a b d^{3} x^{2} \sqrt{d + e x}}{33} + \frac{184 a b d^{2} e x^{3} \sqrt{d + e x}}{99} + \frac{136 a b d e^{2} x^{4} \sqrt{d + e x}}{99} + \frac{4 a b e^{3} x^{5} \sqrt{d + e x}}{11} + \frac{16 b^{2} d^{6} \sqrt{d + e x}}{1287 e^{3}} - \frac{8 b^{2} d^{5} x \sqrt{d + e x}}{1287 e^{2}} + \frac{2 b^{2} d^{4} x^{2} \sqrt{d + e x}}{429 e} + \frac{424 b^{2} d^{3} x^{3} \sqrt{d + e x}}{1287} + \frac{916 b^{2} d^{2} e x^{4} \sqrt{d + e x}}{1287} + \frac{80 b^{2} d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{2 b^{2} e^{3} x^{6} \sqrt{d + e x}}{13} & \text{for}\: e \neq 0 \\d^{\frac{7}{2}} \left(a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*d**4*sqrt(d + e*x)/(9*e) + 8*a**2*d**3*x*sqrt(d + e*x)/9 + 4*a**2*d**2*e*x**2*sqrt(d + e*x)/3 + 8*a**2*d*e**2*x**3*sqrt(d + e*x)/9 + 2*a**2*e**3*x**4*sqrt(d + e*x)/9 - 8*a*b*d**5*sqrt(d + e*x)/(99*e**2) + 4*a*b*d**4*x*sqrt(d + e*x)/(99*e) + 32*a*b*d**3*x**2*sqrt(d + e*x)/33 + 184*a*b*d**2*e*x**3*sqrt(d + e*x)/99 + 136*a*b*d*e**2*x**4*sqrt(d + e*x)/99 + 4*a*b*e**3*x**5*sqrt(d + e*x)/11 + 16*b**2*d**6*sqrt(d + e*x)/(1287*e**3) - 8*b**2*d**5*x*sqrt(d + e*x)/(1287*e**2) + 2*b**2*d**4*x**2*sqrt(d + e*x)/(429*e) + 424*b**2*d**3*x**3*sqrt(d + e*x)/1287 + 916*b**2*d**2*e*x**4*sqrt(d + e*x)/1287 + 80*b**2*d*e**2*x**5*sqrt(d + e*x)/143 + 2*b**2*e**3*x**6*sqrt(d + e*x)/13, Ne(e, 0)), (d**(7/2)*(a**2*x + a*b*x**2 + b**2*x**3/3), True))","A",0
1622,1,355,0,3.582930," ","integrate((e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \frac{2 a^{2} d^{3} \sqrt{d + e x}}{7 e} + \frac{6 a^{2} d^{2} x \sqrt{d + e x}}{7} + \frac{6 a^{2} d e x^{2} \sqrt{d + e x}}{7} + \frac{2 a^{2} e^{2} x^{3} \sqrt{d + e x}}{7} - \frac{8 a b d^{4} \sqrt{d + e x}}{63 e^{2}} + \frac{4 a b d^{3} x \sqrt{d + e x}}{63 e} + \frac{20 a b d^{2} x^{2} \sqrt{d + e x}}{21} + \frac{76 a b d e x^{3} \sqrt{d + e x}}{63} + \frac{4 a b e^{2} x^{4} \sqrt{d + e x}}{9} + \frac{16 b^{2} d^{5} \sqrt{d + e x}}{693 e^{3}} - \frac{8 b^{2} d^{4} x \sqrt{d + e x}}{693 e^{2}} + \frac{2 b^{2} d^{3} x^{2} \sqrt{d + e x}}{231 e} + \frac{226 b^{2} d^{2} x^{3} \sqrt{d + e x}}{693} + \frac{46 b^{2} d e x^{4} \sqrt{d + e x}}{99} + \frac{2 b^{2} e^{2} x^{5} \sqrt{d + e x}}{11} & \text{for}\: e \neq 0 \\d^{\frac{5}{2}} \left(a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*d**3*sqrt(d + e*x)/(7*e) + 6*a**2*d**2*x*sqrt(d + e*x)/7 + 6*a**2*d*e*x**2*sqrt(d + e*x)/7 + 2*a**2*e**2*x**3*sqrt(d + e*x)/7 - 8*a*b*d**4*sqrt(d + e*x)/(63*e**2) + 4*a*b*d**3*x*sqrt(d + e*x)/(63*e) + 20*a*b*d**2*x**2*sqrt(d + e*x)/21 + 76*a*b*d*e*x**3*sqrt(d + e*x)/63 + 4*a*b*e**2*x**4*sqrt(d + e*x)/9 + 16*b**2*d**5*sqrt(d + e*x)/(693*e**3) - 8*b**2*d**4*x*sqrt(d + e*x)/(693*e**2) + 2*b**2*d**3*x**2*sqrt(d + e*x)/(231*e) + 226*b**2*d**2*x**3*sqrt(d + e*x)/693 + 46*b**2*d*e*x**4*sqrt(d + e*x)/99 + 2*b**2*e**2*x**5*sqrt(d + e*x)/11, Ne(e, 0)), (d**(5/2)*(a**2*x + a*b*x**2 + b**2*x**3/3), True))","A",0
1623,1,240,0,10.700404," ","integrate((e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2),x)","a^{2} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{4 a b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{4 a b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}}"," ",0,"a**2*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 4*a*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 4*a*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3","A",0
1624,1,85,0,3.494615," ","integrate((b**2*x**2+2*a*b*x+a**2)*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{b^{2} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{2}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(2 a b e - 2 b^{2} d\right)}{5 e^{2}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{2} e^{2} - 2 a b d e + b^{2} d^{2}\right)}{3 e^{2}}\right)}{e}"," ",0,"2*(b**2*(d + e*x)**(7/2)/(7*e**2) + (d + e*x)**(5/2)*(2*a*b*e - 2*b**2*d)/(5*e**2) + (d + e*x)**(3/2)*(a**2*e**2 - 2*a*b*d*e + b**2*d**2)/(3*e**2))/e","A",0
1625,1,236,0,11.123775," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{2} d}{\sqrt{d + e x}} - 2 a^{2} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{4 a b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{4 a b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{2 b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}}}{e} & \text{for}\: e \neq 0 \\\frac{a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**2*d/sqrt(d + e*x) - 2*a**2*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 4*a*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 4*a*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 2*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2)/e, Ne(e, 0)), ((a**2*x + a*b*x**2 + b**2*x**3/3)/sqrt(d), True))","A",0
1626,1,65,0,13.709980," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(3/2),x)","\frac{2 b^{2} \left(d + e x\right)^{\frac{3}{2}}}{3 e^{3}} + \frac{\sqrt{d + e x} \left(4 a b e - 4 b^{2} d\right)}{e^{3}} - \frac{2 \left(a e - b d\right)^{2}}{e^{3} \sqrt{d + e x}}"," ",0,"2*b**2*(d + e*x)**(3/2)/(3*e**3) + sqrt(d + e*x)*(4*a*b*e - 4*b**2*d)/e**3 - 2*(a*e - b*d)**2/(e**3*sqrt(d + e*x))","A",0
1627,1,265,0,1.323498," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(5/2),x)","\begin{cases} - \frac{2 a^{2} e^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} - \frac{8 a b d e}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} - \frac{12 a b e^{2} x}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{16 b^{2} d^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{24 b^{2} d e x}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{6 b^{2} e^{2} x^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}}{d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*e**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) - 8*a*b*d*e/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) - 12*a*b*e**2*x/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 16*b**2*d**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 24*b**2*d*e*x/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 6*b**2*e**2*x**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)), Ne(e, 0)), ((a**2*x + a*b*x**2 + b**2*x**3/3)/d**(5/2), True))","A",0
1628,1,389,0,3.037499," ","integrate((b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 a^{2} e^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{8 a b d e}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{20 a b e^{2} x}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{16 b^{2} d^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{40 b^{2} d e x}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{30 b^{2} e^{2} x^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a**2*e**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 8*a*b*d*e/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 20*a*b*e**2*x/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 16*b**2*d**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 40*b**2*d*e*x/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 30*b**2*e**2*x**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)), Ne(e, 0)), ((a**2*x + a*b*x**2 + b**2*x**3/3)/d**(7/2), True))","A",0
1629,1,903,0,14.072265," ","integrate((e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\begin{cases} \frac{2 a^{4} d^{4} \sqrt{d + e x}}{9 e} + \frac{8 a^{4} d^{3} x \sqrt{d + e x}}{9} + \frac{4 a^{4} d^{2} e x^{2} \sqrt{d + e x}}{3} + \frac{8 a^{4} d e^{2} x^{3} \sqrt{d + e x}}{9} + \frac{2 a^{4} e^{3} x^{4} \sqrt{d + e x}}{9} - \frac{16 a^{3} b d^{5} \sqrt{d + e x}}{99 e^{2}} + \frac{8 a^{3} b d^{4} x \sqrt{d + e x}}{99 e} + \frac{64 a^{3} b d^{3} x^{2} \sqrt{d + e x}}{33} + \frac{368 a^{3} b d^{2} e x^{3} \sqrt{d + e x}}{99} + \frac{272 a^{3} b d e^{2} x^{4} \sqrt{d + e x}}{99} + \frac{8 a^{3} b e^{3} x^{5} \sqrt{d + e x}}{11} + \frac{32 a^{2} b^{2} d^{6} \sqrt{d + e x}}{429 e^{3}} - \frac{16 a^{2} b^{2} d^{5} x \sqrt{d + e x}}{429 e^{2}} + \frac{4 a^{2} b^{2} d^{4} x^{2} \sqrt{d + e x}}{143 e} + \frac{848 a^{2} b^{2} d^{3} x^{3} \sqrt{d + e x}}{429} + \frac{1832 a^{2} b^{2} d^{2} e x^{4} \sqrt{d + e x}}{429} + \frac{480 a^{2} b^{2} d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{12 a^{2} b^{2} e^{3} x^{6} \sqrt{d + e x}}{13} - \frac{128 a b^{3} d^{7} \sqrt{d + e x}}{6435 e^{4}} + \frac{64 a b^{3} d^{6} x \sqrt{d + e x}}{6435 e^{3}} - \frac{16 a b^{3} d^{5} x^{2} \sqrt{d + e x}}{2145 e^{2}} + \frac{8 a b^{3} d^{4} x^{3} \sqrt{d + e x}}{1287 e} + \frac{1280 a b^{3} d^{3} x^{4} \sqrt{d + e x}}{1287} + \frac{1648 a b^{3} d^{2} e x^{5} \sqrt{d + e x}}{715} + \frac{368 a b^{3} d e^{2} x^{6} \sqrt{d + e x}}{195} + \frac{8 a b^{3} e^{3} x^{7} \sqrt{d + e x}}{15} + \frac{256 b^{4} d^{8} \sqrt{d + e x}}{109395 e^{5}} - \frac{128 b^{4} d^{7} x \sqrt{d + e x}}{109395 e^{4}} + \frac{32 b^{4} d^{6} x^{2} \sqrt{d + e x}}{36465 e^{3}} - \frac{16 b^{4} d^{5} x^{3} \sqrt{d + e x}}{21879 e^{2}} + \frac{14 b^{4} d^{4} x^{4} \sqrt{d + e x}}{21879 e} + \frac{2424 b^{4} d^{3} x^{5} \sqrt{d + e x}}{12155} + \frac{1604 b^{4} d^{2} e x^{6} \sqrt{d + e x}}{3315} + \frac{104 b^{4} d e^{2} x^{7} \sqrt{d + e x}}{255} + \frac{2 b^{4} e^{3} x^{8} \sqrt{d + e x}}{17} & \text{for}\: e \neq 0 \\d^{\frac{7}{2}} \left(a^{4} x + 2 a^{3} b x^{2} + 2 a^{2} b^{2} x^{3} + a b^{3} x^{4} + \frac{b^{4} x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**4*d**4*sqrt(d + e*x)/(9*e) + 8*a**4*d**3*x*sqrt(d + e*x)/9 + 4*a**4*d**2*e*x**2*sqrt(d + e*x)/3 + 8*a**4*d*e**2*x**3*sqrt(d + e*x)/9 + 2*a**4*e**3*x**4*sqrt(d + e*x)/9 - 16*a**3*b*d**5*sqrt(d + e*x)/(99*e**2) + 8*a**3*b*d**4*x*sqrt(d + e*x)/(99*e) + 64*a**3*b*d**3*x**2*sqrt(d + e*x)/33 + 368*a**3*b*d**2*e*x**3*sqrt(d + e*x)/99 + 272*a**3*b*d*e**2*x**4*sqrt(d + e*x)/99 + 8*a**3*b*e**3*x**5*sqrt(d + e*x)/11 + 32*a**2*b**2*d**6*sqrt(d + e*x)/(429*e**3) - 16*a**2*b**2*d**5*x*sqrt(d + e*x)/(429*e**2) + 4*a**2*b**2*d**4*x**2*sqrt(d + e*x)/(143*e) + 848*a**2*b**2*d**3*x**3*sqrt(d + e*x)/429 + 1832*a**2*b**2*d**2*e*x**4*sqrt(d + e*x)/429 + 480*a**2*b**2*d*e**2*x**5*sqrt(d + e*x)/143 + 12*a**2*b**2*e**3*x**6*sqrt(d + e*x)/13 - 128*a*b**3*d**7*sqrt(d + e*x)/(6435*e**4) + 64*a*b**3*d**6*x*sqrt(d + e*x)/(6435*e**3) - 16*a*b**3*d**5*x**2*sqrt(d + e*x)/(2145*e**2) + 8*a*b**3*d**4*x**3*sqrt(d + e*x)/(1287*e) + 1280*a*b**3*d**3*x**4*sqrt(d + e*x)/1287 + 1648*a*b**3*d**2*e*x**5*sqrt(d + e*x)/715 + 368*a*b**3*d*e**2*x**6*sqrt(d + e*x)/195 + 8*a*b**3*e**3*x**7*sqrt(d + e*x)/15 + 256*b**4*d**8*sqrt(d + e*x)/(109395*e**5) - 128*b**4*d**7*x*sqrt(d + e*x)/(109395*e**4) + 32*b**4*d**6*x**2*sqrt(d + e*x)/(36465*e**3) - 16*b**4*d**5*x**3*sqrt(d + e*x)/(21879*e**2) + 14*b**4*d**4*x**4*sqrt(d + e*x)/(21879*e) + 2424*b**4*d**3*x**5*sqrt(d + e*x)/12155 + 1604*b**4*d**2*e*x**6*sqrt(d + e*x)/3315 + 104*b**4*d*e**2*x**7*sqrt(d + e*x)/255 + 2*b**4*e**3*x**8*sqrt(d + e*x)/17, Ne(e, 0)), (d**(7/2)*(a**4*x + 2*a**3*b*x**2 + 2*a**2*b**2*x**3 + a*b**3*x**4 + b**4*x**5/5), True))","A",0
1630,1,960,0,35.256090," ","integrate((e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{4} d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 a^{4} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 a^{4} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{8 a^{3} b d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{16 a^{3} b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{8 a^{3} b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{12 a^{2} b^{2} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{24 a^{2} b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{12 a^{2} b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{8 a b^{3} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{16 a b^{3} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{8 a b^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{2 b^{4} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{4 b^{4} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 b^{4} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}}"," ",0,"a**4*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a**4*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*a**4*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 8*a**3*b*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 16*a**3*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 8*a**3*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 12*a**2*b**2*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 24*a**2*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 12*a**2*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 8*a*b**3*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 16*a*b**3*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 8*a*b**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 2*b**4*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 4*b**4*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*b**4*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5","A",0
1631,1,559,0,21.715256," ","integrate((e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{4} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{4} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{8 a^{3} b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{8 a^{3} b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{12 a^{2} b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{12 a^{2} b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{8 a b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{8 a b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 b^{4} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{2 b^{4} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}}"," ",0,"a**4*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**4*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 8*a**3*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 8*a**3*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 12*a**2*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 12*a**2*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 8*a*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 8*a*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*b**4*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 2*b**4*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5","A",0
1632,1,223,0,5.278794," ","integrate((b**2*x**2+2*a*b*x+a**2)**2*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{b^{4} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{4}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(4 a b^{3} e - 4 b^{4} d\right)}{9 e^{4}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(6 a^{2} b^{2} e^{2} - 12 a b^{3} d e + 6 b^{4} d^{2}\right)}{7 e^{4}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(4 a^{3} b e^{3} - 12 a^{2} b^{2} d e^{2} + 12 a b^{3} d^{2} e - 4 b^{4} d^{3}\right)}{5 e^{4}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{4} e^{4} - 4 a^{3} b d e^{3} + 6 a^{2} b^{2} d^{2} e^{2} - 4 a b^{3} d^{3} e + b^{4} d^{4}\right)}{3 e^{4}}\right)}{e}"," ",0,"2*(b**4*(d + e*x)**(11/2)/(11*e**4) + (d + e*x)**(9/2)*(4*a*b**3*e - 4*b**4*d)/(9*e**4) + (d + e*x)**(7/2)*(6*a**2*b**2*e**2 - 12*a*b**3*d*e + 6*b**4*d**2)/(7*e**4) + (d + e*x)**(5/2)*(4*a**3*b*e**3 - 12*a**2*b**2*d*e**2 + 12*a*b**3*d**2*e - 4*b**4*d**3)/(5*e**4) + (d + e*x)**(3/2)*(a**4*e**4 - 4*a**3*b*d*e**3 + 6*a**2*b**2*d**2*e**2 - 4*a*b**3*d**3*e + b**4*d**4)/(3*e**4))/e","A",0
1633,1,561,0,56.840955," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{4} d}{\sqrt{d + e x}} - 2 a^{4} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{8 a^{3} b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{8 a^{3} b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{12 a^{2} b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{12 a^{2} b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{8 a b^{3} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{8 a b^{3} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{2 b^{4} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{2 b^{4} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}}}{e} & \text{for}\: e \neq 0 \\\frac{a^{4} x + 2 a^{3} b x^{2} + 2 a^{2} b^{2} x^{3} + a b^{3} x^{4} + \frac{b^{4} x^{5}}{5}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**4*d/sqrt(d + e*x) - 2*a**4*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 8*a**3*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 8*a**3*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 12*a**2*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 12*a**2*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 8*a*b**3*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 8*a*b**3*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 2*b**4*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 2*b**4*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4)/e, Ne(e, 0)), ((a**4*x + 2*a**3*b*x**2 + 2*a**2*b**2*x**3 + a*b**3*x**4 + b**4*x**5/5)/sqrt(d), True))","A",0
1634,1,168,0,33.848202," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(3/2),x)","\frac{2 b^{4} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{5}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(8 a b^{3} e - 8 b^{4} d\right)}{5 e^{5}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(12 a^{2} b^{2} e^{2} - 24 a b^{3} d e + 12 b^{4} d^{2}\right)}{3 e^{5}} + \frac{\sqrt{d + e x} \left(8 a^{3} b e^{3} - 24 a^{2} b^{2} d e^{2} + 24 a b^{3} d^{2} e - 8 b^{4} d^{3}\right)}{e^{5}} - \frac{2 \left(a e - b d\right)^{4}}{e^{5} \sqrt{d + e x}}"," ",0,"2*b**4*(d + e*x)**(7/2)/(7*e**5) + (d + e*x)**(5/2)*(8*a*b**3*e - 8*b**4*d)/(5*e**5) + (d + e*x)**(3/2)*(12*a**2*b**2*e**2 - 24*a*b**3*d*e + 12*b**4*d**2)/(3*e**5) + sqrt(d + e*x)*(8*a**3*b*e**3 - 24*a**2*b**2*d*e**2 + 24*a*b**3*d**2*e - 8*b**4*d**3)/e**5 - 2*(a*e - b*d)**4/(e**5*sqrt(d + e*x))","A",0
1635,1,136,0,45.306819," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(5/2),x)","\frac{2 b^{4} \left(d + e x\right)^{\frac{5}{2}}}{5 e^{5}} - \frac{8 b \left(a e - b d\right)^{3}}{e^{5} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(8 a b^{3} e - 8 b^{4} d\right)}{3 e^{5}} + \frac{\sqrt{d + e x} \left(12 a^{2} b^{2} e^{2} - 24 a b^{3} d e + 12 b^{4} d^{2}\right)}{e^{5}} - \frac{2 \left(a e - b d\right)^{4}}{3 e^{5} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"2*b**4*(d + e*x)**(5/2)/(5*e**5) - 8*b*(a*e - b*d)**3/(e**5*sqrt(d + e*x)) + (d + e*x)**(3/2)*(8*a*b**3*e - 8*b**4*d)/(3*e**5) + sqrt(d + e*x)*(12*a**2*b**2*e**2 - 24*a*b**3*d*e + 12*b**4*d**2)/e**5 - 2*(a*e - b*d)**4/(3*e**5*(d + e*x)**(3/2))","A",0
1636,1,1008,0,3.880600," ","integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 a^{4} e^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{16 a^{3} b d e^{3}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{40 a^{3} b e^{4} x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{96 a^{2} b^{2} d^{2} e^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{240 a^{2} b^{2} d e^{3} x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{180 a^{2} b^{2} e^{4} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{384 a b^{3} d^{3} e}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{960 a b^{3} d^{2} e^{2} x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{720 a b^{3} d e^{3} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{120 a b^{3} e^{4} x^{3}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{256 b^{4} d^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{640 b^{4} d^{3} e x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{480 b^{4} d^{2} e^{2} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{80 b^{4} d e^{3} x^{3}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{10 b^{4} e^{4} x^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a^{4} x + 2 a^{3} b x^{2} + 2 a^{2} b^{2} x^{3} + a b^{3} x^{4} + \frac{b^{4} x^{5}}{5}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a**4*e**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 16*a**3*b*d*e**3/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 40*a**3*b*e**4*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 96*a**2*b**2*d**2*e**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 240*a**2*b**2*d*e**3*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 180*a**2*b**2*e**4*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 384*a*b**3*d**3*e/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 960*a*b**3*d**2*e**2*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 720*a*b**3*d*e**3*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 120*a*b**3*e**4*x**3/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 256*b**4*d**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 640*b**4*d**3*e*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 480*b**4*d**2*e**2*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 80*b**4*d*e**3*x**3/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 10*b**4*e**4*x**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)), Ne(e, 0)), ((a**4*x + 2*a**3*b*x**2 + 2*a**2*b**2*x**3 + a*b**3*x**4 + b**4*x**5/5)/d**(7/2), True))","A",0
1637,1,2450,0,82.648485," ","integrate((e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d^{3} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{6 a^{6} d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{6 a^{6} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{2 a^{6} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e} + \frac{12 a^{5} b d^{3} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{36 a^{5} b d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{36 a^{5} b d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{12 a^{5} b \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{2}} + \frac{30 a^{4} b^{2} d^{3} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{90 a^{4} b^{2} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{90 a^{4} b^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{30 a^{4} b^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{3}} + \frac{40 a^{3} b^{3} d^{3} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{120 a^{3} b^{3} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{120 a^{3} b^{3} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{40 a^{3} b^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{4}} + \frac{30 a^{2} b^{4} d^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{90 a^{2} b^{4} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{90 a^{2} b^{4} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{30 a^{2} b^{4} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{5}} + \frac{12 a b^{5} d^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{36 a b^{5} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{36 a b^{5} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{12 a b^{5} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{6}} + \frac{2 b^{6} d^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{6 b^{6} d^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{6 b^{6} d \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}} + \frac{2 b^{6} \left(- \frac{d^{9} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{9 d^{8} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{36 d^{7} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{28 d^{6} \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{126 d^{5} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{126 d^{4} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{28 d^{3} \left(d + e x\right)^{\frac{15}{2}}}{5} + \frac{36 d^{2} \left(d + e x\right)^{\frac{17}{2}}}{17} - \frac{9 d \left(d + e x\right)^{\frac{19}{2}}}{19} + \frac{\left(d + e x\right)^{\frac{21}{2}}}{21}\right)}{e^{7}}"," ",0,"a**6*d**3*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 6*a**6*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 6*a**6*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 2*a**6*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e + 12*a**5*b*d**3*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 36*a**5*b*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 36*a**5*b*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 12*a**5*b*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**2 + 30*a**4*b**2*d**3*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 90*a**4*b**2*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 90*a**4*b**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 30*a**4*b**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**3 + 40*a**3*b**3*d**3*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 120*a**3*b**3*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 120*a**3*b**3*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 40*a**3*b**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**4 + 30*a**2*b**4*d**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 90*a**2*b**4*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 90*a**2*b**4*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 30*a**2*b**4*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**5 + 12*a*b**5*d**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 36*a*b**5*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 36*a*b**5*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 12*a*b**5*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**6 + 2*b**6*d**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 6*b**6*d**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 6*b**6*d*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 2*b**6*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**7","A",0
1638,1,1671,0,57.336432," ","integrate((e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 a^{6} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 a^{6} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{12 a^{5} b d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{24 a^{5} b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{12 a^{5} b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{30 a^{4} b^{2} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{60 a^{4} b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{30 a^{4} b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{40 a^{3} b^{3} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{80 a^{3} b^{3} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{40 a^{3} b^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{30 a^{2} b^{4} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{60 a^{2} b^{4} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{30 a^{2} b^{4} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{12 a b^{5} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{24 a b^{5} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{12 a b^{5} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{2 b^{6} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{4 b^{6} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{2 b^{6} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}}"," ",0,"a**6*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a**6*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*a**6*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 12*a**5*b*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 24*a**5*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 12*a**5*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 30*a**4*b**2*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 60*a**4*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 30*a**4*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 40*a**3*b**3*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 80*a**3*b**3*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 40*a**3*b**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 30*a**2*b**4*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 60*a**2*b**4*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 30*a**2*b**4*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 12*a*b**5*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 24*a*b**5*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 12*a*b**5*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 2*b**6*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 4*b**6*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 2*b**6*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7","A",0
1639,1,1000,0,35.949788," ","integrate((e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{6} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{6} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{12 a^{5} b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{12 a^{5} b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{30 a^{4} b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{30 a^{4} b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{40 a^{3} b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{40 a^{3} b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{30 a^{2} b^{4} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{30 a^{2} b^{4} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{12 a b^{5} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{12 a b^{5} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{2 b^{6} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{2 b^{6} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}}"," ",0,"a**6*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**6*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 12*a**5*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 12*a**5*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 30*a**4*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 30*a**4*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 40*a**3*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 40*a**3*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 30*a**2*b**4*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 30*a**2*b**4*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 12*a*b**5*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 12*a*b**5*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 2*b**6*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 2*b**6*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7","A",0
1640,1,422,0,7.766029," ","integrate((b**2*x**2+2*a*b*x+a**2)**3*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{b^{6} \left(d + e x\right)^{\frac{15}{2}}}{15 e^{6}} + \frac{\left(d + e x\right)^{\frac{13}{2}} \left(6 a b^{5} e - 6 b^{6} d\right)}{13 e^{6}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(15 a^{2} b^{4} e^{2} - 30 a b^{5} d e + 15 b^{6} d^{2}\right)}{11 e^{6}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(20 a^{3} b^{3} e^{3} - 60 a^{2} b^{4} d e^{2} + 60 a b^{5} d^{2} e - 20 b^{6} d^{3}\right)}{9 e^{6}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(15 a^{4} b^{2} e^{4} - 60 a^{3} b^{3} d e^{3} + 90 a^{2} b^{4} d^{2} e^{2} - 60 a b^{5} d^{3} e + 15 b^{6} d^{4}\right)}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(6 a^{5} b e^{5} - 30 a^{4} b^{2} d e^{4} + 60 a^{3} b^{3} d^{2} e^{3} - 60 a^{2} b^{4} d^{3} e^{2} + 30 a b^{5} d^{4} e - 6 b^{6} d^{5}\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{6} e^{6} - 6 a^{5} b d e^{5} + 15 a^{4} b^{2} d^{2} e^{4} - 20 a^{3} b^{3} d^{3} e^{3} + 15 a^{2} b^{4} d^{4} e^{2} - 6 a b^{5} d^{5} e + b^{6} d^{6}\right)}{3 e^{6}}\right)}{e}"," ",0,"2*(b**6*(d + e*x)**(15/2)/(15*e**6) + (d + e*x)**(13/2)*(6*a*b**5*e - 6*b**6*d)/(13*e**6) + (d + e*x)**(11/2)*(15*a**2*b**4*e**2 - 30*a*b**5*d*e + 15*b**6*d**2)/(11*e**6) + (d + e*x)**(9/2)*(20*a**3*b**3*e**3 - 60*a**2*b**4*d*e**2 + 60*a*b**5*d**2*e - 20*b**6*d**3)/(9*e**6) + (d + e*x)**(7/2)*(15*a**4*b**2*e**4 - 60*a**3*b**3*d*e**3 + 90*a**2*b**4*d**2*e**2 - 60*a*b**5*d**3*e + 15*b**6*d**4)/(7*e**6) + (d + e*x)**(5/2)*(6*a**5*b*e**5 - 30*a**4*b**2*d*e**4 + 60*a**3*b**3*d**2*e**3 - 60*a**2*b**4*d**3*e**2 + 30*a*b**5*d**4*e - 6*b**6*d**5)/(5*e**6) + (d + e*x)**(3/2)*(a**6*e**6 - 6*a**5*b*d*e**5 + 15*a**4*b**2*d**2*e**4 - 20*a**3*b**3*d**3*e**3 + 15*a**2*b**4*d**4*e**2 - 6*a*b**5*d**5*e + b**6*d**6)/(3*e**6))/e","B",0
1641,1,1003,0,107.363797," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{6} d}{\sqrt{d + e x}} - 2 a^{6} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{12 a^{5} b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{12 a^{5} b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{30 a^{4} b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{30 a^{4} b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{40 a^{3} b^{3} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{40 a^{3} b^{3} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{30 a^{2} b^{4} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{30 a^{2} b^{4} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{12 a b^{5} d \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{5}} - \frac{12 a b^{5} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} - \frac{2 b^{6} d \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{6}} - \frac{2 b^{6} \left(- \frac{d^{7}}{\sqrt{d + e x}} - 7 d^{6} \sqrt{d + e x} + 7 d^{5} \left(d + e x\right)^{\frac{3}{2}} - 7 d^{4} \left(d + e x\right)^{\frac{5}{2}} + 5 d^{3} \left(d + e x\right)^{\frac{7}{2}} - \frac{7 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{3} + \frac{7 d \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}}}{e} & \text{for}\: e \neq 0 \\\frac{a^{6} x + 3 a^{5} b x^{2} + 5 a^{4} b^{2} x^{3} + 5 a^{3} b^{3} x^{4} + 3 a^{2} b^{4} x^{5} + a b^{5} x^{6} + \frac{b^{6} x^{7}}{7}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**6*d/sqrt(d + e*x) - 2*a**6*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 12*a**5*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 12*a**5*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 30*a**4*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 30*a**4*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 40*a**3*b**3*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 40*a**3*b**3*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 30*a**2*b**4*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 30*a**2*b**4*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 12*a*b**5*d*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**5 - 12*a*b**5*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**5 - 2*b**6*d*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**6 - 2*b**6*(-d**7/sqrt(d + e*x) - 7*d**6*sqrt(d + e*x) + 7*d**5*(d + e*x)**(3/2) - 7*d**4*(d + e*x)**(5/2) + 5*d**3*(d + e*x)**(7/2) - 7*d**2*(d + e*x)**(9/2)/3 + 7*d*(d + e*x)**(11/2)/11 - (d + e*x)**(13/2)/13)/e**6)/e, Ne(e, 0)), ((a**6*x + 3*a**5*b*x**2 + 5*a**4*b**2*x**3 + 5*a**3*b**3*x**4 + 3*a**2*b**4*x**5 + a*b**5*x**6 + b**6*x**7/7)/sqrt(d), True))","A",0
1642,1,333,0,69.697558," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(3/2),x)","\frac{2 b^{6} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{7}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(12 a b^{5} e - 12 b^{6} d\right)}{9 e^{7}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(30 a^{2} b^{4} e^{2} - 60 a b^{5} d e + 30 b^{6} d^{2}\right)}{7 e^{7}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(40 a^{3} b^{3} e^{3} - 120 a^{2} b^{4} d e^{2} + 120 a b^{5} d^{2} e - 40 b^{6} d^{3}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(30 a^{4} b^{2} e^{4} - 120 a^{3} b^{3} d e^{3} + 180 a^{2} b^{4} d^{2} e^{2} - 120 a b^{5} d^{3} e + 30 b^{6} d^{4}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(12 a^{5} b e^{5} - 60 a^{4} b^{2} d e^{4} + 120 a^{3} b^{3} d^{2} e^{3} - 120 a^{2} b^{4} d^{3} e^{2} + 60 a b^{5} d^{4} e - 12 b^{6} d^{5}\right)}{e^{7}} - \frac{2 \left(a e - b d\right)^{6}}{e^{7} \sqrt{d + e x}}"," ",0,"2*b**6*(d + e*x)**(11/2)/(11*e**7) + (d + e*x)**(9/2)*(12*a*b**5*e - 12*b**6*d)/(9*e**7) + (d + e*x)**(7/2)*(30*a**2*b**4*e**2 - 60*a*b**5*d*e + 30*b**6*d**2)/(7*e**7) + (d + e*x)**(5/2)*(40*a**3*b**3*e**3 - 120*a**2*b**4*d*e**2 + 120*a*b**5*d**2*e - 40*b**6*d**3)/(5*e**7) + (d + e*x)**(3/2)*(30*a**4*b**2*e**4 - 120*a**3*b**3*d*e**3 + 180*a**2*b**4*d**2*e**2 - 120*a*b**5*d**3*e + 30*b**6*d**4)/(3*e**7) + sqrt(d + e*x)*(12*a**5*b*e**5 - 60*a**4*b**2*d*e**4 + 120*a**3*b**3*d**2*e**3 - 120*a**2*b**4*d**3*e**2 + 60*a*b**5*d**4*e - 12*b**6*d**5)/e**7 - 2*(a*e - b*d)**6/(e**7*sqrt(d + e*x))","A",0
1643,1,270,0,83.163755," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(5/2),x)","\frac{2 b^{6} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{7}} - \frac{12 b \left(a e - b d\right)^{5}}{e^{7} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(12 a b^{5} e - 12 b^{6} d\right)}{7 e^{7}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(30 a^{2} b^{4} e^{2} - 60 a b^{5} d e + 30 b^{6} d^{2}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(40 a^{3} b^{3} e^{3} - 120 a^{2} b^{4} d e^{2} + 120 a b^{5} d^{2} e - 40 b^{6} d^{3}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(30 a^{4} b^{2} e^{4} - 120 a^{3} b^{3} d e^{3} + 180 a^{2} b^{4} d^{2} e^{2} - 120 a b^{5} d^{3} e + 30 b^{6} d^{4}\right)}{e^{7}} - \frac{2 \left(a e - b d\right)^{6}}{3 e^{7} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"2*b**6*(d + e*x)**(9/2)/(9*e**7) - 12*b*(a*e - b*d)**5/(e**7*sqrt(d + e*x)) + (d + e*x)**(7/2)*(12*a*b**5*e - 12*b**6*d)/(7*e**7) + (d + e*x)**(5/2)*(30*a**2*b**4*e**2 - 60*a*b**5*d*e + 30*b**6*d**2)/(5*e**7) + (d + e*x)**(3/2)*(40*a**3*b**3*e**3 - 120*a**2*b**4*d*e**2 + 120*a*b**5*d**2*e - 40*b**6*d**3)/(3*e**7) + sqrt(d + e*x)*(30*a**4*b**2*e**4 - 120*a**3*b**3*d*e**3 + 180*a**2*b**4*d**2*e**2 - 120*a*b**5*d**3*e + 30*b**6*d**4)/e**7 - 2*(a*e - b*d)**6/(3*e**7*(d + e*x)**(3/2))","A",0
1644,1,221,0,149.325522," ","integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(7/2),x)","\frac{2 b^{6} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{7}} - \frac{30 b^{2} \left(a e - b d\right)^{4}}{e^{7} \sqrt{d + e x}} - \frac{4 b \left(a e - b d\right)^{5}}{e^{7} \left(d + e x\right)^{\frac{3}{2}}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(12 a b^{5} e - 12 b^{6} d\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(30 a^{2} b^{4} e^{2} - 60 a b^{5} d e + 30 b^{6} d^{2}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(40 a^{3} b^{3} e^{3} - 120 a^{2} b^{4} d e^{2} + 120 a b^{5} d^{2} e - 40 b^{6} d^{3}\right)}{e^{7}} - \frac{2 \left(a e - b d\right)^{6}}{5 e^{7} \left(d + e x\right)^{\frac{5}{2}}}"," ",0,"2*b**6*(d + e*x)**(7/2)/(7*e**7) - 30*b**2*(a*e - b*d)**4/(e**7*sqrt(d + e*x)) - 4*b*(a*e - b*d)**5/(e**7*(d + e*x)**(3/2)) + (d + e*x)**(5/2)*(12*a*b**5*e - 12*b**6*d)/(5*e**7) + (d + e*x)**(3/2)*(30*a**2*b**4*e**2 - 60*a*b**5*d*e + 30*b**6*d**2)/(3*e**7) + sqrt(d + e*x)*(40*a**3*b**3*e**3 - 120*a**2*b**4*d*e**2 + 120*a*b**5*d**2*e - 40*b**6*d**3)/e**7 - 2*(a*e - b*d)**6/(5*e**7*(d + e*x)**(5/2))","A",0
1645,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1646,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1647,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1648,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1649,1,573,0,39.846387," ","integrate((e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2),x)","- \frac{2 a e^{2} \sqrt{d + e x}}{2 a^{2} b e^{2} - 2 a b^{2} d e + 2 a b^{2} e^{2} x - 2 b^{3} d e x} + \frac{a e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(- a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{a e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(- a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2} + \frac{d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2} + \frac{2 d e \sqrt{d + e x}}{2 a^{2} e^{2} - 2 a b d e + 2 a b e^{2} x - 2 b^{2} d e x} + \frac{2 e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e}{b} - d}} \right)}}{b^{2} \sqrt{\frac{a e}{b} - d}}"," ",0,"-2*a*e**2*sqrt(d + e*x)/(2*a**2*b*e**2 - 2*a*b**2*d*e + 2*a*b**2*e**2*x - 2*b**3*d*e*x) + a*e**2*sqrt(-1/(b*(a*e - b*d)**3))*log(-a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) + 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) - b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/(2*b) - a*e**2*sqrt(-1/(b*(a*e - b*d)**3))*log(a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) - 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) + b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/(2*b) - d*e*sqrt(-1/(b*(a*e - b*d)**3))*log(-a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) + 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) - b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/2 + d*e*sqrt(-1/(b*(a*e - b*d)**3))*log(a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) - 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) + b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/2 + 2*d*e*sqrt(d + e*x)/(2*a**2*e**2 - 2*a*b*d*e + 2*a*b*e**2*x - 2*b**2*d*e*x) + 2*e*atan(sqrt(d + e*x)/sqrt(a*e/b - d))/(b**2*sqrt(a*e/b - d))","B",0
1650,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2),x)","\int \frac{1}{\left(a + b x\right)^{2} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/((a + b*x)**2*sqrt(d + e*x)), x)","F",0
1651,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2),x)","\int \frac{1}{\left(a + b x\right)^{2} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**2*(d + e*x)**(3/2)), x)","F",0
1652,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2),x)","\int \frac{1}{\left(a + b x\right)^{2} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**2*(d + e*x)**(5/2)), x)","F",0
1653,0,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2),x)","\int \frac{1}{\left(a + b x\right)^{2} \left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**2*(d + e*x)**(7/2)), x)","F",0
1654,-1,0,0,0.000000," ","integrate((e*x+d)**(11/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1655,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1656,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1657,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1658,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1659,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1660,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1661,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1662,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1663,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1664,-1,0,0,0.000000," ","integrate((e*x+d)**(15/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1665,-1,0,0,0.000000," ","integrate((e*x+d)**(13/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1666,-1,0,0,0.000000," ","integrate((e*x+d)**(11/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1667,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1668,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1669,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1670,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1671,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1672,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1673,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1674,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1675,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1676,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1677,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*((b*x+a)**2)**(1/2),x)","\int \left(d + e x\right)^{\frac{3}{2}} \sqrt{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*sqrt((a + b*x)**2), x)","F",0
1678,1,49,0,7.975550," ","integrate((e*x+d)**(1/2)*((b*x+a)**2)**(1/2),x)","\frac{2 a \left(d + e x\right)^{\frac{3}{2}}}{3 e} - \frac{2 b d \left(d + e x\right)^{\frac{3}{2}}}{3 e^{2}} + \frac{2 b \left(d + e x\right)^{\frac{5}{2}}}{5 e^{2}}"," ",0,"2*a*(d + e*x)**(3/2)/(3*e) - 2*b*d*(d + e*x)**(3/2)/(3*e**2) + 2*b*(d + e*x)**(5/2)/(5*e**2)","A",0
1679,0,0,0,0.000000," ","integrate(((b*x+a)**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(a + b x\right)^{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt((a + b*x)**2)/sqrt(d + e*x), x)","F",0
1680,0,0,0,0.000000," ","integrate(((b*x+a)**2)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\sqrt{\left(a + b x\right)^{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt((a + b*x)**2)/(d + e*x)**(3/2), x)","F",0
1681,0,0,0,0.000000," ","integrate(((b*x+a)**2)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\sqrt{\left(a + b x\right)^{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt((a + b*x)**2)/(d + e*x)**(5/2), x)","F",0
1682,-1,0,0,0.000000," ","integrate(((b*x+a)**2)**(1/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1683,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1684,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(d + e x\right)^{\frac{3}{2}} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*((a + b*x)**2)**(3/2), x)","F",0
1685,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)*(e*x+d)**(1/2),x)","\int \sqrt{d + e x} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(d + e*x)*((a + b*x)**2)**(3/2), x)","F",0
1686,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1687,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**(3/2), x)","F",0
1688,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**(5/2), x)","F",0
1689,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(7/2),x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**(7/2), x)","F",0
1690,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(9/2),x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral(((a + b*x)**2)**(3/2)/(d + e*x)**(9/2), x)","F",0
1691,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1692,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1693,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1694,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)*(e*x+d)**(1/2),x)","\int \sqrt{d + e x} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(sqrt(d + e*x)*((a + b*x)**2)**(5/2), x)","F",0
1695,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1696,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1697,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1698,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1699,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1700,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1701,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1702,-1,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1703,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1704,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1705,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/((b*x+a)**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/sqrt((a + b*x)**2), x)","F",0
1706,1,95,0,6.558726," ","integrate((e*x+d)**(1/2)/((b*x+a)**2)**(1/2),x)","\sqrt{- \frac{a e}{b^{3}} + \frac{d}{b^{2}}} \log{\left(- b \sqrt{- \frac{a e}{b^{3}} + \frac{d}{b^{2}}} + \sqrt{d + e x} \right)} - \sqrt{- \frac{a e}{b^{3}} + \frac{d}{b^{2}}} \log{\left(b \sqrt{- \frac{a e}{b^{3}} + \frac{d}{b^{2}}} + \sqrt{d + e x} \right)} + \frac{2 \sqrt{d + e x}}{b}"," ",0,"sqrt(-a*e/b**3 + d/b**2)*log(-b*sqrt(-a*e/b**3 + d/b**2) + sqrt(d + e*x)) - sqrt(-a*e/b**3 + d/b**2)*log(b*sqrt(-a*e/b**3 + d/b**2) + sqrt(d + e*x)) + 2*sqrt(d + e*x)/b","A",0
1707,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/((b*x+a)**2)**(1/2),x)","\int \frac{1}{\sqrt{d + e x} \sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral(1/(sqrt(d + e*x)*sqrt((a + b*x)**2)), x)","F",0
1708,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/((b*x+a)**2)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{3}{2}} \sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(3/2)*sqrt((a + b*x)**2)), x)","F",0
1709,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/((b*x+a)**2)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{5}{2}} \sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(5/2)*sqrt((a + b*x)**2)), x)","F",0
1710,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1711,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1712,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1713,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1714,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1715,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\sqrt{d + e x}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/((a + b*x)**2)**(3/2), x)","F",0
1716,0,0,0,0.000000," ","integrate(1/(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{1}{\sqrt{d + e x} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(d + e*x)*((a + b*x)**2)**(3/2)), x)","F",0
1717,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{3}{2}} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(3/2)*((a + b*x)**2)**(3/2)), x)","F",0
1718,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{5}{2}} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(5/2)*((a + b*x)**2)**(3/2)), x)","F",0
1719,0,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{7}{2}} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(7/2)*((a + b*x)**2)**(3/2)), x)","F",0
1720,-1,0,0,0.000000," ","integrate((e*x+d)**(13/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1721,-1,0,0,0.000000," ","integrate((e*x+d)**(11/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1722,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1723,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1724,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1725,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1726,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1727,-1,0,0,0.000000," ","integrate(1/(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1728,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{3}{2}} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(3/2)*((a + b*x)**2)**(5/2)), x)","F",0
1729,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1730,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1731,-1,0,0,0.000000," ","integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1732,1,8719,0,9.029461," ","integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**2,x)","\begin{cases} d^{m} \left(a^{4} x + 2 a^{3} b x^{2} + 2 a^{2} b^{2} x^{3} + a b^{3} x^{4} + \frac{b^{4} x^{5}}{5}\right) & \text{for}\: e = 0 \\- \frac{3 a^{4} e^{4}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{4 a^{3} b d e^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{16 a^{3} b e^{4} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{6 a^{2} b^{2} d^{2} e^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{24 a^{2} b^{2} d e^{3} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{36 a^{2} b^{2} e^{4} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{12 a b^{3} d^{3} e}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{48 a b^{3} d^{2} e^{2} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{72 a b^{3} d e^{3} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{48 a b^{3} e^{4} x^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{12 b^{4} d^{4} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{25 b^{4} d^{4}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 b^{4} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{88 b^{4} d^{3} e x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{72 b^{4} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{108 b^{4} d^{2} e^{2} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 b^{4} d e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 b^{4} d e^{3} x^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{12 b^{4} e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} & \text{for}\: m = -5 \\- \frac{a^{4} e^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{2 a^{3} b d e^{3}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{6 a^{3} b e^{4} x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{6 a^{2} b^{2} d^{2} e^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{18 a^{2} b^{2} d e^{3} x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{18 a^{2} b^{2} e^{4} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{12 a b^{3} d^{3} e \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{22 a b^{3} d^{3} e}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{36 a b^{3} d^{2} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{54 a b^{3} d^{2} e^{2} x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{36 a b^{3} d e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{36 a b^{3} d e^{3} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{12 a b^{3} e^{4} x^{3} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{12 b^{4} d^{4} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{22 b^{4} d^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 b^{4} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{54 b^{4} d^{3} e x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 b^{4} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 b^{4} d^{2} e^{2} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{12 b^{4} d e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{3 b^{4} e^{4} x^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} & \text{for}\: m = -4 \\- \frac{a^{4} e^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{4 a^{3} b d e^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{8 a^{3} b e^{4} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 a^{2} b^{2} d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{18 a^{2} b^{2} d^{2} e^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 a^{2} b^{2} d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 a^{2} b^{2} d e^{3} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 a^{2} b^{2} e^{4} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{24 a b^{3} d^{3} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{36 a b^{3} d^{3} e}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{48 a b^{3} d^{2} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{48 a b^{3} d^{2} e^{2} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{24 a b^{3} d e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{8 a b^{3} e^{4} x^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 b^{4} d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{18 b^{4} d^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 b^{4} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 b^{4} d^{3} e x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 b^{4} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{4 b^{4} d e^{3} x^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{b^{4} e^{4} x^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} & \text{for}\: m = -3 \\- \frac{3 a^{4} e^{4}}{3 d e^{5} + 3 e^{6} x} + \frac{12 a^{3} b d e^{3} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{12 a^{3} b d e^{3}}{3 d e^{5} + 3 e^{6} x} + \frac{12 a^{3} b e^{4} x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{36 a^{2} b^{2} d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{36 a^{2} b^{2} d^{2} e^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{36 a^{2} b^{2} d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{18 a^{2} b^{2} e^{4} x^{2}}{3 d e^{5} + 3 e^{6} x} + \frac{36 a b^{3} d^{3} e \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{36 a b^{3} d^{3} e}{3 d e^{5} + 3 e^{6} x} + \frac{36 a b^{3} d^{2} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{18 a b^{3} d e^{3} x^{2}}{3 d e^{5} + 3 e^{6} x} + \frac{6 a b^{3} e^{4} x^{3}}{3 d e^{5} + 3 e^{6} x} - \frac{12 b^{4} d^{4} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{12 b^{4} d^{4}}{3 d e^{5} + 3 e^{6} x} - \frac{12 b^{4} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{6 b^{4} d^{2} e^{2} x^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{2 b^{4} d e^{3} x^{3}}{3 d e^{5} + 3 e^{6} x} + \frac{b^{4} e^{4} x^{4}}{3 d e^{5} + 3 e^{6} x} & \text{for}\: m = -2 \\\frac{a^{4} \log{\left(\frac{d}{e} + x \right)}}{e} - \frac{4 a^{3} b d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{4 a^{3} b x}{e} + \frac{6 a^{2} b^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{6 a^{2} b^{2} d x}{e^{2}} + \frac{3 a^{2} b^{2} x^{2}}{e} - \frac{4 a b^{3} d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{4 a b^{3} d^{2} x}{e^{3}} - \frac{2 a b^{3} d x^{2}}{e^{2}} + \frac{4 a b^{3} x^{3}}{3 e} + \frac{b^{4} d^{4} \log{\left(\frac{d}{e} + x \right)}}{e^{5}} - \frac{b^{4} d^{3} x}{e^{4}} + \frac{b^{4} d^{2} x^{2}}{2 e^{3}} - \frac{b^{4} d x^{3}}{3 e^{2}} + \frac{b^{4} x^{4}}{4 e} & \text{for}\: m = -1 \\\frac{a^{4} d e^{4} m^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{14 a^{4} d e^{4} m^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{71 a^{4} d e^{4} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{154 a^{4} d e^{4} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a^{4} d e^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{a^{4} e^{5} m^{4} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{14 a^{4} e^{5} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{71 a^{4} e^{5} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{154 a^{4} e^{5} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a^{4} e^{5} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{4 a^{3} b d^{2} e^{3} m^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{48 a^{3} b d^{2} e^{3} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{188 a^{3} b d^{2} e^{3} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{240 a^{3} b d^{2} e^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{4 a^{3} b d e^{4} m^{4} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{48 a^{3} b d e^{4} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{188 a^{3} b d e^{4} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{240 a^{3} b d e^{4} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{4 a^{3} b e^{5} m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{52 a^{3} b e^{5} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{236 a^{3} b e^{5} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{428 a^{3} b e^{5} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{240 a^{3} b e^{5} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 a^{2} b^{2} d^{3} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{108 a^{2} b^{2} d^{3} e^{2} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{240 a^{2} b^{2} d^{3} e^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 a^{2} b^{2} d^{2} e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{108 a^{2} b^{2} d^{2} e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{240 a^{2} b^{2} d^{2} e^{3} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 a^{2} b^{2} d e^{4} m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{60 a^{2} b^{2} d e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{174 a^{2} b^{2} d e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a^{2} b^{2} d e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 a^{2} b^{2} e^{5} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{72 a^{2} b^{2} e^{5} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{294 a^{2} b^{2} e^{5} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{468 a^{2} b^{2} e^{5} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{240 a^{2} b^{2} e^{5} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{24 a b^{3} d^{4} e m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{120 a b^{3} d^{4} e \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 a b^{3} d^{3} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a b^{3} d^{3} e^{2} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 a b^{3} d^{2} e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{72 a b^{3} d^{2} e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{60 a b^{3} d^{2} e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{4 a b^{3} d e^{4} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{32 a b^{3} d e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{68 a b^{3} d e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 a b^{3} d e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{4 a b^{3} e^{5} m^{4} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{44 a b^{3} e^{5} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{164 a b^{3} e^{5} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{244 a b^{3} e^{5} m x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a b^{3} e^{5} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 b^{4} d^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{24 b^{4} d^{4} e m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 b^{4} d^{3} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 b^{4} d^{3} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{4 b^{4} d^{2} e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 b^{4} d^{2} e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{8 b^{4} d^{2} e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{b^{4} d e^{4} m^{4} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 b^{4} d e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{11 b^{4} d e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 b^{4} d e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{b^{4} e^{5} m^{4} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{10 b^{4} e^{5} m^{3} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{35 b^{4} e^{5} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{50 b^{4} e^{5} m x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 b^{4} e^{5} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a**4*x + 2*a**3*b*x**2 + 2*a**2*b**2*x**3 + a*b**3*x**4 + b**4*x**5/5), Eq(e, 0)), (-3*a**4*e**4/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 4*a**3*b*d*e**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 16*a**3*b*e**4*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 6*a**2*b**2*d**2*e**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 24*a**2*b**2*d*e**3*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 36*a**2*b**2*e**4*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 12*a*b**3*d**3*e/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 48*a*b**3*d**2*e**2*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 72*a*b**3*d*e**3*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 48*a*b**3*e**4*x**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 12*b**4*d**4*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 25*b**4*d**4/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*b**4*d**3*e*x*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 88*b**4*d**3*e*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 72*b**4*d**2*e**2*x**2*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 108*b**4*d**2*e**2*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*b**4*d*e**3*x**3*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*b**4*d*e**3*x**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 12*b**4*e**4*x**4*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4), Eq(m, -5)), (-a**4*e**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 2*a**3*b*d*e**3/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 6*a**3*b*e**4*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 6*a**2*b**2*d**2*e**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 18*a**2*b**2*d*e**3*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 18*a**2*b**2*e**4*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 12*a*b**3*d**3*e*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 22*a*b**3*d**3*e/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 36*a*b**3*d**2*e**2*x*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 54*a*b**3*d**2*e**2*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 36*a*b**3*d*e**3*x**2*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 36*a*b**3*d*e**3*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 12*a*b**3*e**4*x**3*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 12*b**4*d**4*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 22*b**4*d**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*b**4*d**3*e*x*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 54*b**4*d**3*e*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*b**4*d**2*e**2*x**2*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*b**4*d**2*e**2*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 12*b**4*d*e**3*x**3*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 3*b**4*e**4*x**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3), Eq(m, -4)), (-a**4*e**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 4*a**3*b*d*e**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 8*a**3*b*e**4*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*a**2*b**2*d**2*e**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 18*a**2*b**2*d**2*e**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*a**2*b**2*d*e**3*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*a**2*b**2*d*e**3*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*a**2*b**2*e**4*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 24*a*b**3*d**3*e*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 36*a*b**3*d**3*e/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 48*a*b**3*d**2*e**2*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 48*a*b**3*d**2*e**2*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 24*a*b**3*d*e**3*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 8*a*b**3*e**4*x**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*b**4*d**4*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 18*b**4*d**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*b**4*d**3*e*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*b**4*d**3*e*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*b**4*d**2*e**2*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 4*b**4*d*e**3*x**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + b**4*e**4*x**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2), Eq(m, -3)), (-3*a**4*e**4/(3*d*e**5 + 3*e**6*x) + 12*a**3*b*d*e**3*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 12*a**3*b*d*e**3/(3*d*e**5 + 3*e**6*x) + 12*a**3*b*e**4*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 36*a**2*b**2*d**2*e**2*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 36*a**2*b**2*d**2*e**2/(3*d*e**5 + 3*e**6*x) - 36*a**2*b**2*d*e**3*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 18*a**2*b**2*e**4*x**2/(3*d*e**5 + 3*e**6*x) + 36*a*b**3*d**3*e*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 36*a*b**3*d**3*e/(3*d*e**5 + 3*e**6*x) + 36*a*b**3*d**2*e**2*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 18*a*b**3*d*e**3*x**2/(3*d*e**5 + 3*e**6*x) + 6*a*b**3*e**4*x**3/(3*d*e**5 + 3*e**6*x) - 12*b**4*d**4*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 12*b**4*d**4/(3*d*e**5 + 3*e**6*x) - 12*b**4*d**3*e*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 6*b**4*d**2*e**2*x**2/(3*d*e**5 + 3*e**6*x) - 2*b**4*d*e**3*x**3/(3*d*e**5 + 3*e**6*x) + b**4*e**4*x**4/(3*d*e**5 + 3*e**6*x), Eq(m, -2)), (a**4*log(d/e + x)/e - 4*a**3*b*d*log(d/e + x)/e**2 + 4*a**3*b*x/e + 6*a**2*b**2*d**2*log(d/e + x)/e**3 - 6*a**2*b**2*d*x/e**2 + 3*a**2*b**2*x**2/e - 4*a*b**3*d**3*log(d/e + x)/e**4 + 4*a*b**3*d**2*x/e**3 - 2*a*b**3*d*x**2/e**2 + 4*a*b**3*x**3/(3*e) + b**4*d**4*log(d/e + x)/e**5 - b**4*d**3*x/e**4 + b**4*d**2*x**2/(2*e**3) - b**4*d*x**3/(3*e**2) + b**4*x**4/(4*e), Eq(m, -1)), (a**4*d*e**4*m**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 14*a**4*d*e**4*m**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 71*a**4*d*e**4*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 154*a**4*d*e**4*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a**4*d*e**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + a**4*e**5*m**4*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 14*a**4*e**5*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 71*a**4*e**5*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 154*a**4*e**5*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a**4*e**5*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 4*a**3*b*d**2*e**3*m**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 48*a**3*b*d**2*e**3*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 188*a**3*b*d**2*e**3*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 240*a**3*b*d**2*e**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 4*a**3*b*d*e**4*m**4*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 48*a**3*b*d*e**4*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 188*a**3*b*d*e**4*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 240*a**3*b*d*e**4*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 4*a**3*b*e**5*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 52*a**3*b*e**5*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 236*a**3*b*e**5*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 428*a**3*b*e**5*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 240*a**3*b*e**5*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*a**2*b**2*d**3*e**2*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 108*a**2*b**2*d**3*e**2*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 240*a**2*b**2*d**3*e**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*a**2*b**2*d**2*e**3*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 108*a**2*b**2*d**2*e**3*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 240*a**2*b**2*d**2*e**3*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*a**2*b**2*d*e**4*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 60*a**2*b**2*d*e**4*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 174*a**2*b**2*d*e**4*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a**2*b**2*d*e**4*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*a**2*b**2*e**5*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 72*a**2*b**2*e**5*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 294*a**2*b**2*e**5*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 468*a**2*b**2*e**5*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 240*a**2*b**2*e**5*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 24*a*b**3*d**4*e*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 120*a*b**3*d**4*e*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*a*b**3*d**3*e**2*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a*b**3*d**3*e**2*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*a*b**3*d**2*e**3*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 72*a*b**3*d**2*e**3*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 60*a*b**3*d**2*e**3*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 4*a*b**3*d*e**4*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 32*a*b**3*d*e**4*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 68*a*b**3*d*e**4*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*a*b**3*d*e**4*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 4*a*b**3*e**5*m**4*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 44*a*b**3*e**5*m**3*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 164*a*b**3*e**5*m**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 244*a*b**3*e**5*m*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a*b**3*e**5*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*b**4*d**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 24*b**4*d**4*e*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*b**4*d**3*e**2*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*b**4*d**3*e**2*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 4*b**4*d**2*e**3*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*b**4*d**2*e**3*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 8*b**4*d**2*e**3*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + b**4*d*e**4*m**4*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*b**4*d*e**4*m**3*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 11*b**4*d*e**4*m**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*b**4*d*e**4*m*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + b**4*e**5*m**4*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 10*b**4*e**5*m**3*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 35*b**4*e**5*m**2*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 50*b**4*e**5*m*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*b**4*e**5*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5), True))","A",0
1733,1,1506,0,2.073929," ","integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} d^{m} \left(a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}\right) & \text{for}\: e = 0 \\- \frac{a^{2} e^{2}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} - \frac{2 a b d e}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} - \frac{4 a b e^{2} x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 b^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{3 b^{2} d^{2}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 b^{2} d e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 b^{2} d e x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 b^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} & \text{for}\: m = -3 \\- \frac{a^{2} e^{2}}{d e^{3} + e^{4} x} + \frac{2 a b d e \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} + \frac{2 a b d e}{d e^{3} + e^{4} x} + \frac{2 a b e^{2} x \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{2 b^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{2 b^{2} d^{2}}{d e^{3} + e^{4} x} - \frac{2 b^{2} d e x \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} + \frac{b^{2} e^{2} x^{2}}{d e^{3} + e^{4} x} & \text{for}\: m = -2 \\\frac{a^{2} \log{\left(\frac{d}{e} + x \right)}}{e} - \frac{2 a b d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{2 a b x}{e} + \frac{b^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{b^{2} d x}{e^{2}} + \frac{b^{2} x^{2}}{2 e} & \text{for}\: m = -1 \\\frac{a^{2} d e^{2} m^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{5 a^{2} d e^{2} m \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{6 a^{2} d e^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{a^{2} e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{5 a^{2} e^{3} m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{6 a^{2} e^{3} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} - \frac{2 a b d^{2} e m \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} - \frac{6 a b d^{2} e \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{2 a b d e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{6 a b d e^{2} m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{2 a b e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{8 a b e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{6 a b e^{3} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{2 b^{2} d^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} - \frac{2 b^{2} d^{2} e m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{b^{2} d e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{b^{2} d e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{b^{2} e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{3 b^{2} e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{2 b^{2} e^{3} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a**2*x + a*b*x**2 + b**2*x**3/3), Eq(e, 0)), (-a**2*e**2/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) - 2*a*b*d*e/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) - 4*a*b*e**2*x/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*b**2*d**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 3*b**2*d**2/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*b**2*d*e*x*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*b**2*d*e*x/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*b**2*e**2*x**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2), Eq(m, -3)), (-a**2*e**2/(d*e**3 + e**4*x) + 2*a*b*d*e*log(d/e + x)/(d*e**3 + e**4*x) + 2*a*b*d*e/(d*e**3 + e**4*x) + 2*a*b*e**2*x*log(d/e + x)/(d*e**3 + e**4*x) - 2*b**2*d**2*log(d/e + x)/(d*e**3 + e**4*x) - 2*b**2*d**2/(d*e**3 + e**4*x) - 2*b**2*d*e*x*log(d/e + x)/(d*e**3 + e**4*x) + b**2*e**2*x**2/(d*e**3 + e**4*x), Eq(m, -2)), (a**2*log(d/e + x)/e - 2*a*b*d*log(d/e + x)/e**2 + 2*a*b*x/e + b**2*d**2*log(d/e + x)/e**3 - b**2*d*x/e**2 + b**2*x**2/(2*e), Eq(m, -1)), (a**2*d*e**2*m**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 5*a**2*d*e**2*m*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 6*a**2*d*e**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + a**2*e**3*m**2*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 5*a**2*e**3*m*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 6*a**2*e**3*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) - 2*a*b*d**2*e*m*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) - 6*a*b*d**2*e*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 2*a*b*d*e**2*m**2*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 6*a*b*d*e**2*m*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 2*a*b*e**3*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 8*a*b*e**3*m*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 6*a*b*e**3*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 2*b**2*d**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) - 2*b**2*d**2*e*m*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + b**2*d*e**2*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + b**2*d*e**2*m*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + b**2*e**3*m**2*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 3*b**2*e**3*m*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 2*b**2*e**3*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3), True))","A",0
1734,0,0,0,0.000000," ","integrate((e*x+d)**m/(b**2*x**2+2*a*b*x+a**2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*x)**2, x)","F",0
1735,0,0,0,0.000000," ","integrate((e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**2,x)","\int \frac{\left(d + e x\right)^{m}}{\left(a + b x\right)^{4}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*x)**4, x)","F",0
1736,0,0,0,0.000000," ","integrate((e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**3,x)","\int \frac{\left(d + e x\right)^{m}}{\left(a + b x\right)^{6}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*x)**6, x)","F",0
1737,-2,0,0,0.000000," ","integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1738,0,0,0,0.000000," ","integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(d + e x\right)^{m} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)**m*((a + b*x)**2)**(3/2), x)","F",0
1739,0,0,0,0.000000," ","integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(1/2),x)","\int \left(d + e x\right)^{m} \sqrt{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**m*sqrt((a + b*x)**2), x)","F",0
1740,0,0,0,0.000000," ","integrate((e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{m}}{\sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((d + e*x)**m/sqrt((a + b*x)**2), x)","F",0
1741,0,0,0,0.000000," ","integrate((e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**m/((a + b*x)**2)**(3/2), x)","F",0
1742,0,0,0,0.000000," ","integrate((e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**m/((a + b*x)**2)**(5/2), x)","F",0
1743,-2,0,0,0.000000," ","integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1744,0,0,0,0.000000," ","integrate((e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**p,x)","\begin{cases} \left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right) \left(a^{2}\right)^{p} & \text{for}\: b = 0 \\\frac{6 a^{3} e^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{11 a^{3} e^{3}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} - \frac{6 a^{2} b d e^{2}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a^{2} b e^{3} x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{27 a^{2} b e^{3} x}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} - \frac{3 a b^{2} d^{2} e}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} - \frac{18 a b^{2} d e^{2} x}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a b^{2} e^{3} x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a b^{2} e^{3} x^{2}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} - \frac{2 b^{3} d^{3}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} - \frac{9 b^{3} d^{2} e x}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} - \frac{18 b^{3} d e^{2} x^{2}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{6 b^{3} e^{3} x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} & \text{for}\: p = -2 \\\int \frac{\left(d + e x\right)^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: p = - \frac{3}{2} \\\frac{6 a^{3} e^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{3} e^{3}}{2 a b^{4} + 2 b^{5} x} - \frac{12 a^{2} b d e^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} - \frac{12 a^{2} b d e^{2}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{2} b e^{3} x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a b^{2} d^{2} e \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a b^{2} d^{2} e}{2 a b^{4} + 2 b^{5} x} - \frac{12 a b^{2} d e^{2} x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} - \frac{3 a b^{2} e^{3} x^{2}}{2 a b^{4} + 2 b^{5} x} - \frac{2 b^{3} d^{3}}{2 a b^{4} + 2 b^{5} x} + \frac{6 b^{3} d^{2} e x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 b^{3} d e^{2} x^{2}}{2 a b^{4} + 2 b^{5} x} + \frac{b^{3} e^{3} x^{3}}{2 a b^{4} + 2 b^{5} x} & \text{for}\: p = -1 \\\int \frac{\left(d + e x\right)^{3}}{\sqrt{\left(a + b x\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\- \frac{3 a^{4} e^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{6 a^{3} b d e^{2} p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{12 a^{3} b d e^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{6 a^{3} b e^{3} p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} - \frac{6 a^{2} b^{2} d^{2} e p^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} - \frac{21 a^{2} b^{2} d^{2} e p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} - \frac{18 a^{2} b^{2} d^{2} e \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} - \frac{12 a^{2} b^{2} d e^{2} p^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} - \frac{24 a^{2} b^{2} d e^{2} p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} - \frac{6 a^{2} b^{2} e^{3} p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} - \frac{3 a^{2} b^{2} e^{3} p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{4 a b^{3} d^{3} p^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{18 a b^{3} d^{3} p^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{26 a b^{3} d^{3} p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{12 a b^{3} d^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{12 a b^{3} d^{2} e p^{3} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{42 a b^{3} d^{2} e p^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{36 a b^{3} d^{2} e p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{12 a b^{3} d e^{2} p^{3} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{30 a b^{3} d e^{2} p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{12 a b^{3} d e^{2} p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{4 a b^{3} e^{3} p^{3} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{6 a b^{3} e^{3} p^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{2 a b^{3} e^{3} p x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{4 b^{4} d^{3} p^{3} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{18 b^{4} d^{3} p^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{26 b^{4} d^{3} p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{12 b^{4} d^{3} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{12 b^{4} d^{2} e p^{3} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{48 b^{4} d^{2} e p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{57 b^{4} d^{2} e p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{18 b^{4} d^{2} e x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{12 b^{4} d e^{2} p^{3} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{42 b^{4} d e^{2} p^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{42 b^{4} d e^{2} p x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{12 b^{4} d e^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{4 b^{4} e^{3} p^{3} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{12 b^{4} e^{3} p^{2} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{11 b^{4} e^{3} p x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} + \frac{3 b^{4} e^{3} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 40 b^{4} p^{3} + 70 b^{4} p^{2} + 50 b^{4} p + 12 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4)*(a**2)**p, Eq(b, 0)), (6*a**3*e**3*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 11*a**3*e**3/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) - 6*a**2*b*d*e**2/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a**2*b*e**3*x*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 27*a**2*b*e**3*x/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) - 3*a*b**2*d**2*e/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) - 18*a*b**2*d*e**2*x/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a*b**2*e**3*x**2*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a*b**2*e**3*x**2/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) - 2*b**3*d**3/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) - 9*b**3*d**2*e*x/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) - 18*b**3*d*e**2*x**2/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 6*b**3*e**3*x**3*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3), Eq(p, -2)), (Integral((d + e*x)**3/((a + b*x)**2)**(3/2), x), Eq(p, -3/2)), (6*a**3*e**3*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a**3*e**3/(2*a*b**4 + 2*b**5*x) - 12*a**2*b*d*e**2*log(a/b + x)/(2*a*b**4 + 2*b**5*x) - 12*a**2*b*d*e**2/(2*a*b**4 + 2*b**5*x) + 6*a**2*b*e**3*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a*b**2*d**2*e*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a*b**2*d**2*e/(2*a*b**4 + 2*b**5*x) - 12*a*b**2*d*e**2*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) - 3*a*b**2*e**3*x**2/(2*a*b**4 + 2*b**5*x) - 2*b**3*d**3/(2*a*b**4 + 2*b**5*x) + 6*b**3*d**2*e*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*b**3*d*e**2*x**2/(2*a*b**4 + 2*b**5*x) + b**3*e**3*x**3/(2*a*b**4 + 2*b**5*x), Eq(p, -1)), (Integral((d + e*x)**3/sqrt((a + b*x)**2), x), Eq(p, -1/2)), (-3*a**4*e**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 6*a**3*b*d*e**2*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 12*a**3*b*d*e**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 6*a**3*b*e**3*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) - 6*a**2*b**2*d**2*e*p**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) - 21*a**2*b**2*d**2*e*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) - 18*a**2*b**2*d**2*e*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) - 12*a**2*b**2*d*e**2*p**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) - 24*a**2*b**2*d*e**2*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) - 6*a**2*b**2*e**3*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) - 3*a**2*b**2*e**3*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 4*a*b**3*d**3*p**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 18*a*b**3*d**3*p**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 26*a*b**3*d**3*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 12*a*b**3*d**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 12*a*b**3*d**2*e*p**3*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 42*a*b**3*d**2*e*p**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 36*a*b**3*d**2*e*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 12*a*b**3*d*e**2*p**3*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 30*a*b**3*d*e**2*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 12*a*b**3*d*e**2*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 4*a*b**3*e**3*p**3*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 6*a*b**3*e**3*p**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 2*a*b**3*e**3*p*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 4*b**4*d**3*p**3*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 18*b**4*d**3*p**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 26*b**4*d**3*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 12*b**4*d**3*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 12*b**4*d**2*e*p**3*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 48*b**4*d**2*e*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 57*b**4*d**2*e*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 18*b**4*d**2*e*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 12*b**4*d*e**2*p**3*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 42*b**4*d*e**2*p**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 42*b**4*d*e**2*p*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 12*b**4*d*e**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 4*b**4*e**3*p**3*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 12*b**4*e**3*p**2*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 11*b**4*e**3*p*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4) + 3*b**4*e**3*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 40*b**4*p**3 + 70*b**4*p**2 + 50*b**4*p + 12*b**4), True))","F",0
1745,0,0,0,0.000000," ","integrate((e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**p,x)","\begin{cases} \left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right) \left(a^{2}\right)^{p} & \text{for}\: b = 0 \\\int \frac{\left(d + e x\right)^{2}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: p = - \frac{3}{2} \\- \frac{2 a^{2} e^{2} \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} - \frac{2 a^{2} e^{2}}{a b^{3} + b^{4} x} + \frac{2 a b d e \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} + \frac{2 a b d e}{a b^{3} + b^{4} x} - \frac{2 a b e^{2} x \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} - \frac{b^{2} d^{2}}{a b^{3} + b^{4} x} + \frac{2 b^{2} d e x \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} + \frac{b^{2} e^{2} x^{2}}{a b^{3} + b^{4} x} & \text{for}\: p = -1 \\\int \frac{\left(d + e x\right)^{2}}{\sqrt{\left(a + b x\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{a^{3} e^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} - \frac{2 a^{2} b d e p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} - \frac{3 a^{2} b d e \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} - \frac{2 a^{2} b e^{2} p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{2 a b^{2} d^{2} p^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{5 a b^{2} d^{2} p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{3 a b^{2} d^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{4 a b^{2} d e p^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{6 a b^{2} d e p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{2 a b^{2} e^{2} p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{a b^{2} e^{2} p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{2 b^{3} d^{2} p^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{5 b^{3} d^{2} p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{3 b^{3} d^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{4 b^{3} d e p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{8 b^{3} d e p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{3 b^{3} d e x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{2 b^{3} e^{2} p^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{3 b^{3} e^{2} p x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} + \frac{b^{3} e^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 12 b^{3} p^{2} + 11 b^{3} p + 3 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((d**2*x + d*e*x**2 + e**2*x**3/3)*(a**2)**p, Eq(b, 0)), (Integral((d + e*x)**2/((a + b*x)**2)**(3/2), x), Eq(p, -3/2)), (-2*a**2*e**2*log(a/b + x)/(a*b**3 + b**4*x) - 2*a**2*e**2/(a*b**3 + b**4*x) + 2*a*b*d*e*log(a/b + x)/(a*b**3 + b**4*x) + 2*a*b*d*e/(a*b**3 + b**4*x) - 2*a*b*e**2*x*log(a/b + x)/(a*b**3 + b**4*x) - b**2*d**2/(a*b**3 + b**4*x) + 2*b**2*d*e*x*log(a/b + x)/(a*b**3 + b**4*x) + b**2*e**2*x**2/(a*b**3 + b**4*x), Eq(p, -1)), (Integral((d + e*x)**2/sqrt((a + b*x)**2), x), Eq(p, -1/2)), (a**3*e**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) - 2*a**2*b*d*e*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) - 3*a**2*b*d*e*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) - 2*a**2*b*e**2*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 2*a*b**2*d**2*p**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 5*a*b**2*d**2*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 3*a*b**2*d**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 4*a*b**2*d*e*p**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 6*a*b**2*d*e*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 2*a*b**2*e**2*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + a*b**2*e**2*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 2*b**3*d**2*p**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 5*b**3*d**2*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 3*b**3*d**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 4*b**3*d*e*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 8*b**3*d*e*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 3*b**3*d*e*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 2*b**3*e**2*p**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + 3*b**3*e**2*p*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3) + b**3*e**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 12*b**3*p**2 + 11*b**3*p + 3*b**3), True))","F",0
1746,0,0,0,0.000000," ","integrate((e*x+d)*(b**2*x**2+2*a*b*x+a**2)**p,x)","\begin{cases} \left(d x + \frac{e x^{2}}{2}\right) \left(a^{2}\right)^{p} & \text{for}\: b = 0 \\\frac{a e \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} + \frac{a e}{a b^{2} + b^{3} x} - \frac{b d}{a b^{2} + b^{3} x} + \frac{b e x \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} & \text{for}\: p = -1 \\\int \frac{d + e x}{\sqrt{\left(a + b x\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\- \frac{a^{2} e \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 6 b^{2} p + 2 b^{2}} + \frac{2 a b d p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 6 b^{2} p + 2 b^{2}} + \frac{2 a b d \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 6 b^{2} p + 2 b^{2}} + \frac{2 a b e p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 6 b^{2} p + 2 b^{2}} + \frac{2 b^{2} d p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 6 b^{2} p + 2 b^{2}} + \frac{2 b^{2} d x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 6 b^{2} p + 2 b^{2}} + \frac{2 b^{2} e p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 6 b^{2} p + 2 b^{2}} + \frac{b^{2} e x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 6 b^{2} p + 2 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((d*x + e*x**2/2)*(a**2)**p, Eq(b, 0)), (a*e*log(a/b + x)/(a*b**2 + b**3*x) + a*e/(a*b**2 + b**3*x) - b*d/(a*b**2 + b**3*x) + b*e*x*log(a/b + x)/(a*b**2 + b**3*x), Eq(p, -1)), (Integral((d + e*x)/sqrt((a + b*x)**2), x), Eq(p, -1/2)), (-a**2*e*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 6*b**2*p + 2*b**2) + 2*a*b*d*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 6*b**2*p + 2*b**2) + 2*a*b*d*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 6*b**2*p + 2*b**2) + 2*a*b*e*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 6*b**2*p + 2*b**2) + 2*b**2*d*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 6*b**2*p + 2*b**2) + 2*b**2*d*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 6*b**2*p + 2*b**2) + 2*b**2*e*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 6*b**2*p + 2*b**2) + b**2*e*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 6*b**2*p + 2*b**2), True))","F",0
1747,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**p,x)","\begin{cases} \frac{x}{\sqrt{a^{2}}} & \text{for}\: b = 0 \wedge p = - \frac{1}{2} \\x \left(a^{2}\right)^{p} & \text{for}\: b = 0 \\\int \frac{1}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{a \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{2 b p + b} + \frac{b x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{2 b p + b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/sqrt(a**2), Eq(b, 0) & Eq(p, -1/2)), (x*(a**2)**p, Eq(b, 0)), (Integral(1/sqrt(a**2 + 2*a*b*x + b**2*x**2), x), Eq(p, -1/2)), (a*(a**2 + 2*a*b*x + b**2*x**2)**p/(2*b*p + b) + b*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(2*b*p + b), True))","F",0
1748,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**p/(e*x+d),x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{p}}{d + e x}\, dx"," ",0,"Integral(((a + b*x)**2)**p/(d + e*x), x)","F",0
1749,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**p/(e*x+d)**2,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(((a + b*x)**2)**p/(d + e*x)**2, x)","F",0
1750,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**p/(e*x+d)**3,x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{p}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(((a + b*x)**2)**p/(d + e*x)**3, x)","F",0
1751,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**p,x)","\int \left(d + e x\right)^{\frac{3}{2}} \left(\left(a + b x\right)^{2}\right)^{p}\, dx"," ",0,"Integral((d + e*x)**(3/2)*((a + b*x)**2)**p, x)","F",0
1752,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(b**2*x**2+2*a*b*x+a**2)**p,x)","\int \sqrt{d + e x} \left(\left(a + b x\right)^{2}\right)^{p}\, dx"," ",0,"Integral(sqrt(d + e*x)*((a + b*x)**2)**p, x)","F",0
1753,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**p/(e*x+d)**(1/2),x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{p}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(((a + b*x)**2)**p/sqrt(d + e*x), x)","F",0
1754,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**p/(e*x+d)**(3/2),x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{p}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((a + b*x)**2)**p/(d + e*x)**(3/2), x)","F",0
1755,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2)**p/(e*x+d)**(5/2),x)","\int \frac{\left(\left(a + b x\right)^{2}\right)^{p}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(((a + b*x)**2)**p/(d + e*x)**(5/2), x)","F",0
1756,-2,0,0,0.000000," ","integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(5+p),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1757,-2,0,0,0.000000," ","integrate((e*x+d)**(-3-2*p)*(b**2*x**2+2*a*b*x+a**2)**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1758,0,0,0,0.000000," ","integrate((e*x+d)*(4*x**2+12*x+9)**p,x)","\begin{cases} - \frac{2 d}{8 x + 12} + \frac{2 e x \log{\left(x + \frac{3}{2} \right)}}{8 x + 12} + \frac{3 e \log{\left(x + \frac{3}{2} \right)}}{8 x + 12} + \frac{3 e}{8 x + 12} & \text{for}\: p = -1 \\\int \frac{d + e x}{\sqrt{\left(2 x + 3\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{8 d p x \left(4 x^{2} + 12 x + 9\right)^{p}}{16 p^{2} + 24 p + 8} + \frac{12 d p \left(4 x^{2} + 12 x + 9\right)^{p}}{16 p^{2} + 24 p + 8} + \frac{8 d x \left(4 x^{2} + 12 x + 9\right)^{p}}{16 p^{2} + 24 p + 8} + \frac{12 d \left(4 x^{2} + 12 x + 9\right)^{p}}{16 p^{2} + 24 p + 8} + \frac{8 e p x^{2} \left(4 x^{2} + 12 x + 9\right)^{p}}{16 p^{2} + 24 p + 8} + \frac{12 e p x \left(4 x^{2} + 12 x + 9\right)^{p}}{16 p^{2} + 24 p + 8} + \frac{4 e x^{2} \left(4 x^{2} + 12 x + 9\right)^{p}}{16 p^{2} + 24 p + 8} - \frac{9 e \left(4 x^{2} + 12 x + 9\right)^{p}}{16 p^{2} + 24 p + 8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*d/(8*x + 12) + 2*e*x*log(x + 3/2)/(8*x + 12) + 3*e*log(x + 3/2)/(8*x + 12) + 3*e/(8*x + 12), Eq(p, -1)), (Integral((d + e*x)/sqrt((2*x + 3)**2), x), Eq(p, -1/2)), (8*d*p*x*(4*x**2 + 12*x + 9)**p/(16*p**2 + 24*p + 8) + 12*d*p*(4*x**2 + 12*x + 9)**p/(16*p**2 + 24*p + 8) + 8*d*x*(4*x**2 + 12*x + 9)**p/(16*p**2 + 24*p + 8) + 12*d*(4*x**2 + 12*x + 9)**p/(16*p**2 + 24*p + 8) + 8*e*p*x**2*(4*x**2 + 12*x + 9)**p/(16*p**2 + 24*p + 8) + 12*e*p*x*(4*x**2 + 12*x + 9)**p/(16*p**2 + 24*p + 8) + 4*e*x**2*(4*x**2 + 12*x + 9)**p/(16*p**2 + 24*p + 8) - 9*e*(4*x**2 + 12*x + 9)**p/(16*p**2 + 24*p + 8), True))","F",0
1759,1,100,0,0.113197," ","integrate((b*x+a)**3*(a*c+(a*d+b*c)*x+b*d*x**2),x)","a^{4} c x + \frac{b^{4} d x^{6}}{6} + x^{5} \left(\frac{4 a b^{3} d}{5} + \frac{b^{4} c}{5}\right) + x^{4} \left(\frac{3 a^{2} b^{2} d}{2} + a b^{3} c\right) + x^{3} \left(\frac{4 a^{3} b d}{3} + 2 a^{2} b^{2} c\right) + x^{2} \left(\frac{a^{4} d}{2} + 2 a^{3} b c\right)"," ",0,"a**4*c*x + b**4*d*x**6/6 + x**5*(4*a*b**3*d/5 + b**4*c/5) + x**4*(3*a**2*b**2*d/2 + a*b**3*c) + x**3*(4*a**3*b*d/3 + 2*a**2*b**2*c) + x**2*(a**4*d/2 + 2*a**3*b*c)","B",0
1760,1,73,0,0.085834," ","integrate((b*x+a)**2*(a*c+(a*d+b*c)*x+b*d*x**2),x)","a^{3} c x + \frac{b^{3} d x^{5}}{5} + x^{4} \left(\frac{3 a b^{2} d}{4} + \frac{b^{3} c}{4}\right) + x^{3} \left(a^{2} b d + a b^{2} c\right) + x^{2} \left(\frac{a^{3} d}{2} + \frac{3 a^{2} b c}{2}\right)"," ",0,"a**3*c*x + b**3*d*x**5/5 + x**4*(3*a*b**2*d/4 + b**3*c/4) + x**3*(a**2*b*d + a*b**2*c) + x**2*(a**3*d/2 + 3*a**2*b*c/2)","B",0
1761,1,49,0,0.074401," ","integrate((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x**2),x)","a^{2} c x + \frac{b^{2} d x^{4}}{4} + x^{3} \left(\frac{2 a b d}{3} + \frac{b^{2} c}{3}\right) + x^{2} \left(\frac{a^{2} d}{2} + a b c\right)"," ",0,"a**2*c*x + b**2*d*x**4/4 + x**3*(2*a*b*d/3 + b**2*c/3) + x**2*(a**2*d/2 + a*b*c)","A",0
1762,1,26,0,0.065238," ","integrate(a*c+(a*d+b*c)*x+b*d*x**2,x)","a c x + \frac{b d x^{3}}{3} + x^{2} \left(\frac{a d}{2} + \frac{b c}{2}\right)"," ",0,"a*c*x + b*d*x**3/3 + x**2*(a*d/2 + b*c/2)","A",0
1763,1,8,0,0.095736," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)/(b*x+a),x)","c x + \frac{d x^{2}}{2}"," ",0,"c*x + d*x**2/2","A",0
1764,1,20,0,0.176543," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)/(b*x+a)**2,x)","\frac{d x}{b} - \frac{\left(a d - b c\right) \log{\left(a + b x \right)}}{b^{2}}"," ",0,"d*x/b - (a*d - b*c)*log(a + b*x)/b**2","A",0
1765,1,27,0,0.207099," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)/(b*x+a)**3,x)","\frac{a d - b c}{a b^{2} + b^{3} x} + \frac{d \log{\left(a + b x \right)}}{b^{2}}"," ",0,"(a*d - b*c)/(a*b**2 + b**3*x) + d*log(a + b*x)/b**2","A",0
1766,1,39,0,0.298289," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)/(b*x+a)**4,x)","\frac{- a d - b c - 2 b d x}{2 a^{2} b^{2} + 4 a b^{3} x + 2 b^{4} x^{2}}"," ",0,"(-a*d - b*c - 2*b*d*x)/(2*a**2*b**2 + 4*a*b**3*x + 2*b**4*x**2)","A",0
1767,1,53,0,0.403993," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)/(b*x+a)**5,x)","\frac{- a d - 2 b c - 3 b d x}{6 a^{3} b^{2} + 18 a^{2} b^{3} x + 18 a b^{4} x^{2} + 6 b^{5} x^{3}}"," ",0,"(-a*d - 2*b*c - 3*b*d*x)/(6*a**3*b**2 + 18*a**2*b**3*x + 18*a*b**4*x**2 + 6*b**5*x**3)","A",0
1768,1,65,0,0.515911," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)/(b*x+a)**6,x)","\frac{- a d - 3 b c - 4 b d x}{12 a^{4} b^{2} + 48 a^{3} b^{3} x + 72 a^{2} b^{4} x^{2} + 48 a b^{5} x^{3} + 12 b^{6} x^{4}}"," ",0,"(-a*d - 3*b*c - 4*b*d*x)/(12*a**4*b**2 + 48*a**3*b**3*x + 72*a**2*b**4*x**2 + 48*a*b**5*x**3 + 12*b**6*x**4)","B",0
1769,1,218,0,0.132761," ","integrate((b*x+a)**3*(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","a^{5} c^{2} x + \frac{b^{5} d^{2} x^{8}}{8} + x^{7} \left(\frac{5 a b^{4} d^{2}}{7} + \frac{2 b^{5} c d}{7}\right) + x^{6} \left(\frac{5 a^{2} b^{3} d^{2}}{3} + \frac{5 a b^{4} c d}{3} + \frac{b^{5} c^{2}}{6}\right) + x^{5} \left(2 a^{3} b^{2} d^{2} + 4 a^{2} b^{3} c d + a b^{4} c^{2}\right) + x^{4} \left(\frac{5 a^{4} b d^{2}}{4} + 5 a^{3} b^{2} c d + \frac{5 a^{2} b^{3} c^{2}}{2}\right) + x^{3} \left(\frac{a^{5} d^{2}}{3} + \frac{10 a^{4} b c d}{3} + \frac{10 a^{3} b^{2} c^{2}}{3}\right) + x^{2} \left(a^{5} c d + \frac{5 a^{4} b c^{2}}{2}\right)"," ",0,"a**5*c**2*x + b**5*d**2*x**8/8 + x**7*(5*a*b**4*d**2/7 + 2*b**5*c*d/7) + x**6*(5*a**2*b**3*d**2/3 + 5*a*b**4*c*d/3 + b**5*c**2/6) + x**5*(2*a**3*b**2*d**2 + 4*a**2*b**3*c*d + a*b**4*c**2) + x**4*(5*a**4*b*d**2/4 + 5*a**3*b**2*c*d + 5*a**2*b**3*c**2/2) + x**3*(a**5*d**2/3 + 10*a**4*b*c*d/3 + 10*a**3*b**2*c**2/3) + x**2*(a**5*c*d + 5*a**4*b*c**2/2)","B",0
1770,1,168,0,0.117831," ","integrate((b*x+a)**2*(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","a^{4} c^{2} x + \frac{b^{4} d^{2} x^{7}}{7} + x^{6} \left(\frac{2 a b^{3} d^{2}}{3} + \frac{b^{4} c d}{3}\right) + x^{5} \left(\frac{6 a^{2} b^{2} d^{2}}{5} + \frac{8 a b^{3} c d}{5} + \frac{b^{4} c^{2}}{5}\right) + x^{4} \left(a^{3} b d^{2} + 3 a^{2} b^{2} c d + a b^{3} c^{2}\right) + x^{3} \left(\frac{a^{4} d^{2}}{3} + \frac{8 a^{3} b c d}{3} + 2 a^{2} b^{2} c^{2}\right) + x^{2} \left(a^{4} c d + 2 a^{3} b c^{2}\right)"," ",0,"a**4*c**2*x + b**4*d**2*x**7/7 + x**6*(2*a*b**3*d**2/3 + b**4*c*d/3) + x**5*(6*a**2*b**2*d**2/5 + 8*a*b**3*c*d/5 + b**4*c**2/5) + x**4*(a**3*b*d**2 + 3*a**2*b**2*c*d + a*b**3*c**2) + x**3*(a**4*d**2/3 + 8*a**3*b*c*d/3 + 2*a**2*b**2*c**2) + x**2*(a**4*c*d + 2*a**3*b*c**2)","B",0
1771,1,133,0,0.108637," ","integrate((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","a^{3} c^{2} x + \frac{b^{3} d^{2} x^{6}}{6} + x^{5} \left(\frac{3 a b^{2} d^{2}}{5} + \frac{2 b^{3} c d}{5}\right) + x^{4} \left(\frac{3 a^{2} b d^{2}}{4} + \frac{3 a b^{2} c d}{2} + \frac{b^{3} c^{2}}{4}\right) + x^{3} \left(\frac{a^{3} d^{2}}{3} + 2 a^{2} b c d + a b^{2} c^{2}\right) + x^{2} \left(a^{3} c d + \frac{3 a^{2} b c^{2}}{2}\right)"," ",0,"a**3*c**2*x + b**3*d**2*x**6/6 + x**5*(3*a*b**2*d**2/5 + 2*b**3*c*d/5) + x**4*(3*a**2*b*d**2/4 + 3*a*b**2*c*d/2 + b**3*c**2/4) + x**3*(a**3*d**2/3 + 2*a**2*b*c*d + a*b**2*c**2) + x**2*(a**3*c*d + 3*a**2*b*c**2/2)","B",0
1772,1,87,0,0.088744," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","a^{2} c^{2} x + \frac{b^{2} d^{2} x^{5}}{5} + x^{4} \left(\frac{a b d^{2}}{2} + \frac{b^{2} c d}{2}\right) + x^{3} \left(\frac{a^{2} d^{2}}{3} + \frac{4 a b c d}{3} + \frac{b^{2} c^{2}}{3}\right) + x^{2} \left(a^{2} c d + a b c^{2}\right)"," ",0,"a**2*c**2*x + b**2*d**2*x**5/5 + x**4*(a*b*d**2/2 + b**2*c*d/2) + x**3*(a**2*d**2/3 + 4*a*b*c*d/3 + b**2*c**2/3) + x**2*(a**2*c*d + a*b*c**2)","A",0
1773,1,49,0,0.133497," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2/(b*x+a),x)","a c^{2} x + \frac{b d^{2} x^{4}}{4} + x^{3} \left(\frac{a d^{2}}{3} + \frac{2 b c d}{3}\right) + x^{2} \left(a c d + \frac{b c^{2}}{2}\right)"," ",0,"a*c**2*x + b*d**2*x**4/4 + x**3*(a*d**2/3 + 2*b*c*d/3) + x**2*(a*c*d + b*c**2/2)","A",0
1774,1,19,0,0.129192," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2/(b*x+a)**2,x)","c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3}"," ",0,"c**2*x + c*d*x**2 + d**2*x**3/3","B",0
1775,1,44,0,0.292183," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2/(b*x+a)**3,x)","x \left(- \frac{a d^{2}}{b^{2}} + \frac{2 c d}{b}\right) + \frac{d^{2} x^{2}}{2 b} + \frac{\left(a d - b c\right)^{2} \log{\left(a + b x \right)}}{b^{3}}"," ",0,"x*(-a*d**2/b**2 + 2*c*d/b) + d**2*x**2/(2*b) + (a*d - b*c)**2*log(a + b*x)/b**3","A",0
1776,1,60,0,0.416162," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2/(b*x+a)**4,x)","\frac{- a^{2} d^{2} + 2 a b c d - b^{2} c^{2}}{a b^{3} + b^{4} x} + \frac{d^{2} x}{b^{2}} - \frac{2 d \left(a d - b c\right) \log{\left(a + b x \right)}}{b^{3}}"," ",0,"(-a**2*d**2 + 2*a*b*c*d - b**2*c**2)/(a*b**3 + b**4*x) + d**2*x/b**2 - 2*d*(a*d - b*c)*log(a + b*x)/b**3","A",0
1777,1,80,0,0.539958," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2/(b*x+a)**5,x)","\frac{3 a^{2} d^{2} - 2 a b c d - b^{2} c^{2} + x \left(4 a b d^{2} - 4 b^{2} c d\right)}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{d^{2} \log{\left(a + b x \right)}}{b^{3}}"," ",0,"(3*a**2*d**2 - 2*a*b*c*d - b**2*c**2 + x*(4*a*b*d**2 - 4*b**2*c*d))/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + d**2*log(a + b*x)/b**3","A",0
1778,1,88,0,0.696962," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2/(b*x+a)**6,x)","\frac{- a^{2} d^{2} - a b c d - b^{2} c^{2} - 3 b^{2} d^{2} x^{2} + x \left(- 3 a b d^{2} - 3 b^{2} c d\right)}{3 a^{3} b^{3} + 9 a^{2} b^{4} x + 9 a b^{5} x^{2} + 3 b^{6} x^{3}}"," ",0,"(-a**2*d**2 - a*b*c*d - b**2*c**2 - 3*b**2*d**2*x**2 + x*(-3*a*b*d**2 - 3*b**2*c*d))/(3*a**3*b**3 + 9*a**2*b**4*x + 9*a*b**5*x**2 + 3*b**6*x**3)","B",0
1779,1,104,0,0.843550," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2/(b*x+a)**7,x)","\frac{- a^{2} d^{2} - 2 a b c d - 3 b^{2} c^{2} - 6 b^{2} d^{2} x^{2} + x \left(- 4 a b d^{2} - 8 b^{2} c d\right)}{12 a^{4} b^{3} + 48 a^{3} b^{4} x + 72 a^{2} b^{5} x^{2} + 48 a b^{6} x^{3} + 12 b^{7} x^{4}}"," ",0,"(-a**2*d**2 - 2*a*b*c*d - 3*b**2*c**2 - 6*b**2*d**2*x**2 + x*(-4*a*b*d**2 - 8*b**2*c*d))/(12*a**4*b**3 + 48*a**3*b**4*x + 72*a**2*b**5*x**2 + 48*a*b**6*x**3 + 12*b**7*x**4)","A",0
1780,1,116,0,1.077545," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2/(b*x+a)**8,x)","\frac{- a^{2} d^{2} - 3 a b c d - 6 b^{2} c^{2} - 10 b^{2} d^{2} x^{2} + x \left(- 5 a b d^{2} - 15 b^{2} c d\right)}{30 a^{5} b^{3} + 150 a^{4} b^{4} x + 300 a^{3} b^{5} x^{2} + 300 a^{2} b^{6} x^{3} + 150 a b^{7} x^{4} + 30 b^{8} x^{5}}"," ",0,"(-a**2*d**2 - 3*a*b*c*d - 6*b**2*c**2 - 10*b**2*d**2*x**2 + x*(-5*a*b*d**2 - 15*b**2*c*d))/(30*a**5*b**3 + 150*a**4*b**4*x + 300*a**3*b**5*x**2 + 300*a**2*b**6*x**3 + 150*a*b**7*x**4 + 30*b**8*x**5)","B",0
1781,1,128,0,1.355658," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2/(b*x+a)**9,x)","\frac{- a^{2} d^{2} - 4 a b c d - 10 b^{2} c^{2} - 15 b^{2} d^{2} x^{2} + x \left(- 6 a b d^{2} - 24 b^{2} c d\right)}{60 a^{6} b^{3} + 360 a^{5} b^{4} x + 900 a^{4} b^{5} x^{2} + 1200 a^{3} b^{6} x^{3} + 900 a^{2} b^{7} x^{4} + 360 a b^{8} x^{5} + 60 b^{9} x^{6}}"," ",0,"(-a**2*d**2 - 4*a*b*c*d - 10*b**2*c**2 - 15*b**2*d**2*x**2 + x*(-6*a*b*d**2 - 24*b**2*c*d))/(60*a**6*b**3 + 360*a**5*b**4*x + 900*a**4*b**5*x**2 + 1200*a**3*b**6*x**3 + 900*a**2*b**7*x**4 + 360*a*b**8*x**5 + 60*b**9*x**6)","B",0
1782,1,139,0,1.947408," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**2/(b*x+a)**10,x)","\frac{- a^{2} d^{2} - 5 a b c d - 15 b^{2} c^{2} - 21 b^{2} d^{2} x^{2} + x \left(- 7 a b d^{2} - 35 b^{2} c d\right)}{105 a^{7} b^{3} + 735 a^{6} b^{4} x + 2205 a^{5} b^{5} x^{2} + 3675 a^{4} b^{6} x^{3} + 3675 a^{3} b^{7} x^{4} + 2205 a^{2} b^{8} x^{5} + 735 a b^{9} x^{6} + 105 b^{10} x^{7}}"," ",0,"(-a**2*d**2 - 5*a*b*c*d - 15*b**2*c**2 - 21*b**2*d**2*x**2 + x*(-7*a*b*d**2 - 35*b**2*c*d))/(105*a**7*b**3 + 735*a**6*b**4*x + 2205*a**5*b**5*x**2 + 3675*a**4*b**6*x**3 + 3675*a**3*b**7*x**4 + 2205*a**2*b**8*x**5 + 735*a*b**9*x**6 + 105*b**10*x**7)","B",0
1783,1,364,0,0.164305," ","integrate((b*x+a)**3*(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","a^{6} c^{3} x + \frac{b^{6} d^{3} x^{10}}{10} + x^{9} \left(\frac{2 a b^{5} d^{3}}{3} + \frac{b^{6} c d^{2}}{3}\right) + x^{8} \left(\frac{15 a^{2} b^{4} d^{3}}{8} + \frac{9 a b^{5} c d^{2}}{4} + \frac{3 b^{6} c^{2} d}{8}\right) + x^{7} \left(\frac{20 a^{3} b^{3} d^{3}}{7} + \frac{45 a^{2} b^{4} c d^{2}}{7} + \frac{18 a b^{5} c^{2} d}{7} + \frac{b^{6} c^{3}}{7}\right) + x^{6} \left(\frac{5 a^{4} b^{2} d^{3}}{2} + 10 a^{3} b^{3} c d^{2} + \frac{15 a^{2} b^{4} c^{2} d}{2} + a b^{5} c^{3}\right) + x^{5} \left(\frac{6 a^{5} b d^{3}}{5} + 9 a^{4} b^{2} c d^{2} + 12 a^{3} b^{3} c^{2} d + 3 a^{2} b^{4} c^{3}\right) + x^{4} \left(\frac{a^{6} d^{3}}{4} + \frac{9 a^{5} b c d^{2}}{2} + \frac{45 a^{4} b^{2} c^{2} d}{4} + 5 a^{3} b^{3} c^{3}\right) + x^{3} \left(a^{6} c d^{2} + 6 a^{5} b c^{2} d + 5 a^{4} b^{2} c^{3}\right) + x^{2} \left(\frac{3 a^{6} c^{2} d}{2} + 3 a^{5} b c^{3}\right)"," ",0,"a**6*c**3*x + b**6*d**3*x**10/10 + x**9*(2*a*b**5*d**3/3 + b**6*c*d**2/3) + x**8*(15*a**2*b**4*d**3/8 + 9*a*b**5*c*d**2/4 + 3*b**6*c**2*d/8) + x**7*(20*a**3*b**3*d**3/7 + 45*a**2*b**4*c*d**2/7 + 18*a*b**5*c**2*d/7 + b**6*c**3/7) + x**6*(5*a**4*b**2*d**3/2 + 10*a**3*b**3*c*d**2 + 15*a**2*b**4*c**2*d/2 + a*b**5*c**3) + x**5*(6*a**5*b*d**3/5 + 9*a**4*b**2*c*d**2 + 12*a**3*b**3*c**2*d + 3*a**2*b**4*c**3) + x**4*(a**6*d**3/4 + 9*a**5*b*c*d**2/2 + 45*a**4*b**2*c**2*d/4 + 5*a**3*b**3*c**3) + x**3*(a**6*c*d**2 + 6*a**5*b*c**2*d + 5*a**4*b**2*c**3) + x**2*(3*a**6*c**2*d/2 + 3*a**5*b*c**3)","B",0
1784,1,308,0,0.148788," ","integrate((b*x+a)**2*(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","a^{5} c^{3} x + \frac{b^{5} d^{3} x^{9}}{9} + x^{8} \left(\frac{5 a b^{4} d^{3}}{8} + \frac{3 b^{5} c d^{2}}{8}\right) + x^{7} \left(\frac{10 a^{2} b^{3} d^{3}}{7} + \frac{15 a b^{4} c d^{2}}{7} + \frac{3 b^{5} c^{2} d}{7}\right) + x^{6} \left(\frac{5 a^{3} b^{2} d^{3}}{3} + 5 a^{2} b^{3} c d^{2} + \frac{5 a b^{4} c^{2} d}{2} + \frac{b^{5} c^{3}}{6}\right) + x^{5} \left(a^{4} b d^{3} + 6 a^{3} b^{2} c d^{2} + 6 a^{2} b^{3} c^{2} d + a b^{4} c^{3}\right) + x^{4} \left(\frac{a^{5} d^{3}}{4} + \frac{15 a^{4} b c d^{2}}{4} + \frac{15 a^{3} b^{2} c^{2} d}{2} + \frac{5 a^{2} b^{3} c^{3}}{2}\right) + x^{3} \left(a^{5} c d^{2} + 5 a^{4} b c^{2} d + \frac{10 a^{3} b^{2} c^{3}}{3}\right) + x^{2} \left(\frac{3 a^{5} c^{2} d}{2} + \frac{5 a^{4} b c^{3}}{2}\right)"," ",0,"a**5*c**3*x + b**5*d**3*x**9/9 + x**8*(5*a*b**4*d**3/8 + 3*b**5*c*d**2/8) + x**7*(10*a**2*b**3*d**3/7 + 15*a*b**4*c*d**2/7 + 3*b**5*c**2*d/7) + x**6*(5*a**3*b**2*d**3/3 + 5*a**2*b**3*c*d**2 + 5*a*b**4*c**2*d/2 + b**5*c**3/6) + x**5*(a**4*b*d**3 + 6*a**3*b**2*c*d**2 + 6*a**2*b**3*c**2*d + a*b**4*c**3) + x**4*(a**5*d**3/4 + 15*a**4*b*c*d**2/4 + 15*a**3*b**2*c**2*d/2 + 5*a**2*b**3*c**3/2) + x**3*(a**5*c*d**2 + 5*a**4*b*c**2*d + 10*a**3*b**2*c**3/3) + x**2*(3*a**5*c**2*d/2 + 5*a**4*b*c**3/2)","B",0
1785,1,243,0,0.130349," ","integrate((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","a^{4} c^{3} x + \frac{b^{4} d^{3} x^{8}}{8} + x^{7} \left(\frac{4 a b^{3} d^{3}}{7} + \frac{3 b^{4} c d^{2}}{7}\right) + x^{6} \left(a^{2} b^{2} d^{3} + 2 a b^{3} c d^{2} + \frac{b^{4} c^{2} d}{2}\right) + x^{5} \left(\frac{4 a^{3} b d^{3}}{5} + \frac{18 a^{2} b^{2} c d^{2}}{5} + \frac{12 a b^{3} c^{2} d}{5} + \frac{b^{4} c^{3}}{5}\right) + x^{4} \left(\frac{a^{4} d^{3}}{4} + 3 a^{3} b c d^{2} + \frac{9 a^{2} b^{2} c^{2} d}{2} + a b^{3} c^{3}\right) + x^{3} \left(a^{4} c d^{2} + 4 a^{3} b c^{2} d + 2 a^{2} b^{2} c^{3}\right) + x^{2} \left(\frac{3 a^{4} c^{2} d}{2} + 2 a^{3} b c^{3}\right)"," ",0,"a**4*c**3*x + b**4*d**3*x**8/8 + x**7*(4*a*b**3*d**3/7 + 3*b**4*c*d**2/7) + x**6*(a**2*b**2*d**3 + 2*a*b**3*c*d**2 + b**4*c**2*d/2) + x**5*(4*a**3*b*d**3/5 + 18*a**2*b**2*c*d**2/5 + 12*a*b**3*c**2*d/5 + b**4*c**3/5) + x**4*(a**4*d**3/4 + 3*a**3*b*c*d**2 + 9*a**2*b**2*c**2*d/2 + a*b**3*c**3) + x**3*(a**4*c*d**2 + 4*a**3*b*c**2*d + 2*a**2*b**2*c**3) + x**2*(3*a**4*c**2*d/2 + 2*a**3*b*c**3)","B",0
1786,1,190,0,0.114223," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","a^{3} c^{3} x + \frac{b^{3} d^{3} x^{7}}{7} + x^{6} \left(\frac{a b^{2} d^{3}}{2} + \frac{b^{3} c d^{2}}{2}\right) + x^{5} \left(\frac{3 a^{2} b d^{3}}{5} + \frac{9 a b^{2} c d^{2}}{5} + \frac{3 b^{3} c^{2} d}{5}\right) + x^{4} \left(\frac{a^{3} d^{3}}{4} + \frac{9 a^{2} b c d^{2}}{4} + \frac{9 a b^{2} c^{2} d}{4} + \frac{b^{3} c^{3}}{4}\right) + x^{3} \left(a^{3} c d^{2} + 3 a^{2} b c^{2} d + a b^{2} c^{3}\right) + x^{2} \left(\frac{3 a^{3} c^{2} d}{2} + \frac{3 a^{2} b c^{3}}{2}\right)"," ",0,"a**3*c**3*x + b**3*d**3*x**7/7 + x**6*(a*b**2*d**3/2 + b**3*c*d**2/2) + x**5*(3*a**2*b*d**3/5 + 9*a*b**2*c*d**2/5 + 3*b**3*c**2*d/5) + x**4*(a**3*d**3/4 + 9*a**2*b*c*d**2/4 + 9*a*b**2*c**2*d/4 + b**3*c**3/4) + x**3*(a**3*c*d**2 + 3*a**2*b*c**2*d + a*b**2*c**3) + x**2*(3*a**3*c**2*d/2 + 3*a**2*b*c**3/2)","B",0
1787,1,133,0,0.171088," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a),x)","a^{2} c^{3} x + \frac{b^{2} d^{3} x^{6}}{6} + x^{5} \left(\frac{2 a b d^{3}}{5} + \frac{3 b^{2} c d^{2}}{5}\right) + x^{4} \left(\frac{a^{2} d^{3}}{4} + \frac{3 a b c d^{2}}{2} + \frac{3 b^{2} c^{2} d}{4}\right) + x^{3} \left(a^{2} c d^{2} + 2 a b c^{2} d + \frac{b^{2} c^{3}}{3}\right) + x^{2} \left(\frac{3 a^{2} c^{2} d}{2} + a b c^{3}\right)"," ",0,"a**2*c**3*x + b**2*d**3*x**6/6 + x**5*(2*a*b*d**3/5 + 3*b**2*c*d**2/5) + x**4*(a**2*d**3/4 + 3*a*b*c*d**2/2 + 3*b**2*c**2*d/4) + x**3*(a**2*c*d**2 + 2*a*b*c**2*d + b**2*c**3/3) + x**2*(3*a**2*c**2*d/2 + a*b*c**3)","B",0
1788,1,73,0,0.168370," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**2,x)","a c^{3} x + \frac{b d^{3} x^{5}}{5} + x^{4} \left(\frac{a d^{3}}{4} + \frac{3 b c d^{2}}{4}\right) + x^{3} \left(a c d^{2} + b c^{2} d\right) + x^{2} \left(\frac{3 a c^{2} d}{2} + \frac{b c^{3}}{2}\right)"," ",0,"a*c**3*x + b*d**3*x**5/5 + x**4*(a*d**3/4 + 3*b*c*d**2/4) + x**3*(a*c*d**2 + b*c**2*d) + x**2*(3*a*c**2*d/2 + b*c**3/2)","B",0
1789,1,32,0,0.162097," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**3,x)","c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4}"," ",0,"c**3*x + 3*c**2*d*x**2/2 + c*d**2*x**3 + d**3*x**4/4","B",0
1790,1,83,0,0.398473," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**4,x)","x^{2} \left(- \frac{a d^{3}}{2 b^{2}} + \frac{3 c d^{2}}{2 b}\right) + x \left(\frac{a^{2} d^{3}}{b^{3}} - \frac{3 a c d^{2}}{b^{2}} + \frac{3 c^{2} d}{b}\right) + \frac{d^{3} x^{3}}{3 b} - \frac{\left(a d - b c\right)^{3} \log{\left(a + b x \right)}}{b^{4}}"," ",0,"x**2*(-a*d**3/(2*b**2) + 3*c*d**2/(2*b)) + x*(a**2*d**3/b**3 - 3*a*c*d**2/b**2 + 3*c**2*d/b) + d**3*x**3/(3*b) - (a*d - b*c)**3*log(a + b*x)/b**4","A",0
1791,1,102,0,0.663080," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**5,x)","x \left(- \frac{2 a d^{3}}{b^{3}} + \frac{3 c d^{2}}{b^{2}}\right) + \frac{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}}{a b^{4} + b^{5} x} + \frac{d^{3} x^{2}}{2 b^{2}} + \frac{3 d \left(a d - b c\right)^{2} \log{\left(a + b x \right)}}{b^{4}}"," ",0,"x*(-2*a*d**3/b**3 + 3*c*d**2/b**2) + (a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3)/(a*b**4 + b**5*x) + d**3*x**2/(2*b**2) + 3*d*(a*d - b*c)**2*log(a + b*x)/b**4","A",0
1792,1,128,0,0.965820," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**6,x)","\frac{- 5 a^{3} d^{3} + 9 a^{2} b c d^{2} - 3 a b^{2} c^{2} d - b^{3} c^{3} + x \left(- 6 a^{2} b d^{3} + 12 a b^{2} c d^{2} - 6 b^{3} c^{2} d\right)}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{d^{3} x}{b^{3}} - \frac{3 d^{2} \left(a d - b c\right) \log{\left(a + b x \right)}}{b^{4}}"," ",0,"(-5*a**3*d**3 + 9*a**2*b*c*d**2 - 3*a*b**2*c**2*d - b**3*c**3 + x*(-6*a**2*b*d**3 + 12*a*b**2*c*d**2 - 6*b**3*c**2*d))/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + d**3*x/b**3 - 3*d**2*(a*d - b*c)*log(a + b*x)/b**4","A",0
1793,1,148,0,1.290149," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**7,x)","\frac{11 a^{3} d^{3} - 6 a^{2} b c d^{2} - 3 a b^{2} c^{2} d - 2 b^{3} c^{3} + x^{2} \left(18 a b^{2} d^{3} - 18 b^{3} c d^{2}\right) + x \left(27 a^{2} b d^{3} - 18 a b^{2} c d^{2} - 9 b^{3} c^{2} d\right)}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{d^{3} \log{\left(a + b x \right)}}{b^{4}}"," ",0,"(11*a**3*d**3 - 6*a**2*b*c*d**2 - 3*a*b**2*c**2*d - 2*b**3*c**3 + x**2*(18*a*b**2*d**3 - 18*b**3*c*d**2) + x*(27*a**2*b*d**3 - 18*a*b**2*c*d**2 - 9*b**3*c**2*d))/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + d**3*log(a + b*x)/b**4","A",0
1794,1,155,0,1.973948," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**8,x)","\frac{- a^{3} d^{3} - a^{2} b c d^{2} - a b^{2} c^{2} d - b^{3} c^{3} - 4 b^{3} d^{3} x^{3} + x^{2} \left(- 6 a b^{2} d^{3} - 6 b^{3} c d^{2}\right) + x \left(- 4 a^{2} b d^{3} - 4 a b^{2} c d^{2} - 4 b^{3} c^{2} d\right)}{4 a^{4} b^{4} + 16 a^{3} b^{5} x + 24 a^{2} b^{6} x^{2} + 16 a b^{7} x^{3} + 4 b^{8} x^{4}}"," ",0,"(-a**3*d**3 - a**2*b*c*d**2 - a*b**2*c**2*d - b**3*c**3 - 4*b**3*d**3*x**3 + x**2*(-6*a*b**2*d**3 - 6*b**3*c*d**2) + x*(-4*a**2*b*d**3 - 4*a*b**2*c*d**2 - 4*b**3*c**2*d))/(4*a**4*b**4 + 16*a**3*b**5*x + 24*a**2*b**6*x**2 + 16*a*b**7*x**3 + 4*b**8*x**4)","B",0
1795,1,172,0,2.906663," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**9,x)","\frac{- a^{3} d^{3} - 2 a^{2} b c d^{2} - 3 a b^{2} c^{2} d - 4 b^{3} c^{3} - 10 b^{3} d^{3} x^{3} + x^{2} \left(- 10 a b^{2} d^{3} - 20 b^{3} c d^{2}\right) + x \left(- 5 a^{2} b d^{3} - 10 a b^{2} c d^{2} - 15 b^{3} c^{2} d\right)}{20 a^{5} b^{4} + 100 a^{4} b^{5} x + 200 a^{3} b^{6} x^{2} + 200 a^{2} b^{7} x^{3} + 100 a b^{8} x^{4} + 20 b^{9} x^{5}}"," ",0,"(-a**3*d**3 - 2*a**2*b*c*d**2 - 3*a*b**2*c**2*d - 4*b**3*c**3 - 10*b**3*d**3*x**3 + x**2*(-10*a*b**2*d**3 - 20*b**3*c*d**2) + x*(-5*a**2*b*d**3 - 10*a*b**2*c*d**2 - 15*b**3*c**2*d))/(20*a**5*b**4 + 100*a**4*b**5*x + 200*a**3*b**6*x**2 + 200*a**2*b**7*x**3 + 100*a*b**8*x**4 + 20*b**9*x**5)","B",0
1796,1,184,0,5.039274," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**10,x)","\frac{- a^{3} d^{3} - 3 a^{2} b c d^{2} - 6 a b^{2} c^{2} d - 10 b^{3} c^{3} - 20 b^{3} d^{3} x^{3} + x^{2} \left(- 15 a b^{2} d^{3} - 45 b^{3} c d^{2}\right) + x \left(- 6 a^{2} b d^{3} - 18 a b^{2} c d^{2} - 36 b^{3} c^{2} d\right)}{60 a^{6} b^{4} + 360 a^{5} b^{5} x + 900 a^{4} b^{6} x^{2} + 1200 a^{3} b^{7} x^{3} + 900 a^{2} b^{8} x^{4} + 360 a b^{9} x^{5} + 60 b^{10} x^{6}}"," ",0,"(-a**3*d**3 - 3*a**2*b*c*d**2 - 6*a*b**2*c**2*d - 10*b**3*c**3 - 20*b**3*d**3*x**3 + x**2*(-15*a*b**2*d**3 - 45*b**3*c*d**2) + x*(-6*a**2*b*d**3 - 18*a*b**2*c*d**2 - 36*b**3*c**2*d))/(60*a**6*b**4 + 360*a**5*b**5*x + 900*a**4*b**6*x**2 + 1200*a**3*b**7*x**3 + 900*a**2*b**8*x**4 + 360*a*b**9*x**5 + 60*b**10*x**6)","B",0
1797,1,196,0,9.168355," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**11,x)","\frac{- a^{3} d^{3} - 4 a^{2} b c d^{2} - 10 a b^{2} c^{2} d - 20 b^{3} c^{3} - 35 b^{3} d^{3} x^{3} + x^{2} \left(- 21 a b^{2} d^{3} - 84 b^{3} c d^{2}\right) + x \left(- 7 a^{2} b d^{3} - 28 a b^{2} c d^{2} - 70 b^{3} c^{2} d\right)}{140 a^{7} b^{4} + 980 a^{6} b^{5} x + 2940 a^{5} b^{6} x^{2} + 4900 a^{4} b^{7} x^{3} + 4900 a^{3} b^{8} x^{4} + 2940 a^{2} b^{9} x^{5} + 980 a b^{10} x^{6} + 140 b^{11} x^{7}}"," ",0,"(-a**3*d**3 - 4*a**2*b*c*d**2 - 10*a*b**2*c**2*d - 20*b**3*c**3 - 35*b**3*d**3*x**3 + x**2*(-21*a*b**2*d**3 - 84*b**3*c*d**2) + x*(-7*a**2*b*d**3 - 28*a*b**2*c*d**2 - 70*b**3*c**2*d))/(140*a**7*b**4 + 980*a**6*b**5*x + 2940*a**5*b**6*x**2 + 4900*a**4*b**7*x**3 + 4900*a**3*b**8*x**4 + 2940*a**2*b**9*x**5 + 980*a*b**10*x**6 + 140*b**11*x**7)","B",0
1798,1,207,0,17.824814," ","integrate((a*c+(a*d+b*c)*x+b*d*x**2)**3/(b*x+a)**12,x)","\frac{- a^{3} d^{3} - 5 a^{2} b c d^{2} - 15 a b^{2} c^{2} d - 35 b^{3} c^{3} - 56 b^{3} d^{3} x^{3} + x^{2} \left(- 28 a b^{2} d^{3} - 140 b^{3} c d^{2}\right) + x \left(- 8 a^{2} b d^{3} - 40 a b^{2} c d^{2} - 120 b^{3} c^{2} d\right)}{280 a^{8} b^{4} + 2240 a^{7} b^{5} x + 7840 a^{6} b^{6} x^{2} + 15680 a^{5} b^{7} x^{3} + 19600 a^{4} b^{8} x^{4} + 15680 a^{3} b^{9} x^{5} + 7840 a^{2} b^{10} x^{6} + 2240 a b^{11} x^{7} + 280 b^{12} x^{8}}"," ",0,"(-a**3*d**3 - 5*a**2*b*c*d**2 - 15*a*b**2*c**2*d - 35*b**3*c**3 - 56*b**3*d**3*x**3 + x**2*(-28*a*b**2*d**3 - 140*b**3*c*d**2) + x*(-8*a**2*b*d**3 - 40*a*b**2*c*d**2 - 120*b**3*c**2*d))/(280*a**8*b**4 + 2240*a**7*b**5*x + 7840*a**6*b**6*x**2 + 15680*a**5*b**7*x**3 + 19600*a**4*b**8*x**4 + 15680*a**3*b**9*x**5 + 7840*a**2*b**10*x**6 + 2240*a*b**11*x**7 + 280*b**12*x**8)","B",0
1799,1,209,0,0.575282," ","integrate((b*x+a)**6/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{b^{5} x^{5}}{5 d} + x^{4} \left(\frac{5 a b^{4}}{4 d} - \frac{b^{5} c}{4 d^{2}}\right) + x^{3} \left(\frac{10 a^{2} b^{3}}{3 d} - \frac{5 a b^{4} c}{3 d^{2}} + \frac{b^{5} c^{2}}{3 d^{3}}\right) + x^{2} \left(\frac{5 a^{3} b^{2}}{d} - \frac{5 a^{2} b^{3} c}{d^{2}} + \frac{5 a b^{4} c^{2}}{2 d^{3}} - \frac{b^{5} c^{3}}{2 d^{4}}\right) + x \left(\frac{5 a^{4} b}{d} - \frac{10 a^{3} b^{2} c}{d^{2}} + \frac{10 a^{2} b^{3} c^{2}}{d^{3}} - \frac{5 a b^{4} c^{3}}{d^{4}} + \frac{b^{5} c^{4}}{d^{5}}\right) + \frac{\left(a d - b c\right)^{5} \log{\left(c + d x \right)}}{d^{6}}"," ",0,"b**5*x**5/(5*d) + x**4*(5*a*b**4/(4*d) - b**5*c/(4*d**2)) + x**3*(10*a**2*b**3/(3*d) - 5*a*b**4*c/(3*d**2) + b**5*c**2/(3*d**3)) + x**2*(5*a**3*b**2/d - 5*a**2*b**3*c/d**2 + 5*a*b**4*c**2/(2*d**3) - b**5*c**3/(2*d**4)) + x*(5*a**4*b/d - 10*a**3*b**2*c/d**2 + 10*a**2*b**3*c**2/d**3 - 5*a*b**4*c**3/d**4 + b**5*c**4/d**5) + (a*d - b*c)**5*log(c + d*x)/d**6","B",0
1800,1,136,0,0.457838," ","integrate((b*x+a)**5/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{b^{4} x^{4}}{4 d} + x^{3} \left(\frac{4 a b^{3}}{3 d} - \frac{b^{4} c}{3 d^{2}}\right) + x^{2} \left(\frac{3 a^{2} b^{2}}{d} - \frac{2 a b^{3} c}{d^{2}} + \frac{b^{4} c^{2}}{2 d^{3}}\right) + x \left(\frac{4 a^{3} b}{d} - \frac{6 a^{2} b^{2} c}{d^{2}} + \frac{4 a b^{3} c^{2}}{d^{3}} - \frac{b^{4} c^{3}}{d^{4}}\right) + \frac{\left(a d - b c\right)^{4} \log{\left(c + d x \right)}}{d^{5}}"," ",0,"b**4*x**4/(4*d) + x**3*(4*a*b**3/(3*d) - b**4*c/(3*d**2)) + x**2*(3*a**2*b**2/d - 2*a*b**3*c/d**2 + b**4*c**2/(2*d**3)) + x*(4*a**3*b/d - 6*a**2*b**2*c/d**2 + 4*a*b**3*c**2/d**3 - b**4*c**3/d**4) + (a*d - b*c)**4*log(c + d*x)/d**5","A",0
1801,1,83,0,0.366640," ","integrate((b*x+a)**4/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{b^{3} x^{3}}{3 d} + x^{2} \left(\frac{3 a b^{2}}{2 d} - \frac{b^{3} c}{2 d^{2}}\right) + x \left(\frac{3 a^{2} b}{d} - \frac{3 a b^{2} c}{d^{2}} + \frac{b^{3} c^{2}}{d^{3}}\right) + \frac{\left(a d - b c\right)^{3} \log{\left(c + d x \right)}}{d^{4}}"," ",0,"b**3*x**3/(3*d) + x**2*(3*a*b**2/(2*d) - b**3*c/(2*d**2)) + x*(3*a**2*b/d - 3*a*b**2*c/d**2 + b**3*c**2/d**3) + (a*d - b*c)**3*log(c + d*x)/d**4","A",0
1802,1,44,0,0.258198," ","integrate((b*x+a)**3/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{b^{2} x^{2}}{2 d} + x \left(\frac{2 a b}{d} - \frac{b^{2} c}{d^{2}}\right) + \frac{\left(a d - b c\right)^{2} \log{\left(c + d x \right)}}{d^{3}}"," ",0,"b**2*x**2/(2*d) + x*(2*a*b/d - b**2*c/d**2) + (a*d - b*c)**2*log(c + d*x)/d**3","A",0
1803,1,20,0,0.174209," ","integrate((b*x+a)**2/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{b x}{d} + \frac{\left(a d - b c\right) \log{\left(c + d x \right)}}{d^{2}}"," ",0,"b*x/d + (a*d - b*c)*log(c + d*x)/d**2","A",0
1804,1,7,0,0.080155," ","integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{\log{\left(c + d x \right)}}{d}"," ",0,"log(c + d*x)/d","A",0
1805,1,128,0,0.348552," ","integrate(1/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{\log{\left(x + \frac{- \frac{a^{2} d^{2}}{a d - b c} + \frac{2 a b c d}{a d - b c} + a d - \frac{b^{2} c^{2}}{a d - b c} + b c}{2 b d} \right)}}{a d - b c} - \frac{\log{\left(x + \frac{\frac{a^{2} d^{2}}{a d - b c} - \frac{2 a b c d}{a d - b c} + a d + \frac{b^{2} c^{2}}{a d - b c} + b c}{2 b d} \right)}}{a d - b c}"," ",0,"log(x + (-a**2*d**2/(a*d - b*c) + 2*a*b*c*d/(a*d - b*c) + a*d - b**2*c**2/(a*d - b*c) + b*c)/(2*b*d))/(a*d - b*c) - log(x + (a**2*d**2/(a*d - b*c) - 2*a*b*c*d/(a*d - b*c) + a*d + b**2*c**2/(a*d - b*c) + b*c)/(2*b*d))/(a*d - b*c)","B",0
1806,1,233,0,0.805753," ","integrate(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{d \log{\left(x + \frac{- \frac{a^{3} d^{4}}{\left(a d - b c\right)^{2}} + \frac{3 a^{2} b c d^{3}}{\left(a d - b c\right)^{2}} - \frac{3 a b^{2} c^{2} d^{2}}{\left(a d - b c\right)^{2}} + a d^{2} + \frac{b^{3} c^{3} d}{\left(a d - b c\right)^{2}} + b c d}{2 b d^{2}} \right)}}{\left(a d - b c\right)^{2}} - \frac{d \log{\left(x + \frac{\frac{a^{3} d^{4}}{\left(a d - b c\right)^{2}} - \frac{3 a^{2} b c d^{3}}{\left(a d - b c\right)^{2}} + \frac{3 a b^{2} c^{2} d^{2}}{\left(a d - b c\right)^{2}} + a d^{2} - \frac{b^{3} c^{3} d}{\left(a d - b c\right)^{2}} + b c d}{2 b d^{2}} \right)}}{\left(a d - b c\right)^{2}} + \frac{1}{a^{2} d - a b c + x \left(a b d - b^{2} c\right)}"," ",0,"d*log(x + (-a**3*d**4/(a*d - b*c)**2 + 3*a**2*b*c*d**3/(a*d - b*c)**2 - 3*a*b**2*c**2*d**2/(a*d - b*c)**2 + a*d**2 + b**3*c**3*d/(a*d - b*c)**2 + b*c*d)/(2*b*d**2))/(a*d - b*c)**2 - d*log(x + (a**3*d**4/(a*d - b*c)**2 - 3*a**2*b*c*d**3/(a*d - b*c)**2 + 3*a*b**2*c**2*d**2/(a*d - b*c)**2 + a*d**2 - b**3*c**3*d/(a*d - b*c)**2 + b*c*d)/(2*b*d**2))/(a*d - b*c)**2 + 1/(a**2*d - a*b*c + x*(a*b*d - b**2*c))","B",0
1807,1,381,0,1.125161," ","integrate(1/(b*x+a)**2/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{d^{2} \log{\left(x + \frac{- \frac{a^{4} d^{6}}{\left(a d - b c\right)^{3}} + \frac{4 a^{3} b c d^{5}}{\left(a d - b c\right)^{3}} - \frac{6 a^{2} b^{2} c^{2} d^{4}}{\left(a d - b c\right)^{3}} + \frac{4 a b^{3} c^{3} d^{3}}{\left(a d - b c\right)^{3}} + a d^{3} - \frac{b^{4} c^{4} d^{2}}{\left(a d - b c\right)^{3}} + b c d^{2}}{2 b d^{3}} \right)}}{\left(a d - b c\right)^{3}} - \frac{d^{2} \log{\left(x + \frac{\frac{a^{4} d^{6}}{\left(a d - b c\right)^{3}} - \frac{4 a^{3} b c d^{5}}{\left(a d - b c\right)^{3}} + \frac{6 a^{2} b^{2} c^{2} d^{4}}{\left(a d - b c\right)^{3}} - \frac{4 a b^{3} c^{3} d^{3}}{\left(a d - b c\right)^{3}} + a d^{3} + \frac{b^{4} c^{4} d^{2}}{\left(a d - b c\right)^{3}} + b c d^{2}}{2 b d^{3}} \right)}}{\left(a d - b c\right)^{3}} + \frac{3 a d - b c + 2 b d x}{2 a^{4} d^{2} - 4 a^{3} b c d + 2 a^{2} b^{2} c^{2} + x^{2} \left(2 a^{2} b^{2} d^{2} - 4 a b^{3} c d + 2 b^{4} c^{2}\right) + x \left(4 a^{3} b d^{2} - 8 a^{2} b^{2} c d + 4 a b^{3} c^{2}\right)}"," ",0,"d**2*log(x + (-a**4*d**6/(a*d - b*c)**3 + 4*a**3*b*c*d**5/(a*d - b*c)**3 - 6*a**2*b**2*c**2*d**4/(a*d - b*c)**3 + 4*a*b**3*c**3*d**3/(a*d - b*c)**3 + a*d**3 - b**4*c**4*d**2/(a*d - b*c)**3 + b*c*d**2)/(2*b*d**3))/(a*d - b*c)**3 - d**2*log(x + (a**4*d**6/(a*d - b*c)**3 - 4*a**3*b*c*d**5/(a*d - b*c)**3 + 6*a**2*b**2*c**2*d**4/(a*d - b*c)**3 - 4*a*b**3*c**3*d**3/(a*d - b*c)**3 + a*d**3 + b**4*c**4*d**2/(a*d - b*c)**3 + b*c*d**2)/(2*b*d**3))/(a*d - b*c)**3 + (3*a*d - b*c + 2*b*d*x)/(2*a**4*d**2 - 4*a**3*b*c*d + 2*a**2*b**2*c**2 + x**2*(2*a**2*b**2*d**2 - 4*a*b**3*c*d + 2*b**4*c**2) + x*(4*a**3*b*d**2 - 8*a**2*b**2*c*d + 4*a*b**3*c**2))","B",0
1808,1,570,0,1.549519," ","integrate(1/(b*x+a)**3/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{d^{3} \log{\left(x + \frac{- \frac{a^{5} d^{8}}{\left(a d - b c\right)^{4}} + \frac{5 a^{4} b c d^{7}}{\left(a d - b c\right)^{4}} - \frac{10 a^{3} b^{2} c^{2} d^{6}}{\left(a d - b c\right)^{4}} + \frac{10 a^{2} b^{3} c^{3} d^{5}}{\left(a d - b c\right)^{4}} - \frac{5 a b^{4} c^{4} d^{4}}{\left(a d - b c\right)^{4}} + a d^{4} + \frac{b^{5} c^{5} d^{3}}{\left(a d - b c\right)^{4}} + b c d^{3}}{2 b d^{4}} \right)}}{\left(a d - b c\right)^{4}} - \frac{d^{3} \log{\left(x + \frac{\frac{a^{5} d^{8}}{\left(a d - b c\right)^{4}} - \frac{5 a^{4} b c d^{7}}{\left(a d - b c\right)^{4}} + \frac{10 a^{3} b^{2} c^{2} d^{6}}{\left(a d - b c\right)^{4}} - \frac{10 a^{2} b^{3} c^{3} d^{5}}{\left(a d - b c\right)^{4}} + \frac{5 a b^{4} c^{4} d^{4}}{\left(a d - b c\right)^{4}} + a d^{4} - \frac{b^{5} c^{5} d^{3}}{\left(a d - b c\right)^{4}} + b c d^{3}}{2 b d^{4}} \right)}}{\left(a d - b c\right)^{4}} + \frac{11 a^{2} d^{2} - 7 a b c d + 2 b^{2} c^{2} + 6 b^{2} d^{2} x^{2} + x \left(15 a b d^{2} - 3 b^{2} c d\right)}{6 a^{6} d^{3} - 18 a^{5} b c d^{2} + 18 a^{4} b^{2} c^{2} d - 6 a^{3} b^{3} c^{3} + x^{3} \left(6 a^{3} b^{3} d^{3} - 18 a^{2} b^{4} c d^{2} + 18 a b^{5} c^{2} d - 6 b^{6} c^{3}\right) + x^{2} \left(18 a^{4} b^{2} d^{3} - 54 a^{3} b^{3} c d^{2} + 54 a^{2} b^{4} c^{2} d - 18 a b^{5} c^{3}\right) + x \left(18 a^{5} b d^{3} - 54 a^{4} b^{2} c d^{2} + 54 a^{3} b^{3} c^{2} d - 18 a^{2} b^{4} c^{3}\right)}"," ",0,"d**3*log(x + (-a**5*d**8/(a*d - b*c)**4 + 5*a**4*b*c*d**7/(a*d - b*c)**4 - 10*a**3*b**2*c**2*d**6/(a*d - b*c)**4 + 10*a**2*b**3*c**3*d**5/(a*d - b*c)**4 - 5*a*b**4*c**4*d**4/(a*d - b*c)**4 + a*d**4 + b**5*c**5*d**3/(a*d - b*c)**4 + b*c*d**3)/(2*b*d**4))/(a*d - b*c)**4 - d**3*log(x + (a**5*d**8/(a*d - b*c)**4 - 5*a**4*b*c*d**7/(a*d - b*c)**4 + 10*a**3*b**2*c**2*d**6/(a*d - b*c)**4 - 10*a**2*b**3*c**3*d**5/(a*d - b*c)**4 + 5*a*b**4*c**4*d**4/(a*d - b*c)**4 + a*d**4 - b**5*c**5*d**3/(a*d - b*c)**4 + b*c*d**3)/(2*b*d**4))/(a*d - b*c)**4 + (11*a**2*d**2 - 7*a*b*c*d + 2*b**2*c**2 + 6*b**2*d**2*x**2 + x*(15*a*b*d**2 - 3*b**2*c*d))/(6*a**6*d**3 - 18*a**5*b*c*d**2 + 18*a**4*b**2*c**2*d - 6*a**3*b**3*c**3 + x**3*(6*a**3*b**3*d**3 - 18*a**2*b**4*c*d**2 + 18*a*b**5*c**2*d - 6*b**6*c**3) + x**2*(18*a**4*b**2*d**3 - 54*a**3*b**3*c*d**2 + 54*a**2*b**4*c**2*d - 18*a*b**5*c**3) + x*(18*a**5*b*d**3 - 54*a**4*b**2*c*d**2 + 54*a**3*b**3*c**2*d - 18*a**2*b**4*c**3))","B",0
1809,1,802,0,2.156297," ","integrate(1/(b*x+a)**4/(a*c+(a*d+b*c)*x+b*d*x**2),x)","\frac{d^{4} \log{\left(x + \frac{- \frac{a^{6} d^{10}}{\left(a d - b c\right)^{5}} + \frac{6 a^{5} b c d^{9}}{\left(a d - b c\right)^{5}} - \frac{15 a^{4} b^{2} c^{2} d^{8}}{\left(a d - b c\right)^{5}} + \frac{20 a^{3} b^{3} c^{3} d^{7}}{\left(a d - b c\right)^{5}} - \frac{15 a^{2} b^{4} c^{4} d^{6}}{\left(a d - b c\right)^{5}} + \frac{6 a b^{5} c^{5} d^{5}}{\left(a d - b c\right)^{5}} + a d^{5} - \frac{b^{6} c^{6} d^{4}}{\left(a d - b c\right)^{5}} + b c d^{4}}{2 b d^{5}} \right)}}{\left(a d - b c\right)^{5}} - \frac{d^{4} \log{\left(x + \frac{\frac{a^{6} d^{10}}{\left(a d - b c\right)^{5}} - \frac{6 a^{5} b c d^{9}}{\left(a d - b c\right)^{5}} + \frac{15 a^{4} b^{2} c^{2} d^{8}}{\left(a d - b c\right)^{5}} - \frac{20 a^{3} b^{3} c^{3} d^{7}}{\left(a d - b c\right)^{5}} + \frac{15 a^{2} b^{4} c^{4} d^{6}}{\left(a d - b c\right)^{5}} - \frac{6 a b^{5} c^{5} d^{5}}{\left(a d - b c\right)^{5}} + a d^{5} + \frac{b^{6} c^{6} d^{4}}{\left(a d - b c\right)^{5}} + b c d^{4}}{2 b d^{5}} \right)}}{\left(a d - b c\right)^{5}} + \frac{25 a^{3} d^{3} - 23 a^{2} b c d^{2} + 13 a b^{2} c^{2} d - 3 b^{3} c^{3} + 12 b^{3} d^{3} x^{3} + x^{2} \left(42 a b^{2} d^{3} - 6 b^{3} c d^{2}\right) + x \left(52 a^{2} b d^{3} - 20 a b^{2} c d^{2} + 4 b^{3} c^{2} d\right)}{12 a^{8} d^{4} - 48 a^{7} b c d^{3} + 72 a^{6} b^{2} c^{2} d^{2} - 48 a^{5} b^{3} c^{3} d + 12 a^{4} b^{4} c^{4} + x^{4} \left(12 a^{4} b^{4} d^{4} - 48 a^{3} b^{5} c d^{3} + 72 a^{2} b^{6} c^{2} d^{2} - 48 a b^{7} c^{3} d + 12 b^{8} c^{4}\right) + x^{3} \left(48 a^{5} b^{3} d^{4} - 192 a^{4} b^{4} c d^{3} + 288 a^{3} b^{5} c^{2} d^{2} - 192 a^{2} b^{6} c^{3} d + 48 a b^{7} c^{4}\right) + x^{2} \left(72 a^{6} b^{2} d^{4} - 288 a^{5} b^{3} c d^{3} + 432 a^{4} b^{4} c^{2} d^{2} - 288 a^{3} b^{5} c^{3} d + 72 a^{2} b^{6} c^{4}\right) + x \left(48 a^{7} b d^{4} - 192 a^{6} b^{2} c d^{3} + 288 a^{5} b^{3} c^{2} d^{2} - 192 a^{4} b^{4} c^{3} d + 48 a^{3} b^{5} c^{4}\right)}"," ",0,"d**4*log(x + (-a**6*d**10/(a*d - b*c)**5 + 6*a**5*b*c*d**9/(a*d - b*c)**5 - 15*a**4*b**2*c**2*d**8/(a*d - b*c)**5 + 20*a**3*b**3*c**3*d**7/(a*d - b*c)**5 - 15*a**2*b**4*c**4*d**6/(a*d - b*c)**5 + 6*a*b**5*c**5*d**5/(a*d - b*c)**5 + a*d**5 - b**6*c**6*d**4/(a*d - b*c)**5 + b*c*d**4)/(2*b*d**5))/(a*d - b*c)**5 - d**4*log(x + (a**6*d**10/(a*d - b*c)**5 - 6*a**5*b*c*d**9/(a*d - b*c)**5 + 15*a**4*b**2*c**2*d**8/(a*d - b*c)**5 - 20*a**3*b**3*c**3*d**7/(a*d - b*c)**5 + 15*a**2*b**4*c**4*d**6/(a*d - b*c)**5 - 6*a*b**5*c**5*d**5/(a*d - b*c)**5 + a*d**5 + b**6*c**6*d**4/(a*d - b*c)**5 + b*c*d**4)/(2*b*d**5))/(a*d - b*c)**5 + (25*a**3*d**3 - 23*a**2*b*c*d**2 + 13*a*b**2*c**2*d - 3*b**3*c**3 + 12*b**3*d**3*x**3 + x**2*(42*a*b**2*d**3 - 6*b**3*c*d**2) + x*(52*a**2*b*d**3 - 20*a*b**2*c*d**2 + 4*b**3*c**2*d))/(12*a**8*d**4 - 48*a**7*b*c*d**3 + 72*a**6*b**2*c**2*d**2 - 48*a**5*b**3*c**3*d + 12*a**4*b**4*c**4 + x**4*(12*a**4*b**4*d**4 - 48*a**3*b**5*c*d**3 + 72*a**2*b**6*c**2*d**2 - 48*a*b**7*c**3*d + 12*b**8*c**4) + x**3*(48*a**5*b**3*d**4 - 192*a**4*b**4*c*d**3 + 288*a**3*b**5*c**2*d**2 - 192*a**2*b**6*c**3*d + 48*a*b**7*c**4) + x**2*(72*a**6*b**2*d**4 - 288*a**5*b**3*c*d**3 + 432*a**4*b**4*c**2*d**2 - 288*a**3*b**5*c**3*d + 72*a**2*b**6*c**4) + x*(48*a**7*b*d**4 - 192*a**6*b**2*c*d**3 + 288*a**5*b**3*c**2*d**2 - 192*a**4*b**4*c**3*d + 48*a**3*b**5*c**4))","B",0
1810,1,155,0,0.769332," ","integrate((b*x+a)**6/(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","\frac{b^{4} x^{3}}{3 d^{2}} + \frac{4 b \left(a d - b c\right)^{3} \log{\left(c + d x \right)}}{d^{5}} + x^{2} \left(\frac{2 a b^{3}}{d^{2}} - \frac{b^{4} c}{d^{3}}\right) + x \left(\frac{6 a^{2} b^{2}}{d^{2}} - \frac{8 a b^{3} c}{d^{3}} + \frac{3 b^{4} c^{2}}{d^{4}}\right) + \frac{- a^{4} d^{4} + 4 a^{3} b c d^{3} - 6 a^{2} b^{2} c^{2} d^{2} + 4 a b^{3} c^{3} d - b^{4} c^{4}}{c d^{5} + d^{6} x}"," ",0,"b**4*x**3/(3*d**2) + 4*b*(a*d - b*c)**3*log(c + d*x)/d**5 + x**2*(2*a*b**3/d**2 - b**4*c/d**3) + x*(6*a**2*b**2/d**2 - 8*a*b**3*c/d**3 + 3*b**4*c**2/d**4) + (-a**4*d**4 + 4*a**3*b*c*d**3 - 6*a**2*b**2*c**2*d**2 + 4*a*b**3*c**3*d - b**4*c**4)/(c*d**5 + d**6*x)","A",0
1811,1,102,0,0.562569," ","integrate((b*x+a)**5/(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","\frac{b^{3} x^{2}}{2 d^{2}} + \frac{3 b \left(a d - b c\right)^{2} \log{\left(c + d x \right)}}{d^{4}} + x \left(\frac{3 a b^{2}}{d^{2}} - \frac{2 b^{3} c}{d^{3}}\right) + \frac{- a^{3} d^{3} + 3 a^{2} b c d^{2} - 3 a b^{2} c^{2} d + b^{3} c^{3}}{c d^{4} + d^{5} x}"," ",0,"b**3*x**2/(2*d**2) + 3*b*(a*d - b*c)**2*log(c + d*x)/d**4 + x*(3*a*b**2/d**2 - 2*b**3*c/d**3) + (-a**3*d**3 + 3*a**2*b*c*d**2 - 3*a*b**2*c**2*d + b**3*c**3)/(c*d**4 + d**5*x)","A",0
1812,1,60,0,0.398341," ","integrate((b*x+a)**4/(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","\frac{b^{2} x}{d^{2}} + \frac{2 b \left(a d - b c\right) \log{\left(c + d x \right)}}{d^{3}} + \frac{- a^{2} d^{2} + 2 a b c d - b^{2} c^{2}}{c d^{3} + d^{4} x}"," ",0,"b**2*x/d**2 + 2*b*(a*d - b*c)*log(c + d*x)/d**3 + (-a**2*d**2 + 2*a*b*c*d - b**2*c**2)/(c*d**3 + d**4*x)","A",0
1813,1,27,0,0.239485," ","integrate((b*x+a)**3/(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","\frac{b \log{\left(c + d x \right)}}{d^{2}} + \frac{- a d + b c}{c d^{2} + d^{3} x}"," ",0,"b*log(c + d*x)/d**2 + (-a*d + b*c)/(c*d**2 + d**3*x)","A",0
1814,1,10,0,0.169799," ","integrate((b*x+a)**2/(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","- \frac{1}{c d + d^{2} x}"," ",0,"-1/(c*d + d**2*x)","A",0
1815,1,233,0,0.721710," ","integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","- \frac{b \log{\left(x + \frac{- \frac{a^{3} b d^{3}}{\left(a d - b c\right)^{2}} + \frac{3 a^{2} b^{2} c d^{2}}{\left(a d - b c\right)^{2}} - \frac{3 a b^{3} c^{2} d}{\left(a d - b c\right)^{2}} + a b d + \frac{b^{4} c^{3}}{\left(a d - b c\right)^{2}} + b^{2} c}{2 b^{2} d} \right)}}{\left(a d - b c\right)^{2}} + \frac{b \log{\left(x + \frac{\frac{a^{3} b d^{3}}{\left(a d - b c\right)^{2}} - \frac{3 a^{2} b^{2} c d^{2}}{\left(a d - b c\right)^{2}} + \frac{3 a b^{3} c^{2} d}{\left(a d - b c\right)^{2}} + a b d - \frac{b^{4} c^{3}}{\left(a d - b c\right)^{2}} + b^{2} c}{2 b^{2} d} \right)}}{\left(a d - b c\right)^{2}} - \frac{1}{a c d - b c^{2} + x \left(a d^{2} - b c d\right)}"," ",0,"-b*log(x + (-a**3*b*d**3/(a*d - b*c)**2 + 3*a**2*b**2*c*d**2/(a*d - b*c)**2 - 3*a*b**3*c**2*d/(a*d - b*c)**2 + a*b*d + b**4*c**3/(a*d - b*c)**2 + b**2*c)/(2*b**2*d))/(a*d - b*c)**2 + b*log(x + (a**3*b*d**3/(a*d - b*c)**2 - 3*a**2*b**2*c*d**2/(a*d - b*c)**2 + 3*a*b**3*c**2*d/(a*d - b*c)**2 + a*b*d - b**4*c**3/(a*d - b*c)**2 + b**2*c)/(2*b**2*d))/(a*d - b*c)**2 - 1/(a*c*d - b*c**2 + x*(a*d**2 - b*c*d))","B",0
1816,1,406,0,1.151270," ","integrate(1/(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","- \frac{2 b d \log{\left(x + \frac{- \frac{2 a^{4} b d^{5}}{\left(a d - b c\right)^{3}} + \frac{8 a^{3} b^{2} c d^{4}}{\left(a d - b c\right)^{3}} - \frac{12 a^{2} b^{3} c^{2} d^{3}}{\left(a d - b c\right)^{3}} + \frac{8 a b^{4} c^{3} d^{2}}{\left(a d - b c\right)^{3}} + 2 a b d^{2} - \frac{2 b^{5} c^{4} d}{\left(a d - b c\right)^{3}} + 2 b^{2} c d}{4 b^{2} d^{2}} \right)}}{\left(a d - b c\right)^{3}} + \frac{2 b d \log{\left(x + \frac{\frac{2 a^{4} b d^{5}}{\left(a d - b c\right)^{3}} - \frac{8 a^{3} b^{2} c d^{4}}{\left(a d - b c\right)^{3}} + \frac{12 a^{2} b^{3} c^{2} d^{3}}{\left(a d - b c\right)^{3}} - \frac{8 a b^{4} c^{3} d^{2}}{\left(a d - b c\right)^{3}} + 2 a b d^{2} + \frac{2 b^{5} c^{4} d}{\left(a d - b c\right)^{3}} + 2 b^{2} c d}{4 b^{2} d^{2}} \right)}}{\left(a d - b c\right)^{3}} + \frac{- a d - b c - 2 b d x}{a^{3} c d^{2} - 2 a^{2} b c^{2} d + a b^{2} c^{3} + x^{2} \left(a^{2} b d^{3} - 2 a b^{2} c d^{2} + b^{3} c^{2} d\right) + x \left(a^{3} d^{3} - a^{2} b c d^{2} - a b^{2} c^{2} d + b^{3} c^{3}\right)}"," ",0,"-2*b*d*log(x + (-2*a**4*b*d**5/(a*d - b*c)**3 + 8*a**3*b**2*c*d**4/(a*d - b*c)**3 - 12*a**2*b**3*c**2*d**3/(a*d - b*c)**3 + 8*a*b**4*c**3*d**2/(a*d - b*c)**3 + 2*a*b*d**2 - 2*b**5*c**4*d/(a*d - b*c)**3 + 2*b**2*c*d)/(4*b**2*d**2))/(a*d - b*c)**3 + 2*b*d*log(x + (2*a**4*b*d**5/(a*d - b*c)**3 - 8*a**3*b**2*c*d**4/(a*d - b*c)**3 + 12*a**2*b**3*c**2*d**3/(a*d - b*c)**3 - 8*a*b**4*c**3*d**2/(a*d - b*c)**3 + 2*a*b*d**2 + 2*b**5*c**4*d/(a*d - b*c)**3 + 2*b**2*c*d)/(4*b**2*d**2))/(a*d - b*c)**3 + (-a*d - b*c - 2*b*d*x)/(a**3*c*d**2 - 2*a**2*b*c**2*d + a*b**2*c**3 + x**2*(a**2*b*d**3 - 2*a*b**2*c*d**2 + b**3*c**2*d) + x*(a**3*d**3 - a**2*b*c*d**2 - a*b**2*c**2*d + b**3*c**3))","B",0
1817,1,634,0,1.982294," ","integrate(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x**2)**2,x)","- \frac{3 b d^{2} \log{\left(x + \frac{- \frac{3 a^{5} b d^{7}}{\left(a d - b c\right)^{4}} + \frac{15 a^{4} b^{2} c d^{6}}{\left(a d - b c\right)^{4}} - \frac{30 a^{3} b^{3} c^{2} d^{5}}{\left(a d - b c\right)^{4}} + \frac{30 a^{2} b^{4} c^{3} d^{4}}{\left(a d - b c\right)^{4}} - \frac{15 a b^{5} c^{4} d^{3}}{\left(a d - b c\right)^{4}} + 3 a b d^{3} + \frac{3 b^{6} c^{5} d^{2}}{\left(a d - b c\right)^{4}} + 3 b^{2} c d^{2}}{6 b^{2} d^{3}} \right)}}{\left(a d - b c\right)^{4}} + \frac{3 b d^{2} \log{\left(x + \frac{\frac{3 a^{5} b d^{7}}{\left(a d - b c\right)^{4}} - \frac{15 a^{4} b^{2} c d^{6}}{\left(a d - b c\right)^{4}} + \frac{30 a^{3} b^{3} c^{2} d^{5}}{\left(a d - b c\right)^{4}} - \frac{30 a^{2} b^{4} c^{3} d^{4}}{\left(a d - b c\right)^{4}} + \frac{15 a b^{5} c^{4} d^{3}}{\left(a d - b c\right)^{4}} + 3 a b d^{3} - \frac{3 b^{6} c^{5} d^{2}}{\left(a d - b c\right)^{4}} + 3 b^{2} c d^{2}}{6 b^{2} d^{3}} \right)}}{\left(a d - b c\right)^{4}} + \frac{- 2 a^{2} d^{2} - 5 a b c d + b^{2} c^{2} - 6 b^{2} d^{2} x^{2} + x \left(- 9 a b d^{2} - 3 b^{2} c d\right)}{2 a^{5} c d^{3} - 6 a^{4} b c^{2} d^{2} + 6 a^{3} b^{2} c^{3} d - 2 a^{2} b^{3} c^{4} + x^{3} \left(2 a^{3} b^{2} d^{4} - 6 a^{2} b^{3} c d^{3} + 6 a b^{4} c^{2} d^{2} - 2 b^{5} c^{3} d\right) + x^{2} \left(4 a^{4} b d^{4} - 10 a^{3} b^{2} c d^{3} + 6 a^{2} b^{3} c^{2} d^{2} + 2 a b^{4} c^{3} d - 2 b^{5} c^{4}\right) + x \left(2 a^{5} d^{4} - 2 a^{4} b c d^{3} - 6 a^{3} b^{2} c^{2} d^{2} + 10 a^{2} b^{3} c^{3} d - 4 a b^{4} c^{4}\right)}"," ",0,"-3*b*d**2*log(x + (-3*a**5*b*d**7/(a*d - b*c)**4 + 15*a**4*b**2*c*d**6/(a*d - b*c)**4 - 30*a**3*b**3*c**2*d**5/(a*d - b*c)**4 + 30*a**2*b**4*c**3*d**4/(a*d - b*c)**4 - 15*a*b**5*c**4*d**3/(a*d - b*c)**4 + 3*a*b*d**3 + 3*b**6*c**5*d**2/(a*d - b*c)**4 + 3*b**2*c*d**2)/(6*b**2*d**3))/(a*d - b*c)**4 + 3*b*d**2*log(x + (3*a**5*b*d**7/(a*d - b*c)**4 - 15*a**4*b**2*c*d**6/(a*d - b*c)**4 + 30*a**3*b**3*c**2*d**5/(a*d - b*c)**4 - 30*a**2*b**4*c**3*d**4/(a*d - b*c)**4 + 15*a*b**5*c**4*d**3/(a*d - b*c)**4 + 3*a*b*d**3 - 3*b**6*c**5*d**2/(a*d - b*c)**4 + 3*b**2*c*d**2)/(6*b**2*d**3))/(a*d - b*c)**4 + (-2*a**2*d**2 - 5*a*b*c*d + b**2*c**2 - 6*b**2*d**2*x**2 + x*(-9*a*b*d**2 - 3*b**2*c*d))/(2*a**5*c*d**3 - 6*a**4*b*c**2*d**2 + 6*a**3*b**2*c**3*d - 2*a**2*b**3*c**4 + x**3*(2*a**3*b**2*d**4 - 6*a**2*b**3*c*d**3 + 6*a*b**4*c**2*d**2 - 2*b**5*c**3*d) + x**2*(4*a**4*b*d**4 - 10*a**3*b**2*c*d**3 + 6*a**2*b**3*c**2*d**2 + 2*a*b**4*c**3*d - 2*b**5*c**4) + x*(2*a**5*d**4 - 2*a**4*b*c*d**3 - 6*a**3*b**2*c**2*d**2 + 10*a**2*b**3*c**3*d - 4*a*b**4*c**4))","B",0
1818,1,258,0,2.039434," ","integrate((b*x+a)**8/(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","\frac{b^{5} x^{3}}{3 d^{3}} + \frac{10 b^{2} \left(a d - b c\right)^{3} \log{\left(c + d x \right)}}{d^{6}} + x^{2} \left(\frac{5 a b^{4}}{2 d^{3}} - \frac{3 b^{5} c}{2 d^{4}}\right) + x \left(\frac{10 a^{2} b^{3}}{d^{3}} - \frac{15 a b^{4} c}{d^{4}} + \frac{6 b^{5} c^{2}}{d^{5}}\right) + \frac{- a^{5} d^{5} - 5 a^{4} b c d^{4} + 30 a^{3} b^{2} c^{2} d^{3} - 50 a^{2} b^{3} c^{3} d^{2} + 35 a b^{4} c^{4} d - 9 b^{5} c^{5} + x \left(- 10 a^{4} b d^{5} + 40 a^{3} b^{2} c d^{4} - 60 a^{2} b^{3} c^{2} d^{3} + 40 a b^{4} c^{3} d^{2} - 10 b^{5} c^{4} d\right)}{2 c^{2} d^{6} + 4 c d^{7} x + 2 d^{8} x^{2}}"," ",0,"b**5*x**3/(3*d**3) + 10*b**2*(a*d - b*c)**3*log(c + d*x)/d**6 + x**2*(5*a*b**4/(2*d**3) - 3*b**5*c/(2*d**4)) + x*(10*a**2*b**3/d**3 - 15*a*b**4*c/d**4 + 6*b**5*c**2/d**5) + (-a**5*d**5 - 5*a**4*b*c*d**4 + 30*a**3*b**2*c**2*d**3 - 50*a**2*b**3*c**3*d**2 + 35*a*b**4*c**4*d - 9*b**5*c**5 + x*(-10*a**4*b*d**5 + 40*a**3*b**2*c*d**4 - 60*a**2*b**3*c**2*d**3 + 40*a*b**4*c**3*d**2 - 10*b**5*c**4*d))/(2*c**2*d**6 + 4*c*d**7*x + 2*d**8*x**2)","B",0
1819,1,185,0,1.367540," ","integrate((b*x+a)**7/(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","\frac{b^{4} x^{2}}{2 d^{3}} + \frac{6 b^{2} \left(a d - b c\right)^{2} \log{\left(c + d x \right)}}{d^{5}} + x \left(\frac{4 a b^{3}}{d^{3}} - \frac{3 b^{4} c}{d^{4}}\right) + \frac{- a^{4} d^{4} - 4 a^{3} b c d^{3} + 18 a^{2} b^{2} c^{2} d^{2} - 20 a b^{3} c^{3} d + 7 b^{4} c^{4} + x \left(- 8 a^{3} b d^{4} + 24 a^{2} b^{2} c d^{3} - 24 a b^{3} c^{2} d^{2} + 8 b^{4} c^{3} d\right)}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}}"," ",0,"b**4*x**2/(2*d**3) + 6*b**2*(a*d - b*c)**2*log(c + d*x)/d**5 + x*(4*a*b**3/d**3 - 3*b**4*c/d**4) + (-a**4*d**4 - 4*a**3*b*c*d**3 + 18*a**2*b**2*c**2*d**2 - 20*a*b**3*c**3*d + 7*b**4*c**4 + x*(-8*a**3*b*d**4 + 24*a**2*b**2*c*d**3 - 24*a*b**3*c**2*d**2 + 8*b**4*c**3*d))/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2)","A",0
1820,1,128,0,0.943967," ","integrate((b*x+a)**6/(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","\frac{b^{3} x}{d^{3}} + \frac{3 b^{2} \left(a d - b c\right) \log{\left(c + d x \right)}}{d^{4}} + \frac{- a^{3} d^{3} - 3 a^{2} b c d^{2} + 9 a b^{2} c^{2} d - 5 b^{3} c^{3} + x \left(- 6 a^{2} b d^{3} + 12 a b^{2} c d^{2} - 6 b^{3} c^{2} d\right)}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}}"," ",0,"b**3*x/d**3 + 3*b**2*(a*d - b*c)*log(c + d*x)/d**4 + (-a**3*d**3 - 3*a**2*b*c*d**2 + 9*a*b**2*c**2*d - 5*b**3*c**3 + x*(-6*a**2*b*d**3 + 12*a*b**2*c*d**2 - 6*b**3*c**2*d))/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2)","A",0
1821,1,80,0,0.541527," ","integrate((b*x+a)**5/(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","\frac{b^{2} \log{\left(c + d x \right)}}{d^{3}} + \frac{- a^{2} d^{2} - 2 a b c d + 3 b^{2} c^{2} + x \left(- 4 a b d^{2} + 4 b^{2} c d\right)}{2 c^{2} d^{3} + 4 c d^{4} x + 2 d^{5} x^{2}}"," ",0,"b**2*log(c + d*x)/d**3 + (-a**2*d**2 - 2*a*b*c*d + 3*b**2*c**2 + x*(-4*a*b*d**2 + 4*b**2*c*d))/(2*c**2*d**3 + 4*c*d**4*x + 2*d**5*x**2)","A",0
1822,1,39,0,0.339662," ","integrate((b*x+a)**4/(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","\frac{- a d - b c - 2 b d x}{2 c^{2} d^{2} + 4 c d^{3} x + 2 d^{4} x^{2}}"," ",0,"(-a*d - b*c - 2*b*d*x)/(2*c**2*d**2 + 4*c*d**3*x + 2*d**4*x**2)","A",0
1823,1,26,0,0.256776," ","integrate((b*x+a)**3/(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","- \frac{1}{2 c^{2} d + 4 c d^{2} x + 2 d^{3} x^{2}}"," ",0,"-1/(2*c**2*d + 4*c*d**2*x + 2*d**3*x**2)","B",0
1824,1,381,0,1.164185," ","integrate((b*x+a)**2/(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","\frac{b^{2} \log{\left(x + \frac{- \frac{a^{4} b^{2} d^{4}}{\left(a d - b c\right)^{3}} + \frac{4 a^{3} b^{3} c d^{3}}{\left(a d - b c\right)^{3}} - \frac{6 a^{2} b^{4} c^{2} d^{2}}{\left(a d - b c\right)^{3}} + \frac{4 a b^{5} c^{3} d}{\left(a d - b c\right)^{3}} + a b^{2} d - \frac{b^{6} c^{4}}{\left(a d - b c\right)^{3}} + b^{3} c}{2 b^{3} d} \right)}}{\left(a d - b c\right)^{3}} - \frac{b^{2} \log{\left(x + \frac{\frac{a^{4} b^{2} d^{4}}{\left(a d - b c\right)^{3}} - \frac{4 a^{3} b^{3} c d^{3}}{\left(a d - b c\right)^{3}} + \frac{6 a^{2} b^{4} c^{2} d^{2}}{\left(a d - b c\right)^{3}} - \frac{4 a b^{5} c^{3} d}{\left(a d - b c\right)^{3}} + a b^{2} d + \frac{b^{6} c^{4}}{\left(a d - b c\right)^{3}} + b^{3} c}{2 b^{3} d} \right)}}{\left(a d - b c\right)^{3}} + \frac{- a d + 3 b c + 2 b d x}{2 a^{2} c^{2} d^{2} - 4 a b c^{3} d + 2 b^{2} c^{4} + x^{2} \left(2 a^{2} d^{4} - 4 a b c d^{3} + 2 b^{2} c^{2} d^{2}\right) + x \left(4 a^{2} c d^{3} - 8 a b c^{2} d^{2} + 4 b^{2} c^{3} d\right)}"," ",0,"b**2*log(x + (-a**4*b**2*d**4/(a*d - b*c)**3 + 4*a**3*b**3*c*d**3/(a*d - b*c)**3 - 6*a**2*b**4*c**2*d**2/(a*d - b*c)**3 + 4*a*b**5*c**3*d/(a*d - b*c)**3 + a*b**2*d - b**6*c**4/(a*d - b*c)**3 + b**3*c)/(2*b**3*d))/(a*d - b*c)**3 - b**2*log(x + (a**4*b**2*d**4/(a*d - b*c)**3 - 4*a**3*b**3*c*d**3/(a*d - b*c)**3 + 6*a**2*b**4*c**2*d**2/(a*d - b*c)**3 - 4*a*b**5*c**3*d/(a*d - b*c)**3 + a*b**2*d + b**6*c**4/(a*d - b*c)**3 + b**3*c)/(2*b**3*d))/(a*d - b*c)**3 + (-a*d + 3*b*c + 2*b*d*x)/(2*a**2*c**2*d**2 - 4*a*b*c**3*d + 2*b**2*c**4 + x**2*(2*a**2*d**4 - 4*a*b*c*d**3 + 2*b**2*c**2*d**2) + x*(4*a**2*c*d**3 - 8*a*b*c**2*d**2 + 4*b**2*c**3*d))","B",0
1825,1,632,0,1.800630," ","integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","\frac{3 b^{2} d \log{\left(x + \frac{- \frac{3 a^{5} b^{2} d^{6}}{\left(a d - b c\right)^{4}} + \frac{15 a^{4} b^{3} c d^{5}}{\left(a d - b c\right)^{4}} - \frac{30 a^{3} b^{4} c^{2} d^{4}}{\left(a d - b c\right)^{4}} + \frac{30 a^{2} b^{5} c^{3} d^{3}}{\left(a d - b c\right)^{4}} - \frac{15 a b^{6} c^{4} d^{2}}{\left(a d - b c\right)^{4}} + 3 a b^{2} d^{2} + \frac{3 b^{7} c^{5} d}{\left(a d - b c\right)^{4}} + 3 b^{3} c d}{6 b^{3} d^{2}} \right)}}{\left(a d - b c\right)^{4}} - \frac{3 b^{2} d \log{\left(x + \frac{\frac{3 a^{5} b^{2} d^{6}}{\left(a d - b c\right)^{4}} - \frac{15 a^{4} b^{3} c d^{5}}{\left(a d - b c\right)^{4}} + \frac{30 a^{3} b^{4} c^{2} d^{4}}{\left(a d - b c\right)^{4}} - \frac{30 a^{2} b^{5} c^{3} d^{3}}{\left(a d - b c\right)^{4}} + \frac{15 a b^{6} c^{4} d^{2}}{\left(a d - b c\right)^{4}} + 3 a b^{2} d^{2} - \frac{3 b^{7} c^{5} d}{\left(a d - b c\right)^{4}} + 3 b^{3} c d}{6 b^{3} d^{2}} \right)}}{\left(a d - b c\right)^{4}} + \frac{- a^{2} d^{2} + 5 a b c d + 2 b^{2} c^{2} + 6 b^{2} d^{2} x^{2} + x \left(3 a b d^{2} + 9 b^{2} c d\right)}{2 a^{4} c^{2} d^{3} - 6 a^{3} b c^{3} d^{2} + 6 a^{2} b^{2} c^{4} d - 2 a b^{3} c^{5} + x^{3} \left(2 a^{3} b d^{5} - 6 a^{2} b^{2} c d^{4} + 6 a b^{3} c^{2} d^{3} - 2 b^{4} c^{3} d^{2}\right) + x^{2} \left(2 a^{4} d^{5} - 2 a^{3} b c d^{4} - 6 a^{2} b^{2} c^{2} d^{3} + 10 a b^{3} c^{3} d^{2} - 4 b^{4} c^{4} d\right) + x \left(4 a^{4} c d^{4} - 10 a^{3} b c^{2} d^{3} + 6 a^{2} b^{2} c^{3} d^{2} + 2 a b^{3} c^{4} d - 2 b^{4} c^{5}\right)}"," ",0,"3*b**2*d*log(x + (-3*a**5*b**2*d**6/(a*d - b*c)**4 + 15*a**4*b**3*c*d**5/(a*d - b*c)**4 - 30*a**3*b**4*c**2*d**4/(a*d - b*c)**4 + 30*a**2*b**5*c**3*d**3/(a*d - b*c)**4 - 15*a*b**6*c**4*d**2/(a*d - b*c)**4 + 3*a*b**2*d**2 + 3*b**7*c**5*d/(a*d - b*c)**4 + 3*b**3*c*d)/(6*b**3*d**2))/(a*d - b*c)**4 - 3*b**2*d*log(x + (3*a**5*b**2*d**6/(a*d - b*c)**4 - 15*a**4*b**3*c*d**5/(a*d - b*c)**4 + 30*a**3*b**4*c**2*d**4/(a*d - b*c)**4 - 30*a**2*b**5*c**3*d**3/(a*d - b*c)**4 + 15*a*b**6*c**4*d**2/(a*d - b*c)**4 + 3*a*b**2*d**2 - 3*b**7*c**5*d/(a*d - b*c)**4 + 3*b**3*c*d)/(6*b**3*d**2))/(a*d - b*c)**4 + (-a**2*d**2 + 5*a*b*c*d + 2*b**2*c**2 + 6*b**2*d**2*x**2 + x*(3*a*b*d**2 + 9*b**2*c*d))/(2*a**4*c**2*d**3 - 6*a**3*b*c**3*d**2 + 6*a**2*b**2*c**4*d - 2*a*b**3*c**5 + x**3*(2*a**3*b*d**5 - 6*a**2*b**2*c*d**4 + 6*a*b**3*c**2*d**3 - 2*b**4*c**3*d**2) + x**2*(2*a**4*d**5 - 2*a**3*b*c*d**4 - 6*a**2*b**2*c**2*d**3 + 10*a*b**3*c**3*d**2 - 4*b**4*c**4*d) + x*(4*a**4*c*d**4 - 10*a**3*b*c**2*d**3 + 6*a**2*b**2*c**3*d**2 + 2*a*b**3*c**4*d - 2*b**4*c**5))","B",0
1826,1,881,0,2.481713," ","integrate(1/(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","\frac{6 b^{2} d^{2} \log{\left(x + \frac{- \frac{6 a^{6} b^{2} d^{8}}{\left(a d - b c\right)^{5}} + \frac{36 a^{5} b^{3} c d^{7}}{\left(a d - b c\right)^{5}} - \frac{90 a^{4} b^{4} c^{2} d^{6}}{\left(a d - b c\right)^{5}} + \frac{120 a^{3} b^{5} c^{3} d^{5}}{\left(a d - b c\right)^{5}} - \frac{90 a^{2} b^{6} c^{4} d^{4}}{\left(a d - b c\right)^{5}} + \frac{36 a b^{7} c^{5} d^{3}}{\left(a d - b c\right)^{5}} + 6 a b^{2} d^{3} - \frac{6 b^{8} c^{6} d^{2}}{\left(a d - b c\right)^{5}} + 6 b^{3} c d^{2}}{12 b^{3} d^{3}} \right)}}{\left(a d - b c\right)^{5}} - \frac{6 b^{2} d^{2} \log{\left(x + \frac{\frac{6 a^{6} b^{2} d^{8}}{\left(a d - b c\right)^{5}} - \frac{36 a^{5} b^{3} c d^{7}}{\left(a d - b c\right)^{5}} + \frac{90 a^{4} b^{4} c^{2} d^{6}}{\left(a d - b c\right)^{5}} - \frac{120 a^{3} b^{5} c^{3} d^{5}}{\left(a d - b c\right)^{5}} + \frac{90 a^{2} b^{6} c^{4} d^{4}}{\left(a d - b c\right)^{5}} - \frac{36 a b^{7} c^{5} d^{3}}{\left(a d - b c\right)^{5}} + 6 a b^{2} d^{3} + \frac{6 b^{8} c^{6} d^{2}}{\left(a d - b c\right)^{5}} + 6 b^{3} c d^{2}}{12 b^{3} d^{3}} \right)}}{\left(a d - b c\right)^{5}} + \frac{- a^{3} d^{3} + 7 a^{2} b c d^{2} + 7 a b^{2} c^{2} d - b^{3} c^{3} + 12 b^{3} d^{3} x^{3} + x^{2} \left(18 a b^{2} d^{3} + 18 b^{3} c d^{2}\right) + x \left(4 a^{2} b d^{3} + 28 a b^{2} c d^{2} + 4 b^{3} c^{2} d\right)}{2 a^{6} c^{2} d^{4} - 8 a^{5} b c^{3} d^{3} + 12 a^{4} b^{2} c^{4} d^{2} - 8 a^{3} b^{3} c^{5} d + 2 a^{2} b^{4} c^{6} + x^{4} \left(2 a^{4} b^{2} d^{6} - 8 a^{3} b^{3} c d^{5} + 12 a^{2} b^{4} c^{2} d^{4} - 8 a b^{5} c^{3} d^{3} + 2 b^{6} c^{4} d^{2}\right) + x^{3} \left(4 a^{5} b d^{6} - 12 a^{4} b^{2} c d^{5} + 8 a^{3} b^{3} c^{2} d^{4} + 8 a^{2} b^{4} c^{3} d^{3} - 12 a b^{5} c^{4} d^{2} + 4 b^{6} c^{5} d\right) + x^{2} \left(2 a^{6} d^{6} - 18 a^{4} b^{2} c^{2} d^{4} + 32 a^{3} b^{3} c^{3} d^{3} - 18 a^{2} b^{4} c^{4} d^{2} + 2 b^{6} c^{6}\right) + x \left(4 a^{6} c d^{5} - 12 a^{5} b c^{2} d^{4} + 8 a^{4} b^{2} c^{3} d^{3} + 8 a^{3} b^{3} c^{4} d^{2} - 12 a^{2} b^{4} c^{5} d + 4 a b^{5} c^{6}\right)}"," ",0,"6*b**2*d**2*log(x + (-6*a**6*b**2*d**8/(a*d - b*c)**5 + 36*a**5*b**3*c*d**7/(a*d - b*c)**5 - 90*a**4*b**4*c**2*d**6/(a*d - b*c)**5 + 120*a**3*b**5*c**3*d**5/(a*d - b*c)**5 - 90*a**2*b**6*c**4*d**4/(a*d - b*c)**5 + 36*a*b**7*c**5*d**3/(a*d - b*c)**5 + 6*a*b**2*d**3 - 6*b**8*c**6*d**2/(a*d - b*c)**5 + 6*b**3*c*d**2)/(12*b**3*d**3))/(a*d - b*c)**5 - 6*b**2*d**2*log(x + (6*a**6*b**2*d**8/(a*d - b*c)**5 - 36*a**5*b**3*c*d**7/(a*d - b*c)**5 + 90*a**4*b**4*c**2*d**6/(a*d - b*c)**5 - 120*a**3*b**5*c**3*d**5/(a*d - b*c)**5 + 90*a**2*b**6*c**4*d**4/(a*d - b*c)**5 - 36*a*b**7*c**5*d**3/(a*d - b*c)**5 + 6*a*b**2*d**3 + 6*b**8*c**6*d**2/(a*d - b*c)**5 + 6*b**3*c*d**2)/(12*b**3*d**3))/(a*d - b*c)**5 + (-a**3*d**3 + 7*a**2*b*c*d**2 + 7*a*b**2*c**2*d - b**3*c**3 + 12*b**3*d**3*x**3 + x**2*(18*a*b**2*d**3 + 18*b**3*c*d**2) + x*(4*a**2*b*d**3 + 28*a*b**2*c*d**2 + 4*b**3*c**2*d))/(2*a**6*c**2*d**4 - 8*a**5*b*c**3*d**3 + 12*a**4*b**2*c**4*d**2 - 8*a**3*b**3*c**5*d + 2*a**2*b**4*c**6 + x**4*(2*a**4*b**2*d**6 - 8*a**3*b**3*c*d**5 + 12*a**2*b**4*c**2*d**4 - 8*a*b**5*c**3*d**3 + 2*b**6*c**4*d**2) + x**3*(4*a**5*b*d**6 - 12*a**4*b**2*c*d**5 + 8*a**3*b**3*c**2*d**4 + 8*a**2*b**4*c**3*d**3 - 12*a*b**5*c**4*d**2 + 4*b**6*c**5*d) + x**2*(2*a**6*d**6 - 18*a**4*b**2*c**2*d**4 + 32*a**3*b**3*c**3*d**3 - 18*a**2*b**4*c**4*d**2 + 2*b**6*c**6) + x*(4*a**6*c*d**5 - 12*a**5*b*c**2*d**4 + 8*a**4*b**2*c**3*d**3 + 8*a**3*b**3*c**4*d**2 - 12*a**2*b**4*c**5*d + 4*a*b**5*c**6))","B",0
1827,1,1217,0,3.539645," ","integrate(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x**2)**3,x)","\frac{10 b^{2} d^{3} \log{\left(x + \frac{- \frac{10 a^{7} b^{2} d^{10}}{\left(a d - b c\right)^{6}} + \frac{70 a^{6} b^{3} c d^{9}}{\left(a d - b c\right)^{6}} - \frac{210 a^{5} b^{4} c^{2} d^{8}}{\left(a d - b c\right)^{6}} + \frac{350 a^{4} b^{5} c^{3} d^{7}}{\left(a d - b c\right)^{6}} - \frac{350 a^{3} b^{6} c^{4} d^{6}}{\left(a d - b c\right)^{6}} + \frac{210 a^{2} b^{7} c^{5} d^{5}}{\left(a d - b c\right)^{6}} - \frac{70 a b^{8} c^{6} d^{4}}{\left(a d - b c\right)^{6}} + 10 a b^{2} d^{4} + \frac{10 b^{9} c^{7} d^{3}}{\left(a d - b c\right)^{6}} + 10 b^{3} c d^{3}}{20 b^{3} d^{4}} \right)}}{\left(a d - b c\right)^{6}} - \frac{10 b^{2} d^{3} \log{\left(x + \frac{\frac{10 a^{7} b^{2} d^{10}}{\left(a d - b c\right)^{6}} - \frac{70 a^{6} b^{3} c d^{9}}{\left(a d - b c\right)^{6}} + \frac{210 a^{5} b^{4} c^{2} d^{8}}{\left(a d - b c\right)^{6}} - \frac{350 a^{4} b^{5} c^{3} d^{7}}{\left(a d - b c\right)^{6}} + \frac{350 a^{3} b^{6} c^{4} d^{6}}{\left(a d - b c\right)^{6}} - \frac{210 a^{2} b^{7} c^{5} d^{5}}{\left(a d - b c\right)^{6}} + \frac{70 a b^{8} c^{6} d^{4}}{\left(a d - b c\right)^{6}} + 10 a b^{2} d^{4} - \frac{10 b^{9} c^{7} d^{3}}{\left(a d - b c\right)^{6}} + 10 b^{3} c d^{3}}{20 b^{3} d^{4}} \right)}}{\left(a d - b c\right)^{6}} + \frac{- 3 a^{4} d^{4} + 27 a^{3} b c d^{3} + 47 a^{2} b^{2} c^{2} d^{2} - 13 a b^{3} c^{3} d + 2 b^{4} c^{4} + 60 b^{4} d^{4} x^{4} + x^{3} \left(150 a b^{3} d^{4} + 90 b^{4} c d^{3}\right) + x^{2} \left(110 a^{2} b^{2} d^{4} + 230 a b^{3} c d^{3} + 20 b^{4} c^{2} d^{2}\right) + x \left(15 a^{3} b d^{4} + 175 a^{2} b^{2} c d^{3} + 55 a b^{3} c^{2} d^{2} - 5 b^{4} c^{3} d\right)}{6 a^{8} c^{2} d^{5} - 30 a^{7} b c^{3} d^{4} + 60 a^{6} b^{2} c^{4} d^{3} - 60 a^{5} b^{3} c^{5} d^{2} + 30 a^{4} b^{4} c^{6} d - 6 a^{3} b^{5} c^{7} + x^{5} \left(6 a^{5} b^{3} d^{7} - 30 a^{4} b^{4} c d^{6} + 60 a^{3} b^{5} c^{2} d^{5} - 60 a^{2} b^{6} c^{3} d^{4} + 30 a b^{7} c^{4} d^{3} - 6 b^{8} c^{5} d^{2}\right) + x^{4} \left(18 a^{6} b^{2} d^{7} - 78 a^{5} b^{3} c d^{6} + 120 a^{4} b^{4} c^{2} d^{5} - 60 a^{3} b^{5} c^{3} d^{4} - 30 a^{2} b^{6} c^{4} d^{3} + 42 a b^{7} c^{5} d^{2} - 12 b^{8} c^{6} d\right) + x^{3} \left(18 a^{7} b d^{7} - 54 a^{6} b^{2} c d^{6} + 6 a^{5} b^{3} c^{2} d^{5} + 150 a^{4} b^{4} c^{3} d^{4} - 210 a^{3} b^{5} c^{4} d^{3} + 102 a^{2} b^{6} c^{5} d^{2} - 6 a b^{7} c^{6} d - 6 b^{8} c^{7}\right) + x^{2} \left(6 a^{8} d^{7} + 6 a^{7} b c d^{6} - 102 a^{6} b^{2} c^{2} d^{5} + 210 a^{5} b^{3} c^{3} d^{4} - 150 a^{4} b^{4} c^{4} d^{3} - 6 a^{3} b^{5} c^{5} d^{2} + 54 a^{2} b^{6} c^{6} d - 18 a b^{7} c^{7}\right) + x \left(12 a^{8} c d^{6} - 42 a^{7} b c^{2} d^{5} + 30 a^{6} b^{2} c^{3} d^{4} + 60 a^{5} b^{3} c^{4} d^{3} - 120 a^{4} b^{4} c^{5} d^{2} + 78 a^{3} b^{5} c^{6} d - 18 a^{2} b^{6} c^{7}\right)}"," ",0,"10*b**2*d**3*log(x + (-10*a**7*b**2*d**10/(a*d - b*c)**6 + 70*a**6*b**3*c*d**9/(a*d - b*c)**6 - 210*a**5*b**4*c**2*d**8/(a*d - b*c)**6 + 350*a**4*b**5*c**3*d**7/(a*d - b*c)**6 - 350*a**3*b**6*c**4*d**6/(a*d - b*c)**6 + 210*a**2*b**7*c**5*d**5/(a*d - b*c)**6 - 70*a*b**8*c**6*d**4/(a*d - b*c)**6 + 10*a*b**2*d**4 + 10*b**9*c**7*d**3/(a*d - b*c)**6 + 10*b**3*c*d**3)/(20*b**3*d**4))/(a*d - b*c)**6 - 10*b**2*d**3*log(x + (10*a**7*b**2*d**10/(a*d - b*c)**6 - 70*a**6*b**3*c*d**9/(a*d - b*c)**6 + 210*a**5*b**4*c**2*d**8/(a*d - b*c)**6 - 350*a**4*b**5*c**3*d**7/(a*d - b*c)**6 + 350*a**3*b**6*c**4*d**6/(a*d - b*c)**6 - 210*a**2*b**7*c**5*d**5/(a*d - b*c)**6 + 70*a*b**8*c**6*d**4/(a*d - b*c)**6 + 10*a*b**2*d**4 - 10*b**9*c**7*d**3/(a*d - b*c)**6 + 10*b**3*c*d**3)/(20*b**3*d**4))/(a*d - b*c)**6 + (-3*a**4*d**4 + 27*a**3*b*c*d**3 + 47*a**2*b**2*c**2*d**2 - 13*a*b**3*c**3*d + 2*b**4*c**4 + 60*b**4*d**4*x**4 + x**3*(150*a*b**3*d**4 + 90*b**4*c*d**3) + x**2*(110*a**2*b**2*d**4 + 230*a*b**3*c*d**3 + 20*b**4*c**2*d**2) + x*(15*a**3*b*d**4 + 175*a**2*b**2*c*d**3 + 55*a*b**3*c**2*d**2 - 5*b**4*c**3*d))/(6*a**8*c**2*d**5 - 30*a**7*b*c**3*d**4 + 60*a**6*b**2*c**4*d**3 - 60*a**5*b**3*c**5*d**2 + 30*a**4*b**4*c**6*d - 6*a**3*b**5*c**7 + x**5*(6*a**5*b**3*d**7 - 30*a**4*b**4*c*d**6 + 60*a**3*b**5*c**2*d**5 - 60*a**2*b**6*c**3*d**4 + 30*a*b**7*c**4*d**3 - 6*b**8*c**5*d**2) + x**4*(18*a**6*b**2*d**7 - 78*a**5*b**3*c*d**6 + 120*a**4*b**4*c**2*d**5 - 60*a**3*b**5*c**3*d**4 - 30*a**2*b**6*c**4*d**3 + 42*a*b**7*c**5*d**2 - 12*b**8*c**6*d) + x**3*(18*a**7*b*d**7 - 54*a**6*b**2*c*d**6 + 6*a**5*b**3*c**2*d**5 + 150*a**4*b**4*c**3*d**4 - 210*a**3*b**5*c**4*d**3 + 102*a**2*b**6*c**5*d**2 - 6*a*b**7*c**6*d - 6*b**8*c**7) + x**2*(6*a**8*d**7 + 6*a**7*b*c*d**6 - 102*a**6*b**2*c**2*d**5 + 210*a**5*b**3*c**3*d**4 - 150*a**4*b**4*c**4*d**3 - 6*a**3*b**5*c**5*d**2 + 54*a**2*b**6*c**6*d - 18*a*b**7*c**7) + x*(12*a**8*c*d**6 - 42*a**7*b*c**2*d**5 + 30*a**6*b**2*c**3*d**4 + 60*a**5*b**3*c**4*d**3 - 120*a**4*b**4*c**5*d**2 + 78*a**3*b**5*c**6*d - 18*a**2*b**6*c**7))","B",0
1828,1,136,0,0.094805," ","integrate((e*x+d)**4*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","a d^{5} e x + \frac{c d e^{5} x^{7}}{7} + x^{6} \left(\frac{a e^{6}}{6} + \frac{5 c d^{2} e^{4}}{6}\right) + x^{5} \left(a d e^{5} + 2 c d^{3} e^{3}\right) + x^{4} \left(\frac{5 a d^{2} e^{4}}{2} + \frac{5 c d^{4} e^{2}}{2}\right) + x^{3} \left(\frac{10 a d^{3} e^{3}}{3} + \frac{5 c d^{5} e}{3}\right) + x^{2} \left(\frac{5 a d^{4} e^{2}}{2} + \frac{c d^{6}}{2}\right)"," ",0,"a*d**5*e*x + c*d*e**5*x**7/7 + x**6*(a*e**6/6 + 5*c*d**2*e**4/6) + x**5*(a*d*e**5 + 2*c*d**3*e**3) + x**4*(5*a*d**2*e**4/2 + 5*c*d**4*e**2/2) + x**3*(10*a*d**3*e**3/3 + 5*c*d**5*e/3) + x**2*(5*a*d**4*e**2/2 + c*d**6/2)","B",0
1829,1,107,0,0.091243," ","integrate((e*x+d)**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","a d^{4} e x + \frac{c d e^{4} x^{6}}{6} + x^{5} \left(\frac{a e^{5}}{5} + \frac{4 c d^{2} e^{3}}{5}\right) + x^{4} \left(a d e^{4} + \frac{3 c d^{3} e^{2}}{2}\right) + x^{3} \left(2 a d^{2} e^{3} + \frac{4 c d^{4} e}{3}\right) + x^{2} \left(2 a d^{3} e^{2} + \frac{c d^{5}}{2}\right)"," ",0,"a*d**4*e*x + c*d*e**4*x**6/6 + x**5*(a*e**5/5 + 4*c*d**2*e**3/5) + x**4*(a*d*e**4 + 3*c*d**3*e**2/2) + x**3*(2*a*d**2*e**3 + 4*c*d**4*e/3) + x**2*(2*a*d**3*e**2 + c*d**5/2)","B",0
1830,1,80,0,0.082748," ","integrate((e*x+d)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","a d^{3} e x + \frac{c d e^{3} x^{5}}{5} + x^{4} \left(\frac{a e^{4}}{4} + \frac{3 c d^{2} e^{2}}{4}\right) + x^{3} \left(a d e^{3} + c d^{3} e\right) + x^{2} \left(\frac{3 a d^{2} e^{2}}{2} + \frac{c d^{4}}{2}\right)"," ",0,"a*d**3*e*x + c*d*e**3*x**5/5 + x**4*(a*e**4/4 + 3*c*d**2*e**2/4) + x**3*(a*d*e**3 + c*d**3*e) + x**2*(3*a*d**2*e**2/2 + c*d**4/2)","B",0
1831,1,56,0,0.075095," ","integrate((e*x+d)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","a d^{2} e x + \frac{c d e^{2} x^{4}}{4} + x^{3} \left(\frac{a e^{3}}{3} + \frac{2 c d^{2} e}{3}\right) + x^{2} \left(a d e^{2} + \frac{c d^{3}}{2}\right)"," ",0,"a*d**2*e*x + c*d*e**2*x**4/4 + x**3*(a*e**3/3 + 2*c*d**2*e/3) + x**2*(a*d*e**2 + c*d**3/2)","A",0
1832,1,32,0,0.069886," ","integrate(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2,x)","a d e x + \frac{c d e x^{3}}{3} + x^{2} \left(\frac{a e^{2}}{2} + \frac{c d^{2}}{2}\right)"," ",0,"a*d*e*x + c*d*e*x**3/3 + x**2*(a*e**2/2 + c*d**2/2)","A",0
1833,1,12,0,0.081558," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d),x)","a e x + \frac{c d x^{2}}{2}"," ",0,"a*e*x + c*d*x**2/2","A",0
1834,1,26,0,0.184880," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**2,x)","\frac{c d x}{e} + \frac{\left(a e^{2} - c d^{2}\right) \log{\left(d + e x \right)}}{e^{2}}"," ",0,"c*d*x/e + (a*e**2 - c*d**2)*log(d + e*x)/e**2","A",0
1835,1,32,0,0.214882," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**3,x)","\frac{c d \log{\left(d + e x \right)}}{e^{2}} + \frac{- a e^{2} + c d^{2}}{d e^{2} + e^{3} x}"," ",0,"c*d*log(d + e*x)/e**2 + (-a*e**2 + c*d**2)/(d*e**2 + e**3*x)","A",0
1836,1,44,0,0.308953," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**4,x)","\frac{- a e^{2} - c d^{2} - 2 c d e x}{2 d^{2} e^{2} + 4 d e^{3} x + 2 e^{4} x^{2}}"," ",0,"(-a*e**2 - c*d**2 - 2*c*d*e*x)/(2*d**2*e**2 + 4*d*e**3*x + 2*e**4*x**2)","A",0
1837,1,58,0,0.384816," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**5,x)","\frac{- 2 a e^{2} - c d^{2} - 3 c d e x}{6 d^{3} e^{2} + 18 d^{2} e^{3} x + 18 d e^{4} x^{2} + 6 e^{5} x^{3}}"," ",0,"(-2*a*e**2 - c*d**2 - 3*c*d*e*x)/(6*d**3*e**2 + 18*d**2*e**3*x + 18*d*e**4*x**2 + 6*e**5*x**3)","A",0
1838,1,70,0,0.636971," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**6,x)","\frac{- 3 a e^{2} - c d^{2} - 4 c d e x}{12 d^{4} e^{2} + 48 d^{3} e^{3} x + 72 d^{2} e^{4} x^{2} + 48 d e^{5} x^{3} + 12 e^{6} x^{4}}"," ",0,"(-3*a*e**2 - c*d**2 - 4*c*d*e*x)/(12*d**4*e**2 + 48*d**3*e**3*x + 72*d**2*e**4*x**2 + 48*d*e**5*x**3 + 12*e**6*x**4)","B",0
1839,1,185,0,0.123878," ","integrate((e*x+d)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","a^{2} d^{4} e^{2} x + \frac{c^{2} d^{2} e^{4} x^{7}}{7} + x^{6} \left(\frac{a c d e^{5}}{3} + \frac{2 c^{2} d^{3} e^{3}}{3}\right) + x^{5} \left(\frac{a^{2} e^{6}}{5} + \frac{8 a c d^{2} e^{4}}{5} + \frac{6 c^{2} d^{4} e^{2}}{5}\right) + x^{4} \left(a^{2} d e^{5} + 3 a c d^{3} e^{3} + c^{2} d^{5} e\right) + x^{3} \left(2 a^{2} d^{2} e^{4} + \frac{8 a c d^{4} e^{2}}{3} + \frac{c^{2} d^{6}}{3}\right) + x^{2} \left(2 a^{2} d^{3} e^{3} + a c d^{5} e\right)"," ",0,"a**2*d**4*e**2*x + c**2*d**2*e**4*x**7/7 + x**6*(a*c*d*e**5/3 + 2*c**2*d**3*e**3/3) + x**5*(a**2*e**6/5 + 8*a*c*d**2*e**4/5 + 6*c**2*d**4*e**2/5) + x**4*(a**2*d*e**5 + 3*a*c*d**3*e**3 + c**2*d**5*e) + x**3*(2*a**2*d**2*e**4 + 8*a*c*d**4*e**2/3 + c**2*d**6/3) + x**2*(2*a**2*d**3*e**3 + a*c*d**5*e)","B",0
1840,1,150,0,0.106409," ","integrate((e*x+d)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","a^{2} d^{3} e^{2} x + \frac{c^{2} d^{2} e^{3} x^{6}}{6} + x^{5} \left(\frac{2 a c d e^{4}}{5} + \frac{3 c^{2} d^{3} e^{2}}{5}\right) + x^{4} \left(\frac{a^{2} e^{5}}{4} + \frac{3 a c d^{2} e^{3}}{2} + \frac{3 c^{2} d^{4} e}{4}\right) + x^{3} \left(a^{2} d e^{4} + 2 a c d^{3} e^{2} + \frac{c^{2} d^{5}}{3}\right) + x^{2} \left(\frac{3 a^{2} d^{2} e^{3}}{2} + a c d^{4} e\right)"," ",0,"a**2*d**3*e**2*x + c**2*d**2*e**3*x**6/6 + x**5*(2*a*c*d*e**4/5 + 3*c**2*d**3*e**2/5) + x**4*(a**2*e**5/4 + 3*a*c*d**2*e**3/2 + 3*c**2*d**4*e/4) + x**3*(a**2*d*e**4 + 2*a*c*d**3*e**2 + c**2*d**5/3) + x**2*(3*a**2*d**2*e**3/2 + a*c*d**4*e)","B",0
1841,1,104,0,0.092609," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","a^{2} d^{2} e^{2} x + \frac{c^{2} d^{2} e^{2} x^{5}}{5} + x^{4} \left(\frac{a c d e^{3}}{2} + \frac{c^{2} d^{3} e}{2}\right) + x^{3} \left(\frac{a^{2} e^{4}}{3} + \frac{4 a c d^{2} e^{2}}{3} + \frac{c^{2} d^{4}}{3}\right) + x^{2} \left(a^{2} d e^{3} + a c d^{3} e\right)"," ",0,"a**2*d**2*e**2*x + c**2*d**2*e**2*x**5/5 + x**4*(a*c*d*e**3/2 + c**2*d**3*e/2) + x**3*(a**2*e**4/3 + 4*a*c*d**2*e**2/3 + c**2*d**4/3) + x**2*(a**2*d*e**3 + a*c*d**3*e)","A",0
1842,1,66,0,0.128606," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d),x)","a^{2} d e^{2} x + \frac{c^{2} d^{2} e x^{4}}{4} + x^{3} \left(\frac{2 a c d e^{2}}{3} + \frac{c^{2} d^{3}}{3}\right) + x^{2} \left(\frac{a^{2} e^{3}}{2} + a c d^{2} e\right)"," ",0,"a**2*d*e**2*x + c**2*d**2*e*x**4/4 + x**3*(2*a*c*d*e**2/3 + c**2*d**3/3) + x**2*(a**2*e**3/2 + a*c*d**2*e)","A",0
1843,1,29,0,0.128446," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**2,x)","a^{2} e^{2} x + a c d e x^{2} + \frac{c^{2} d^{2} x^{3}}{3}"," ",0,"a**2*e**2*x + a*c*d*e*x**2 + c**2*d**2*x**3/3","B",0
1844,1,53,0,0.288773," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**3,x)","\frac{c^{2} d^{2} x^{2}}{2 e} + x \left(2 a c d - \frac{c^{2} d^{3}}{e^{2}}\right) + \frac{\left(a e^{2} - c d^{2}\right)^{2} \log{\left(d + e x \right)}}{e^{3}}"," ",0,"c**2*d**2*x**2/(2*e) + x*(2*a*c*d - c**2*d**3/e**2) + (a*e**2 - c*d**2)**2*log(d + e*x)/e**3","A",0
1845,1,71,0,0.424050," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**4,x)","\frac{c^{2} d^{2} x}{e^{2}} + \frac{2 c d \left(a e^{2} - c d^{2}\right) \log{\left(d + e x \right)}}{e^{3}} + \frac{- a^{2} e^{4} + 2 a c d^{2} e^{2} - c^{2} d^{4}}{d e^{3} + e^{4} x}"," ",0,"c**2*d**2*x/e**2 + 2*c*d*(a*e**2 - c*d**2)*log(d + e*x)/e**3 + (-a**2*e**4 + 2*a*c*d**2*e**2 - c**2*d**4)/(d*e**3 + e**4*x)","A",0
1846,1,90,0,0.561070," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**5,x)","\frac{c^{2} d^{2} \log{\left(d + e x \right)}}{e^{3}} + \frac{- a^{2} e^{4} - 2 a c d^{2} e^{2} + 3 c^{2} d^{4} + x \left(- 4 a c d e^{3} + 4 c^{2} d^{3} e\right)}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}}"," ",0,"c**2*d**2*log(d + e*x)/e**3 + (-a**2*e**4 - 2*a*c*d**2*e**2 + 3*c**2*d**4 + x*(-4*a*c*d*e**3 + 4*c**2*d**3*e))/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2)","A",0
1847,1,99,0,0.741266," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**6,x)","\frac{- a^{2} e^{4} - a c d^{2} e^{2} - c^{2} d^{4} - 3 c^{2} d^{2} e^{2} x^{2} + x \left(- 3 a c d e^{3} - 3 c^{2} d^{3} e\right)}{3 d^{3} e^{3} + 9 d^{2} e^{4} x + 9 d e^{5} x^{2} + 3 e^{6} x^{3}}"," ",0,"(-a**2*e**4 - a*c*d**2*e**2 - c**2*d**4 - 3*c**2*d**2*e**2*x**2 + x*(-3*a*c*d*e**3 - 3*c**2*d**3*e))/(3*d**3*e**3 + 9*d**2*e**4*x + 9*d*e**5*x**2 + 3*e**6*x**3)","B",0
1848,1,114,0,0.969476," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**7,x)","\frac{- 3 a^{2} e^{4} - 2 a c d^{2} e^{2} - c^{2} d^{4} - 6 c^{2} d^{2} e^{2} x^{2} + x \left(- 8 a c d e^{3} - 4 c^{2} d^{3} e\right)}{12 d^{4} e^{3} + 48 d^{3} e^{4} x + 72 d^{2} e^{5} x^{2} + 48 d e^{6} x^{3} + 12 e^{7} x^{4}}"," ",0,"(-3*a**2*e**4 - 2*a*c*d**2*e**2 - c**2*d**4 - 6*c**2*d**2*e**2*x**2 + x*(-8*a*c*d*e**3 - 4*c**2*d**3*e))/(12*d**4*e**3 + 48*d**3*e**4*x + 72*d**2*e**5*x**2 + 48*d*e**6*x**3 + 12*e**7*x**4)","A",0
1849,1,126,0,1.416839," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**8,x)","\frac{- 6 a^{2} e^{4} - 3 a c d^{2} e^{2} - c^{2} d^{4} - 10 c^{2} d^{2} e^{2} x^{2} + x \left(- 15 a c d e^{3} - 5 c^{2} d^{3} e\right)}{30 d^{5} e^{3} + 150 d^{4} e^{4} x + 300 d^{3} e^{5} x^{2} + 300 d^{2} e^{6} x^{3} + 150 d e^{7} x^{4} + 30 e^{8} x^{5}}"," ",0,"(-6*a**2*e**4 - 3*a*c*d**2*e**2 - c**2*d**4 - 10*c**2*d**2*e**2*x**2 + x*(-15*a*c*d*e**3 - 5*c**2*d**3*e))/(30*d**5*e**3 + 150*d**4*e**4*x + 300*d**3*e**5*x**2 + 300*d**2*e**6*x**3 + 150*d*e**7*x**4 + 30*e**8*x**5)","A",0
1850,1,138,0,2.361526," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**9,x)","\frac{- 10 a^{2} e^{4} - 4 a c d^{2} e^{2} - c^{2} d^{4} - 15 c^{2} d^{2} e^{2} x^{2} + x \left(- 24 a c d e^{3} - 6 c^{2} d^{3} e\right)}{60 d^{6} e^{3} + 360 d^{5} e^{4} x + 900 d^{4} e^{5} x^{2} + 1200 d^{3} e^{6} x^{3} + 900 d^{2} e^{7} x^{4} + 360 d e^{8} x^{5} + 60 e^{9} x^{6}}"," ",0,"(-10*a**2*e**4 - 4*a*c*d**2*e**2 - c**2*d**4 - 15*c**2*d**2*e**2*x**2 + x*(-24*a*c*d*e**3 - 6*c**2*d**3*e))/(60*d**6*e**3 + 360*d**5*e**4*x + 900*d**4*e**5*x**2 + 1200*d**3*e**6*x**3 + 900*d**2*e**7*x**4 + 360*d*e**8*x**5 + 60*e**9*x**6)","B",0
1851,1,335,0,0.178431," ","integrate((e*x+d)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","a^{3} d^{5} e^{3} x + \frac{c^{3} d^{3} e^{5} x^{9}}{9} + x^{8} \left(\frac{3 a c^{2} d^{2} e^{6}}{8} + \frac{5 c^{3} d^{4} e^{4}}{8}\right) + x^{7} \left(\frac{3 a^{2} c d e^{7}}{7} + \frac{15 a c^{2} d^{3} e^{5}}{7} + \frac{10 c^{3} d^{5} e^{3}}{7}\right) + x^{6} \left(\frac{a^{3} e^{8}}{6} + \frac{5 a^{2} c d^{2} e^{6}}{2} + 5 a c^{2} d^{4} e^{4} + \frac{5 c^{3} d^{6} e^{2}}{3}\right) + x^{5} \left(a^{3} d e^{7} + 6 a^{2} c d^{3} e^{5} + 6 a c^{2} d^{5} e^{3} + c^{3} d^{7} e\right) + x^{4} \left(\frac{5 a^{3} d^{2} e^{6}}{2} + \frac{15 a^{2} c d^{4} e^{4}}{2} + \frac{15 a c^{2} d^{6} e^{2}}{4} + \frac{c^{3} d^{8}}{4}\right) + x^{3} \left(\frac{10 a^{3} d^{3} e^{5}}{3} + 5 a^{2} c d^{5} e^{3} + a c^{2} d^{7} e\right) + x^{2} \left(\frac{5 a^{3} d^{4} e^{4}}{2} + \frac{3 a^{2} c d^{6} e^{2}}{2}\right)"," ",0,"a**3*d**5*e**3*x + c**3*d**3*e**5*x**9/9 + x**8*(3*a*c**2*d**2*e**6/8 + 5*c**3*d**4*e**4/8) + x**7*(3*a**2*c*d*e**7/7 + 15*a*c**2*d**3*e**5/7 + 10*c**3*d**5*e**3/7) + x**6*(a**3*e**8/6 + 5*a**2*c*d**2*e**6/2 + 5*a*c**2*d**4*e**4 + 5*c**3*d**6*e**2/3) + x**5*(a**3*d*e**7 + 6*a**2*c*d**3*e**5 + 6*a*c**2*d**5*e**3 + c**3*d**7*e) + x**4*(5*a**3*d**2*e**6/2 + 15*a**2*c*d**4*e**4/2 + 15*a*c**2*d**6*e**2/4 + c**3*d**8/4) + x**3*(10*a**3*d**3*e**5/3 + 5*a**2*c*d**5*e**3 + a*c**2*d**7*e) + x**2*(5*a**3*d**4*e**4/2 + 3*a**2*c*d**6*e**2/2)","B",0
1852,1,270,0,0.140976," ","integrate((e*x+d)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","a^{3} d^{4} e^{3} x + \frac{c^{3} d^{3} e^{4} x^{8}}{8} + x^{7} \left(\frac{3 a c^{2} d^{2} e^{5}}{7} + \frac{4 c^{3} d^{4} e^{3}}{7}\right) + x^{6} \left(\frac{a^{2} c d e^{6}}{2} + 2 a c^{2} d^{3} e^{4} + c^{3} d^{5} e^{2}\right) + x^{5} \left(\frac{a^{3} e^{7}}{5} + \frac{12 a^{2} c d^{2} e^{5}}{5} + \frac{18 a c^{2} d^{4} e^{3}}{5} + \frac{4 c^{3} d^{6} e}{5}\right) + x^{4} \left(a^{3} d e^{6} + \frac{9 a^{2} c d^{3} e^{4}}{2} + 3 a c^{2} d^{5} e^{2} + \frac{c^{3} d^{7}}{4}\right) + x^{3} \left(2 a^{3} d^{2} e^{5} + 4 a^{2} c d^{4} e^{3} + a c^{2} d^{6} e\right) + x^{2} \left(2 a^{3} d^{3} e^{4} + \frac{3 a^{2} c d^{5} e^{2}}{2}\right)"," ",0,"a**3*d**4*e**3*x + c**3*d**3*e**4*x**8/8 + x**7*(3*a*c**2*d**2*e**5/7 + 4*c**3*d**4*e**3/7) + x**6*(a**2*c*d*e**6/2 + 2*a*c**2*d**3*e**4 + c**3*d**5*e**2) + x**5*(a**3*e**7/5 + 12*a**2*c*d**2*e**5/5 + 18*a*c**2*d**4*e**3/5 + 4*c**3*d**6*e/5) + x**4*(a**3*d*e**6 + 9*a**2*c*d**3*e**4/2 + 3*a*c**2*d**5*e**2 + c**3*d**7/4) + x**3*(2*a**3*d**2*e**5 + 4*a**2*c*d**4*e**3 + a*c**2*d**6*e) + x**2*(2*a**3*d**3*e**4 + 3*a**2*c*d**5*e**2/2)","B",0
1853,1,218,0,0.115368," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","a^{3} d^{3} e^{3} x + \frac{c^{3} d^{3} e^{3} x^{7}}{7} + x^{6} \left(\frac{a c^{2} d^{2} e^{4}}{2} + \frac{c^{3} d^{4} e^{2}}{2}\right) + x^{5} \left(\frac{3 a^{2} c d e^{5}}{5} + \frac{9 a c^{2} d^{3} e^{3}}{5} + \frac{3 c^{3} d^{5} e}{5}\right) + x^{4} \left(\frac{a^{3} e^{6}}{4} + \frac{9 a^{2} c d^{2} e^{4}}{4} + \frac{9 a c^{2} d^{4} e^{2}}{4} + \frac{c^{3} d^{6}}{4}\right) + x^{3} \left(a^{3} d e^{5} + 3 a^{2} c d^{3} e^{3} + a c^{2} d^{5} e\right) + x^{2} \left(\frac{3 a^{3} d^{2} e^{4}}{2} + \frac{3 a^{2} c d^{4} e^{2}}{2}\right)"," ",0,"a**3*d**3*e**3*x + c**3*d**3*e**3*x**7/7 + x**6*(a*c**2*d**2*e**4/2 + c**3*d**4*e**2/2) + x**5*(3*a**2*c*d*e**5/5 + 9*a*c**2*d**3*e**3/5 + 3*c**3*d**5*e/5) + x**4*(a**3*e**6/4 + 9*a**2*c*d**2*e**4/4 + 9*a*c**2*d**4*e**2/4 + c**3*d**6/4) + x**3*(a**3*d*e**5 + 3*a**2*c*d**3*e**3 + a*c**2*d**5*e) + x**2*(3*a**3*d**2*e**4/2 + 3*a**2*c*d**4*e**2/2)","B",0
1854,1,160,0,0.176888," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d),x)","a^{3} d^{2} e^{3} x + \frac{c^{3} d^{3} e^{2} x^{6}}{6} + x^{5} \left(\frac{3 a c^{2} d^{2} e^{3}}{5} + \frac{2 c^{3} d^{4} e}{5}\right) + x^{4} \left(\frac{3 a^{2} c d e^{4}}{4} + \frac{3 a c^{2} d^{3} e^{2}}{2} + \frac{c^{3} d^{5}}{4}\right) + x^{3} \left(\frac{a^{3} e^{5}}{3} + 2 a^{2} c d^{2} e^{3} + a c^{2} d^{4} e\right) + x^{2} \left(a^{3} d e^{4} + \frac{3 a^{2} c d^{3} e^{2}}{2}\right)"," ",0,"a**3*d**2*e**3*x + c**3*d**3*e**2*x**6/6 + x**5*(3*a*c**2*d**2*e**3/5 + 2*c**3*d**4*e/5) + x**4*(3*a**2*c*d*e**4/4 + 3*a*c**2*d**3*e**2/2 + c**3*d**5/4) + x**3*(a**3*e**5/3 + 2*a**2*c*d**2*e**3 + a*c**2*d**4*e) + x**2*(a**3*d*e**4 + 3*a**2*c*d**3*e**2/2)","A",0
1855,1,100,0,0.174086," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**2,x)","a^{3} d e^{3} x + \frac{c^{3} d^{3} e x^{5}}{5} + x^{4} \left(\frac{3 a c^{2} d^{2} e^{2}}{4} + \frac{c^{3} d^{4}}{4}\right) + x^{3} \left(a^{2} c d e^{3} + a c^{2} d^{3} e\right) + x^{2} \left(\frac{a^{3} e^{4}}{2} + \frac{3 a^{2} c d^{2} e^{2}}{2}\right)"," ",0,"a**3*d*e**3*x + c**3*d**3*e*x**5/5 + x**4*(3*a*c**2*d**2*e**2/4 + c**3*d**4/4) + x**3*(a**2*c*d*e**3 + a*c**2*d**3*e) + x**2*(a**3*e**4/2 + 3*a**2*c*d**2*e**2/2)","B",0
1856,1,49,0,0.173422," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**3,x)","a^{3} e^{3} x + \frac{3 a^{2} c d e^{2} x^{2}}{2} + a c^{2} d^{2} e x^{3} + \frac{c^{3} d^{3} x^{4}}{4}"," ",0,"a**3*e**3*x + 3*a**2*c*d*e**2*x**2/2 + a*c**2*d**2*e*x**3 + c**3*d**3*x**4/4","B",0
1857,1,95,0,0.407024," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**4,x)","\frac{c^{3} d^{3} x^{3}}{3 e} + x^{2} \left(\frac{3 a c^{2} d^{2}}{2} - \frac{c^{3} d^{4}}{2 e^{2}}\right) + x \left(3 a^{2} c d e - \frac{3 a c^{2} d^{3}}{e} + \frac{c^{3} d^{5}}{e^{3}}\right) + \frac{\left(a e^{2} - c d^{2}\right)^{3} \log{\left(d + e x \right)}}{e^{4}}"," ",0,"c**3*d**3*x**3/(3*e) + x**2*(3*a*c**2*d**2/2 - c**3*d**4/(2*e**2)) + x*(3*a**2*c*d*e - 3*a*c**2*d**3/e + c**3*d**5/e**3) + (a*e**2 - c*d**2)**3*log(d + e*x)/e**4","A",0
1858,1,117,0,0.658177," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**5,x)","\frac{c^{3} d^{3} x^{2}}{2 e^{2}} + \frac{3 c d \left(a e^{2} - c d^{2}\right)^{2} \log{\left(d + e x \right)}}{e^{4}} + x \left(\frac{3 a c^{2} d^{2}}{e} - \frac{2 c^{3} d^{4}}{e^{3}}\right) + \frac{- a^{3} e^{6} + 3 a^{2} c d^{2} e^{4} - 3 a c^{2} d^{4} e^{2} + c^{3} d^{6}}{d e^{4} + e^{5} x}"," ",0,"c**3*d**3*x**2/(2*e**2) + 3*c*d*(a*e**2 - c*d**2)**2*log(d + e*x)/e**4 + x*(3*a*c**2*d**2/e - 2*c**3*d**4/e**3) + (-a**3*e**6 + 3*a**2*c*d**2*e**4 - 3*a*c**2*d**4*e**2 + c**3*d**6)/(d*e**4 + e**5*x)","A",0
1859,1,144,0,1.171263," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**6,x)","\frac{c^{3} d^{3} x}{e^{3}} + \frac{3 c^{2} d^{2} \left(a e^{2} - c d^{2}\right) \log{\left(d + e x \right)}}{e^{4}} + \frac{- a^{3} e^{6} - 3 a^{2} c d^{2} e^{4} + 9 a c^{2} d^{4} e^{2} - 5 c^{3} d^{6} + x \left(- 6 a^{2} c d e^{5} + 12 a c^{2} d^{3} e^{3} - 6 c^{3} d^{5} e\right)}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}}"," ",0,"c**3*d**3*x/e**3 + 3*c**2*d**2*(a*e**2 - c*d**2)*log(d + e*x)/e**4 + (-a**3*e**6 - 3*a**2*c*d**2*e**4 + 9*a*c**2*d**4*e**2 - 5*c**3*d**6 + x*(-6*a**2*c*d*e**5 + 12*a*c**2*d**3*e**3 - 6*c**3*d**5*e))/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2)","A",0
1860,1,163,0,2.156360," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**7,x)","\frac{c^{3} d^{3} \log{\left(d + e x \right)}}{e^{4}} + \frac{- 2 a^{3} e^{6} - 3 a^{2} c d^{2} e^{4} - 6 a c^{2} d^{4} e^{2} + 11 c^{3} d^{6} + x^{2} \left(- 18 a c^{2} d^{2} e^{4} + 18 c^{3} d^{4} e^{2}\right) + x \left(- 9 a^{2} c d e^{5} - 18 a c^{2} d^{3} e^{3} + 27 c^{3} d^{5} e\right)}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}}"," ",0,"c**3*d**3*log(d + e*x)/e**4 + (-2*a**3*e**6 - 3*a**2*c*d**2*e**4 - 6*a*c**2*d**4*e**2 + 11*c**3*d**6 + x**2*(-18*a*c**2*d**2*e**4 + 18*c**3*d**4*e**2) + x*(-9*a**2*c*d*e**5 - 18*a*c**2*d**3*e**3 + 27*c**3*d**5*e))/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3)","A",0
1861,1,170,0,4.738808," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**8,x)","\frac{- a^{3} e^{6} - a^{2} c d^{2} e^{4} - a c^{2} d^{4} e^{2} - c^{3} d^{6} - 4 c^{3} d^{3} e^{3} x^{3} + x^{2} \left(- 6 a c^{2} d^{2} e^{4} - 6 c^{3} d^{4} e^{2}\right) + x \left(- 4 a^{2} c d e^{5} - 4 a c^{2} d^{3} e^{3} - 4 c^{3} d^{5} e\right)}{4 d^{4} e^{4} + 16 d^{3} e^{5} x + 24 d^{2} e^{6} x^{2} + 16 d e^{7} x^{3} + 4 e^{8} x^{4}}"," ",0,"(-a**3*e**6 - a**2*c*d**2*e**4 - a*c**2*d**4*e**2 - c**3*d**6 - 4*c**3*d**3*e**3*x**3 + x**2*(-6*a*c**2*d**2*e**4 - 6*c**3*d**4*e**2) + x*(-4*a**2*c*d*e**5 - 4*a*c**2*d**3*e**3 - 4*c**3*d**5*e))/(4*d**4*e**4 + 16*d**3*e**5*x + 24*d**2*e**6*x**2 + 16*d*e**7*x**3 + 4*e**8*x**4)","B",0
1862,1,187,0,7.256664," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**9,x)","\frac{- 4 a^{3} e^{6} - 3 a^{2} c d^{2} e^{4} - 2 a c^{2} d^{4} e^{2} - c^{3} d^{6} - 10 c^{3} d^{3} e^{3} x^{3} + x^{2} \left(- 20 a c^{2} d^{2} e^{4} - 10 c^{3} d^{4} e^{2}\right) + x \left(- 15 a^{2} c d e^{5} - 10 a c^{2} d^{3} e^{3} - 5 c^{3} d^{5} e\right)}{20 d^{5} e^{4} + 100 d^{4} e^{5} x + 200 d^{3} e^{6} x^{2} + 200 d^{2} e^{7} x^{3} + 100 d e^{8} x^{4} + 20 e^{9} x^{5}}"," ",0,"(-4*a**3*e**6 - 3*a**2*c*d**2*e**4 - 2*a*c**2*d**4*e**2 - c**3*d**6 - 10*c**3*d**3*e**3*x**3 + x**2*(-20*a*c**2*d**2*e**4 - 10*c**3*d**4*e**2) + x*(-15*a**2*c*d*e**5 - 10*a*c**2*d**3*e**3 - 5*c**3*d**5*e))/(20*d**5*e**4 + 100*d**4*e**5*x + 200*d**3*e**6*x**2 + 200*d**2*e**7*x**3 + 100*d*e**8*x**4 + 20*e**9*x**5)","B",0
1863,1,199,0,31.839715," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**10,x)","\frac{- 10 a^{3} e^{6} - 6 a^{2} c d^{2} e^{4} - 3 a c^{2} d^{4} e^{2} - c^{3} d^{6} - 20 c^{3} d^{3} e^{3} x^{3} + x^{2} \left(- 45 a c^{2} d^{2} e^{4} - 15 c^{3} d^{4} e^{2}\right) + x \left(- 36 a^{2} c d e^{5} - 18 a c^{2} d^{3} e^{3} - 6 c^{3} d^{5} e\right)}{60 d^{6} e^{4} + 360 d^{5} e^{5} x + 900 d^{4} e^{6} x^{2} + 1200 d^{3} e^{7} x^{3} + 900 d^{2} e^{8} x^{4} + 360 d e^{9} x^{5} + 60 e^{10} x^{6}}"," ",0,"(-10*a**3*e**6 - 6*a**2*c*d**2*e**4 - 3*a*c**2*d**4*e**2 - c**3*d**6 - 20*c**3*d**3*e**3*x**3 + x**2*(-45*a*c**2*d**2*e**4 - 15*c**3*d**4*e**2) + x*(-36*a**2*c*d*e**5 - 18*a*c**2*d**3*e**3 - 6*c**3*d**5*e))/(60*d**6*e**4 + 360*d**5*e**5*x + 900*d**4*e**6*x**2 + 1200*d**3*e**7*x**3 + 900*d**2*e**8*x**4 + 360*d*e**9*x**5 + 60*e**10*x**6)","A",0
1864,1,211,0,72.750091," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**11,x)","\frac{- 20 a^{3} e^{6} - 10 a^{2} c d^{2} e^{4} - 4 a c^{2} d^{4} e^{2} - c^{3} d^{6} - 35 c^{3} d^{3} e^{3} x^{3} + x^{2} \left(- 84 a c^{2} d^{2} e^{4} - 21 c^{3} d^{4} e^{2}\right) + x \left(- 70 a^{2} c d e^{5} - 28 a c^{2} d^{3} e^{3} - 7 c^{3} d^{5} e\right)}{140 d^{7} e^{4} + 980 d^{6} e^{5} x + 2940 d^{5} e^{6} x^{2} + 4900 d^{4} e^{7} x^{3} + 4900 d^{3} e^{8} x^{4} + 2940 d^{2} e^{9} x^{5} + 980 d e^{10} x^{6} + 140 e^{11} x^{7}}"," ",0,"(-20*a**3*e**6 - 10*a**2*c*d**2*e**4 - 4*a*c**2*d**4*e**2 - c**3*d**6 - 35*c**3*d**3*e**3*x**3 + x**2*(-84*a*c**2*d**2*e**4 - 21*c**3*d**4*e**2) + x*(-70*a**2*c*d*e**5 - 28*a*c**2*d**3*e**3 - 7*c**3*d**5*e))/(140*d**7*e**4 + 980*d**6*e**5*x + 2940*d**5*e**6*x**2 + 4900*d**4*e**7*x**3 + 4900*d**3*e**8*x**4 + 2940*d**2*e**9*x**5 + 980*d*e**10*x**6 + 140*e**11*x**7)","B",0
1865,1,153,0,0.519103," ","integrate((e*x+d)**5/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","x^{3} \left(- \frac{a e^{5}}{3 c^{2} d^{2}} + \frac{4 e^{3}}{3 c}\right) + x^{2} \left(\frac{a^{2} e^{6}}{2 c^{3} d^{3}} - \frac{2 a e^{4}}{c^{2} d} + \frac{3 d e^{2}}{c}\right) + x \left(- \frac{a^{3} e^{7}}{c^{4} d^{4}} + \frac{4 a^{2} e^{5}}{c^{3} d^{2}} - \frac{6 a e^{3}}{c^{2}} + \frac{4 d^{2} e}{c}\right) + \frac{e^{4} x^{4}}{4 c d} + \frac{\left(a e^{2} - c d^{2}\right)^{4} \log{\left(a e + c d x \right)}}{c^{5} d^{5}}"," ",0,"x**3*(-a*e**5/(3*c**2*d**2) + 4*e**3/(3*c)) + x**2*(a**2*e**6/(2*c**3*d**3) - 2*a*e**4/(c**2*d) + 3*d*e**2/c) + x*(-a**3*e**7/(c**4*d**4) + 4*a**2*e**5/(c**3*d**2) - 6*a*e**3/c**2 + 4*d**2*e/c) + e**4*x**4/(4*c*d) + (a*e**2 - c*d**2)**4*log(a*e + c*d*x)/(c**5*d**5)","A",0
1866,1,99,0,0.379245," ","integrate((e*x+d)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","x^{2} \left(- \frac{a e^{4}}{2 c^{2} d^{2}} + \frac{3 e^{2}}{2 c}\right) + x \left(\frac{a^{2} e^{5}}{c^{3} d^{3}} - \frac{3 a e^{3}}{c^{2} d} + \frac{3 d e}{c}\right) + \frac{e^{3} x^{3}}{3 c d} - \frac{\left(a e^{2} - c d^{2}\right)^{3} \log{\left(a e + c d x \right)}}{c^{4} d^{4}}"," ",0,"x**2*(-a*e**4/(2*c**2*d**2) + 3*e**2/(2*c)) + x*(a**2*e**5/(c**3*d**3) - 3*a*e**3/(c**2*d) + 3*d*e/c) + e**3*x**3/(3*c*d) - (a*e**2 - c*d**2)**3*log(a*e + c*d*x)/(c**4*d**4)","A",0
1867,1,58,0,0.283762," ","integrate((e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","x \left(- \frac{a e^{3}}{c^{2} d^{2}} + \frac{2 e}{c}\right) + \frac{e^{2} x^{2}}{2 c d} + \frac{\left(a e^{2} - c d^{2}\right)^{2} \log{\left(a e + c d x \right)}}{c^{3} d^{3}}"," ",0,"x*(-a*e**3/(c**2*d**2) + 2*e/c) + e**2*x**2/(2*c*d) + (a*e**2 - c*d**2)**2*log(a*e + c*d*x)/(c**3*d**3)","A",0
1868,1,32,0,0.190405," ","integrate((e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\frac{e x}{c d} - \frac{\left(a e^{2} - c d^{2}\right) \log{\left(a e + c d x \right)}}{c^{2} d^{2}}"," ",0,"e*x/(c*d) - (a*e**2 - c*d**2)*log(a*e + c*d*x)/(c**2*d**2)","A",0
1869,1,12,0,0.089376," ","integrate((e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\frac{\log{\left(a e + c d x \right)}}{c d}"," ",0,"log(a*e + c*d*x)/(c*d)","A",0
1870,1,172,0,0.372930," ","integrate(1/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\frac{\log{\left(x + \frac{- \frac{a^{2} e^{4}}{a e^{2} - c d^{2}} + \frac{2 a c d^{2} e^{2}}{a e^{2} - c d^{2}} + a e^{2} - \frac{c^{2} d^{4}}{a e^{2} - c d^{2}} + c d^{2}}{2 c d e} \right)}}{a e^{2} - c d^{2}} - \frac{\log{\left(x + \frac{\frac{a^{2} e^{4}}{a e^{2} - c d^{2}} - \frac{2 a c d^{2} e^{2}}{a e^{2} - c d^{2}} + a e^{2} + \frac{c^{2} d^{4}}{a e^{2} - c d^{2}} + c d^{2}}{2 c d e} \right)}}{a e^{2} - c d^{2}}"," ",0,"log(x + (-a**2*e**4/(a*e**2 - c*d**2) + 2*a*c*d**2*e**2/(a*e**2 - c*d**2) + a*e**2 - c**2*d**4/(a*e**2 - c*d**2) + c*d**2)/(2*c*d*e))/(a*e**2 - c*d**2) - log(x + (a**2*e**4/(a*e**2 - c*d**2) - 2*a*c*d**2*e**2/(a*e**2 - c*d**2) + a*e**2 + c**2*d**4/(a*e**2 - c*d**2) + c*d**2)/(2*c*d*e))/(a*e**2 - c*d**2)","B",0
1871,1,301,0,0.785647," ","integrate(1/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","- \frac{c d \log{\left(x + \frac{- \frac{a^{3} c d e^{6}}{\left(a e^{2} - c d^{2}\right)^{2}} + \frac{3 a^{2} c^{2} d^{3} e^{4}}{\left(a e^{2} - c d^{2}\right)^{2}} - \frac{3 a c^{3} d^{5} e^{2}}{\left(a e^{2} - c d^{2}\right)^{2}} + a c d e^{2} + \frac{c^{4} d^{7}}{\left(a e^{2} - c d^{2}\right)^{2}} + c^{2} d^{3}}{2 c^{2} d^{2} e} \right)}}{\left(a e^{2} - c d^{2}\right)^{2}} + \frac{c d \log{\left(x + \frac{\frac{a^{3} c d e^{6}}{\left(a e^{2} - c d^{2}\right)^{2}} - \frac{3 a^{2} c^{2} d^{3} e^{4}}{\left(a e^{2} - c d^{2}\right)^{2}} + \frac{3 a c^{3} d^{5} e^{2}}{\left(a e^{2} - c d^{2}\right)^{2}} + a c d e^{2} - \frac{c^{4} d^{7}}{\left(a e^{2} - c d^{2}\right)^{2}} + c^{2} d^{3}}{2 c^{2} d^{2} e} \right)}}{\left(a e^{2} - c d^{2}\right)^{2}} - \frac{1}{a d e^{2} - c d^{3} + x \left(a e^{3} - c d^{2} e\right)}"," ",0,"-c*d*log(x + (-a**3*c*d*e**6/(a*e**2 - c*d**2)**2 + 3*a**2*c**2*d**3*e**4/(a*e**2 - c*d**2)**2 - 3*a*c**3*d**5*e**2/(a*e**2 - c*d**2)**2 + a*c*d*e**2 + c**4*d**7/(a*e**2 - c*d**2)**2 + c**2*d**3)/(2*c**2*d**2*e))/(a*e**2 - c*d**2)**2 + c*d*log(x + (a**3*c*d*e**6/(a*e**2 - c*d**2)**2 - 3*a**2*c**2*d**3*e**4/(a*e**2 - c*d**2)**2 + 3*a*c**3*d**5*e**2/(a*e**2 - c*d**2)**2 + a*c*d*e**2 - c**4*d**7/(a*e**2 - c*d**2)**2 + c**2*d**3)/(2*c**2*d**2*e))/(a*e**2 - c*d**2)**2 - 1/(a*d*e**2 - c*d**3 + x*(a*e**3 - c*d**2*e))","B",0
1872,1,471,0,1.197562," ","integrate(1/(e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\frac{c^{2} d^{2} \log{\left(x + \frac{- \frac{a^{4} c^{2} d^{2} e^{8}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{4 a^{3} c^{3} d^{4} e^{6}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{6 a^{2} c^{4} d^{6} e^{4}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{4 a c^{5} d^{8} e^{2}}{\left(a e^{2} - c d^{2}\right)^{3}} + a c^{2} d^{2} e^{2} - \frac{c^{6} d^{10}}{\left(a e^{2} - c d^{2}\right)^{3}} + c^{3} d^{4}}{2 c^{3} d^{3} e} \right)}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{c^{2} d^{2} \log{\left(x + \frac{\frac{a^{4} c^{2} d^{2} e^{8}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{4 a^{3} c^{3} d^{4} e^{6}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{6 a^{2} c^{4} d^{6} e^{4}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{4 a c^{5} d^{8} e^{2}}{\left(a e^{2} - c d^{2}\right)^{3}} + a c^{2} d^{2} e^{2} + \frac{c^{6} d^{10}}{\left(a e^{2} - c d^{2}\right)^{3}} + c^{3} d^{4}}{2 c^{3} d^{3} e} \right)}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{- a e^{2} + 3 c d^{2} + 2 c d e x}{2 a^{2} d^{2} e^{4} - 4 a c d^{4} e^{2} + 2 c^{2} d^{6} + x^{2} \left(2 a^{2} e^{6} - 4 a c d^{2} e^{4} + 2 c^{2} d^{4} e^{2}\right) + x \left(4 a^{2} d e^{5} - 8 a c d^{3} e^{3} + 4 c^{2} d^{5} e\right)}"," ",0,"c**2*d**2*log(x + (-a**4*c**2*d**2*e**8/(a*e**2 - c*d**2)**3 + 4*a**3*c**3*d**4*e**6/(a*e**2 - c*d**2)**3 - 6*a**2*c**4*d**6*e**4/(a*e**2 - c*d**2)**3 + 4*a*c**5*d**8*e**2/(a*e**2 - c*d**2)**3 + a*c**2*d**2*e**2 - c**6*d**10/(a*e**2 - c*d**2)**3 + c**3*d**4)/(2*c**3*d**3*e))/(a*e**2 - c*d**2)**3 - c**2*d**2*log(x + (a**4*c**2*d**2*e**8/(a*e**2 - c*d**2)**3 - 4*a**3*c**3*d**4*e**6/(a*e**2 - c*d**2)**3 + 6*a**2*c**4*d**6*e**4/(a*e**2 - c*d**2)**3 - 4*a*c**5*d**8*e**2/(a*e**2 - c*d**2)**3 + a*c**2*d**2*e**2 + c**6*d**10/(a*e**2 - c*d**2)**3 + c**3*d**4)/(2*c**3*d**3*e))/(a*e**2 - c*d**2)**3 + (-a*e**2 + 3*c*d**2 + 2*c*d*e*x)/(2*a**2*d**2*e**4 - 4*a*c*d**4*e**2 + 2*c**2*d**6 + x**2*(2*a**2*e**6 - 4*a*c*d**2*e**4 + 2*c**2*d**4*e**2) + x*(4*a**2*d*e**5 - 8*a*c*d**3*e**3 + 4*c**2*d**5*e))","B",0
1873,1,672,0,1.685321," ","integrate(1/(e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","- \frac{c^{3} d^{3} \log{\left(x + \frac{- \frac{a^{5} c^{3} d^{3} e^{10}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{5 a^{4} c^{4} d^{5} e^{8}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{10 a^{3} c^{5} d^{7} e^{6}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{10 a^{2} c^{6} d^{9} e^{4}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{5 a c^{7} d^{11} e^{2}}{\left(a e^{2} - c d^{2}\right)^{4}} + a c^{3} d^{3} e^{2} + \frac{c^{8} d^{13}}{\left(a e^{2} - c d^{2}\right)^{4}} + c^{4} d^{5}}{2 c^{4} d^{4} e} \right)}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{c^{3} d^{3} \log{\left(x + \frac{\frac{a^{5} c^{3} d^{3} e^{10}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{5 a^{4} c^{4} d^{5} e^{8}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{10 a^{3} c^{5} d^{7} e^{6}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{10 a^{2} c^{6} d^{9} e^{4}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{5 a c^{7} d^{11} e^{2}}{\left(a e^{2} - c d^{2}\right)^{4}} + a c^{3} d^{3} e^{2} - \frac{c^{8} d^{13}}{\left(a e^{2} - c d^{2}\right)^{4}} + c^{4} d^{5}}{2 c^{4} d^{4} e} \right)}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{- 2 a^{2} e^{4} + 7 a c d^{2} e^{2} - 11 c^{2} d^{4} - 6 c^{2} d^{2} e^{2} x^{2} + x \left(3 a c d e^{3} - 15 c^{2} d^{3} e\right)}{6 a^{3} d^{3} e^{6} - 18 a^{2} c d^{5} e^{4} + 18 a c^{2} d^{7} e^{2} - 6 c^{3} d^{9} + x^{3} \left(6 a^{3} e^{9} - 18 a^{2} c d^{2} e^{7} + 18 a c^{2} d^{4} e^{5} - 6 c^{3} d^{6} e^{3}\right) + x^{2} \left(18 a^{3} d e^{8} - 54 a^{2} c d^{3} e^{6} + 54 a c^{2} d^{5} e^{4} - 18 c^{3} d^{7} e^{2}\right) + x \left(18 a^{3} d^{2} e^{7} - 54 a^{2} c d^{4} e^{5} + 54 a c^{2} d^{6} e^{3} - 18 c^{3} d^{8} e\right)}"," ",0,"-c**3*d**3*log(x + (-a**5*c**3*d**3*e**10/(a*e**2 - c*d**2)**4 + 5*a**4*c**4*d**5*e**8/(a*e**2 - c*d**2)**4 - 10*a**3*c**5*d**7*e**6/(a*e**2 - c*d**2)**4 + 10*a**2*c**6*d**9*e**4/(a*e**2 - c*d**2)**4 - 5*a*c**7*d**11*e**2/(a*e**2 - c*d**2)**4 + a*c**3*d**3*e**2 + c**8*d**13/(a*e**2 - c*d**2)**4 + c**4*d**5)/(2*c**4*d**4*e))/(a*e**2 - c*d**2)**4 + c**3*d**3*log(x + (a**5*c**3*d**3*e**10/(a*e**2 - c*d**2)**4 - 5*a**4*c**4*d**5*e**8/(a*e**2 - c*d**2)**4 + 10*a**3*c**5*d**7*e**6/(a*e**2 - c*d**2)**4 - 10*a**2*c**6*d**9*e**4/(a*e**2 - c*d**2)**4 + 5*a*c**7*d**11*e**2/(a*e**2 - c*d**2)**4 + a*c**3*d**3*e**2 - c**8*d**13/(a*e**2 - c*d**2)**4 + c**4*d**5)/(2*c**4*d**4*e))/(a*e**2 - c*d**2)**4 + (-2*a**2*e**4 + 7*a*c*d**2*e**2 - 11*c**2*d**4 - 6*c**2*d**2*e**2*x**2 + x*(3*a*c*d*e**3 - 15*c**2*d**3*e))/(6*a**3*d**3*e**6 - 18*a**2*c*d**5*e**4 + 18*a*c**2*d**7*e**2 - 6*c**3*d**9 + x**3*(6*a**3*e**9 - 18*a**2*c*d**2*e**7 + 18*a*c**2*d**4*e**5 - 6*c**3*d**6*e**3) + x**2*(18*a**3*d*e**8 - 54*a**2*c*d**3*e**6 + 54*a*c**2*d**5*e**4 - 18*c**3*d**7*e**2) + x*(18*a**3*d**2*e**7 - 54*a**2*c*d**4*e**5 + 54*a*c**2*d**6*e**3 - 18*c**3*d**8*e))","B",0
1874,1,345,0,1.731378," ","integrate((e*x+d)**8/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","x^{4} \left(- \frac{a e^{7}}{2 c^{3} d^{3}} + \frac{3 e^{5}}{2 c^{2} d}\right) + x^{3} \left(\frac{a^{2} e^{8}}{c^{4} d^{4}} - \frac{4 a e^{6}}{c^{3} d^{2}} + \frac{5 e^{4}}{c^{2}}\right) + x^{2} \left(- \frac{2 a^{3} e^{9}}{c^{5} d^{5}} + \frac{9 a^{2} e^{7}}{c^{4} d^{3}} - \frac{15 a e^{5}}{c^{3} d} + \frac{10 d e^{3}}{c^{2}}\right) + x \left(\frac{5 a^{4} e^{10}}{c^{6} d^{6}} - \frac{24 a^{3} e^{8}}{c^{5} d^{4}} + \frac{45 a^{2} e^{6}}{c^{4} d^{2}} - \frac{40 a e^{4}}{c^{3}} + \frac{15 d^{2} e^{2}}{c^{2}}\right) + \frac{- a^{6} e^{12} + 6 a^{5} c d^{2} e^{10} - 15 a^{4} c^{2} d^{4} e^{8} + 20 a^{3} c^{3} d^{6} e^{6} - 15 a^{2} c^{4} d^{8} e^{4} + 6 a c^{5} d^{10} e^{2} - c^{6} d^{12}}{a c^{7} d^{7} e + c^{8} d^{8} x} + \frac{e^{6} x^{5}}{5 c^{2} d^{2}} - \frac{6 e \left(a e^{2} - c d^{2}\right)^{5} \log{\left(a e + c d x \right)}}{c^{7} d^{7}}"," ",0,"x**4*(-a*e**7/(2*c**3*d**3) + 3*e**5/(2*c**2*d)) + x**3*(a**2*e**8/(c**4*d**4) - 4*a*e**6/(c**3*d**2) + 5*e**4/c**2) + x**2*(-2*a**3*e**9/(c**5*d**5) + 9*a**2*e**7/(c**4*d**3) - 15*a*e**5/(c**3*d) + 10*d*e**3/c**2) + x*(5*a**4*e**10/(c**6*d**6) - 24*a**3*e**8/(c**5*d**4) + 45*a**2*e**6/(c**4*d**2) - 40*a*e**4/c**3 + 15*d**2*e**2/c**2) + (-a**6*e**12 + 6*a**5*c*d**2*e**10 - 15*a**4*c**2*d**4*e**8 + 20*a**3*c**3*d**6*e**6 - 15*a**2*c**4*d**8*e**4 + 6*a*c**5*d**10*e**2 - c**6*d**12)/(a*c**7*d**7*e + c**8*d**8*x) + e**6*x**5/(5*c**2*d**2) - 6*e*(a*e**2 - c*d**2)**5*log(a*e + c*d*x)/(c**7*d**7)","A",0
1875,1,264,0,1.194504," ","integrate((e*x+d)**7/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","x^{3} \left(- \frac{2 a e^{6}}{3 c^{3} d^{3}} + \frac{5 e^{4}}{3 c^{2} d}\right) + x^{2} \left(\frac{3 a^{2} e^{7}}{2 c^{4} d^{4}} - \frac{5 a e^{5}}{c^{3} d^{2}} + \frac{5 e^{3}}{c^{2}}\right) + x \left(- \frac{4 a^{3} e^{8}}{c^{5} d^{5}} + \frac{15 a^{2} e^{6}}{c^{4} d^{3}} - \frac{20 a e^{4}}{c^{3} d} + \frac{10 d e^{2}}{c^{2}}\right) + \frac{a^{5} e^{10} - 5 a^{4} c d^{2} e^{8} + 10 a^{3} c^{2} d^{4} e^{6} - 10 a^{2} c^{3} d^{6} e^{4} + 5 a c^{4} d^{8} e^{2} - c^{5} d^{10}}{a c^{6} d^{6} e + c^{7} d^{7} x} + \frac{e^{5} x^{4}}{4 c^{2} d^{2}} + \frac{5 e \left(a e^{2} - c d^{2}\right)^{4} \log{\left(a e + c d x \right)}}{c^{6} d^{6}}"," ",0,"x**3*(-2*a*e**6/(3*c**3*d**3) + 5*e**4/(3*c**2*d)) + x**2*(3*a**2*e**7/(2*c**4*d**4) - 5*a*e**5/(c**3*d**2) + 5*e**3/c**2) + x*(-4*a**3*e**8/(c**5*d**5) + 15*a**2*e**6/(c**4*d**3) - 20*a*e**4/(c**3*d) + 10*d*e**2/c**2) + (a**5*e**10 - 5*a**4*c*d**2*e**8 + 10*a**3*c**2*d**4*e**6 - 10*a**2*c**3*d**6*e**4 + 5*a*c**4*d**8*e**2 - c**5*d**10)/(a*c**6*d**6*e + c**7*d**7*x) + e**5*x**4/(4*c**2*d**2) + 5*e*(a*e**2 - c*d**2)**4*log(a*e + c*d*x)/(c**6*d**6)","A",0
1876,1,185,0,0.882808," ","integrate((e*x+d)**6/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","x^{2} \left(- \frac{a e^{5}}{c^{3} d^{3}} + \frac{2 e^{3}}{c^{2} d}\right) + x \left(\frac{3 a^{2} e^{6}}{c^{4} d^{4}} - \frac{8 a e^{4}}{c^{3} d^{2}} + \frac{6 e^{2}}{c^{2}}\right) + \frac{- a^{4} e^{8} + 4 a^{3} c d^{2} e^{6} - 6 a^{2} c^{2} d^{4} e^{4} + 4 a c^{3} d^{6} e^{2} - c^{4} d^{8}}{a c^{5} d^{5} e + c^{6} d^{6} x} + \frac{e^{4} x^{3}}{3 c^{2} d^{2}} - \frac{4 e \left(a e^{2} - c d^{2}\right)^{3} \log{\left(a e + c d x \right)}}{c^{5} d^{5}}"," ",0,"x**2*(-a*e**5/(c**3*d**3) + 2*e**3/(c**2*d)) + x*(3*a**2*e**6/(c**4*d**4) - 8*a*e**4/(c**3*d**2) + 6*e**2/c**2) + (-a**4*e**8 + 4*a**3*c*d**2*e**6 - 6*a**2*c**2*d**4*e**4 + 4*a*c**3*d**6*e**2 - c**4*d**8)/(a*c**5*d**5*e + c**6*d**6*x) + e**4*x**3/(3*c**2*d**2) - 4*e*(a*e**2 - c*d**2)**3*log(a*e + c*d*x)/(c**5*d**5)","A",0
1877,1,131,0,0.640389," ","integrate((e*x+d)**5/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","x \left(- \frac{2 a e^{4}}{c^{3} d^{3}} + \frac{3 e^{2}}{c^{2} d}\right) + \frac{a^{3} e^{6} - 3 a^{2} c d^{2} e^{4} + 3 a c^{2} d^{4} e^{2} - c^{3} d^{6}}{a c^{4} d^{4} e + c^{5} d^{5} x} + \frac{e^{3} x^{2}}{2 c^{2} d^{2}} + \frac{3 e \left(a e^{2} - c d^{2}\right)^{2} \log{\left(a e + c d x \right)}}{c^{4} d^{4}}"," ",0,"x*(-2*a*e**4/(c**3*d**3) + 3*e**2/(c**2*d)) + (a**3*e**6 - 3*a**2*c*d**2*e**4 + 3*a*c**2*d**4*e**2 - c**3*d**6)/(a*c**4*d**4*e + c**5*d**5*x) + e**3*x**2/(2*c**2*d**2) + 3*e*(a*e**2 - c*d**2)**2*log(a*e + c*d*x)/(c**4*d**4)","A",0
1878,1,85,0,0.435509," ","integrate((e*x+d)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\frac{- a^{2} e^{4} + 2 a c d^{2} e^{2} - c^{2} d^{4}}{a c^{3} d^{3} e + c^{4} d^{4} x} + \frac{e^{2} x}{c^{2} d^{2}} - \frac{2 e \left(a e^{2} - c d^{2}\right) \log{\left(a e + c d x \right)}}{c^{3} d^{3}}"," ",0,"(-a**2*e**4 + 2*a*c*d**2*e**2 - c**2*d**4)/(a*c**3*d**3*e + c**4*d**4*x) + e**2*x/(c**2*d**2) - 2*e*(a*e**2 - c*d**2)*log(a*e + c*d*x)/(c**3*d**3)","A",0
1879,1,46,0,0.254241," ","integrate((e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\frac{a e^{2} - c d^{2}}{a c^{2} d^{2} e + c^{3} d^{3} x} + \frac{e \log{\left(a e + c d x \right)}}{c^{2} d^{2}}"," ",0,"(a*e**2 - c*d**2)/(a*c**2*d**2*e + c**3*d**3*x) + e*log(a*e + c*d*x)/(c**2*d**2)","A",0
1880,1,17,0,0.192973," ","integrate((e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","- \frac{1}{a c d e + c^{2} d^{2} x}"," ",0,"-1/(a*c*d*e + c**2*d**2*x)","A",0
1881,1,287,0,0.789081," ","integrate((e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\frac{e \log{\left(x + \frac{- \frac{a^{3} e^{7}}{\left(a e^{2} - c d^{2}\right)^{2}} + \frac{3 a^{2} c d^{2} e^{5}}{\left(a e^{2} - c d^{2}\right)^{2}} - \frac{3 a c^{2} d^{4} e^{3}}{\left(a e^{2} - c d^{2}\right)^{2}} + a e^{3} + \frac{c^{3} d^{6} e}{\left(a e^{2} - c d^{2}\right)^{2}} + c d^{2} e}{2 c d e^{2}} \right)}}{\left(a e^{2} - c d^{2}\right)^{2}} - \frac{e \log{\left(x + \frac{\frac{a^{3} e^{7}}{\left(a e^{2} - c d^{2}\right)^{2}} - \frac{3 a^{2} c d^{2} e^{5}}{\left(a e^{2} - c d^{2}\right)^{2}} + \frac{3 a c^{2} d^{4} e^{3}}{\left(a e^{2} - c d^{2}\right)^{2}} + a e^{3} - \frac{c^{3} d^{6} e}{\left(a e^{2} - c d^{2}\right)^{2}} + c d^{2} e}{2 c d e^{2}} \right)}}{\left(a e^{2} - c d^{2}\right)^{2}} + \frac{1}{a^{2} e^{3} - a c d^{2} e + x \left(a c d e^{2} - c^{2} d^{3}\right)}"," ",0,"e*log(x + (-a**3*e**7/(a*e**2 - c*d**2)**2 + 3*a**2*c*d**2*e**5/(a*e**2 - c*d**2)**2 - 3*a*c**2*d**4*e**3/(a*e**2 - c*d**2)**2 + a*e**3 + c**3*d**6*e/(a*e**2 - c*d**2)**2 + c*d**2*e)/(2*c*d*e**2))/(a*e**2 - c*d**2)**2 - e*log(x + (a**3*e**7/(a*e**2 - c*d**2)**2 - 3*a**2*c*d**2*e**5/(a*e**2 - c*d**2)**2 + 3*a*c**2*d**4*e**3/(a*e**2 - c*d**2)**2 + a*e**3 - c**3*d**6*e/(a*e**2 - c*d**2)**2 + c*d**2*e)/(2*c*d*e**2))/(a*e**2 - c*d**2)**2 + 1/(a**2*e**3 - a*c*d**2*e + x*(a*c*d*e**2 - c**2*d**3))","B",0
1882,1,486,0,1.272406," ","integrate(1/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","- \frac{2 c d e \log{\left(x + \frac{- \frac{2 a^{4} c d e^{9}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{8 a^{3} c^{2} d^{3} e^{7}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{12 a^{2} c^{3} d^{5} e^{5}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{8 a c^{4} d^{7} e^{3}}{\left(a e^{2} - c d^{2}\right)^{3}} + 2 a c d e^{3} - \frac{2 c^{5} d^{9} e}{\left(a e^{2} - c d^{2}\right)^{3}} + 2 c^{2} d^{3} e}{4 c^{2} d^{2} e^{2}} \right)}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{2 c d e \log{\left(x + \frac{\frac{2 a^{4} c d e^{9}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{8 a^{3} c^{2} d^{3} e^{7}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{12 a^{2} c^{3} d^{5} e^{5}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{8 a c^{4} d^{7} e^{3}}{\left(a e^{2} - c d^{2}\right)^{3}} + 2 a c d e^{3} + \frac{2 c^{5} d^{9} e}{\left(a e^{2} - c d^{2}\right)^{3}} + 2 c^{2} d^{3} e}{4 c^{2} d^{2} e^{2}} \right)}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{- a e^{2} - c d^{2} - 2 c d e x}{a^{3} d e^{5} - 2 a^{2} c d^{3} e^{3} + a c^{2} d^{5} e + x^{2} \left(a^{2} c d e^{5} - 2 a c^{2} d^{3} e^{3} + c^{3} d^{5} e\right) + x \left(a^{3} e^{6} - a^{2} c d^{2} e^{4} - a c^{2} d^{4} e^{2} + c^{3} d^{6}\right)}"," ",0,"-2*c*d*e*log(x + (-2*a**4*c*d*e**9/(a*e**2 - c*d**2)**3 + 8*a**3*c**2*d**3*e**7/(a*e**2 - c*d**2)**3 - 12*a**2*c**3*d**5*e**5/(a*e**2 - c*d**2)**3 + 8*a*c**4*d**7*e**3/(a*e**2 - c*d**2)**3 + 2*a*c*d*e**3 - 2*c**5*d**9*e/(a*e**2 - c*d**2)**3 + 2*c**2*d**3*e)/(4*c**2*d**2*e**2))/(a*e**2 - c*d**2)**3 + 2*c*d*e*log(x + (2*a**4*c*d*e**9/(a*e**2 - c*d**2)**3 - 8*a**3*c**2*d**3*e**7/(a*e**2 - c*d**2)**3 + 12*a**2*c**3*d**5*e**5/(a*e**2 - c*d**2)**3 - 8*a*c**4*d**7*e**3/(a*e**2 - c*d**2)**3 + 2*a*c*d*e**3 + 2*c**5*d**9*e/(a*e**2 - c*d**2)**3 + 2*c**2*d**3*e)/(4*c**2*d**2*e**2))/(a*e**2 - c*d**2)**3 + (-a*e**2 - c*d**2 - 2*c*d*e*x)/(a**3*d*e**5 - 2*a**2*c*d**3*e**3 + a*c**2*d**5*e + x**2*(a**2*c*d*e**5 - 2*a*c**2*d**3*e**3 + c**3*d**5*e) + x*(a**3*e**6 - a**2*c*d**2*e**4 - a*c**2*d**4*e**2 + c**3*d**6))","B",0
1883,1,734,0,1.944791," ","integrate(1/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\frac{3 c^{2} d^{2} e \log{\left(x + \frac{- \frac{3 a^{5} c^{2} d^{2} e^{11}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{15 a^{4} c^{3} d^{4} e^{9}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{30 a^{3} c^{4} d^{6} e^{7}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{30 a^{2} c^{5} d^{8} e^{5}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{15 a c^{6} d^{10} e^{3}}{\left(a e^{2} - c d^{2}\right)^{4}} + 3 a c^{2} d^{2} e^{3} + \frac{3 c^{7} d^{12} e}{\left(a e^{2} - c d^{2}\right)^{4}} + 3 c^{3} d^{4} e}{6 c^{3} d^{3} e^{2}} \right)}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{3 c^{2} d^{2} e \log{\left(x + \frac{\frac{3 a^{5} c^{2} d^{2} e^{11}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{15 a^{4} c^{3} d^{4} e^{9}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{30 a^{3} c^{4} d^{6} e^{7}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{30 a^{2} c^{5} d^{8} e^{5}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{15 a c^{6} d^{10} e^{3}}{\left(a e^{2} - c d^{2}\right)^{4}} + 3 a c^{2} d^{2} e^{3} - \frac{3 c^{7} d^{12} e}{\left(a e^{2} - c d^{2}\right)^{4}} + 3 c^{3} d^{4} e}{6 c^{3} d^{3} e^{2}} \right)}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{- a^{2} e^{4} + 5 a c d^{2} e^{2} + 2 c^{2} d^{4} + 6 c^{2} d^{2} e^{2} x^{2} + x \left(3 a c d e^{3} + 9 c^{2} d^{3} e\right)}{2 a^{4} d^{2} e^{7} - 6 a^{3} c d^{4} e^{5} + 6 a^{2} c^{2} d^{6} e^{3} - 2 a c^{3} d^{8} e + x^{3} \left(2 a^{3} c d e^{8} - 6 a^{2} c^{2} d^{3} e^{6} + 6 a c^{3} d^{5} e^{4} - 2 c^{4} d^{7} e^{2}\right) + x^{2} \left(2 a^{4} e^{9} - 2 a^{3} c d^{2} e^{7} - 6 a^{2} c^{2} d^{4} e^{5} + 10 a c^{3} d^{6} e^{3} - 4 c^{4} d^{8} e\right) + x \left(4 a^{4} d e^{8} - 10 a^{3} c d^{3} e^{6} + 6 a^{2} c^{2} d^{5} e^{4} + 2 a c^{3} d^{7} e^{2} - 2 c^{4} d^{9}\right)}"," ",0,"3*c**2*d**2*e*log(x + (-3*a**5*c**2*d**2*e**11/(a*e**2 - c*d**2)**4 + 15*a**4*c**3*d**4*e**9/(a*e**2 - c*d**2)**4 - 30*a**3*c**4*d**6*e**7/(a*e**2 - c*d**2)**4 + 30*a**2*c**5*d**8*e**5/(a*e**2 - c*d**2)**4 - 15*a*c**6*d**10*e**3/(a*e**2 - c*d**2)**4 + 3*a*c**2*d**2*e**3 + 3*c**7*d**12*e/(a*e**2 - c*d**2)**4 + 3*c**3*d**4*e)/(6*c**3*d**3*e**2))/(a*e**2 - c*d**2)**4 - 3*c**2*d**2*e*log(x + (3*a**5*c**2*d**2*e**11/(a*e**2 - c*d**2)**4 - 15*a**4*c**3*d**4*e**9/(a*e**2 - c*d**2)**4 + 30*a**3*c**4*d**6*e**7/(a*e**2 - c*d**2)**4 - 30*a**2*c**5*d**8*e**5/(a*e**2 - c*d**2)**4 + 15*a*c**6*d**10*e**3/(a*e**2 - c*d**2)**4 + 3*a*c**2*d**2*e**3 - 3*c**7*d**12*e/(a*e**2 - c*d**2)**4 + 3*c**3*d**4*e)/(6*c**3*d**3*e**2))/(a*e**2 - c*d**2)**4 + (-a**2*e**4 + 5*a*c*d**2*e**2 + 2*c**2*d**4 + 6*c**2*d**2*e**2*x**2 + x*(3*a*c*d*e**3 + 9*c**2*d**3*e))/(2*a**4*d**2*e**7 - 6*a**3*c*d**4*e**5 + 6*a**2*c**2*d**6*e**3 - 2*a*c**3*d**8*e + x**3*(2*a**3*c*d*e**8 - 6*a**2*c**2*d**3*e**6 + 6*a*c**3*d**5*e**4 - 2*c**4*d**7*e**2) + x**2*(2*a**4*e**9 - 2*a**3*c*d**2*e**7 - 6*a**2*c**2*d**4*e**5 + 10*a*c**3*d**6*e**3 - 4*c**4*d**8*e) + x*(4*a**4*d*e**8 - 10*a**3*c*d**3*e**6 + 6*a**2*c**2*d**5*e**4 + 2*a*c**3*d**7*e**2 - 2*c**4*d**9))","B",0
1884,1,996,0,2.843683," ","integrate(1/(e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","- \frac{4 c^{3} d^{3} e \log{\left(x + \frac{- \frac{4 a^{6} c^{3} d^{3} e^{13}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{24 a^{5} c^{4} d^{5} e^{11}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{60 a^{4} c^{5} d^{7} e^{9}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{80 a^{3} c^{6} d^{9} e^{7}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{60 a^{2} c^{7} d^{11} e^{5}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{24 a c^{8} d^{13} e^{3}}{\left(a e^{2} - c d^{2}\right)^{5}} + 4 a c^{3} d^{3} e^{3} - \frac{4 c^{9} d^{15} e}{\left(a e^{2} - c d^{2}\right)^{5}} + 4 c^{4} d^{5} e}{8 c^{4} d^{4} e^{2}} \right)}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{4 c^{3} d^{3} e \log{\left(x + \frac{\frac{4 a^{6} c^{3} d^{3} e^{13}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{24 a^{5} c^{4} d^{5} e^{11}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{60 a^{4} c^{5} d^{7} e^{9}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{80 a^{3} c^{6} d^{9} e^{7}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{60 a^{2} c^{7} d^{11} e^{5}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{24 a c^{8} d^{13} e^{3}}{\left(a e^{2} - c d^{2}\right)^{5}} + 4 a c^{3} d^{3} e^{3} + \frac{4 c^{9} d^{15} e}{\left(a e^{2} - c d^{2}\right)^{5}} + 4 c^{4} d^{5} e}{8 c^{4} d^{4} e^{2}} \right)}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{- a^{3} e^{6} + 5 a^{2} c d^{2} e^{4} - 13 a c^{2} d^{4} e^{2} - 3 c^{3} d^{6} - 12 c^{3} d^{3} e^{3} x^{3} + x^{2} \left(- 6 a c^{2} d^{2} e^{4} - 30 c^{3} d^{4} e^{2}\right) + x \left(2 a^{2} c d e^{5} - 16 a c^{2} d^{3} e^{3} - 22 c^{3} d^{5} e\right)}{3 a^{5} d^{3} e^{9} - 12 a^{4} c d^{5} e^{7} + 18 a^{3} c^{2} d^{7} e^{5} - 12 a^{2} c^{3} d^{9} e^{3} + 3 a c^{4} d^{11} e + x^{4} \left(3 a^{4} c d e^{11} - 12 a^{3} c^{2} d^{3} e^{9} + 18 a^{2} c^{3} d^{5} e^{7} - 12 a c^{4} d^{7} e^{5} + 3 c^{5} d^{9} e^{3}\right) + x^{3} \left(3 a^{5} e^{12} - 3 a^{4} c d^{2} e^{10} - 18 a^{3} c^{2} d^{4} e^{8} + 42 a^{2} c^{3} d^{6} e^{6} - 33 a c^{4} d^{8} e^{4} + 9 c^{5} d^{10} e^{2}\right) + x^{2} \left(9 a^{5} d e^{11} - 27 a^{4} c d^{3} e^{9} + 18 a^{3} c^{2} d^{5} e^{7} + 18 a^{2} c^{3} d^{7} e^{5} - 27 a c^{4} d^{9} e^{3} + 9 c^{5} d^{11} e\right) + x \left(9 a^{5} d^{2} e^{10} - 33 a^{4} c d^{4} e^{8} + 42 a^{3} c^{2} d^{6} e^{6} - 18 a^{2} c^{3} d^{8} e^{4} - 3 a c^{4} d^{10} e^{2} + 3 c^{5} d^{12}\right)}"," ",0,"-4*c**3*d**3*e*log(x + (-4*a**6*c**3*d**3*e**13/(a*e**2 - c*d**2)**5 + 24*a**5*c**4*d**5*e**11/(a*e**2 - c*d**2)**5 - 60*a**4*c**5*d**7*e**9/(a*e**2 - c*d**2)**5 + 80*a**3*c**6*d**9*e**7/(a*e**2 - c*d**2)**5 - 60*a**2*c**7*d**11*e**5/(a*e**2 - c*d**2)**5 + 24*a*c**8*d**13*e**3/(a*e**2 - c*d**2)**5 + 4*a*c**3*d**3*e**3 - 4*c**9*d**15*e/(a*e**2 - c*d**2)**5 + 4*c**4*d**5*e)/(8*c**4*d**4*e**2))/(a*e**2 - c*d**2)**5 + 4*c**3*d**3*e*log(x + (4*a**6*c**3*d**3*e**13/(a*e**2 - c*d**2)**5 - 24*a**5*c**4*d**5*e**11/(a*e**2 - c*d**2)**5 + 60*a**4*c**5*d**7*e**9/(a*e**2 - c*d**2)**5 - 80*a**3*c**6*d**9*e**7/(a*e**2 - c*d**2)**5 + 60*a**2*c**7*d**11*e**5/(a*e**2 - c*d**2)**5 - 24*a*c**8*d**13*e**3/(a*e**2 - c*d**2)**5 + 4*a*c**3*d**3*e**3 + 4*c**9*d**15*e/(a*e**2 - c*d**2)**5 + 4*c**4*d**5*e)/(8*c**4*d**4*e**2))/(a*e**2 - c*d**2)**5 + (-a**3*e**6 + 5*a**2*c*d**2*e**4 - 13*a*c**2*d**4*e**2 - 3*c**3*d**6 - 12*c**3*d**3*e**3*x**3 + x**2*(-6*a*c**2*d**2*e**4 - 30*c**3*d**4*e**2) + x*(2*a**2*c*d*e**5 - 16*a*c**2*d**3*e**3 - 22*c**3*d**5*e))/(3*a**5*d**3*e**9 - 12*a**4*c*d**5*e**7 + 18*a**3*c**2*d**7*e**5 - 12*a**2*c**3*d**9*e**3 + 3*a*c**4*d**11*e + x**4*(3*a**4*c*d*e**11 - 12*a**3*c**2*d**3*e**9 + 18*a**2*c**3*d**5*e**7 - 12*a*c**4*d**7*e**5 + 3*c**5*d**9*e**3) + x**3*(3*a**5*e**12 - 3*a**4*c*d**2*e**10 - 18*a**3*c**2*d**4*e**8 + 42*a**2*c**3*d**6*e**6 - 33*a*c**4*d**8*e**4 + 9*c**5*d**10*e**2) + x**2*(9*a**5*d*e**11 - 27*a**4*c*d**3*e**9 + 18*a**3*c**2*d**5*e**7 + 18*a**2*c**3*d**7*e**5 - 27*a*c**4*d**9*e**3 + 9*c**5*d**11*e) + x*(9*a**5*d**2*e**10 - 33*a**4*c*d**4*e**8 + 42*a**3*c**2*d**6*e**6 - 18*a**2*c**3*d**8*e**4 - 3*a*c**4*d**10*e**2 + 3*c**5*d**12))","B",0
1885,1,386,0,7.529296," ","integrate((e*x+d)**9/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","x^{3} \left(- \frac{a e^{7}}{c^{4} d^{4}} + \frac{2 e^{5}}{c^{3} d^{2}}\right) + x^{2} \left(\frac{3 a^{2} e^{8}}{c^{5} d^{5}} - \frac{9 a e^{6}}{c^{4} d^{3}} + \frac{15 e^{4}}{2 c^{3} d}\right) + x \left(- \frac{10 a^{3} e^{9}}{c^{6} d^{6}} + \frac{36 a^{2} e^{7}}{c^{5} d^{4}} - \frac{45 a e^{5}}{c^{4} d^{2}} + \frac{20 e^{3}}{c^{3}}\right) + \frac{11 a^{6} e^{12} - 54 a^{5} c d^{2} e^{10} + 105 a^{4} c^{2} d^{4} e^{8} - 100 a^{3} c^{3} d^{6} e^{6} + 45 a^{2} c^{4} d^{8} e^{4} - 6 a c^{5} d^{10} e^{2} - c^{6} d^{12} + x \left(12 a^{5} c d e^{11} - 60 a^{4} c^{2} d^{3} e^{9} + 120 a^{3} c^{3} d^{5} e^{7} - 120 a^{2} c^{4} d^{7} e^{5} + 60 a c^{5} d^{9} e^{3} - 12 c^{6} d^{11} e\right)}{2 a^{2} c^{7} d^{7} e^{2} + 4 a c^{8} d^{8} e x + 2 c^{9} d^{9} x^{2}} + \frac{e^{6} x^{4}}{4 c^{3} d^{3}} + \frac{15 e^{2} \left(a e^{2} - c d^{2}\right)^{4} \log{\left(a e + c d x \right)}}{c^{7} d^{7}}"," ",0,"x**3*(-a*e**7/(c**4*d**4) + 2*e**5/(c**3*d**2)) + x**2*(3*a**2*e**8/(c**5*d**5) - 9*a*e**6/(c**4*d**3) + 15*e**4/(2*c**3*d)) + x*(-10*a**3*e**9/(c**6*d**6) + 36*a**2*e**7/(c**5*d**4) - 45*a*e**5/(c**4*d**2) + 20*e**3/c**3) + (11*a**6*e**12 - 54*a**5*c*d**2*e**10 + 105*a**4*c**2*d**4*e**8 - 100*a**3*c**3*d**6*e**6 + 45*a**2*c**4*d**8*e**4 - 6*a*c**5*d**10*e**2 - c**6*d**12 + x*(12*a**5*c*d*e**11 - 60*a**4*c**2*d**3*e**9 + 120*a**3*c**3*d**5*e**7 - 120*a**2*c**4*d**7*e**5 + 60*a*c**5*d**9*e**3 - 12*c**6*d**11*e))/(2*a**2*c**7*d**7*e**2 + 4*a*c**8*d**8*e*x + 2*c**9*d**9*x**2) + e**6*x**4/(4*c**3*d**3) + 15*e**2*(a*e**2 - c*d**2)**4*log(a*e + c*d*x)/(c**7*d**7)","A",0
1886,1,303,0,4.853569," ","integrate((e*x+d)**8/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","x^{2} \left(- \frac{3 a e^{6}}{2 c^{4} d^{4}} + \frac{5 e^{4}}{2 c^{3} d^{2}}\right) + x \left(\frac{6 a^{2} e^{7}}{c^{5} d^{5}} - \frac{15 a e^{5}}{c^{4} d^{3}} + \frac{10 e^{3}}{c^{3} d}\right) + \frac{- 9 a^{5} e^{10} + 35 a^{4} c d^{2} e^{8} - 50 a^{3} c^{2} d^{4} e^{6} + 30 a^{2} c^{3} d^{6} e^{4} - 5 a c^{4} d^{8} e^{2} - c^{5} d^{10} + x \left(- 10 a^{4} c d e^{9} + 40 a^{3} c^{2} d^{3} e^{7} - 60 a^{2} c^{3} d^{5} e^{5} + 40 a c^{4} d^{7} e^{3} - 10 c^{5} d^{9} e\right)}{2 a^{2} c^{6} d^{6} e^{2} + 4 a c^{7} d^{7} e x + 2 c^{8} d^{8} x^{2}} + \frac{e^{5} x^{3}}{3 c^{3} d^{3}} - \frac{10 e^{2} \left(a e^{2} - c d^{2}\right)^{3} \log{\left(a e + c d x \right)}}{c^{6} d^{6}}"," ",0,"x**2*(-3*a*e**6/(2*c**4*d**4) + 5*e**4/(2*c**3*d**2)) + x*(6*a**2*e**7/(c**5*d**5) - 15*a*e**5/(c**4*d**3) + 10*e**3/(c**3*d)) + (-9*a**5*e**10 + 35*a**4*c*d**2*e**8 - 50*a**3*c**2*d**4*e**6 + 30*a**2*c**3*d**6*e**4 - 5*a*c**4*d**8*e**2 - c**5*d**10 + x*(-10*a**4*c*d*e**9 + 40*a**3*c**2*d**3*e**7 - 60*a**2*c**3*d**5*e**5 + 40*a*c**4*d**7*e**3 - 10*c**5*d**9*e))/(2*a**2*c**6*d**6*e**2 + 4*a*c**7*d**7*e*x + 2*c**8*d**8*x**2) + e**5*x**3/(3*c**3*d**3) - 10*e**2*(a*e**2 - c*d**2)**3*log(a*e + c*d*x)/(c**6*d**6)","A",0
1887,1,226,0,2.156837," ","integrate((e*x+d)**7/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","x \left(- \frac{3 a e^{5}}{c^{4} d^{4}} + \frac{4 e^{3}}{c^{3} d^{2}}\right) + \frac{7 a^{4} e^{8} - 20 a^{3} c d^{2} e^{6} + 18 a^{2} c^{2} d^{4} e^{4} - 4 a c^{3} d^{6} e^{2} - c^{4} d^{8} + x \left(8 a^{3} c d e^{7} - 24 a^{2} c^{2} d^{3} e^{5} + 24 a c^{3} d^{5} e^{3} - 8 c^{4} d^{7} e\right)}{2 a^{2} c^{5} d^{5} e^{2} + 4 a c^{6} d^{6} e x + 2 c^{7} d^{7} x^{2}} + \frac{e^{4} x^{2}}{2 c^{3} d^{3}} + \frac{6 e^{2} \left(a e^{2} - c d^{2}\right)^{2} \log{\left(a e + c d x \right)}}{c^{5} d^{5}}"," ",0,"x*(-3*a*e**5/(c**4*d**4) + 4*e**3/(c**3*d**2)) + (7*a**4*e**8 - 20*a**3*c*d**2*e**6 + 18*a**2*c**2*d**4*e**4 - 4*a*c**3*d**6*e**2 - c**4*d**8 + x*(8*a**3*c*d*e**7 - 24*a**2*c**2*d**3*e**5 + 24*a*c**3*d**5*e**3 - 8*c**4*d**7*e))/(2*a**2*c**5*d**5*e**2 + 4*a*c**6*d**6*e*x + 2*c**7*d**7*x**2) + e**4*x**2/(2*c**3*d**3) + 6*e**2*(a*e**2 - c*d**2)**2*log(a*e + c*d*x)/(c**5*d**5)","A",0
1888,1,163,0,1.043355," ","integrate((e*x+d)**6/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\frac{- 5 a^{3} e^{6} + 9 a^{2} c d^{2} e^{4} - 3 a c^{2} d^{4} e^{2} - c^{3} d^{6} + x \left(- 6 a^{2} c d e^{5} + 12 a c^{2} d^{3} e^{3} - 6 c^{3} d^{5} e\right)}{2 a^{2} c^{4} d^{4} e^{2} + 4 a c^{5} d^{5} e x + 2 c^{6} d^{6} x^{2}} + \frac{e^{3} x}{c^{3} d^{3}} - \frac{3 e^{2} \left(a e^{2} - c d^{2}\right) \log{\left(a e + c d x \right)}}{c^{4} d^{4}}"," ",0,"(-5*a**3*e**6 + 9*a**2*c*d**2*e**4 - 3*a*c**2*d**4*e**2 - c**3*d**6 + x*(-6*a**2*c*d*e**5 + 12*a*c**2*d**3*e**3 - 6*c**3*d**5*e))/(2*a**2*c**4*d**4*e**2 + 4*a*c**5*d**5*e*x + 2*c**6*d**6*x**2) + e**3*x/(c**3*d**3) - 3*e**2*(a*e**2 - c*d**2)*log(a*e + c*d*x)/(c**4*d**4)","A",0
1889,1,109,0,0.606941," ","integrate((e*x+d)**5/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\frac{3 a^{2} e^{4} - 2 a c d^{2} e^{2} - c^{2} d^{4} + x \left(4 a c d e^{3} - 4 c^{2} d^{3} e\right)}{2 a^{2} c^{3} d^{3} e^{2} + 4 a c^{4} d^{4} e x + 2 c^{5} d^{5} x^{2}} + \frac{e^{2} \log{\left(a e + c d x \right)}}{c^{3} d^{3}}"," ",0,"(3*a**2*e**4 - 2*a*c*d**2*e**2 - c**2*d**4 + x*(4*a*c*d*e**3 - 4*c**2*d**3*e))/(2*a**2*c**3*d**3*e**2 + 4*a*c**4*d**4*e*x + 2*c**5*d**5*x**2) + e**2*log(a*e + c*d*x)/(c**3*d**3)","A",0
1890,1,60,0,0.381243," ","integrate((e*x+d)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\frac{- a e^{2} - c d^{2} - 2 c d e x}{2 a^{2} c^{2} d^{2} e^{2} + 4 a c^{3} d^{3} e x + 2 c^{4} d^{4} x^{2}}"," ",0,"(-a*e**2 - c*d**2 - 2*c*d*e*x)/(2*a**2*c**2*d**2*e**2 + 4*a*c**3*d**3*e*x + 2*c**4*d**4*x**2)","B",0
1891,1,39,0,0.293668," ","integrate((e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","- \frac{1}{2 a^{2} c d e^{2} + 4 a c^{2} d^{2} e x + 2 c^{3} d^{3} x^{2}}"," ",0,"-1/(2*a**2*c*d*e**2 + 4*a*c**2*d**2*e*x + 2*c**3*d**3*x**2)","B",0
1892,1,457,0,1.259962," ","integrate((e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\frac{e^{2} \log{\left(x + \frac{- \frac{a^{4} e^{10}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{4 a^{3} c d^{2} e^{8}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{6 a^{2} c^{2} d^{4} e^{6}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{4 a c^{3} d^{6} e^{4}}{\left(a e^{2} - c d^{2}\right)^{3}} + a e^{4} - \frac{c^{4} d^{8} e^{2}}{\left(a e^{2} - c d^{2}\right)^{3}} + c d^{2} e^{2}}{2 c d e^{3}} \right)}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{e^{2} \log{\left(x + \frac{\frac{a^{4} e^{10}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{4 a^{3} c d^{2} e^{8}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{6 a^{2} c^{2} d^{4} e^{6}}{\left(a e^{2} - c d^{2}\right)^{3}} - \frac{4 a c^{3} d^{6} e^{4}}{\left(a e^{2} - c d^{2}\right)^{3}} + a e^{4} + \frac{c^{4} d^{8} e^{2}}{\left(a e^{2} - c d^{2}\right)^{3}} + c d^{2} e^{2}}{2 c d e^{3}} \right)}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{3 a e^{2} - c d^{2} + 2 c d e x}{2 a^{4} e^{6} - 4 a^{3} c d^{2} e^{4} + 2 a^{2} c^{2} d^{4} e^{2} + x^{2} \left(2 a^{2} c^{2} d^{2} e^{4} - 4 a c^{3} d^{4} e^{2} + 2 c^{4} d^{6}\right) + x \left(4 a^{3} c d e^{5} - 8 a^{2} c^{2} d^{3} e^{3} + 4 a c^{3} d^{5} e\right)}"," ",0,"e**2*log(x + (-a**4*e**10/(a*e**2 - c*d**2)**3 + 4*a**3*c*d**2*e**8/(a*e**2 - c*d**2)**3 - 6*a**2*c**2*d**4*e**6/(a*e**2 - c*d**2)**3 + 4*a*c**3*d**6*e**4/(a*e**2 - c*d**2)**3 + a*e**4 - c**4*d**8*e**2/(a*e**2 - c*d**2)**3 + c*d**2*e**2)/(2*c*d*e**3))/(a*e**2 - c*d**2)**3 - e**2*log(x + (a**4*e**10/(a*e**2 - c*d**2)**3 - 4*a**3*c*d**2*e**8/(a*e**2 - c*d**2)**3 + 6*a**2*c**2*d**4*e**6/(a*e**2 - c*d**2)**3 - 4*a*c**3*d**6*e**4/(a*e**2 - c*d**2)**3 + a*e**4 + c**4*d**8*e**2/(a*e**2 - c*d**2)**3 + c*d**2*e**2)/(2*c*d*e**3))/(a*e**2 - c*d**2)**3 + (3*a*e**2 - c*d**2 + 2*c*d*e*x)/(2*a**4*e**6 - 4*a**3*c*d**2*e**4 + 2*a**2*c**2*d**4*e**2 + x**2*(2*a**2*c**2*d**2*e**4 - 4*a*c**3*d**4*e**2 + 2*c**4*d**6) + x*(4*a**3*c*d*e**5 - 8*a**2*c**2*d**3*e**3 + 4*a*c**3*d**5*e))","B",0
1893,1,736,0,2.106156," ","integrate((e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","- \frac{3 c d e^{2} \log{\left(x + \frac{- \frac{3 a^{5} c d e^{12}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{15 a^{4} c^{2} d^{3} e^{10}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{30 a^{3} c^{3} d^{5} e^{8}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{30 a^{2} c^{4} d^{7} e^{6}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{15 a c^{5} d^{9} e^{4}}{\left(a e^{2} - c d^{2}\right)^{4}} + 3 a c d e^{4} + \frac{3 c^{6} d^{11} e^{2}}{\left(a e^{2} - c d^{2}\right)^{4}} + 3 c^{2} d^{3} e^{2}}{6 c^{2} d^{2} e^{3}} \right)}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{3 c d e^{2} \log{\left(x + \frac{\frac{3 a^{5} c d e^{12}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{15 a^{4} c^{2} d^{3} e^{10}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{30 a^{3} c^{3} d^{5} e^{8}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{30 a^{2} c^{4} d^{7} e^{6}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{15 a c^{5} d^{9} e^{4}}{\left(a e^{2} - c d^{2}\right)^{4}} + 3 a c d e^{4} - \frac{3 c^{6} d^{11} e^{2}}{\left(a e^{2} - c d^{2}\right)^{4}} + 3 c^{2} d^{3} e^{2}}{6 c^{2} d^{2} e^{3}} \right)}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{- 2 a^{2} e^{4} - 5 a c d^{2} e^{2} + c^{2} d^{4} - 6 c^{2} d^{2} e^{2} x^{2} + x \left(- 9 a c d e^{3} - 3 c^{2} d^{3} e\right)}{2 a^{5} d e^{8} - 6 a^{4} c d^{3} e^{6} + 6 a^{3} c^{2} d^{5} e^{4} - 2 a^{2} c^{3} d^{7} e^{2} + x^{3} \left(2 a^{3} c^{2} d^{2} e^{7} - 6 a^{2} c^{3} d^{4} e^{5} + 6 a c^{4} d^{6} e^{3} - 2 c^{5} d^{8} e\right) + x^{2} \left(4 a^{4} c d e^{8} - 10 a^{3} c^{2} d^{3} e^{6} + 6 a^{2} c^{3} d^{5} e^{4} + 2 a c^{4} d^{7} e^{2} - 2 c^{5} d^{9}\right) + x \left(2 a^{5} e^{9} - 2 a^{4} c d^{2} e^{7} - 6 a^{3} c^{2} d^{4} e^{5} + 10 a^{2} c^{3} d^{6} e^{3} - 4 a c^{4} d^{8} e\right)}"," ",0,"-3*c*d*e**2*log(x + (-3*a**5*c*d*e**12/(a*e**2 - c*d**2)**4 + 15*a**4*c**2*d**3*e**10/(a*e**2 - c*d**2)**4 - 30*a**3*c**3*d**5*e**8/(a*e**2 - c*d**2)**4 + 30*a**2*c**4*d**7*e**6/(a*e**2 - c*d**2)**4 - 15*a*c**5*d**9*e**4/(a*e**2 - c*d**2)**4 + 3*a*c*d*e**4 + 3*c**6*d**11*e**2/(a*e**2 - c*d**2)**4 + 3*c**2*d**3*e**2)/(6*c**2*d**2*e**3))/(a*e**2 - c*d**2)**4 + 3*c*d*e**2*log(x + (3*a**5*c*d*e**12/(a*e**2 - c*d**2)**4 - 15*a**4*c**2*d**3*e**10/(a*e**2 - c*d**2)**4 + 30*a**3*c**3*d**5*e**8/(a*e**2 - c*d**2)**4 - 30*a**2*c**4*d**7*e**6/(a*e**2 - c*d**2)**4 + 15*a*c**5*d**9*e**4/(a*e**2 - c*d**2)**4 + 3*a*c*d*e**4 - 3*c**6*d**11*e**2/(a*e**2 - c*d**2)**4 + 3*c**2*d**3*e**2)/(6*c**2*d**2*e**3))/(a*e**2 - c*d**2)**4 + (-2*a**2*e**4 - 5*a*c*d**2*e**2 + c**2*d**4 - 6*c**2*d**2*e**2*x**2 + x*(-9*a*c*d*e**3 - 3*c**2*d**3*e))/(2*a**5*d*e**8 - 6*a**4*c*d**3*e**6 + 6*a**3*c**2*d**5*e**4 - 2*a**2*c**3*d**7*e**2 + x**3*(2*a**3*c**2*d**2*e**7 - 6*a**2*c**3*d**4*e**5 + 6*a*c**4*d**6*e**3 - 2*c**5*d**8*e) + x**2*(4*a**4*c*d*e**8 - 10*a**3*c**2*d**3*e**6 + 6*a**2*c**3*d**5*e**4 + 2*a*c**4*d**7*e**2 - 2*c**5*d**9) + x*(2*a**5*e**9 - 2*a**4*c*d**2*e**7 - 6*a**3*c**2*d**4*e**5 + 10*a**2*c**3*d**6*e**3 - 4*a*c**4*d**8*e))","B",0
1894,1,1001,0,2.730840," ","integrate(1/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\frac{6 c^{2} d^{2} e^{2} \log{\left(x + \frac{- \frac{6 a^{6} c^{2} d^{2} e^{14}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{36 a^{5} c^{3} d^{4} e^{12}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{90 a^{4} c^{4} d^{6} e^{10}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{120 a^{3} c^{5} d^{8} e^{8}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{90 a^{2} c^{6} d^{10} e^{6}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{36 a c^{7} d^{12} e^{4}}{\left(a e^{2} - c d^{2}\right)^{5}} + 6 a c^{2} d^{2} e^{4} - \frac{6 c^{8} d^{14} e^{2}}{\left(a e^{2} - c d^{2}\right)^{5}} + 6 c^{3} d^{4} e^{2}}{12 c^{3} d^{3} e^{3}} \right)}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{6 c^{2} d^{2} e^{2} \log{\left(x + \frac{\frac{6 a^{6} c^{2} d^{2} e^{14}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{36 a^{5} c^{3} d^{4} e^{12}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{90 a^{4} c^{4} d^{6} e^{10}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{120 a^{3} c^{5} d^{8} e^{8}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{90 a^{2} c^{6} d^{10} e^{6}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{36 a c^{7} d^{12} e^{4}}{\left(a e^{2} - c d^{2}\right)^{5}} + 6 a c^{2} d^{2} e^{4} + \frac{6 c^{8} d^{14} e^{2}}{\left(a e^{2} - c d^{2}\right)^{5}} + 6 c^{3} d^{4} e^{2}}{12 c^{3} d^{3} e^{3}} \right)}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{- a^{3} e^{6} + 7 a^{2} c d^{2} e^{4} + 7 a c^{2} d^{4} e^{2} - c^{3} d^{6} + 12 c^{3} d^{3} e^{3} x^{3} + x^{2} \left(18 a c^{2} d^{2} e^{4} + 18 c^{3} d^{4} e^{2}\right) + x \left(4 a^{2} c d e^{5} + 28 a c^{2} d^{3} e^{3} + 4 c^{3} d^{5} e\right)}{2 a^{6} d^{2} e^{10} - 8 a^{5} c d^{4} e^{8} + 12 a^{4} c^{2} d^{6} e^{6} - 8 a^{3} c^{3} d^{8} e^{4} + 2 a^{2} c^{4} d^{10} e^{2} + x^{4} \left(2 a^{4} c^{2} d^{2} e^{10} - 8 a^{3} c^{3} d^{4} e^{8} + 12 a^{2} c^{4} d^{6} e^{6} - 8 a c^{5} d^{8} e^{4} + 2 c^{6} d^{10} e^{2}\right) + x^{3} \left(4 a^{5} c d e^{11} - 12 a^{4} c^{2} d^{3} e^{9} + 8 a^{3} c^{3} d^{5} e^{7} + 8 a^{2} c^{4} d^{7} e^{5} - 12 a c^{5} d^{9} e^{3} + 4 c^{6} d^{11} e\right) + x^{2} \left(2 a^{6} e^{12} - 18 a^{4} c^{2} d^{4} e^{8} + 32 a^{3} c^{3} d^{6} e^{6} - 18 a^{2} c^{4} d^{8} e^{4} + 2 c^{6} d^{12}\right) + x \left(4 a^{6} d e^{11} - 12 a^{5} c d^{3} e^{9} + 8 a^{4} c^{2} d^{5} e^{7} + 8 a^{3} c^{3} d^{7} e^{5} - 12 a^{2} c^{4} d^{9} e^{3} + 4 a c^{5} d^{11} e\right)}"," ",0,"6*c**2*d**2*e**2*log(x + (-6*a**6*c**2*d**2*e**14/(a*e**2 - c*d**2)**5 + 36*a**5*c**3*d**4*e**12/(a*e**2 - c*d**2)**5 - 90*a**4*c**4*d**6*e**10/(a*e**2 - c*d**2)**5 + 120*a**3*c**5*d**8*e**8/(a*e**2 - c*d**2)**5 - 90*a**2*c**6*d**10*e**6/(a*e**2 - c*d**2)**5 + 36*a*c**7*d**12*e**4/(a*e**2 - c*d**2)**5 + 6*a*c**2*d**2*e**4 - 6*c**8*d**14*e**2/(a*e**2 - c*d**2)**5 + 6*c**3*d**4*e**2)/(12*c**3*d**3*e**3))/(a*e**2 - c*d**2)**5 - 6*c**2*d**2*e**2*log(x + (6*a**6*c**2*d**2*e**14/(a*e**2 - c*d**2)**5 - 36*a**5*c**3*d**4*e**12/(a*e**2 - c*d**2)**5 + 90*a**4*c**4*d**6*e**10/(a*e**2 - c*d**2)**5 - 120*a**3*c**5*d**8*e**8/(a*e**2 - c*d**2)**5 + 90*a**2*c**6*d**10*e**6/(a*e**2 - c*d**2)**5 - 36*a*c**7*d**12*e**4/(a*e**2 - c*d**2)**5 + 6*a*c**2*d**2*e**4 + 6*c**8*d**14*e**2/(a*e**2 - c*d**2)**5 + 6*c**3*d**4*e**2)/(12*c**3*d**3*e**3))/(a*e**2 - c*d**2)**5 + (-a**3*e**6 + 7*a**2*c*d**2*e**4 + 7*a*c**2*d**4*e**2 - c**3*d**6 + 12*c**3*d**3*e**3*x**3 + x**2*(18*a*c**2*d**2*e**4 + 18*c**3*d**4*e**2) + x*(4*a**2*c*d*e**5 + 28*a*c**2*d**3*e**3 + 4*c**3*d**5*e))/(2*a**6*d**2*e**10 - 8*a**5*c*d**4*e**8 + 12*a**4*c**2*d**6*e**6 - 8*a**3*c**3*d**8*e**4 + 2*a**2*c**4*d**10*e**2 + x**4*(2*a**4*c**2*d**2*e**10 - 8*a**3*c**3*d**4*e**8 + 12*a**2*c**4*d**6*e**6 - 8*a*c**5*d**8*e**4 + 2*c**6*d**10*e**2) + x**3*(4*a**5*c*d*e**11 - 12*a**4*c**2*d**3*e**9 + 8*a**3*c**3*d**5*e**7 + 8*a**2*c**4*d**7*e**5 - 12*a*c**5*d**9*e**3 + 4*c**6*d**11*e) + x**2*(2*a**6*e**12 - 18*a**4*c**2*d**4*e**8 + 32*a**3*c**3*d**6*e**6 - 18*a**2*c**4*d**8*e**4 + 2*c**6*d**12) + x*(4*a**6*d*e**11 - 12*a**5*c*d**3*e**9 + 8*a**4*c**2*d**5*e**7 + 8*a**3*c**3*d**7*e**5 - 12*a**2*c**4*d**9*e**3 + 4*a*c**5*d**11*e))","B",0
1895,1,1357,0,4.465886," ","integrate(1/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","- \frac{10 c^{3} d^{3} e^{2} \log{\left(x + \frac{- \frac{10 a^{7} c^{3} d^{3} e^{16}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{70 a^{6} c^{4} d^{5} e^{14}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{210 a^{5} c^{5} d^{7} e^{12}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{350 a^{4} c^{6} d^{9} e^{10}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{350 a^{3} c^{7} d^{11} e^{8}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{210 a^{2} c^{8} d^{13} e^{6}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{70 a c^{9} d^{15} e^{4}}{\left(a e^{2} - c d^{2}\right)^{6}} + 10 a c^{3} d^{3} e^{4} + \frac{10 c^{10} d^{17} e^{2}}{\left(a e^{2} - c d^{2}\right)^{6}} + 10 c^{4} d^{5} e^{2}}{20 c^{4} d^{4} e^{3}} \right)}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{10 c^{3} d^{3} e^{2} \log{\left(x + \frac{\frac{10 a^{7} c^{3} d^{3} e^{16}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{70 a^{6} c^{4} d^{5} e^{14}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{210 a^{5} c^{5} d^{7} e^{12}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{350 a^{4} c^{6} d^{9} e^{10}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{350 a^{3} c^{7} d^{11} e^{8}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{210 a^{2} c^{8} d^{13} e^{6}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{70 a c^{9} d^{15} e^{4}}{\left(a e^{2} - c d^{2}\right)^{6}} + 10 a c^{3} d^{3} e^{4} - \frac{10 c^{10} d^{17} e^{2}}{\left(a e^{2} - c d^{2}\right)^{6}} + 10 c^{4} d^{5} e^{2}}{20 c^{4} d^{4} e^{3}} \right)}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{- 2 a^{4} e^{8} + 13 a^{3} c d^{2} e^{6} - 47 a^{2} c^{2} d^{4} e^{4} - 27 a c^{3} d^{6} e^{2} + 3 c^{4} d^{8} - 60 c^{4} d^{4} e^{4} x^{4} + x^{3} \left(- 90 a c^{3} d^{3} e^{5} - 150 c^{4} d^{5} e^{3}\right) + x^{2} \left(- 20 a^{2} c^{2} d^{2} e^{6} - 230 a c^{3} d^{4} e^{4} - 110 c^{4} d^{6} e^{2}\right) + x \left(5 a^{3} c d e^{7} - 55 a^{2} c^{2} d^{3} e^{5} - 175 a c^{3} d^{5} e^{3} - 15 c^{4} d^{7} e\right)}{6 a^{7} d^{3} e^{12} - 30 a^{6} c d^{5} e^{10} + 60 a^{5} c^{2} d^{7} e^{8} - 60 a^{4} c^{3} d^{9} e^{6} + 30 a^{3} c^{4} d^{11} e^{4} - 6 a^{2} c^{5} d^{13} e^{2} + x^{5} \left(6 a^{5} c^{2} d^{2} e^{13} - 30 a^{4} c^{3} d^{4} e^{11} + 60 a^{3} c^{4} d^{6} e^{9} - 60 a^{2} c^{5} d^{8} e^{7} + 30 a c^{6} d^{10} e^{5} - 6 c^{7} d^{12} e^{3}\right) + x^{4} \left(12 a^{6} c d e^{14} - 42 a^{5} c^{2} d^{3} e^{12} + 30 a^{4} c^{3} d^{5} e^{10} + 60 a^{3} c^{4} d^{7} e^{8} - 120 a^{2} c^{5} d^{9} e^{6} + 78 a c^{6} d^{11} e^{4} - 18 c^{7} d^{13} e^{2}\right) + x^{3} \left(6 a^{7} e^{15} + 6 a^{6} c d^{2} e^{13} - 102 a^{5} c^{2} d^{4} e^{11} + 210 a^{4} c^{3} d^{6} e^{9} - 150 a^{3} c^{4} d^{8} e^{7} - 6 a^{2} c^{5} d^{10} e^{5} + 54 a c^{6} d^{12} e^{3} - 18 c^{7} d^{14} e\right) + x^{2} \left(18 a^{7} d e^{14} - 54 a^{6} c d^{3} e^{12} + 6 a^{5} c^{2} d^{5} e^{10} + 150 a^{4} c^{3} d^{7} e^{8} - 210 a^{3} c^{4} d^{9} e^{6} + 102 a^{2} c^{5} d^{11} e^{4} - 6 a c^{6} d^{13} e^{2} - 6 c^{7} d^{15}\right) + x \left(18 a^{7} d^{2} e^{13} - 78 a^{6} c d^{4} e^{11} + 120 a^{5} c^{2} d^{6} e^{9} - 60 a^{4} c^{3} d^{8} e^{7} - 30 a^{3} c^{4} d^{10} e^{5} + 42 a^{2} c^{5} d^{12} e^{3} - 12 a c^{6} d^{14} e\right)}"," ",0,"-10*c**3*d**3*e**2*log(x + (-10*a**7*c**3*d**3*e**16/(a*e**2 - c*d**2)**6 + 70*a**6*c**4*d**5*e**14/(a*e**2 - c*d**2)**6 - 210*a**5*c**5*d**7*e**12/(a*e**2 - c*d**2)**6 + 350*a**4*c**6*d**9*e**10/(a*e**2 - c*d**2)**6 - 350*a**3*c**7*d**11*e**8/(a*e**2 - c*d**2)**6 + 210*a**2*c**8*d**13*e**6/(a*e**2 - c*d**2)**6 - 70*a*c**9*d**15*e**4/(a*e**2 - c*d**2)**6 + 10*a*c**3*d**3*e**4 + 10*c**10*d**17*e**2/(a*e**2 - c*d**2)**6 + 10*c**4*d**5*e**2)/(20*c**4*d**4*e**3))/(a*e**2 - c*d**2)**6 + 10*c**3*d**3*e**2*log(x + (10*a**7*c**3*d**3*e**16/(a*e**2 - c*d**2)**6 - 70*a**6*c**4*d**5*e**14/(a*e**2 - c*d**2)**6 + 210*a**5*c**5*d**7*e**12/(a*e**2 - c*d**2)**6 - 350*a**4*c**6*d**9*e**10/(a*e**2 - c*d**2)**6 + 350*a**3*c**7*d**11*e**8/(a*e**2 - c*d**2)**6 - 210*a**2*c**8*d**13*e**6/(a*e**2 - c*d**2)**6 + 70*a*c**9*d**15*e**4/(a*e**2 - c*d**2)**6 + 10*a*c**3*d**3*e**4 - 10*c**10*d**17*e**2/(a*e**2 - c*d**2)**6 + 10*c**4*d**5*e**2)/(20*c**4*d**4*e**3))/(a*e**2 - c*d**2)**6 + (-2*a**4*e**8 + 13*a**3*c*d**2*e**6 - 47*a**2*c**2*d**4*e**4 - 27*a*c**3*d**6*e**2 + 3*c**4*d**8 - 60*c**4*d**4*e**4*x**4 + x**3*(-90*a*c**3*d**3*e**5 - 150*c**4*d**5*e**3) + x**2*(-20*a**2*c**2*d**2*e**6 - 230*a*c**3*d**4*e**4 - 110*c**4*d**6*e**2) + x*(5*a**3*c*d*e**7 - 55*a**2*c**2*d**3*e**5 - 175*a*c**3*d**5*e**3 - 15*c**4*d**7*e))/(6*a**7*d**3*e**12 - 30*a**6*c*d**5*e**10 + 60*a**5*c**2*d**7*e**8 - 60*a**4*c**3*d**9*e**6 + 30*a**3*c**4*d**11*e**4 - 6*a**2*c**5*d**13*e**2 + x**5*(6*a**5*c**2*d**2*e**13 - 30*a**4*c**3*d**4*e**11 + 60*a**3*c**4*d**6*e**9 - 60*a**2*c**5*d**8*e**7 + 30*a*c**6*d**10*e**5 - 6*c**7*d**12*e**3) + x**4*(12*a**6*c*d*e**14 - 42*a**5*c**2*d**3*e**12 + 30*a**4*c**3*d**5*e**10 + 60*a**3*c**4*d**7*e**8 - 120*a**2*c**5*d**9*e**6 + 78*a*c**6*d**11*e**4 - 18*c**7*d**13*e**2) + x**3*(6*a**7*e**15 + 6*a**6*c*d**2*e**13 - 102*a**5*c**2*d**4*e**11 + 210*a**4*c**3*d**6*e**9 - 150*a**3*c**4*d**8*e**7 - 6*a**2*c**5*d**10*e**5 + 54*a*c**6*d**12*e**3 - 18*c**7*d**14*e) + x**2*(18*a**7*d*e**14 - 54*a**6*c*d**3*e**12 + 6*a**5*c**2*d**5*e**10 + 150*a**4*c**3*d**7*e**8 - 210*a**3*c**4*d**9*e**6 + 102*a**2*c**5*d**11*e**4 - 6*a*c**6*d**13*e**2 - 6*c**7*d**15) + x*(18*a**7*d**2*e**13 - 78*a**6*c*d**4*e**11 + 120*a**5*c**2*d**6*e**9 - 60*a**4*c**3*d**8*e**7 - 30*a**3*c**4*d**10*e**5 + 42*a**2*c**5*d**12*e**3 - 12*a*c**6*d**14*e))","B",0
1896,1,425,0,102.951139," ","integrate((e*x+d)**10/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","x^{2} \left(- \frac{2 a e^{7}}{c^{5} d^{5}} + \frac{3 e^{5}}{c^{4} d^{3}}\right) + x \left(\frac{10 a^{2} e^{8}}{c^{6} d^{6}} - \frac{24 a e^{6}}{c^{5} d^{4}} + \frac{15 e^{4}}{c^{4} d^{2}}\right) + \frac{- 37 a^{6} e^{12} + 141 a^{5} c d^{2} e^{10} - 195 a^{4} c^{2} d^{4} e^{8} + 110 a^{3} c^{3} d^{6} e^{6} - 15 a^{2} c^{4} d^{8} e^{4} - 3 a c^{5} d^{10} e^{2} - c^{6} d^{12} + x^{2} \left(- 45 a^{4} c^{2} d^{2} e^{10} + 180 a^{3} c^{3} d^{4} e^{8} - 270 a^{2} c^{4} d^{6} e^{6} + 180 a c^{5} d^{8} e^{4} - 45 c^{6} d^{10} e^{2}\right) + x \left(- 81 a^{5} c d e^{11} + 315 a^{4} c^{2} d^{3} e^{9} - 450 a^{3} c^{3} d^{5} e^{7} + 270 a^{2} c^{4} d^{7} e^{5} - 45 a c^{5} d^{9} e^{3} - 9 c^{6} d^{11} e\right)}{3 a^{3} c^{7} d^{7} e^{3} + 9 a^{2} c^{8} d^{8} e^{2} x + 9 a c^{9} d^{9} e x^{2} + 3 c^{10} d^{10} x^{3}} + \frac{e^{6} x^{3}}{3 c^{4} d^{4}} - \frac{20 e^{3} \left(a e^{2} - c d^{2}\right)^{3} \log{\left(a e + c d x \right)}}{c^{7} d^{7}}"," ",0,"x**2*(-2*a*e**7/(c**5*d**5) + 3*e**5/(c**4*d**3)) + x*(10*a**2*e**8/(c**6*d**6) - 24*a*e**6/(c**5*d**4) + 15*e**4/(c**4*d**2)) + (-37*a**6*e**12 + 141*a**5*c*d**2*e**10 - 195*a**4*c**2*d**4*e**8 + 110*a**3*c**3*d**6*e**6 - 15*a**2*c**4*d**8*e**4 - 3*a*c**5*d**10*e**2 - c**6*d**12 + x**2*(-45*a**4*c**2*d**2*e**10 + 180*a**3*c**3*d**4*e**8 - 270*a**2*c**4*d**6*e**6 + 180*a*c**5*d**8*e**4 - 45*c**6*d**10*e**2) + x*(-81*a**5*c*d*e**11 + 315*a**4*c**2*d**3*e**9 - 450*a**3*c**3*d**5*e**7 + 270*a**2*c**4*d**7*e**5 - 45*a*c**5*d**9*e**3 - 9*c**6*d**11*e))/(3*a**3*c**7*d**7*e**3 + 9*a**2*c**8*d**8*e**2*x + 9*a*c**9*d**9*e*x**2 + 3*c**10*d**10*x**3) + e**6*x**3/(3*c**4*d**4) - 20*e**3*(a*e**2 - c*d**2)**3*log(a*e + c*d*x)/(c**7*d**7)","B",0
1897,1,337,0,37.645184," ","integrate((e*x+d)**9/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","x \left(- \frac{4 a e^{6}}{c^{5} d^{5}} + \frac{5 e^{4}}{c^{4} d^{3}}\right) + \frac{47 a^{5} e^{10} - 130 a^{4} c d^{2} e^{8} + 110 a^{3} c^{2} d^{4} e^{6} - 20 a^{2} c^{3} d^{6} e^{4} - 5 a c^{4} d^{8} e^{2} - 2 c^{5} d^{10} + x^{2} \left(60 a^{3} c^{2} d^{2} e^{8} - 180 a^{2} c^{3} d^{4} e^{6} + 180 a c^{4} d^{6} e^{4} - 60 c^{5} d^{8} e^{2}\right) + x \left(105 a^{4} c d e^{9} - 300 a^{3} c^{2} d^{3} e^{7} + 270 a^{2} c^{3} d^{5} e^{5} - 60 a c^{4} d^{7} e^{3} - 15 c^{5} d^{9} e\right)}{6 a^{3} c^{6} d^{6} e^{3} + 18 a^{2} c^{7} d^{7} e^{2} x + 18 a c^{8} d^{8} e x^{2} + 6 c^{9} d^{9} x^{3}} + \frac{e^{5} x^{2}}{2 c^{4} d^{4}} + \frac{10 e^{3} \left(a e^{2} - c d^{2}\right)^{2} \log{\left(a e + c d x \right)}}{c^{6} d^{6}}"," ",0,"x*(-4*a*e**6/(c**5*d**5) + 5*e**4/(c**4*d**3)) + (47*a**5*e**10 - 130*a**4*c*d**2*e**8 + 110*a**3*c**2*d**4*e**6 - 20*a**2*c**3*d**6*e**4 - 5*a*c**4*d**8*e**2 - 2*c**5*d**10 + x**2*(60*a**3*c**2*d**2*e**8 - 180*a**2*c**3*d**4*e**6 + 180*a*c**4*d**6*e**4 - 60*c**5*d**8*e**2) + x*(105*a**4*c*d*e**9 - 300*a**3*c**2*d**3*e**7 + 270*a**2*c**3*d**5*e**5 - 60*a*c**4*d**7*e**3 - 15*c**5*d**9*e))/(6*a**3*c**6*d**6*e**3 + 18*a**2*c**7*d**7*e**2*x + 18*a*c**8*d**8*e*x**2 + 6*c**9*d**9*x**3) + e**5*x**2/(2*c**4*d**4) + 10*e**3*(a*e**2 - c*d**2)**2*log(a*e + c*d*x)/(c**6*d**6)","A",0
1898,1,257,0,9.441033," ","integrate((e*x+d)**8/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","\frac{- 13 a^{4} e^{8} + 22 a^{3} c d^{2} e^{6} - 6 a^{2} c^{2} d^{4} e^{4} - 2 a c^{3} d^{6} e^{2} - c^{4} d^{8} + x^{2} \left(- 18 a^{2} c^{2} d^{2} e^{6} + 36 a c^{3} d^{4} e^{4} - 18 c^{4} d^{6} e^{2}\right) + x \left(- 30 a^{3} c d e^{7} + 54 a^{2} c^{2} d^{3} e^{5} - 18 a c^{3} d^{5} e^{3} - 6 c^{4} d^{7} e\right)}{3 a^{3} c^{5} d^{5} e^{3} + 9 a^{2} c^{6} d^{6} e^{2} x + 9 a c^{7} d^{7} e x^{2} + 3 c^{8} d^{8} x^{3}} + \frac{e^{4} x}{c^{4} d^{4}} - \frac{4 e^{3} \left(a e^{2} - c d^{2}\right) \log{\left(a e + c d x \right)}}{c^{5} d^{5}}"," ",0,"(-13*a**4*e**8 + 22*a**3*c*d**2*e**6 - 6*a**2*c**2*d**4*e**4 - 2*a*c**3*d**6*e**2 - c**4*d**8 + x**2*(-18*a**2*c**2*d**2*e**6 + 36*a*c**3*d**4*e**4 - 18*c**4*d**6*e**2) + x*(-30*a**3*c*d*e**7 + 54*a**2*c**2*d**3*e**5 - 18*a*c**3*d**5*e**3 - 6*c**4*d**7*e))/(3*a**3*c**5*d**5*e**3 + 9*a**2*c**6*d**6*e**2*x + 9*a*c**7*d**7*e*x**2 + 3*c**8*d**8*x**3) + e**4*x/(c**4*d**4) - 4*e**3*(a*e**2 - c*d**2)*log(a*e + c*d*x)/(c**5*d**5)","A",0
1899,1,189,0,2.632529," ","integrate((e*x+d)**7/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","\frac{11 a^{3} e^{6} - 6 a^{2} c d^{2} e^{4} - 3 a c^{2} d^{4} e^{2} - 2 c^{3} d^{6} + x^{2} \left(18 a c^{2} d^{2} e^{4} - 18 c^{3} d^{4} e^{2}\right) + x \left(27 a^{2} c d e^{5} - 18 a c^{2} d^{3} e^{3} - 9 c^{3} d^{5} e\right)}{6 a^{3} c^{4} d^{4} e^{3} + 18 a^{2} c^{5} d^{5} e^{2} x + 18 a c^{6} d^{6} e x^{2} + 6 c^{7} d^{7} x^{3}} + \frac{e^{3} \log{\left(a e + c d x \right)}}{c^{4} d^{4}}"," ",0,"(11*a**3*e**6 - 6*a**2*c*d**2*e**4 - 3*a*c**2*d**4*e**2 - 2*c**3*d**6 + x**2*(18*a*c**2*d**2*e**4 - 18*c**3*d**4*e**2) + x*(27*a**2*c*d*e**5 - 18*a*c**2*d**3*e**3 - 9*c**3*d**5*e))/(6*a**3*c**4*d**4*e**3 + 18*a**2*c**5*d**5*e**2*x + 18*a*c**6*d**6*e*x**2 + 6*c**7*d**7*x**3) + e**3*log(a*e + c*d*x)/(c**4*d**4)","A",0
1900,1,121,0,0.855899," ","integrate((e*x+d)**6/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","\frac{- a^{2} e^{4} - a c d^{2} e^{2} - c^{2} d^{4} - 3 c^{2} d^{2} e^{2} x^{2} + x \left(- 3 a c d e^{3} - 3 c^{2} d^{3} e\right)}{3 a^{3} c^{3} d^{3} e^{3} + 9 a^{2} c^{4} d^{4} e^{2} x + 9 a c^{5} d^{5} e x^{2} + 3 c^{6} d^{6} x^{3}}"," ",0,"(-a**2*e**4 - a*c*d**2*e**2 - c**2*d**4 - 3*c**2*d**2*e**2*x**2 + x*(-3*a*c*d*e**3 - 3*c**2*d**3*e))/(3*a**3*c**3*d**3*e**3 + 9*a**2*c**4*d**4*e**2*x + 9*a*c**5*d**5*e*x**2 + 3*c**6*d**6*x**3)","B",0
1901,1,80,0,0.580024," ","integrate((e*x+d)**5/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","\frac{- a e^{2} - 2 c d^{2} - 3 c d e x}{6 a^{3} c^{2} d^{2} e^{3} + 18 a^{2} c^{3} d^{3} e^{2} x + 18 a c^{4} d^{4} e x^{2} + 6 c^{5} d^{5} x^{3}}"," ",0,"(-a*e**2 - 2*c*d**2 - 3*c*d*e*x)/(6*a**3*c**2*d**2*e**3 + 18*a**2*c**3*d**3*e**2*x + 18*a*c**4*d**4*e*x**2 + 6*c**5*d**5*x**3)","A",0
1902,1,58,0,0.436365," ","integrate((e*x+d)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","- \frac{1}{3 a^{3} c d e^{3} + 9 a^{2} c^{2} d^{2} e^{2} x + 9 a c^{3} d^{3} e x^{2} + 3 c^{4} d^{4} x^{3}}"," ",0,"-1/(3*a**3*c*d*e**3 + 9*a**2*c**2*d**2*e**2*x + 9*a*c**3*d**3*e*x**2 + 3*c**4*d**4*x**3)","B",0
1903,1,668,0,1.903021," ","integrate((e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","\frac{e^{3} \log{\left(x + \frac{- \frac{a^{5} e^{13}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{5 a^{4} c d^{2} e^{11}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{10 a^{3} c^{2} d^{4} e^{9}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{10 a^{2} c^{3} d^{6} e^{7}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{5 a c^{4} d^{8} e^{5}}{\left(a e^{2} - c d^{2}\right)^{4}} + a e^{5} + \frac{c^{5} d^{10} e^{3}}{\left(a e^{2} - c d^{2}\right)^{4}} + c d^{2} e^{3}}{2 c d e^{4}} \right)}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{e^{3} \log{\left(x + \frac{\frac{a^{5} e^{13}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{5 a^{4} c d^{2} e^{11}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{10 a^{3} c^{2} d^{4} e^{9}}{\left(a e^{2} - c d^{2}\right)^{4}} - \frac{10 a^{2} c^{3} d^{6} e^{7}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{5 a c^{4} d^{8} e^{5}}{\left(a e^{2} - c d^{2}\right)^{4}} + a e^{5} - \frac{c^{5} d^{10} e^{3}}{\left(a e^{2} - c d^{2}\right)^{4}} + c d^{2} e^{3}}{2 c d e^{4}} \right)}}{\left(a e^{2} - c d^{2}\right)^{4}} + \frac{11 a^{2} e^{4} - 7 a c d^{2} e^{2} + 2 c^{2} d^{4} + 6 c^{2} d^{2} e^{2} x^{2} + x \left(15 a c d e^{3} - 3 c^{2} d^{3} e\right)}{6 a^{6} e^{9} - 18 a^{5} c d^{2} e^{7} + 18 a^{4} c^{2} d^{4} e^{5} - 6 a^{3} c^{3} d^{6} e^{3} + x^{3} \left(6 a^{3} c^{3} d^{3} e^{6} - 18 a^{2} c^{4} d^{5} e^{4} + 18 a c^{5} d^{7} e^{2} - 6 c^{6} d^{9}\right) + x^{2} \left(18 a^{4} c^{2} d^{2} e^{7} - 54 a^{3} c^{3} d^{4} e^{5} + 54 a^{2} c^{4} d^{6} e^{3} - 18 a c^{5} d^{8} e\right) + x \left(18 a^{5} c d e^{8} - 54 a^{4} c^{2} d^{3} e^{6} + 54 a^{3} c^{3} d^{5} e^{4} - 18 a^{2} c^{4} d^{7} e^{2}\right)}"," ",0,"e**3*log(x + (-a**5*e**13/(a*e**2 - c*d**2)**4 + 5*a**4*c*d**2*e**11/(a*e**2 - c*d**2)**4 - 10*a**3*c**2*d**4*e**9/(a*e**2 - c*d**2)**4 + 10*a**2*c**3*d**6*e**7/(a*e**2 - c*d**2)**4 - 5*a*c**4*d**8*e**5/(a*e**2 - c*d**2)**4 + a*e**5 + c**5*d**10*e**3/(a*e**2 - c*d**2)**4 + c*d**2*e**3)/(2*c*d*e**4))/(a*e**2 - c*d**2)**4 - e**3*log(x + (a**5*e**13/(a*e**2 - c*d**2)**4 - 5*a**4*c*d**2*e**11/(a*e**2 - c*d**2)**4 + 10*a**3*c**2*d**4*e**9/(a*e**2 - c*d**2)**4 - 10*a**2*c**3*d**6*e**7/(a*e**2 - c*d**2)**4 + 5*a*c**4*d**8*e**5/(a*e**2 - c*d**2)**4 + a*e**5 - c**5*d**10*e**3/(a*e**2 - c*d**2)**4 + c*d**2*e**3)/(2*c*d*e**4))/(a*e**2 - c*d**2)**4 + (11*a**2*e**4 - 7*a*c*d**2*e**2 + 2*c**2*d**4 + 6*c**2*d**2*e**2*x**2 + x*(15*a*c*d*e**3 - 3*c**2*d**3*e))/(6*a**6*e**9 - 18*a**5*c*d**2*e**7 + 18*a**4*c**2*d**4*e**5 - 6*a**3*c**3*d**6*e**3 + x**3*(6*a**3*c**3*d**3*e**6 - 18*a**2*c**4*d**5*e**4 + 18*a*c**5*d**7*e**2 - 6*c**6*d**9) + x**2*(18*a**4*c**2*d**2*e**7 - 54*a**3*c**3*d**4*e**5 + 54*a**2*c**4*d**6*e**3 - 18*a*c**5*d**8*e) + x*(18*a**5*c*d*e**8 - 54*a**4*c**2*d**3*e**6 + 54*a**3*c**3*d**5*e**4 - 18*a**2*c**4*d**7*e**2))","B",0
1904,1,1006,0,2.963545," ","integrate((e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","- \frac{4 c d e^{3} \log{\left(x + \frac{- \frac{4 a^{6} c d e^{15}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{24 a^{5} c^{2} d^{3} e^{13}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{60 a^{4} c^{3} d^{5} e^{11}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{80 a^{3} c^{4} d^{7} e^{9}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{60 a^{2} c^{5} d^{9} e^{7}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{24 a c^{6} d^{11} e^{5}}{\left(a e^{2} - c d^{2}\right)^{5}} + 4 a c d e^{5} - \frac{4 c^{7} d^{13} e^{3}}{\left(a e^{2} - c d^{2}\right)^{5}} + 4 c^{2} d^{3} e^{3}}{8 c^{2} d^{2} e^{4}} \right)}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{4 c d e^{3} \log{\left(x + \frac{\frac{4 a^{6} c d e^{15}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{24 a^{5} c^{2} d^{3} e^{13}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{60 a^{4} c^{3} d^{5} e^{11}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{80 a^{3} c^{4} d^{7} e^{9}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{60 a^{2} c^{5} d^{9} e^{7}}{\left(a e^{2} - c d^{2}\right)^{5}} - \frac{24 a c^{6} d^{11} e^{5}}{\left(a e^{2} - c d^{2}\right)^{5}} + 4 a c d e^{5} + \frac{4 c^{7} d^{13} e^{3}}{\left(a e^{2} - c d^{2}\right)^{5}} + 4 c^{2} d^{3} e^{3}}{8 c^{2} d^{2} e^{4}} \right)}}{\left(a e^{2} - c d^{2}\right)^{5}} + \frac{- 3 a^{3} e^{6} - 13 a^{2} c d^{2} e^{4} + 5 a c^{2} d^{4} e^{2} - c^{3} d^{6} - 12 c^{3} d^{3} e^{3} x^{3} + x^{2} \left(- 30 a c^{2} d^{2} e^{4} - 6 c^{3} d^{4} e^{2}\right) + x \left(- 22 a^{2} c d e^{5} - 16 a c^{2} d^{3} e^{3} + 2 c^{3} d^{5} e\right)}{3 a^{7} d e^{11} - 12 a^{6} c d^{3} e^{9} + 18 a^{5} c^{2} d^{5} e^{7} - 12 a^{4} c^{3} d^{7} e^{5} + 3 a^{3} c^{4} d^{9} e^{3} + x^{4} \left(3 a^{4} c^{3} d^{3} e^{9} - 12 a^{3} c^{4} d^{5} e^{7} + 18 a^{2} c^{5} d^{7} e^{5} - 12 a c^{6} d^{9} e^{3} + 3 c^{7} d^{11} e\right) + x^{3} \left(9 a^{5} c^{2} d^{2} e^{10} - 33 a^{4} c^{3} d^{4} e^{8} + 42 a^{3} c^{4} d^{6} e^{6} - 18 a^{2} c^{5} d^{8} e^{4} - 3 a c^{6} d^{10} e^{2} + 3 c^{7} d^{12}\right) + x^{2} \left(9 a^{6} c d e^{11} - 27 a^{5} c^{2} d^{3} e^{9} + 18 a^{4} c^{3} d^{5} e^{7} + 18 a^{3} c^{4} d^{7} e^{5} - 27 a^{2} c^{5} d^{9} e^{3} + 9 a c^{6} d^{11} e\right) + x \left(3 a^{7} e^{12} - 3 a^{6} c d^{2} e^{10} - 18 a^{5} c^{2} d^{4} e^{8} + 42 a^{4} c^{3} d^{6} e^{6} - 33 a^{3} c^{4} d^{8} e^{4} + 9 a^{2} c^{5} d^{10} e^{2}\right)}"," ",0,"-4*c*d*e**3*log(x + (-4*a**6*c*d*e**15/(a*e**2 - c*d**2)**5 + 24*a**5*c**2*d**3*e**13/(a*e**2 - c*d**2)**5 - 60*a**4*c**3*d**5*e**11/(a*e**2 - c*d**2)**5 + 80*a**3*c**4*d**7*e**9/(a*e**2 - c*d**2)**5 - 60*a**2*c**5*d**9*e**7/(a*e**2 - c*d**2)**5 + 24*a*c**6*d**11*e**5/(a*e**2 - c*d**2)**5 + 4*a*c*d*e**5 - 4*c**7*d**13*e**3/(a*e**2 - c*d**2)**5 + 4*c**2*d**3*e**3)/(8*c**2*d**2*e**4))/(a*e**2 - c*d**2)**5 + 4*c*d*e**3*log(x + (4*a**6*c*d*e**15/(a*e**2 - c*d**2)**5 - 24*a**5*c**2*d**3*e**13/(a*e**2 - c*d**2)**5 + 60*a**4*c**3*d**5*e**11/(a*e**2 - c*d**2)**5 - 80*a**3*c**4*d**7*e**9/(a*e**2 - c*d**2)**5 + 60*a**2*c**5*d**9*e**7/(a*e**2 - c*d**2)**5 - 24*a*c**6*d**11*e**5/(a*e**2 - c*d**2)**5 + 4*a*c*d*e**5 + 4*c**7*d**13*e**3/(a*e**2 - c*d**2)**5 + 4*c**2*d**3*e**3)/(8*c**2*d**2*e**4))/(a*e**2 - c*d**2)**5 + (-3*a**3*e**6 - 13*a**2*c*d**2*e**4 + 5*a*c**2*d**4*e**2 - c**3*d**6 - 12*c**3*d**3*e**3*x**3 + x**2*(-30*a*c**2*d**2*e**4 - 6*c**3*d**4*e**2) + x*(-22*a**2*c*d*e**5 - 16*a*c**2*d**3*e**3 + 2*c**3*d**5*e))/(3*a**7*d*e**11 - 12*a**6*c*d**3*e**9 + 18*a**5*c**2*d**5*e**7 - 12*a**4*c**3*d**7*e**5 + 3*a**3*c**4*d**9*e**3 + x**4*(3*a**4*c**3*d**3*e**9 - 12*a**3*c**4*d**5*e**7 + 18*a**2*c**5*d**7*e**5 - 12*a*c**6*d**9*e**3 + 3*c**7*d**11*e) + x**3*(9*a**5*c**2*d**2*e**10 - 33*a**4*c**3*d**4*e**8 + 42*a**3*c**4*d**6*e**6 - 18*a**2*c**5*d**8*e**4 - 3*a*c**6*d**10*e**2 + 3*c**7*d**12) + x**2*(9*a**6*c*d*e**11 - 27*a**5*c**2*d**3*e**9 + 18*a**4*c**3*d**5*e**7 + 18*a**3*c**4*d**7*e**5 - 27*a**2*c**5*d**9*e**3 + 9*a*c**6*d**11*e) + x*(3*a**7*e**12 - 3*a**6*c*d**2*e**10 - 18*a**5*c**2*d**4*e**8 + 42*a**4*c**3*d**6*e**6 - 33*a**3*c**4*d**8*e**4 + 9*a**2*c**5*d**10*e**2))","B",0
1905,1,1363,0,4.788644," ","integrate((e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","\frac{10 c^{2} d^{2} e^{3} \log{\left(x + \frac{- \frac{10 a^{7} c^{2} d^{2} e^{17}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{70 a^{6} c^{3} d^{4} e^{15}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{210 a^{5} c^{4} d^{6} e^{13}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{350 a^{4} c^{5} d^{8} e^{11}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{350 a^{3} c^{6} d^{10} e^{9}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{210 a^{2} c^{7} d^{12} e^{7}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{70 a c^{8} d^{14} e^{5}}{\left(a e^{2} - c d^{2}\right)^{6}} + 10 a c^{2} d^{2} e^{5} + \frac{10 c^{9} d^{16} e^{3}}{\left(a e^{2} - c d^{2}\right)^{6}} + 10 c^{3} d^{4} e^{3}}{20 c^{3} d^{3} e^{4}} \right)}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{10 c^{2} d^{2} e^{3} \log{\left(x + \frac{\frac{10 a^{7} c^{2} d^{2} e^{17}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{70 a^{6} c^{3} d^{4} e^{15}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{210 a^{5} c^{4} d^{6} e^{13}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{350 a^{4} c^{5} d^{8} e^{11}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{350 a^{3} c^{6} d^{10} e^{9}}{\left(a e^{2} - c d^{2}\right)^{6}} - \frac{210 a^{2} c^{7} d^{12} e^{7}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{70 a c^{8} d^{14} e^{5}}{\left(a e^{2} - c d^{2}\right)^{6}} + 10 a c^{2} d^{2} e^{5} - \frac{10 c^{9} d^{16} e^{3}}{\left(a e^{2} - c d^{2}\right)^{6}} + 10 c^{3} d^{4} e^{3}}{20 c^{3} d^{3} e^{4}} \right)}}{\left(a e^{2} - c d^{2}\right)^{6}} + \frac{- 3 a^{4} e^{8} + 27 a^{3} c d^{2} e^{6} + 47 a^{2} c^{2} d^{4} e^{4} - 13 a c^{3} d^{6} e^{2} + 2 c^{4} d^{8} + 60 c^{4} d^{4} e^{4} x^{4} + x^{3} \left(150 a c^{3} d^{3} e^{5} + 90 c^{4} d^{5} e^{3}\right) + x^{2} \left(110 a^{2} c^{2} d^{2} e^{6} + 230 a c^{3} d^{4} e^{4} + 20 c^{4} d^{6} e^{2}\right) + x \left(15 a^{3} c d e^{7} + 175 a^{2} c^{2} d^{3} e^{5} + 55 a c^{3} d^{5} e^{3} - 5 c^{4} d^{7} e\right)}{6 a^{8} d^{2} e^{13} - 30 a^{7} c d^{4} e^{11} + 60 a^{6} c^{2} d^{6} e^{9} - 60 a^{5} c^{3} d^{8} e^{7} + 30 a^{4} c^{4} d^{10} e^{5} - 6 a^{3} c^{5} d^{12} e^{3} + x^{5} \left(6 a^{5} c^{3} d^{3} e^{12} - 30 a^{4} c^{4} d^{5} e^{10} + 60 a^{3} c^{5} d^{7} e^{8} - 60 a^{2} c^{6} d^{9} e^{6} + 30 a c^{7} d^{11} e^{4} - 6 c^{8} d^{13} e^{2}\right) + x^{4} \left(18 a^{6} c^{2} d^{2} e^{13} - 78 a^{5} c^{3} d^{4} e^{11} + 120 a^{4} c^{4} d^{6} e^{9} - 60 a^{3} c^{5} d^{8} e^{7} - 30 a^{2} c^{6} d^{10} e^{5} + 42 a c^{7} d^{12} e^{3} - 12 c^{8} d^{14} e\right) + x^{3} \left(18 a^{7} c d e^{14} - 54 a^{6} c^{2} d^{3} e^{12} + 6 a^{5} c^{3} d^{5} e^{10} + 150 a^{4} c^{4} d^{7} e^{8} - 210 a^{3} c^{5} d^{9} e^{6} + 102 a^{2} c^{6} d^{11} e^{4} - 6 a c^{7} d^{13} e^{2} - 6 c^{8} d^{15}\right) + x^{2} \left(6 a^{8} e^{15} + 6 a^{7} c d^{2} e^{13} - 102 a^{6} c^{2} d^{4} e^{11} + 210 a^{5} c^{3} d^{6} e^{9} - 150 a^{4} c^{4} d^{8} e^{7} - 6 a^{3} c^{5} d^{10} e^{5} + 54 a^{2} c^{6} d^{12} e^{3} - 18 a c^{7} d^{14} e\right) + x \left(12 a^{8} d e^{14} - 42 a^{7} c d^{3} e^{12} + 30 a^{6} c^{2} d^{5} e^{10} + 60 a^{5} c^{3} d^{7} e^{8} - 120 a^{4} c^{4} d^{9} e^{6} + 78 a^{3} c^{5} d^{11} e^{4} - 18 a^{2} c^{6} d^{13} e^{2}\right)}"," ",0,"10*c**2*d**2*e**3*log(x + (-10*a**7*c**2*d**2*e**17/(a*e**2 - c*d**2)**6 + 70*a**6*c**3*d**4*e**15/(a*e**2 - c*d**2)**6 - 210*a**5*c**4*d**6*e**13/(a*e**2 - c*d**2)**6 + 350*a**4*c**5*d**8*e**11/(a*e**2 - c*d**2)**6 - 350*a**3*c**6*d**10*e**9/(a*e**2 - c*d**2)**6 + 210*a**2*c**7*d**12*e**7/(a*e**2 - c*d**2)**6 - 70*a*c**8*d**14*e**5/(a*e**2 - c*d**2)**6 + 10*a*c**2*d**2*e**5 + 10*c**9*d**16*e**3/(a*e**2 - c*d**2)**6 + 10*c**3*d**4*e**3)/(20*c**3*d**3*e**4))/(a*e**2 - c*d**2)**6 - 10*c**2*d**2*e**3*log(x + (10*a**7*c**2*d**2*e**17/(a*e**2 - c*d**2)**6 - 70*a**6*c**3*d**4*e**15/(a*e**2 - c*d**2)**6 + 210*a**5*c**4*d**6*e**13/(a*e**2 - c*d**2)**6 - 350*a**4*c**5*d**8*e**11/(a*e**2 - c*d**2)**6 + 350*a**3*c**6*d**10*e**9/(a*e**2 - c*d**2)**6 - 210*a**2*c**7*d**12*e**7/(a*e**2 - c*d**2)**6 + 70*a*c**8*d**14*e**5/(a*e**2 - c*d**2)**6 + 10*a*c**2*d**2*e**5 - 10*c**9*d**16*e**3/(a*e**2 - c*d**2)**6 + 10*c**3*d**4*e**3)/(20*c**3*d**3*e**4))/(a*e**2 - c*d**2)**6 + (-3*a**4*e**8 + 27*a**3*c*d**2*e**6 + 47*a**2*c**2*d**4*e**4 - 13*a*c**3*d**6*e**2 + 2*c**4*d**8 + 60*c**4*d**4*e**4*x**4 + x**3*(150*a*c**3*d**3*e**5 + 90*c**4*d**5*e**3) + x**2*(110*a**2*c**2*d**2*e**6 + 230*a*c**3*d**4*e**4 + 20*c**4*d**6*e**2) + x*(15*a**3*c*d*e**7 + 175*a**2*c**2*d**3*e**5 + 55*a*c**3*d**5*e**3 - 5*c**4*d**7*e))/(6*a**8*d**2*e**13 - 30*a**7*c*d**4*e**11 + 60*a**6*c**2*d**6*e**9 - 60*a**5*c**3*d**8*e**7 + 30*a**4*c**4*d**10*e**5 - 6*a**3*c**5*d**12*e**3 + x**5*(6*a**5*c**3*d**3*e**12 - 30*a**4*c**4*d**5*e**10 + 60*a**3*c**5*d**7*e**8 - 60*a**2*c**6*d**9*e**6 + 30*a*c**7*d**11*e**4 - 6*c**8*d**13*e**2) + x**4*(18*a**6*c**2*d**2*e**13 - 78*a**5*c**3*d**4*e**11 + 120*a**4*c**4*d**6*e**9 - 60*a**3*c**5*d**8*e**7 - 30*a**2*c**6*d**10*e**5 + 42*a*c**7*d**12*e**3 - 12*c**8*d**14*e) + x**3*(18*a**7*c*d*e**14 - 54*a**6*c**2*d**3*e**12 + 6*a**5*c**3*d**5*e**10 + 150*a**4*c**4*d**7*e**8 - 210*a**3*c**5*d**9*e**6 + 102*a**2*c**6*d**11*e**4 - 6*a*c**7*d**13*e**2 - 6*c**8*d**15) + x**2*(6*a**8*e**15 + 6*a**7*c*d**2*e**13 - 102*a**6*c**2*d**4*e**11 + 210*a**5*c**3*d**6*e**9 - 150*a**4*c**4*d**8*e**7 - 6*a**3*c**5*d**10*e**5 + 54*a**2*c**6*d**12*e**3 - 18*a*c**7*d**14*e) + x*(12*a**8*d*e**14 - 42*a**7*c*d**3*e**12 + 30*a**6*c**2*d**5*e**10 + 60*a**5*c**3*d**7*e**8 - 120*a**4*c**4*d**9*e**6 + 78*a**3*c**5*d**11*e**4 - 18*a**2*c**6*d**13*e**2))","B",0
1906,1,1748,0,6.631509," ","integrate(1/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","- \frac{20 c^{3} d^{3} e^{3} \log{\left(x + \frac{- \frac{20 a^{8} c^{3} d^{3} e^{19}}{\left(a e^{2} - c d^{2}\right)^{7}} + \frac{160 a^{7} c^{4} d^{5} e^{17}}{\left(a e^{2} - c d^{2}\right)^{7}} - \frac{560 a^{6} c^{5} d^{7} e^{15}}{\left(a e^{2} - c d^{2}\right)^{7}} + \frac{1120 a^{5} c^{6} d^{9} e^{13}}{\left(a e^{2} - c d^{2}\right)^{7}} - \frac{1400 a^{4} c^{7} d^{11} e^{11}}{\left(a e^{2} - c d^{2}\right)^{7}} + \frac{1120 a^{3} c^{8} d^{13} e^{9}}{\left(a e^{2} - c d^{2}\right)^{7}} - \frac{560 a^{2} c^{9} d^{15} e^{7}}{\left(a e^{2} - c d^{2}\right)^{7}} + \frac{160 a c^{10} d^{17} e^{5}}{\left(a e^{2} - c d^{2}\right)^{7}} + 20 a c^{3} d^{3} e^{5} - \frac{20 c^{11} d^{19} e^{3}}{\left(a e^{2} - c d^{2}\right)^{7}} + 20 c^{4} d^{5} e^{3}}{40 c^{4} d^{4} e^{4}} \right)}}{\left(a e^{2} - c d^{2}\right)^{7}} + \frac{20 c^{3} d^{3} e^{3} \log{\left(x + \frac{\frac{20 a^{8} c^{3} d^{3} e^{19}}{\left(a e^{2} - c d^{2}\right)^{7}} - \frac{160 a^{7} c^{4} d^{5} e^{17}}{\left(a e^{2} - c d^{2}\right)^{7}} + \frac{560 a^{6} c^{5} d^{7} e^{15}}{\left(a e^{2} - c d^{2}\right)^{7}} - \frac{1120 a^{5} c^{6} d^{9} e^{13}}{\left(a e^{2} - c d^{2}\right)^{7}} + \frac{1400 a^{4} c^{7} d^{11} e^{11}}{\left(a e^{2} - c d^{2}\right)^{7}} - \frac{1120 a^{3} c^{8} d^{13} e^{9}}{\left(a e^{2} - c d^{2}\right)^{7}} + \frac{560 a^{2} c^{9} d^{15} e^{7}}{\left(a e^{2} - c d^{2}\right)^{7}} - \frac{160 a c^{10} d^{17} e^{5}}{\left(a e^{2} - c d^{2}\right)^{7}} + 20 a c^{3} d^{3} e^{5} + \frac{20 c^{11} d^{19} e^{3}}{\left(a e^{2} - c d^{2}\right)^{7}} + 20 c^{4} d^{5} e^{3}}{40 c^{4} d^{4} e^{4}} \right)}}{\left(a e^{2} - c d^{2}\right)^{7}} + \frac{- a^{5} e^{10} + 8 a^{4} c d^{2} e^{8} - 37 a^{3} c^{2} d^{4} e^{6} - 37 a^{2} c^{3} d^{6} e^{4} + 8 a c^{4} d^{8} e^{2} - c^{5} d^{10} - 60 c^{5} d^{5} e^{5} x^{5} + x^{4} \left(- 150 a c^{4} d^{4} e^{6} - 150 c^{5} d^{6} e^{4}\right) + x^{3} \left(- 110 a^{2} c^{3} d^{3} e^{7} - 380 a c^{4} d^{5} e^{5} - 110 c^{5} d^{7} e^{3}\right) + x^{2} \left(- 15 a^{3} c^{2} d^{2} e^{8} - 285 a^{2} c^{3} d^{4} e^{6} - 285 a c^{4} d^{6} e^{4} - 15 c^{5} d^{8} e^{2}\right) + x \left(3 a^{4} c d e^{9} - 42 a^{3} c^{2} d^{3} e^{7} - 222 a^{2} c^{3} d^{5} e^{5} - 42 a c^{4} d^{7} e^{3} + 3 c^{5} d^{9} e\right)}{3 a^{9} d^{3} e^{15} - 18 a^{8} c d^{5} e^{13} + 45 a^{7} c^{2} d^{7} e^{11} - 60 a^{6} c^{3} d^{9} e^{9} + 45 a^{5} c^{4} d^{11} e^{7} - 18 a^{4} c^{5} d^{13} e^{5} + 3 a^{3} c^{6} d^{15} e^{3} + x^{6} \left(3 a^{6} c^{3} d^{3} e^{15} - 18 a^{5} c^{4} d^{5} e^{13} + 45 a^{4} c^{5} d^{7} e^{11} - 60 a^{3} c^{6} d^{9} e^{9} + 45 a^{2} c^{7} d^{11} e^{7} - 18 a c^{8} d^{13} e^{5} + 3 c^{9} d^{15} e^{3}\right) + x^{5} \left(9 a^{7} c^{2} d^{2} e^{16} - 45 a^{6} c^{3} d^{4} e^{14} + 81 a^{5} c^{4} d^{6} e^{12} - 45 a^{4} c^{5} d^{8} e^{10} - 45 a^{3} c^{6} d^{10} e^{8} + 81 a^{2} c^{7} d^{12} e^{6} - 45 a c^{8} d^{14} e^{4} + 9 c^{9} d^{16} e^{2}\right) + x^{4} \left(9 a^{8} c d e^{17} - 27 a^{7} c^{2} d^{3} e^{15} - 18 a^{6} c^{3} d^{5} e^{13} + 171 a^{5} c^{4} d^{7} e^{11} - 270 a^{4} c^{5} d^{9} e^{9} + 171 a^{3} c^{6} d^{11} e^{7} - 18 a^{2} c^{7} d^{13} e^{5} - 27 a c^{8} d^{15} e^{3} + 9 c^{9} d^{17} e\right) + x^{3} \left(3 a^{9} e^{18} + 9 a^{8} c d^{2} e^{16} - 90 a^{7} c^{2} d^{4} e^{14} + 186 a^{6} c^{3} d^{6} e^{12} - 108 a^{5} c^{4} d^{8} e^{10} - 108 a^{4} c^{5} d^{10} e^{8} + 186 a^{3} c^{6} d^{12} e^{6} - 90 a^{2} c^{7} d^{14} e^{4} + 9 a c^{8} d^{16} e^{2} + 3 c^{9} d^{18}\right) + x^{2} \left(9 a^{9} d e^{17} - 27 a^{8} c d^{3} e^{15} - 18 a^{7} c^{2} d^{5} e^{13} + 171 a^{6} c^{3} d^{7} e^{11} - 270 a^{5} c^{4} d^{9} e^{9} + 171 a^{4} c^{5} d^{11} e^{7} - 18 a^{3} c^{6} d^{13} e^{5} - 27 a^{2} c^{7} d^{15} e^{3} + 9 a c^{8} d^{17} e\right) + x \left(9 a^{9} d^{2} e^{16} - 45 a^{8} c d^{4} e^{14} + 81 a^{7} c^{2} d^{6} e^{12} - 45 a^{6} c^{3} d^{8} e^{10} - 45 a^{5} c^{4} d^{10} e^{8} + 81 a^{4} c^{5} d^{12} e^{6} - 45 a^{3} c^{6} d^{14} e^{4} + 9 a^{2} c^{7} d^{16} e^{2}\right)}"," ",0,"-20*c**3*d**3*e**3*log(x + (-20*a**8*c**3*d**3*e**19/(a*e**2 - c*d**2)**7 + 160*a**7*c**4*d**5*e**17/(a*e**2 - c*d**2)**7 - 560*a**6*c**5*d**7*e**15/(a*e**2 - c*d**2)**7 + 1120*a**5*c**6*d**9*e**13/(a*e**2 - c*d**2)**7 - 1400*a**4*c**7*d**11*e**11/(a*e**2 - c*d**2)**7 + 1120*a**3*c**8*d**13*e**9/(a*e**2 - c*d**2)**7 - 560*a**2*c**9*d**15*e**7/(a*e**2 - c*d**2)**7 + 160*a*c**10*d**17*e**5/(a*e**2 - c*d**2)**7 + 20*a*c**3*d**3*e**5 - 20*c**11*d**19*e**3/(a*e**2 - c*d**2)**7 + 20*c**4*d**5*e**3)/(40*c**4*d**4*e**4))/(a*e**2 - c*d**2)**7 + 20*c**3*d**3*e**3*log(x + (20*a**8*c**3*d**3*e**19/(a*e**2 - c*d**2)**7 - 160*a**7*c**4*d**5*e**17/(a*e**2 - c*d**2)**7 + 560*a**6*c**5*d**7*e**15/(a*e**2 - c*d**2)**7 - 1120*a**5*c**6*d**9*e**13/(a*e**2 - c*d**2)**7 + 1400*a**4*c**7*d**11*e**11/(a*e**2 - c*d**2)**7 - 1120*a**3*c**8*d**13*e**9/(a*e**2 - c*d**2)**7 + 560*a**2*c**9*d**15*e**7/(a*e**2 - c*d**2)**7 - 160*a*c**10*d**17*e**5/(a*e**2 - c*d**2)**7 + 20*a*c**3*d**3*e**5 + 20*c**11*d**19*e**3/(a*e**2 - c*d**2)**7 + 20*c**4*d**5*e**3)/(40*c**4*d**4*e**4))/(a*e**2 - c*d**2)**7 + (-a**5*e**10 + 8*a**4*c*d**2*e**8 - 37*a**3*c**2*d**4*e**6 - 37*a**2*c**3*d**6*e**4 + 8*a*c**4*d**8*e**2 - c**5*d**10 - 60*c**5*d**5*e**5*x**5 + x**4*(-150*a*c**4*d**4*e**6 - 150*c**5*d**6*e**4) + x**3*(-110*a**2*c**3*d**3*e**7 - 380*a*c**4*d**5*e**5 - 110*c**5*d**7*e**3) + x**2*(-15*a**3*c**2*d**2*e**8 - 285*a**2*c**3*d**4*e**6 - 285*a*c**4*d**6*e**4 - 15*c**5*d**8*e**2) + x*(3*a**4*c*d*e**9 - 42*a**3*c**2*d**3*e**7 - 222*a**2*c**3*d**5*e**5 - 42*a*c**4*d**7*e**3 + 3*c**5*d**9*e))/(3*a**9*d**3*e**15 - 18*a**8*c*d**5*e**13 + 45*a**7*c**2*d**7*e**11 - 60*a**6*c**3*d**9*e**9 + 45*a**5*c**4*d**11*e**7 - 18*a**4*c**5*d**13*e**5 + 3*a**3*c**6*d**15*e**3 + x**6*(3*a**6*c**3*d**3*e**15 - 18*a**5*c**4*d**5*e**13 + 45*a**4*c**5*d**7*e**11 - 60*a**3*c**6*d**9*e**9 + 45*a**2*c**7*d**11*e**7 - 18*a*c**8*d**13*e**5 + 3*c**9*d**15*e**3) + x**5*(9*a**7*c**2*d**2*e**16 - 45*a**6*c**3*d**4*e**14 + 81*a**5*c**4*d**6*e**12 - 45*a**4*c**5*d**8*e**10 - 45*a**3*c**6*d**10*e**8 + 81*a**2*c**7*d**12*e**6 - 45*a*c**8*d**14*e**4 + 9*c**9*d**16*e**2) + x**4*(9*a**8*c*d*e**17 - 27*a**7*c**2*d**3*e**15 - 18*a**6*c**3*d**5*e**13 + 171*a**5*c**4*d**7*e**11 - 270*a**4*c**5*d**9*e**9 + 171*a**3*c**6*d**11*e**7 - 18*a**2*c**7*d**13*e**5 - 27*a*c**8*d**15*e**3 + 9*c**9*d**17*e) + x**3*(3*a**9*e**18 + 9*a**8*c*d**2*e**16 - 90*a**7*c**2*d**4*e**14 + 186*a**6*c**3*d**6*e**12 - 108*a**5*c**4*d**8*e**10 - 108*a**4*c**5*d**10*e**8 + 186*a**3*c**6*d**12*e**6 - 90*a**2*c**7*d**14*e**4 + 9*a*c**8*d**16*e**2 + 3*c**9*d**18) + x**2*(9*a**9*d*e**17 - 27*a**8*c*d**3*e**15 - 18*a**7*c**2*d**5*e**13 + 171*a**6*c**3*d**7*e**11 - 270*a**5*c**4*d**9*e**9 + 171*a**4*c**5*d**11*e**7 - 18*a**3*c**6*d**13*e**5 - 27*a**2*c**7*d**15*e**3 + 9*a*c**8*d**17*e) + x*(9*a**9*d**2*e**16 - 45*a**8*c*d**4*e**14 + 81*a**7*c**2*d**6*e**12 - 45*a**6*c**3*d**8*e**10 - 45*a**5*c**4*d**10*e**8 + 81*a**4*c**5*d**12*e**6 - 45*a**3*c**6*d**14*e**4 + 9*a**2*c**7*d**16*e**2))","B",0
1907,0,0,0,0.000000," ","integrate((e*x+d)**4*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)^{4}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)**4, x)","F",0
1908,0,0,0,0.000000," ","integrate((e*x+d)**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)^{3}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)**3, x)","F",0
1909,0,0,0,0.000000," ","integrate((e*x+d)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)^{2}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)**2, x)","F",0
1910,0,0,0,0.000000," ","integrate((e*x+d)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x), x)","F",0
1911,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \sqrt{a d e + c d e x^{2} + x \left(a e^{2} + c d^{2}\right)}\, dx"," ",0,"Integral(sqrt(a*d*e + c*d*e*x**2 + x*(a*e**2 + c*d**2)), x)","F",0
1912,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{d + e x}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x), x)","F",0
1913,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x)**2, x)","F",0
1914,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**3,x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x)**3, x)","F",0
1915,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**4,x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x)**4, x)","F",0
1916,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**5,x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x)**5, x)","F",0
1917,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**6,x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x)**6, x)","F",0
1918,0,0,0,0.000000," ","integrate((e*x+d)**4*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{4}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)**4, x)","F",0
1919,0,0,0,0.000000," ","integrate((e*x+d)**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{3}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)**3, x)","F",0
1920,0,0,0,0.000000," ","integrate((e*x+d)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)**2, x)","F",0
1921,0,0,0,0.000000," ","integrate((e*x+d)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x), x)","F",0
1922,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \left(a d e + c d e x^{2} + x \left(a e^{2} + c d^{2}\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*d*e + c*d*e*x**2 + x*(a*e**2 + c*d**2))**(3/2), x)","F",0
1923,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x), x)","F",0
1924,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**2, x)","F",0
1925,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**3,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**3, x)","F",0
1926,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**4,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**4, x)","F",0
1927,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**5,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**5, x)","F",0
1928,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**6,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**6, x)","F",0
1929,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**7,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**7, x)","F",0
1930,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**8,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{8}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**8, x)","F",0
1931,0,0,0,0.000000," ","integrate((e*x+d)**4*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{4}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)*(d + e*x)**4, x)","F",0
1932,0,0,0,0.000000," ","integrate((e*x+d)**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{3}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)*(d + e*x)**3, x)","F",0
1933,0,0,0,0.000000," ","integrate((e*x+d)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{2}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)*(d + e*x)**2, x)","F",0
1934,0,0,0,0.000000," ","integrate((e*x+d)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}} \left(d + e x\right)\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)*(d + e*x), x)","F",0
1935,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \left(a d e + c d e x^{2} + x \left(a e^{2} + c d^{2}\right)\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a*d*e + c*d*e*x**2 + x*(a*e**2 + c*d**2))**(5/2), x)","F",0
1936,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{d + e x}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(d + e*x), x)","F",0
1937,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1938,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(d + e*x)**3, x)","F",0
1939,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(d + e*x)**4, x)","F",0
1940,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**5,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(d + e*x)**5, x)","F",0
1941,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**6,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(d + e*x)**6, x)","F",0
1942,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**7,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(d + e*x)**7, x)","F",0
1943,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**8,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{8}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(d + e*x)**8, x)","F",0
1944,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1945,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1946,0,0,0,0.000000," ","integrate((e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{3}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)**3/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
1947,0,0,0,0.000000," ","integrate((e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{2}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)**2/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
1948,0,0,0,0.000000," ","integrate((e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{d + e x}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
1949,0,0,0,0.000000," ","integrate(1/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{\sqrt{a d e + c d e x^{2} + x \left(a e^{2} + c d^{2}\right)}}\, dx"," ",0,"Integral(1/sqrt(a*d*e + c*d*e*x**2 + x*(a*e**2 + c*d**2)), x)","F",0
1950,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)), x)","F",0
1951,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)**2), x)","F",0
1952,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)**3), x)","F",0
1953,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)**4), x)","F",0
1954,0,0,0,0.000000," ","integrate((e*x+d)**5/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{5}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**5/((d + e*x)*(a*e + c*d*x))**(3/2), x)","F",0
1955,0,0,0,0.000000," ","integrate((e*x+d)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/((d + e*x)*(a*e + c*d*x))**(3/2), x)","F",0
1956,0,0,0,0.000000," ","integrate((e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/((d + e*x)*(a*e + c*d*x))**(3/2), x)","F",0
1957,0,0,0,0.000000," ","integrate((e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/((d + e*x)*(a*e + c*d*x))**(3/2), x)","F",0
1958,0,0,0,0.000000," ","integrate((e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{d + e x}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)/((d + e*x)*(a*e + c*d*x))**(3/2), x)","F",0
1959,0,0,0,0.000000," ","integrate(1/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{\left(a d e + c d e x^{2} + x \left(a e^{2} + c d^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*d*e + c*d*e*x**2 + x*(a*e**2 + c*d**2))**(-3/2), x)","F",0
1960,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
1961,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)**2), x)","F",0
1962,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)**3), x)","F",0
1963,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)**4), x)","F",0
1964,0,0,0,0.000000," ","integrate((e*x+d)**6/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{6}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**6/((d + e*x)*(a*e + c*d*x))**(5/2), x)","F",0
1965,0,0,0,0.000000," ","integrate((e*x+d)**5/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{5}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**5/((d + e*x)*(a*e + c*d*x))**(5/2), x)","F",0
1966,0,0,0,0.000000," ","integrate((e*x+d)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/((d + e*x)*(a*e + c*d*x))**(5/2), x)","F",0
1967,0,0,0,0.000000," ","integrate((e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/((d + e*x)*(a*e + c*d*x))**(5/2), x)","F",0
1968,0,0,0,0.000000," ","integrate((e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/((d + e*x)*(a*e + c*d*x))**(5/2), x)","F",0
1969,0,0,0,0.000000," ","integrate((e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{d + e x}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)/((d + e*x)*(a*e + c*d*x))**(5/2), x)","F",0
1970,0,0,0,0.000000," ","integrate(1/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{1}{\left(a d e + c d e x^{2} + x \left(a e^{2} + c d^{2}\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*d*e + c*d*e*x**2 + x*(a*e**2 + c*d**2))**(-5/2), x)","F",0
1971,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(5/2)*(d + e*x)), x)","F",0
1972,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(5/2)*(d + e*x)**2), x)","F",0
1973,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(5/2)*(d + e*x)**3), x)","F",0
1974,0,0,0,0.000000," ","integrate((e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/3),x)","\int \frac{d + e x}{\sqrt[3]{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)/((d + e*x)*(a*e + c*d*x))**(1/3), x)","F",0
1975,0,0,0,0.000000," ","integrate(1/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/3),x)","\int \frac{1}{\sqrt[3]{a d e + c d e x^{2} + x \left(a e^{2} + c d^{2}\right)}}\, dx"," ",0,"Integral((a*d*e + c*d*e*x**2 + x*(a*e**2 + c*d**2))**(-1/3), x)","F",0
1976,1,235,0,11.908631," ","integrate((e*x+d)**(3/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","a d^{2} e \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + 4 a d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right) + 2 a \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right) + \frac{2 c d^{3} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{4 c d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}}"," ",0,"a*d**2*e*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5) + 2*a*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7) + 2*c*d**3*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 4*c*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2","A",0
1977,1,41,0,3.644047," ","integrate((e*x+d)**(1/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\frac{2 \left(\frac{c d \left(d + e x\right)^{\frac{7}{2}}}{7 e} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(a e^{2} - c d^{2}\right)}{5 e}\right)}{e}"," ",0,"2*(c*d*(d + e*x)**(7/2)/(7*e) + (d + e*x)**(5/2)*(a*e**2 - c*d**2)/(5*e))/e","A",0
1978,1,221,0,26.662331," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a d^{2} e}{\sqrt{d + e x}} - 4 a d e \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 2 a e \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right) - \frac{2 c d^{3} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{4 c d^{2} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{2 c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e}}{e} & \text{for}\: e \neq 0 \\\frac{c d^{\frac{3}{2}} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*d**2*e/sqrt(d + e*x) - 4*a*d*e*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 2*a*e*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3) - 2*c*d**3*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 4*c*d**2*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 2*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e)/e, Ne(e, 0)), (c*d**(3/2)*x**2/2, True))","A",0
1979,1,124,0,11.484534," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**(3/2),x)","\begin{cases} \frac{- \frac{2 a d e}{\sqrt{d + e x}} - 2 a e \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{2 c d^{2} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{2 c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e}}{e} & \text{for}\: e \neq 0 \\\frac{c \sqrt{d} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*d*e/sqrt(d + e*x) - 2*a*e*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 2*c*d**2*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 2*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e)/e, Ne(e, 0)), (c*sqrt(d)*x**2/2, True))","A",0
1980,1,58,0,1.423336," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**(5/2),x)","\begin{cases} - \frac{2 a}{\sqrt{d + e x}} + \frac{4 c d^{2}}{e^{2} \sqrt{d + e x}} + \frac{2 c d x}{e \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c x^{2}}{2 \sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a/sqrt(d + e*x) + 4*c*d**2/(e**2*sqrt(d + e*x)) + 2*c*d*x/(e*sqrt(d + e*x)), Ne(e, 0)), (c*x**2/(2*sqrt(d)), True))","A",0
1981,1,126,0,3.177269," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**(7/2),x)","\begin{cases} - \frac{2 a e^{2}}{3 d e^{2} \sqrt{d + e x} + 3 e^{3} x \sqrt{d + e x}} - \frac{4 c d^{2}}{3 d e^{2} \sqrt{d + e x} + 3 e^{3} x \sqrt{d + e x}} - \frac{6 c d e x}{3 d e^{2} \sqrt{d + e x} + 3 e^{3} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c x^{2}}{2 d^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*e**2/(3*d*e**2*sqrt(d + e*x) + 3*e**3*x*sqrt(d + e*x)) - 4*c*d**2/(3*d*e**2*sqrt(d + e*x) + 3*e**3*x*sqrt(d + e*x)) - 6*c*d*e*x/(3*d*e**2*sqrt(d + e*x) + 3*e**3*x*sqrt(d + e*x)), Ne(e, 0)), (c*x**2/(2*d**(3/2)), True))","A",0
1982,1,187,0,6.867783," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**(9/2),x)","\begin{cases} - \frac{6 a e^{2}}{15 d^{2} e^{2} \sqrt{d + e x} + 30 d e^{3} x \sqrt{d + e x} + 15 e^{4} x^{2} \sqrt{d + e x}} - \frac{4 c d^{2}}{15 d^{2} e^{2} \sqrt{d + e x} + 30 d e^{3} x \sqrt{d + e x} + 15 e^{4} x^{2} \sqrt{d + e x}} - \frac{10 c d e x}{15 d^{2} e^{2} \sqrt{d + e x} + 30 d e^{3} x \sqrt{d + e x} + 15 e^{4} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c x^{2}}{2 d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a*e**2/(15*d**2*e**2*sqrt(d + e*x) + 30*d*e**3*x*sqrt(d + e*x) + 15*e**4*x**2*sqrt(d + e*x)) - 4*c*d**2/(15*d**2*e**2*sqrt(d + e*x) + 30*d*e**3*x*sqrt(d + e*x) + 15*e**4*x**2*sqrt(d + e*x)) - 10*c*d*e*x/(15*d**2*e**2*sqrt(d + e*x) + 30*d*e**3*x*sqrt(d + e*x) + 15*e**4*x**2*sqrt(d + e*x)), Ne(e, 0)), (c*x**2/(2*d**(5/2)), True))","A",0
1983,1,248,0,13.207406," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)/(e*x+d)**(11/2),x)","\begin{cases} - \frac{10 a e^{2}}{35 d^{3} e^{2} \sqrt{d + e x} + 105 d^{2} e^{3} x \sqrt{d + e x} + 105 d e^{4} x^{2} \sqrt{d + e x} + 35 e^{5} x^{3} \sqrt{d + e x}} - \frac{4 c d^{2}}{35 d^{3} e^{2} \sqrt{d + e x} + 105 d^{2} e^{3} x \sqrt{d + e x} + 105 d e^{4} x^{2} \sqrt{d + e x} + 35 e^{5} x^{3} \sqrt{d + e x}} - \frac{14 c d e x}{35 d^{3} e^{2} \sqrt{d + e x} + 105 d^{2} e^{3} x \sqrt{d + e x} + 105 d e^{4} x^{2} \sqrt{d + e x} + 35 e^{5} x^{3} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c x^{2}}{2 d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-10*a*e**2/(35*d**3*e**2*sqrt(d + e*x) + 105*d**2*e**3*x*sqrt(d + e*x) + 105*d*e**4*x**2*sqrt(d + e*x) + 35*e**5*x**3*sqrt(d + e*x)) - 4*c*d**2/(35*d**3*e**2*sqrt(d + e*x) + 105*d**2*e**3*x*sqrt(d + e*x) + 105*d*e**4*x**2*sqrt(d + e*x) + 35*e**5*x**3*sqrt(d + e*x)) - 14*c*d*e*x/(35*d**3*e**2*sqrt(d + e*x) + 105*d**2*e**3*x*sqrt(d + e*x) + 105*d*e**4*x**2*sqrt(d + e*x) + 35*e**5*x**3*sqrt(d + e*x)), Ne(e, 0)), (c*x**2/(2*d**(7/2)), True))","A",0
1984,1,97,0,4.404229," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{c^{2} d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{2}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(2 a c d e^{2} - 2 c^{2} d^{3}\right)}{9 e^{2}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(a^{2} e^{4} - 2 a c d^{2} e^{2} + c^{2} d^{4}\right)}{7 e^{2}}\right)}{e}"," ",0,"2*(c**2*d**2*(d + e*x)**(11/2)/(11*e**2) + (d + e*x)**(9/2)*(2*a*c*d*e**2 - 2*c**2*d**3)/(9*e**2) + (d + e*x)**(7/2)*(a**2*e**4 - 2*a*c*d**2*e**2 + c**2*d**4)/(7*e**2))/e","A",0
1985,1,631,0,92.729865," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{2} d^{3} e^{2}}{\sqrt{d + e x}} - 6 a^{2} d^{2} e^{2} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 6 a^{2} d e^{2} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right) - 2 a^{2} e^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right) - 4 a c d^{4} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 12 a c d^{3} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right) - 12 a c d^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right) - 4 a c d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right) - \frac{2 c^{2} d^{5} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{6 c^{2} d^{4} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{6 c^{2} d^{3} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} - \frac{2 c^{2} d^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}}}{e} & \text{for}\: e \neq 0 \\\frac{c^{2} d^{\frac{7}{2}} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**2*d**3*e**2/sqrt(d + e*x) - 6*a**2*d**2*e**2*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 6*a**2*d*e**2*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3) - 2*a**2*e**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5) - 4*a*c*d**4*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 12*a*c*d**3*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3) - 12*a*c*d**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5) - 4*a*c*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7) - 2*c**2*d**5*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 6*c**2*d**4*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 6*c**2*d**3*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**2 - 2*c**2*d**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**2)/e, Ne(e, 0)), (c**2*d**(7/2)*x**3/3, True))","A",0
1986,1,411,0,43.923850," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**(3/2),x)","\begin{cases} \frac{- \frac{2 a^{2} d^{2} e^{2}}{\sqrt{d + e x}} - 4 a^{2} d e^{2} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 2 a^{2} e^{2} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right) - 4 a c d^{3} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 8 a c d^{2} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right) - 4 a c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right) - \frac{2 c^{2} d^{4} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{4 c^{2} d^{3} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{2 c^{2} d^{2} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}}}{e} & \text{for}\: e \neq 0 \\\frac{c^{2} d^{\frac{5}{2}} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**2*d**2*e**2/sqrt(d + e*x) - 4*a**2*d*e**2*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 2*a**2*e**2*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3) - 4*a*c*d**3*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 8*a*c*d**2*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3) - 4*a*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5) - 2*c**2*d**4*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 4*c**2*d**3*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 2*c**2*d**2*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**2)/e, Ne(e, 0)), (c**2*d**(5/2)*x**3/3, True))","A",0
1987,1,236,0,44.157350," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**(5/2),x)","\begin{cases} \frac{- \frac{2 a^{2} d e^{2}}{\sqrt{d + e x}} - 2 a^{2} e^{2} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 4 a c d^{2} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 4 a c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right) - \frac{2 c^{2} d^{3} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 c^{2} d^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}}}{e} & \text{for}\: e \neq 0 \\\frac{c^{2} d^{\frac{3}{2}} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**2*d*e**2/sqrt(d + e*x) - 2*a**2*e**2*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 4*a*c*d**2*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 4*a*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3) - 2*c**2*d**3*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*c**2*d**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2)/e, Ne(e, 0)), (c**2*d**(3/2)*x**3/3, True))","A",0
1988,1,133,0,4.906006," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**(7/2),x)","\begin{cases} - \frac{2 a^{2} e}{\sqrt{d + e x}} + \frac{8 a c d^{2}}{e \sqrt{d + e x}} + \frac{4 a c d x}{\sqrt{d + e x}} - \frac{16 c^{2} d^{4}}{3 e^{3} \sqrt{d + e x}} - \frac{8 c^{2} d^{3} x}{3 e^{2} \sqrt{d + e x}} + \frac{2 c^{2} d^{2} x^{2}}{3 e \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c^{2} \sqrt{d} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*e/sqrt(d + e*x) + 8*a*c*d**2/(e*sqrt(d + e*x)) + 4*a*c*d*x/sqrt(d + e*x) - 16*c**2*d**4/(3*e**3*sqrt(d + e*x)) - 8*c**2*d**3*x/(3*e**2*sqrt(d + e*x)) + 2*c**2*d**2*x**2/(3*e*sqrt(d + e*x)), Ne(e, 0)), (c**2*sqrt(d)*x**3/3, True))","A",0
1989,1,264,0,9.462938," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**(9/2),x)","\begin{cases} - \frac{2 a^{2} e^{4}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} - \frac{8 a c d^{2} e^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} - \frac{12 a c d e^{3} x}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{16 c^{2} d^{4}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{24 c^{2} d^{3} e x}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{6 c^{2} d^{2} e^{2} x^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c^{2} x^{3}}{3 \sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*e**4/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) - 8*a*c*d**2*e**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) - 12*a*c*d*e**3*x/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 16*c**2*d**4/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 24*c**2*d**3*e*x/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 6*c**2*d**2*e**2*x**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)), Ne(e, 0)), (c**2*x**3/(3*sqrt(d)), True))","A",0
1990,1,388,0,17.070937," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**(11/2),x)","\begin{cases} - \frac{6 a^{2} e^{4}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{8 a c d^{2} e^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{20 a c d e^{3} x}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{16 c^{2} d^{4}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{40 c^{2} d^{3} e x}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{30 c^{2} d^{2} e^{2} x^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c^{2} x^{3}}{3 d^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a**2*e**4/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 8*a*c*d**2*e**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 20*a*c*d*e**3*x/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 16*c**2*d**4/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 40*c**2*d**3*e*x/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 30*c**2*d**2*e**2*x**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)), Ne(e, 0)), (c**2*x**3/(3*d**(3/2)), True))","A",0
1991,1,510,0,29.806656," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2/(e*x+d)**(13/2),x)","\begin{cases} - \frac{30 a^{2} e^{4}}{105 d^{3} e^{3} \sqrt{d + e x} + 315 d^{2} e^{4} x \sqrt{d + e x} + 315 d e^{5} x^{2} \sqrt{d + e x} + 105 e^{6} x^{3} \sqrt{d + e x}} - \frac{24 a c d^{2} e^{2}}{105 d^{3} e^{3} \sqrt{d + e x} + 315 d^{2} e^{4} x \sqrt{d + e x} + 315 d e^{5} x^{2} \sqrt{d + e x} + 105 e^{6} x^{3} \sqrt{d + e x}} - \frac{84 a c d e^{3} x}{105 d^{3} e^{3} \sqrt{d + e x} + 315 d^{2} e^{4} x \sqrt{d + e x} + 315 d e^{5} x^{2} \sqrt{d + e x} + 105 e^{6} x^{3} \sqrt{d + e x}} - \frac{16 c^{2} d^{4}}{105 d^{3} e^{3} \sqrt{d + e x} + 315 d^{2} e^{4} x \sqrt{d + e x} + 315 d e^{5} x^{2} \sqrt{d + e x} + 105 e^{6} x^{3} \sqrt{d + e x}} - \frac{56 c^{2} d^{3} e x}{105 d^{3} e^{3} \sqrt{d + e x} + 315 d^{2} e^{4} x \sqrt{d + e x} + 315 d e^{5} x^{2} \sqrt{d + e x} + 105 e^{6} x^{3} \sqrt{d + e x}} - \frac{70 c^{2} d^{2} e^{2} x^{2}}{105 d^{3} e^{3} \sqrt{d + e x} + 315 d^{2} e^{4} x \sqrt{d + e x} + 315 d e^{5} x^{2} \sqrt{d + e x} + 105 e^{6} x^{3} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c^{2} x^{3}}{3 d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*a**2*e**4/(105*d**3*e**3*sqrt(d + e*x) + 315*d**2*e**4*x*sqrt(d + e*x) + 315*d*e**5*x**2*sqrt(d + e*x) + 105*e**6*x**3*sqrt(d + e*x)) - 24*a*c*d**2*e**2/(105*d**3*e**3*sqrt(d + e*x) + 315*d**2*e**4*x*sqrt(d + e*x) + 315*d*e**5*x**2*sqrt(d + e*x) + 105*e**6*x**3*sqrt(d + e*x)) - 84*a*c*d*e**3*x/(105*d**3*e**3*sqrt(d + e*x) + 315*d**2*e**4*x*sqrt(d + e*x) + 315*d*e**5*x**2*sqrt(d + e*x) + 105*e**6*x**3*sqrt(d + e*x)) - 16*c**2*d**4/(105*d**3*e**3*sqrt(d + e*x) + 315*d**2*e**4*x*sqrt(d + e*x) + 315*d*e**5*x**2*sqrt(d + e*x) + 105*e**6*x**3*sqrt(d + e*x)) - 56*c**2*d**3*e*x/(105*d**3*e**3*sqrt(d + e*x) + 315*d**2*e**4*x*sqrt(d + e*x) + 315*d*e**5*x**2*sqrt(d + e*x) + 105*e**6*x**3*sqrt(d + e*x)) - 70*c**2*d**2*e**2*x**2/(105*d**3*e**3*sqrt(d + e*x) + 315*d**2*e**4*x*sqrt(d + e*x) + 315*d*e**5*x**2*sqrt(d + e*x) + 105*e**6*x**3*sqrt(d + e*x)), Ne(e, 0)), (c**2*x**3/(3*d**(5/2)), True))","A",0
1992,1,165,0,5.409348," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{c^{3} d^{3} \left(d + e x\right)^{\frac{15}{2}}}{15 e^{3}} + \frac{\left(d + e x\right)^{\frac{13}{2}} \left(3 a c^{2} d^{2} e^{2} - 3 c^{3} d^{4}\right)}{13 e^{3}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(3 a^{2} c d e^{4} - 6 a c^{2} d^{3} e^{2} + 3 c^{3} d^{5}\right)}{11 e^{3}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(a^{3} e^{6} - 3 a^{2} c d^{2} e^{4} + 3 a c^{2} d^{4} e^{2} - c^{3} d^{6}\right)}{9 e^{3}}\right)}{e}"," ",0,"2*(c**3*d**3*(d + e*x)**(15/2)/(15*e**3) + (d + e*x)**(13/2)*(3*a*c**2*d**2*e**2 - 3*c**3*d**4)/(13*e**3) + (d + e*x)**(11/2)*(3*a**2*c*d*e**4 - 6*a*c**2*d**3*e**2 + 3*c**3*d**5)/(11*e**3) + (d + e*x)**(9/2)*(a**3*e**6 - 3*a**2*c*d**2*e**4 + 3*a*c**2*d**4*e**2 - c**3*d**6)/(9*e**3))/e","A",0
1993,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1994,1,971,0,110.398553," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**(3/2),x)","\begin{cases} \frac{- \frac{2 a^{3} d^{3} e^{3}}{\sqrt{d + e x}} - 6 a^{3} d^{2} e^{3} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 6 a^{3} d e^{3} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right) - 2 a^{3} e^{3} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right) - 6 a^{2} c d^{4} e \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 18 a^{2} c d^{3} e \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right) - 18 a^{2} c d^{2} e \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right) - 6 a^{2} c d e \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right) - \frac{6 a c^{2} d^{5} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{18 a c^{2} d^{4} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} - \frac{18 a c^{2} d^{3} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} - \frac{6 a c^{2} d^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e} - \frac{2 c^{3} d^{6} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{6 c^{3} d^{5} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{6 c^{3} d^{4} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} - \frac{2 c^{3} d^{3} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}}}{e} & \text{for}\: e \neq 0 \\\frac{c^{3} d^{\frac{9}{2}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**3*d**3*e**3/sqrt(d + e*x) - 6*a**3*d**2*e**3*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 6*a**3*d*e**3*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3) - 2*a**3*e**3*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5) - 6*a**2*c*d**4*e*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 18*a**2*c*d**3*e*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3) - 18*a**2*c*d**2*e*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5) - 6*a**2*c*d*e*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7) - 6*a*c**2*d**5*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 18*a*c**2*d**4*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e - 18*a*c**2*d**3*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e - 6*a*c**2*d**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e - 2*c**3*d**6*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 6*c**3*d**5*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 6*c**3*d**4*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**3 - 2*c**3*d**3*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**3)/e, Ne(e, 0)), (c**3*d**(9/2)*x**4/4, True))","A",0
1995,1,644,0,98.843820," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**(5/2),x)","\begin{cases} \frac{- \frac{2 a^{3} d^{2} e^{3}}{\sqrt{d + e x}} - 4 a^{3} d e^{3} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 2 a^{3} e^{3} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right) - 6 a^{2} c d^{3} e \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 12 a^{2} c d^{2} e \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right) - 6 a^{2} c d e \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right) - \frac{6 a c^{2} d^{4} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{12 a c^{2} d^{3} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} - \frac{6 a c^{2} d^{2} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} - \frac{2 c^{3} d^{5} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{4 c^{3} d^{4} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{2 c^{3} d^{3} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}}}{e} & \text{for}\: e \neq 0 \\\frac{c^{3} d^{\frac{7}{2}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**3*d**2*e**3/sqrt(d + e*x) - 4*a**3*d*e**3*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 2*a**3*e**3*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3) - 6*a**2*c*d**3*e*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 12*a**2*c*d**2*e*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3) - 6*a**2*c*d*e*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5) - 6*a*c**2*d**4*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 12*a*c**2*d**3*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e - 6*a*c**2*d**2*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e - 2*c**3*d**5*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 4*c**3*d**4*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 2*c**3*d**3*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**3)/e, Ne(e, 0)), (c**3*d**(7/2)*x**4/4, True))","A",0
1996,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1997,1,230,0,15.478625," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**(9/2),x)","\begin{cases} - \frac{2 a^{3} e^{2}}{\sqrt{d + e x}} + \frac{12 a^{2} c d^{2}}{\sqrt{d + e x}} + \frac{6 a^{2} c d e x}{\sqrt{d + e x}} - \frac{16 a c^{2} d^{4}}{e^{2} \sqrt{d + e x}} - \frac{8 a c^{2} d^{3} x}{e \sqrt{d + e x}} + \frac{2 a c^{2} d^{2} x^{2}}{\sqrt{d + e x}} + \frac{32 c^{3} d^{6}}{5 e^{4} \sqrt{d + e x}} + \frac{16 c^{3} d^{5} x}{5 e^{3} \sqrt{d + e x}} - \frac{4 c^{3} d^{4} x^{2}}{5 e^{2} \sqrt{d + e x}} + \frac{2 c^{3} d^{3} x^{3}}{5 e \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c^{3} d^{\frac{3}{2}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*e**2/sqrt(d + e*x) + 12*a**2*c*d**2/sqrt(d + e*x) + 6*a**2*c*d*e*x/sqrt(d + e*x) - 16*a*c**2*d**4/(e**2*sqrt(d + e*x)) - 8*a*c**2*d**3*x/(e*sqrt(d + e*x)) + 2*a*c**2*d**2*x**2/sqrt(d + e*x) + 32*c**3*d**6/(5*e**4*sqrt(d + e*x)) + 16*c**3*d**5*x/(5*e**3*sqrt(d + e*x)) - 4*c**3*d**4*x**2/(5*e**2*sqrt(d + e*x)) + 2*c**3*d**3*x**3/(5*e*sqrt(d + e*x)), Ne(e, 0)), (c**3*d**(3/2)*x**4/4, True))","A",0
1998,1,450,0,25.513810," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**(11/2),x)","\begin{cases} - \frac{2 a^{3} e^{6}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{12 a^{2} c d^{2} e^{4}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{18 a^{2} c d e^{5} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{48 a c^{2} d^{4} e^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{72 a c^{2} d^{3} e^{3} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{18 a c^{2} d^{2} e^{4} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{32 c^{3} d^{6}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{48 c^{3} d^{5} e x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{12 c^{3} d^{4} e^{2} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{2 c^{3} d^{3} e^{3} x^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c^{3} \sqrt{d} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*e**6/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 12*a**2*c*d**2*e**4/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 18*a**2*c*d*e**5*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 48*a*c**2*d**4*e**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 72*a*c**2*d**3*e**3*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 18*a*c**2*d**2*e**4*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 32*c**3*d**6/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 48*c**3*d**5*e*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 12*c**3*d**4*e**2*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 2*c**3*d**3*e**3*x**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)), Ne(e, 0)), (c**3*sqrt(d)*x**4/4, True))","A",0
1999,1,654,0,42.155702," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**(13/2),x)","\begin{cases} - \frac{2 a^{3} e^{6}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} - \frac{4 a^{2} c d^{2} e^{4}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} - \frac{10 a^{2} c d e^{5} x}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} - \frac{16 a c^{2} d^{4} e^{2}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} - \frac{40 a c^{2} d^{3} e^{3} x}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} - \frac{30 a c^{2} d^{2} e^{4} x^{2}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} + \frac{32 c^{3} d^{6}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} + \frac{80 c^{3} d^{5} e x}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} + \frac{60 c^{3} d^{4} e^{2} x^{2}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} + \frac{10 c^{3} d^{3} e^{3} x^{3}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{c^{3} x^{4}}{4 \sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*e**6/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) - 4*a**2*c*d**2*e**4/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) - 10*a**2*c*d*e**5*x/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) - 16*a*c**2*d**4*e**2/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) - 40*a*c**2*d**3*e**3*x/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) - 30*a*c**2*d**2*e**4*x**2/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) + 32*c**3*d**6/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) + 80*c**3*d**5*e*x/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) + 60*c**3*d**4*e**2*x**2/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) + 10*c**3*d**3*e**3*x**3/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)), Ne(e, 0)), (c**3*x**4/(4*sqrt(d)), True))","A",0
2000,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2001,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2002,1,107,0,65.931209," ","integrate((e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 c d} + \frac{\sqrt{d + e x} \left(- 2 a e^{2} + 2 c d^{2}\right)}{c^{2} d^{2}} + \frac{2 \left(a e^{2} - c d^{2}\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e^{2} - c d^{2}}{c d}}} \right)}}{c^{3} d^{3} \sqrt{\frac{a e^{2} - c d^{2}}{c d}}}"," ",0,"2*(d + e*x)**(3/2)/(3*c*d) + sqrt(d + e*x)*(-2*a*e**2 + 2*c*d**2)/(c**2*d**2) + 2*(a*e**2 - c*d**2)**2*atan(sqrt(d + e*x)/sqrt((a*e**2 - c*d**2)/(c*d)))/(c**3*d**3*sqrt((a*e**2 - c*d**2)/(c*d)))","A",0
2003,1,80,0,11.852295," ","integrate((e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\frac{2 \left(\frac{e \sqrt{d + e x}}{c d} - \frac{e \left(a e^{2} - c d^{2}\right) \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e^{2} - c d^{2}}{c d}}} \right)}}{c^{2} d^{2} \sqrt{\frac{a e^{2} - c d^{2}}{c d}}}\right)}{e}"," ",0,"2*(e*sqrt(d + e*x)/(c*d) - e*(a*e**2 - c*d**2)*atan(sqrt(d + e*x)/sqrt((a*e**2 - c*d**2)/(c*d)))/(c**2*d**2*sqrt((a*e**2 - c*d**2)/(c*d))))/e","A",0
2004,1,48,0,4.845474," ","integrate((e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\frac{2 \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e^{2} - c d^{2}}{c d}}} \right)}}{c d \sqrt{\frac{a e^{2} - c d^{2}}{c d}}}"," ",0,"2*atan(sqrt(d + e*x)/sqrt((a*e**2 - c*d**2)/(c*d)))/(c*d*sqrt((a*e**2 - c*d**2)/(c*d)))","A",0
2005,1,82,0,15.813011," ","integrate(1/(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\frac{2 c d \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{c d}{a e^{2} - c d^{2}}} \sqrt{d + e x}} \right)}}{\sqrt{\frac{c d}{a e^{2} - c d^{2}}} \left(a e^{2} - c d^{2}\right)^{2}} - \frac{2}{\sqrt{d + e x} \left(a e^{2} - c d^{2}\right)}"," ",0,"2*c*d*atan(1/(sqrt(c*d/(a*e**2 - c*d**2))*sqrt(d + e*x)))/(sqrt(c*d/(a*e**2 - c*d**2))*(a*e**2 - c*d**2)**2) - 2/(sqrt(d + e*x)*(a*e**2 - c*d**2))","A",0
2006,1,107,0,15.815237," ","integrate(1/(e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\frac{2 c d}{\sqrt{d + e x} \left(a e^{2} - c d^{2}\right)^{2}} + \frac{2 c d \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e^{2} - c d^{2}}{c d}}} \right)}}{\sqrt{\frac{a e^{2} - c d^{2}}{c d}} \left(a e^{2} - c d^{2}\right)^{2}} - \frac{2}{3 \left(d + e x\right)^{\frac{3}{2}} \left(a e^{2} - c d^{2}\right)}"," ",0,"2*c*d/(sqrt(d + e*x)*(a*e**2 - c*d**2)**2) + 2*c*d*atan(sqrt(d + e*x)/sqrt((a*e**2 - c*d**2)/(c*d)))/(sqrt((a*e**2 - c*d**2)/(c*d))*(a*e**2 - c*d**2)**2) - 2/(3*(d + e*x)**(3/2)*(a*e**2 - c*d**2))","A",0
2007,1,141,0,34.850175," ","integrate(1/(e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","- \frac{2 c^{2} d^{2}}{\sqrt{d + e x} \left(a e^{2} - c d^{2}\right)^{3}} - \frac{2 c^{2} d^{2} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e^{2} - c d^{2}}{c d}}} \right)}}{\sqrt{\frac{a e^{2} - c d^{2}}{c d}} \left(a e^{2} - c d^{2}\right)^{3}} + \frac{2 c d}{3 \left(d + e x\right)^{\frac{3}{2}} \left(a e^{2} - c d^{2}\right)^{2}} - \frac{2}{5 \left(d + e x\right)^{\frac{5}{2}} \left(a e^{2} - c d^{2}\right)}"," ",0,"-2*c**2*d**2/(sqrt(d + e*x)*(a*e**2 - c*d**2)**3) - 2*c**2*d**2*atan(sqrt(d + e*x)/sqrt((a*e**2 - c*d**2)/(c*d)))/(sqrt((a*e**2 - c*d**2)/(c*d))*(a*e**2 - c*d**2)**3) + 2*c*d/(3*(d + e*x)**(3/2)*(a*e**2 - c*d**2)**2) - 2/(5*(d + e*x)**(5/2)*(a*e**2 - c*d**2))","A",0
2008,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2009,-1,0,0,0.000000," ","integrate((e*x+d)**(13/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2010,-1,0,0,0.000000," ","integrate((e*x+d)**(11/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2011,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2012,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2013,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2014,1,309,0,146.589551," ","integrate((e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","- \frac{e \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} \log{\left(- a^{2} e^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + 2 a c d^{2} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} - c^{2} d^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + \sqrt{d + e x} \right)}}{2} + \frac{e \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} \log{\left(a^{2} e^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} - 2 a c d^{2} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + c^{2} d^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + \sqrt{d + e x} \right)}}{2} + \frac{2 e \sqrt{d + e x}}{2 a^{2} e^{4} - 2 a c d^{2} e^{2} + 2 a c d e^{3} x - 2 c^{2} d^{3} e x}"," ",0,"-e*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3))*log(-a**2*e**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + 2*a*c*d**2*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) - c**2*d**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + sqrt(d + e*x))/2 + e*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3))*log(a**2*e**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) - 2*a*c*d**2*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + c**2*d**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + sqrt(d + e*x))/2 + 2*e*sqrt(d + e*x)/(2*a**2*e**4 - 2*a*c*d**2*e**2 + 2*a*c*d*e**3*x - 2*c**2*d**3*e*x)","B",0
2015,1,452,0,42.329791," ","integrate((e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\frac{c d e \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} \log{\left(- a^{2} e^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + 2 a c d^{2} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} - c^{2} d^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + \sqrt{d + e x} \right)}}{2 a e^{2} - 2 c d^{2}} - \frac{c d e \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} \log{\left(a^{2} e^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} - 2 a c d^{2} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + c^{2} d^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + \sqrt{d + e x} \right)}}{2 a e^{2} - 2 c d^{2}} - \frac{2 c d e \sqrt{d + e x}}{2 a^{3} e^{6} - 4 a^{2} c d^{2} e^{4} + 2 a^{2} c d e^{5} x + 2 a c^{2} d^{4} e^{2} - 4 a c^{2} d^{3} e^{3} x + 2 c^{3} d^{5} e x} - \frac{2 e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e^{2}}{c d} - d}} \right)}}{\left(a e^{2} - c d^{2}\right)^{2} \sqrt{\frac{a e^{2}}{c d} - d}} - \frac{2 e}{\sqrt{d + e x} \left(a e^{2} - c d^{2}\right)^{2}}"," ",0,"c*d*e*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3))*log(-a**2*e**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + 2*a*c*d**2*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) - c**2*d**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + sqrt(d + e*x))/(2*a*e**2 - 2*c*d**2) - c*d*e*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3))*log(a**2*e**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) - 2*a*c*d**2*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + c**2*d**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + sqrt(d + e*x))/(2*a*e**2 - 2*c*d**2) - 2*c*d*e*sqrt(d + e*x)/(2*a**3*e**6 - 4*a**2*c*d**2*e**4 + 2*a**2*c*d*e**5*x + 2*a*c**2*d**4*e**2 - 4*a*c**2*d**3*e**3*x + 2*c**3*d**5*e*x) - 2*e*atan(sqrt(d + e*x)/sqrt(a*e**2/(c*d) - d))/((a*e**2 - c*d**2)**2*sqrt(a*e**2/(c*d) - d)) - 2*e/(sqrt(d + e*x)*(a*e**2 - c*d**2)**2)","B",0
2016,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\int \frac{1}{\left(d + e x\right)^{\frac{5}{2}} \left(a e + c d x\right)^{2}}\, dx"," ",0,"Integral(1/((d + e*x)**(5/2)*(a*e + c*d*x)**2), x)","F",0
2017,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\int \frac{1}{\left(d + e x\right)^{\frac{7}{2}} \left(a e + c d x\right)^{2}}\, dx"," ",0,"Integral(1/((d + e*x)**(7/2)*(a*e + c*d*x)**2), x)","F",0
2018,-1,0,0,0.000000," ","integrate((e*x+d)**(15/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2019,-1,0,0,0.000000," ","integrate((e*x+d)**(13/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2020,-1,0,0,0.000000," ","integrate((e*x+d)**(11/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2021,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2022,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2023,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2024,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2025,1,1826,0,119.851296," ","integrate((e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\frac{10 a c^{2} d^{2} e^{4} \sqrt{d + e x}}{8 a^{4} e^{8} \left(a e^{2} - c d^{2}\right)^{2} - 16 a^{3} c d^{2} e^{6} \left(a e^{2} - c d^{2}\right)^{2} + 16 a^{3} c d e^{7} x \left(a e^{2} - c d^{2}\right)^{2} - 48 a^{2} c^{2} d^{3} e^{5} x \left(a e^{2} - c d^{2}\right)^{2} + 8 a^{2} c^{2} d^{2} e^{4} \left(d + e x\right)^{2} \left(a e^{2} - c d^{2}\right)^{2} + 16 a c^{3} d^{6} e^{2} \left(a e^{2} - c d^{2}\right)^{2} + 48 a c^{3} d^{5} e^{3} x \left(a e^{2} - c d^{2}\right)^{2} - 16 a c^{3} d^{4} e^{2} \left(d + e x\right)^{2} \left(a e^{2} - c d^{2}\right)^{2} - 8 c^{4} d^{8} \left(a e^{2} - c d^{2}\right)^{2} - 16 c^{4} d^{7} e x \left(a e^{2} - c d^{2}\right)^{2} + 8 c^{4} d^{6} \left(d + e x\right)^{2} \left(a e^{2} - c d^{2}\right)^{2}} - \frac{10 c^{3} d^{4} e^{2} \sqrt{d + e x}}{8 a^{4} e^{8} \left(a e^{2} - c d^{2}\right)^{2} - 16 a^{3} c d^{2} e^{6} \left(a e^{2} - c d^{2}\right)^{2} + 16 a^{3} c d e^{7} x \left(a e^{2} - c d^{2}\right)^{2} - 48 a^{2} c^{2} d^{3} e^{5} x \left(a e^{2} - c d^{2}\right)^{2} + 8 a^{2} c^{2} d^{2} e^{4} \left(d + e x\right)^{2} \left(a e^{2} - c d^{2}\right)^{2} + 16 a c^{3} d^{6} e^{2} \left(a e^{2} - c d^{2}\right)^{2} + 48 a c^{3} d^{5} e^{3} x \left(a e^{2} - c d^{2}\right)^{2} - 16 a c^{3} d^{4} e^{2} \left(d + e x\right)^{2} \left(a e^{2} - c d^{2}\right)^{2} - 8 c^{4} d^{8} \left(a e^{2} - c d^{2}\right)^{2} - 16 c^{4} d^{7} e x \left(a e^{2} - c d^{2}\right)^{2} + 8 c^{4} d^{6} \left(d + e x\right)^{2} \left(a e^{2} - c d^{2}\right)^{2}} + \frac{6 c^{3} d^{3} e^{2} \left(d + e x\right)^{\frac{3}{2}}}{8 a^{4} e^{8} \left(a e^{2} - c d^{2}\right)^{2} - 16 a^{3} c d^{2} e^{6} \left(a e^{2} - c d^{2}\right)^{2} + 16 a^{3} c d e^{7} x \left(a e^{2} - c d^{2}\right)^{2} - 48 a^{2} c^{2} d^{3} e^{5} x \left(a e^{2} - c d^{2}\right)^{2} + 8 a^{2} c^{2} d^{2} e^{4} \left(d + e x\right)^{2} \left(a e^{2} - c d^{2}\right)^{2} + 16 a c^{3} d^{6} e^{2} \left(a e^{2} - c d^{2}\right)^{2} + 48 a c^{3} d^{5} e^{3} x \left(a e^{2} - c d^{2}\right)^{2} - 16 a c^{3} d^{4} e^{2} \left(d + e x\right)^{2} \left(a e^{2} - c d^{2}\right)^{2} - 8 c^{4} d^{8} \left(a e^{2} - c d^{2}\right)^{2} - 16 c^{4} d^{7} e x \left(a e^{2} - c d^{2}\right)^{2} + 8 c^{4} d^{6} \left(d + e x\right)^{2} \left(a e^{2} - c d^{2}\right)^{2}} - \frac{3 c^{2} d^{2} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{5}}} \log{\left(- a^{3} e^{6} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{5}}} + 3 a^{2} c d^{2} e^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{5}}} - 3 a c^{2} d^{4} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{5}}} + c^{3} d^{6} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{5}}} + \sqrt{d + e x} \right)}}{8 \left(a e^{2} - c d^{2}\right)^{2}} + \frac{3 c^{2} d^{2} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{5}}} \log{\left(a^{3} e^{6} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{5}}} - 3 a^{2} c d^{2} e^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{5}}} + 3 a c^{2} d^{4} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{5}}} - c^{3} d^{6} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{5}}} + \sqrt{d + e x} \right)}}{8 \left(a e^{2} - c d^{2}\right)^{2}} - \frac{c^{2} d^{2} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} \log{\left(- a^{2} e^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + 2 a c d^{2} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} - c^{2} d^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + \sqrt{d + e x} \right)}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{c^{2} d^{2} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} \log{\left(a^{2} e^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} - 2 a c d^{2} e^{2} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + c^{2} d^{4} \sqrt{- \frac{1}{c d \left(a e^{2} - c d^{2}\right)^{3}}} + \sqrt{d + e x} \right)}}{\left(a e^{2} - c d^{2}\right)^{3}} + \frac{4 c^{2} d^{2} e^{2} \sqrt{d + e x}}{2 a^{2} e^{4} \left(a e^{2} - c d^{2}\right)^{3} - 2 a c d^{2} e^{2} \left(a e^{2} - c d^{2}\right)^{3} + 2 a c d e^{3} x \left(a e^{2} - c d^{2}\right)^{3} - 2 c^{2} d^{3} e x \left(a e^{2} - c d^{2}\right)^{3}} + \frac{6 c d e^{2} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e^{2}}{c d} - d}} \right)}}{\left(a e^{2} - c d^{2}\right)^{4} \sqrt{\frac{a e^{2}}{c d} - d}} + \frac{6 c d e^{2}}{\sqrt{d + e x} \left(a e^{2} - c d^{2}\right)^{4}} - \frac{2 e^{2}}{3 \left(d + e x\right)^{\frac{3}{2}} \left(a e^{2} - c d^{2}\right)^{3}}"," ",0,"10*a*c**2*d**2*e**4*sqrt(d + e*x)/(8*a**4*e**8*(a*e**2 - c*d**2)**2 - 16*a**3*c*d**2*e**6*(a*e**2 - c*d**2)**2 + 16*a**3*c*d*e**7*x*(a*e**2 - c*d**2)**2 - 48*a**2*c**2*d**3*e**5*x*(a*e**2 - c*d**2)**2 + 8*a**2*c**2*d**2*e**4*(d + e*x)**2*(a*e**2 - c*d**2)**2 + 16*a*c**3*d**6*e**2*(a*e**2 - c*d**2)**2 + 48*a*c**3*d**5*e**3*x*(a*e**2 - c*d**2)**2 - 16*a*c**3*d**4*e**2*(d + e*x)**2*(a*e**2 - c*d**2)**2 - 8*c**4*d**8*(a*e**2 - c*d**2)**2 - 16*c**4*d**7*e*x*(a*e**2 - c*d**2)**2 + 8*c**4*d**6*(d + e*x)**2*(a*e**2 - c*d**2)**2) - 10*c**3*d**4*e**2*sqrt(d + e*x)/(8*a**4*e**8*(a*e**2 - c*d**2)**2 - 16*a**3*c*d**2*e**6*(a*e**2 - c*d**2)**2 + 16*a**3*c*d*e**7*x*(a*e**2 - c*d**2)**2 - 48*a**2*c**2*d**3*e**5*x*(a*e**2 - c*d**2)**2 + 8*a**2*c**2*d**2*e**4*(d + e*x)**2*(a*e**2 - c*d**2)**2 + 16*a*c**3*d**6*e**2*(a*e**2 - c*d**2)**2 + 48*a*c**3*d**5*e**3*x*(a*e**2 - c*d**2)**2 - 16*a*c**3*d**4*e**2*(d + e*x)**2*(a*e**2 - c*d**2)**2 - 8*c**4*d**8*(a*e**2 - c*d**2)**2 - 16*c**4*d**7*e*x*(a*e**2 - c*d**2)**2 + 8*c**4*d**6*(d + e*x)**2*(a*e**2 - c*d**2)**2) + 6*c**3*d**3*e**2*(d + e*x)**(3/2)/(8*a**4*e**8*(a*e**2 - c*d**2)**2 - 16*a**3*c*d**2*e**6*(a*e**2 - c*d**2)**2 + 16*a**3*c*d*e**7*x*(a*e**2 - c*d**2)**2 - 48*a**2*c**2*d**3*e**5*x*(a*e**2 - c*d**2)**2 + 8*a**2*c**2*d**2*e**4*(d + e*x)**2*(a*e**2 - c*d**2)**2 + 16*a*c**3*d**6*e**2*(a*e**2 - c*d**2)**2 + 48*a*c**3*d**5*e**3*x*(a*e**2 - c*d**2)**2 - 16*a*c**3*d**4*e**2*(d + e*x)**2*(a*e**2 - c*d**2)**2 - 8*c**4*d**8*(a*e**2 - c*d**2)**2 - 16*c**4*d**7*e*x*(a*e**2 - c*d**2)**2 + 8*c**4*d**6*(d + e*x)**2*(a*e**2 - c*d**2)**2) - 3*c**2*d**2*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**5))*log(-a**3*e**6*sqrt(-1/(c*d*(a*e**2 - c*d**2)**5)) + 3*a**2*c*d**2*e**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**5)) - 3*a*c**2*d**4*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**5)) + c**3*d**6*sqrt(-1/(c*d*(a*e**2 - c*d**2)**5)) + sqrt(d + e*x))/(8*(a*e**2 - c*d**2)**2) + 3*c**2*d**2*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**5))*log(a**3*e**6*sqrt(-1/(c*d*(a*e**2 - c*d**2)**5)) - 3*a**2*c*d**2*e**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**5)) + 3*a*c**2*d**4*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**5)) - c**3*d**6*sqrt(-1/(c*d*(a*e**2 - c*d**2)**5)) + sqrt(d + e*x))/(8*(a*e**2 - c*d**2)**2) - c**2*d**2*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3))*log(-a**2*e**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + 2*a*c*d**2*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) - c**2*d**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + sqrt(d + e*x))/(a*e**2 - c*d**2)**3 + c**2*d**2*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3))*log(a**2*e**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) - 2*a*c*d**2*e**2*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + c**2*d**4*sqrt(-1/(c*d*(a*e**2 - c*d**2)**3)) + sqrt(d + e*x))/(a*e**2 - c*d**2)**3 + 4*c**2*d**2*e**2*sqrt(d + e*x)/(2*a**2*e**4*(a*e**2 - c*d**2)**3 - 2*a*c*d**2*e**2*(a*e**2 - c*d**2)**3 + 2*a*c*d*e**3*x*(a*e**2 - c*d**2)**3 - 2*c**2*d**3*e*x*(a*e**2 - c*d**2)**3) + 6*c*d*e**2*atan(sqrt(d + e*x)/sqrt(a*e**2/(c*d) - d))/((a*e**2 - c*d**2)**4*sqrt(a*e**2/(c*d) - d)) + 6*c*d*e**2/(sqrt(d + e*x)*(a*e**2 - c*d**2)**4) - 2*e**2/(3*(d + e*x)**(3/2)*(a*e**2 - c*d**2)**3)","B",0
2026,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2027,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2028,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2029,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)**(3/2), x)","F",0
2030,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \sqrt{\left(d + e x\right) \left(a e + c d x\right)} \sqrt{d + e x}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*sqrt(d + e*x), x)","F",0
2031,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/sqrt(d + e*x), x)","F",0
2032,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x)**(3/2), x)","F",0
2033,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x)**(5/2), x)","F",0
2034,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2035,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2036,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2037,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)**(3/2), x)","F",0
2038,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \sqrt{d + e x}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)*sqrt(d + e*x), x)","F",0
2039,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/sqrt(d + e*x), x)","F",0
2040,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**(3/2), x)","F",0
2041,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**(5/2), x)","F",0
2042,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2043,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2044,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2045,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2046,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2047,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2048,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2049,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2050,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2051,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2052,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2053,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2054,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2055,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2056,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2057,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2058,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{5}{2}}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)**(5/2)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
2059,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
2060,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
2061,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/(sqrt((d + e*x)*(a*e + c*d*x))*sqrt(d + e*x)), x)","F",0
2062,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)**(3/2)), x)","F",0
2063,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)**(5/2)), x)","F",0
2064,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2065,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2066,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2067,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/((d + e*x)*(a*e + c*d*x))**(3/2), x)","F",0
2068,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{\sqrt{d + e x}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/((d + e*x)*(a*e + c*d*x))**(3/2), x)","F",0
2069,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(3/2)*sqrt(d + e*x)), x)","F",0
2070,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)**(3/2)), x)","F",0
2071,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)**(5/2)), x)","F",0
2072,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2073,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2074,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2075,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/((d + e*x)*(a*e + c*d*x))**(5/2), x)","F",0
2076,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{\sqrt{d + e x}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/((d + e*x)*(a*e + c*d*x))**(5/2), x)","F",0
2077,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(5/2)*sqrt(d + e*x)), x)","F",0
2078,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(5/2)*(d + e*x)**(3/2)), x)","F",0
2079,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2080,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2081,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/(sqrt(-(-d + e*x)*(d + e*x))*sqrt(d + e*x)), x)","F",0
2082,0,0,0,0.000000," ","integrate(1/(e*x-d)**(1/2)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \sqrt{- d + e x}}\, dx"," ",0,"Integral(1/(sqrt(-(-d + e*x)*(d + e*x))*sqrt(-d + e*x)), x)","F",0
2083,0,0,0,0.000000," ","integrate((e*x+d)**(2/3)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{2}{3}}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)**(2/3)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
2084,1,7164,0,14.299550," ","integrate((e*x+d)**m*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\begin{cases} \frac{c^{3} d^{6} d^{m} x^{4}}{4} & \text{for}\: e = 0 \\- \frac{2 a^{3} e^{6}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 a^{2} c d^{2} e^{4}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{9 a^{2} c d e^{5} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 a c^{2} d^{4} e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{18 a c^{2} d^{3} e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{18 a c^{2} d^{2} e^{4} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 c^{3} d^{6} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{11 c^{3} d^{6}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c^{3} d^{5} e x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{27 c^{3} d^{5} e x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c^{3} d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c^{3} d^{4} e^{2} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 c^{3} d^{3} e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} & \text{for}\: m = -7 \\- \frac{a^{3} e^{6}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{3 a^{2} c d^{2} e^{4}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 a^{2} c d e^{5} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{6 a c^{2} d^{4} e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{9 a c^{2} d^{4} e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{12 a c^{2} d^{3} e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{12 a c^{2} d^{3} e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{6 a c^{2} d^{2} e^{4} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 c^{3} d^{6} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{15 c^{3} d^{6}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 c^{3} d^{5} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{24 c^{3} d^{5} e x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 c^{3} d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 c^{3} d^{4} e^{2} x^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 c^{3} d^{3} e^{3} x^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} & \text{for}\: m = -6 \\- \frac{2 a^{3} e^{6}}{2 d e^{4} + 2 e^{5} x} + \frac{6 a^{2} c d^{2} e^{4} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 a^{2} c d^{2} e^{4}}{2 d e^{4} + 2 e^{5} x} + \frac{6 a^{2} c d e^{5} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{12 a c^{2} d^{4} e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{30 a c^{2} d^{4} e^{2}}{2 d e^{4} + 2 e^{5} x} - \frac{12 a c^{2} d^{3} e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{18 a c^{2} d^{3} e^{3} x}{2 d e^{4} + 2 e^{5} x} + \frac{6 a c^{2} d^{2} e^{4} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{6 c^{3} d^{6} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{12 c^{3} d^{6}}{2 d e^{4} + 2 e^{5} x} + \frac{6 c^{3} d^{5} e x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 c^{3} d^{5} e x}{2 d e^{4} + 2 e^{5} x} - \frac{3 c^{3} d^{4} e^{2} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{c^{3} d^{3} e^{3} x^{3}}{2 d e^{4} + 2 e^{5} x} & \text{for}\: m = -5 \\a^{3} e^{2} \log{\left(\frac{d}{e} + x \right)} - 3 a^{2} c d^{2} \log{\left(\frac{d}{e} + x \right)} + 3 a^{2} c d e x + \frac{3 a c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{e^{2}} - \frac{3 a c^{2} d^{3} x}{e} + \frac{3 a c^{2} d^{2} x^{2}}{2} - \frac{c^{3} d^{6} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{c^{3} d^{5} x}{e^{3}} - \frac{c^{3} d^{4} x^{2}}{2 e^{2}} + \frac{c^{3} d^{3} x^{3}}{3 e} & \text{for}\: m = -4 \\\frac{a^{3} d^{4} e^{6} m^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{18 a^{3} d^{4} e^{6} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{107 a^{3} d^{4} e^{6} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{210 a^{3} d^{4} e^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{4 a^{3} d^{3} e^{7} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{72 a^{3} d^{3} e^{7} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{428 a^{3} d^{3} e^{7} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{840 a^{3} d^{3} e^{7} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{6 a^{3} d^{2} e^{8} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{108 a^{3} d^{2} e^{8} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{642 a^{3} d^{2} e^{8} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{1260 a^{3} d^{2} e^{8} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{4 a^{3} d e^{9} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{72 a^{3} d e^{9} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{428 a^{3} d e^{9} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{840 a^{3} d e^{9} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{a^{3} e^{10} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{18 a^{3} e^{10} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{107 a^{3} e^{10} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{210 a^{3} e^{10} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} - \frac{3 a^{2} c d^{6} e^{4} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} - \frac{39 a^{2} c d^{6} e^{4} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} - \frac{126 a^{2} c d^{6} e^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{3 a^{2} c d^{5} e^{5} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{39 a^{2} c d^{5} e^{5} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{126 a^{2} c d^{5} e^{5} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{12 a^{2} c d^{4} e^{6} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{186 a^{2} c d^{4} e^{6} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{894 a^{2} c d^{4} e^{6} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{1260 a^{2} c d^{4} e^{6} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{18 a^{2} c d^{3} e^{7} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{294 a^{2} c d^{3} e^{7} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{1536 a^{2} c d^{3} e^{7} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{2520 a^{2} c d^{3} e^{7} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{12 a^{2} c d^{2} e^{8} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{201 a^{2} c d^{2} e^{8} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{1089 a^{2} c d^{2} e^{8} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{1890 a^{2} c d^{2} e^{8} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{3 a^{2} c d e^{9} m^{3} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{51 a^{2} c d e^{9} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{282 a^{2} c d e^{9} m x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{504 a^{2} c d e^{9} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{6 a c^{2} d^{8} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{42 a c^{2} d^{8} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} - \frac{6 a c^{2} d^{7} e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} - \frac{42 a c^{2} d^{7} e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{3 a c^{2} d^{6} e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{24 a c^{2} d^{6} e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{21 a c^{2} d^{6} e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{12 a c^{2} d^{5} e^{5} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{156 a c^{2} d^{5} e^{5} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{624 a c^{2} d^{5} e^{5} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{840 a c^{2} d^{5} e^{5} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{18 a c^{2} d^{4} e^{6} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{264 a c^{2} d^{4} e^{6} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{1236 a c^{2} d^{4} e^{6} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{1890 a c^{2} d^{4} e^{6} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{12 a c^{2} d^{3} e^{7} m^{3} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{186 a c^{2} d^{3} e^{7} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{930 a c^{2} d^{3} e^{7} m x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{1512 a c^{2} d^{3} e^{7} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{3 a c^{2} d^{2} e^{8} m^{3} x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{48 a c^{2} d^{2} e^{8} m^{2} x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{249 a c^{2} d^{2} e^{8} m x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{420 a c^{2} d^{2} e^{8} x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} - \frac{6 c^{3} d^{10} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{6 c^{3} d^{9} e m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} - \frac{3 c^{3} d^{8} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} - \frac{3 c^{3} d^{8} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{c^{3} d^{7} e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{3 c^{3} d^{7} e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{2 c^{3} d^{7} e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{4 c^{3} d^{6} e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{42 c^{3} d^{6} e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{158 c^{3} d^{6} e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{210 c^{3} d^{6} e^{4} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{6 c^{3} d^{5} e^{5} m^{3} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{78 c^{3} d^{5} e^{5} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{342 c^{3} d^{5} e^{5} m x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{504 c^{3} d^{5} e^{5} x^{5} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{4 c^{3} d^{4} e^{6} m^{3} x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{57 c^{3} d^{4} e^{6} m^{2} x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{269 c^{3} d^{4} e^{6} m x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{420 c^{3} d^{4} e^{6} x^{6} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{c^{3} d^{3} e^{7} m^{3} x^{7} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{15 c^{3} d^{3} e^{7} m^{2} x^{7} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{74 c^{3} d^{3} e^{7} m x^{7} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} + \frac{120 c^{3} d^{3} e^{7} x^{7} \left(d + e x\right)^{m}}{e^{4} m^{4} + 22 e^{4} m^{3} + 179 e^{4} m^{2} + 638 e^{4} m + 840 e^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*d**6*d**m*x**4/4, Eq(e, 0)), (-2*a**3*e**6/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*a**2*c*d**2*e**4/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 9*a**2*c*d*e**5*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*a*c**2*d**4*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 18*a*c**2*d**3*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 18*a*c**2*d**2*e**4*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*c**3*d**6*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 11*c**3*d**6/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c**3*d**5*e*x*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 27*c**3*d**5*e*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c**3*d**4*e**2*x**2*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c**3*d**4*e**2*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*c**3*d**3*e**3*x**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3), Eq(m, -7)), (-a**3*e**6/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 3*a**2*c*d**2*e**4/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*a**2*c*d*e**5*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 6*a*c**2*d**4*e**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 9*a*c**2*d**4*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 12*a*c**2*d**3*e**3*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 12*a*c**2*d**3*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 6*a*c**2*d**2*e**4*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*c**3*d**6*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 15*c**3*d**6/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*c**3*d**5*e*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 24*c**3*d**5*e*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*c**3*d**4*e**2*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*c**3*d**4*e**2*x**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*c**3*d**3*e**3*x**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2), Eq(m, -6)), (-2*a**3*e**6/(2*d*e**4 + 2*e**5*x) + 6*a**2*c*d**2*e**4*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*a**2*c*d**2*e**4/(2*d*e**4 + 2*e**5*x) + 6*a**2*c*d*e**5*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 12*a*c**2*d**4*e**2*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 30*a*c**2*d**4*e**2/(2*d*e**4 + 2*e**5*x) - 12*a*c**2*d**3*e**3*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 18*a*c**2*d**3*e**3*x/(2*d*e**4 + 2*e**5*x) + 6*a*c**2*d**2*e**4*x**2/(2*d*e**4 + 2*e**5*x) + 6*c**3*d**6*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 12*c**3*d**6/(2*d*e**4 + 2*e**5*x) + 6*c**3*d**5*e*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*c**3*d**5*e*x/(2*d*e**4 + 2*e**5*x) - 3*c**3*d**4*e**2*x**2/(2*d*e**4 + 2*e**5*x) + c**3*d**3*e**3*x**3/(2*d*e**4 + 2*e**5*x), Eq(m, -5)), (a**3*e**2*log(d/e + x) - 3*a**2*c*d**2*log(d/e + x) + 3*a**2*c*d*e*x + 3*a*c**2*d**4*log(d/e + x)/e**2 - 3*a*c**2*d**3*x/e + 3*a*c**2*d**2*x**2/2 - c**3*d**6*log(d/e + x)/e**4 + c**3*d**5*x/e**3 - c**3*d**4*x**2/(2*e**2) + c**3*d**3*x**3/(3*e), Eq(m, -4)), (a**3*d**4*e**6*m**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 18*a**3*d**4*e**6*m**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 107*a**3*d**4*e**6*m*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 210*a**3*d**4*e**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 4*a**3*d**3*e**7*m**3*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 72*a**3*d**3*e**7*m**2*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 428*a**3*d**3*e**7*m*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 840*a**3*d**3*e**7*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 6*a**3*d**2*e**8*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 108*a**3*d**2*e**8*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 642*a**3*d**2*e**8*m*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 1260*a**3*d**2*e**8*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 4*a**3*d*e**9*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 72*a**3*d*e**9*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 428*a**3*d*e**9*m*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 840*a**3*d*e**9*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + a**3*e**10*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 18*a**3*e**10*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 107*a**3*e**10*m*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 210*a**3*e**10*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) - 3*a**2*c*d**6*e**4*m**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) - 39*a**2*c*d**6*e**4*m*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) - 126*a**2*c*d**6*e**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 3*a**2*c*d**5*e**5*m**3*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 39*a**2*c*d**5*e**5*m**2*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 126*a**2*c*d**5*e**5*m*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 12*a**2*c*d**4*e**6*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 186*a**2*c*d**4*e**6*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 894*a**2*c*d**4*e**6*m*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 1260*a**2*c*d**4*e**6*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 18*a**2*c*d**3*e**7*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 294*a**2*c*d**3*e**7*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 1536*a**2*c*d**3*e**7*m*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 2520*a**2*c*d**3*e**7*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 12*a**2*c*d**2*e**8*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 201*a**2*c*d**2*e**8*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 1089*a**2*c*d**2*e**8*m*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 1890*a**2*c*d**2*e**8*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 3*a**2*c*d*e**9*m**3*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 51*a**2*c*d*e**9*m**2*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 282*a**2*c*d*e**9*m*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 504*a**2*c*d*e**9*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 6*a*c**2*d**8*e**2*m*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 42*a*c**2*d**8*e**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) - 6*a*c**2*d**7*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) - 42*a*c**2*d**7*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 3*a*c**2*d**6*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 24*a*c**2*d**6*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 21*a*c**2*d**6*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 12*a*c**2*d**5*e**5*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 156*a*c**2*d**5*e**5*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 624*a*c**2*d**5*e**5*m*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 840*a*c**2*d**5*e**5*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 18*a*c**2*d**4*e**6*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 264*a*c**2*d**4*e**6*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 1236*a*c**2*d**4*e**6*m*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 1890*a*c**2*d**4*e**6*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 12*a*c**2*d**3*e**7*m**3*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 186*a*c**2*d**3*e**7*m**2*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 930*a*c**2*d**3*e**7*m*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 1512*a*c**2*d**3*e**7*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 3*a*c**2*d**2*e**8*m**3*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 48*a*c**2*d**2*e**8*m**2*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 249*a*c**2*d**2*e**8*m*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 420*a*c**2*d**2*e**8*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) - 6*c**3*d**10*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 6*c**3*d**9*e*m*x*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) - 3*c**3*d**8*e**2*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) - 3*c**3*d**8*e**2*m*x**2*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + c**3*d**7*e**3*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 3*c**3*d**7*e**3*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 2*c**3*d**7*e**3*m*x**3*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 4*c**3*d**6*e**4*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 42*c**3*d**6*e**4*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 158*c**3*d**6*e**4*m*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 210*c**3*d**6*e**4*x**4*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 6*c**3*d**5*e**5*m**3*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 78*c**3*d**5*e**5*m**2*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 342*c**3*d**5*e**5*m*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 504*c**3*d**5*e**5*x**5*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 4*c**3*d**4*e**6*m**3*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 57*c**3*d**4*e**6*m**2*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 269*c**3*d**4*e**6*m*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 420*c**3*d**4*e**6*x**6*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + c**3*d**3*e**7*m**3*x**7*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 15*c**3*d**3*e**7*m**2*x**7*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 74*c**3*d**3*e**7*m*x**7*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4) + 120*c**3*d**3*e**7*x**7*(d + e*x)**m/(e**4*m**4 + 22*e**4*m**3 + 179*e**4*m**2 + 638*e**4*m + 840*e**4), True))","A",0
2085,1,2494,0,4.695252," ","integrate((e*x+d)**m*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\begin{cases} \frac{c^{2} d^{4} d^{m} x^{3}}{3} & \text{for}\: e = 0 \\- \frac{a^{2} e^{4}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} - \frac{2 a c d^{2} e^{2}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} - \frac{4 a c d e^{3} x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{3 c^{2} d^{4}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 c^{2} d^{3} e x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 c^{2} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} & \text{for}\: m = -5 \\- \frac{a^{2} e^{4}}{d e^{3} + e^{4} x} + \frac{2 a c d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} + \frac{2 a c d^{2} e^{2}}{d e^{3} + e^{4} x} + \frac{2 a c d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{2 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{4 c^{2} d^{4}}{d e^{3} + e^{4} x} - \frac{2 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{2 c^{2} d^{3} e x}{d e^{3} + e^{4} x} + \frac{c^{2} d^{2} e^{2} x^{2}}{d e^{3} + e^{4} x} & \text{for}\: m = -4 \\a^{2} e \log{\left(\frac{d}{e} + x \right)} - \frac{2 a c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e} + 2 a c d x + \frac{c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{c^{2} d^{3} x}{e^{2}} + \frac{c^{2} d^{2} x^{2}}{2 e} & \text{for}\: m = -3 \\\frac{a^{2} d^{3} e^{4} m^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{9 a^{2} d^{3} e^{4} m \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{20 a^{2} d^{3} e^{4} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{3 a^{2} d^{2} e^{5} m^{2} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{27 a^{2} d^{2} e^{5} m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{60 a^{2} d^{2} e^{5} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{3 a^{2} d e^{6} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{27 a^{2} d e^{6} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{60 a^{2} d e^{6} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{a^{2} e^{7} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{9 a^{2} e^{7} m x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{20 a^{2} e^{7} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} - \frac{2 a c d^{5} e^{2} m \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} - \frac{10 a c d^{5} e^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{2 a c d^{4} e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{10 a c d^{4} e^{3} m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{6 a c d^{3} e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{42 a c d^{3} e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{60 a c d^{3} e^{4} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{6 a c d^{2} e^{5} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{46 a c d^{2} e^{5} m x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{80 a c d^{2} e^{5} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{2 a c d e^{6} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{16 a c d e^{6} m x^{4} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{30 a c d e^{6} x^{4} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{2 c^{2} d^{7} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} - \frac{2 c^{2} d^{6} e m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{c^{2} d^{5} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{c^{2} d^{5} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{3 c^{2} d^{4} e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{15 c^{2} d^{4} e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{20 c^{2} d^{4} e^{3} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{3 c^{2} d^{3} e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{19 c^{2} d^{3} e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{30 c^{2} d^{3} e^{4} x^{4} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{c^{2} d^{2} e^{5} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{7 c^{2} d^{2} e^{5} m x^{5} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} + \frac{12 c^{2} d^{2} e^{5} x^{5} \left(d + e x\right)^{m}}{e^{3} m^{3} + 12 e^{3} m^{2} + 47 e^{3} m + 60 e^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*d**4*d**m*x**3/3, Eq(e, 0)), (-a**2*e**4/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) - 2*a*c*d**2*e**2/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) - 4*a*c*d*e**3*x/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*c**2*d**4*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 3*c**2*d**4/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*c**2*d**3*e*x*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*c**2*d**3*e*x/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*c**2*d**2*e**2*x**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2), Eq(m, -5)), (-a**2*e**4/(d*e**3 + e**4*x) + 2*a*c*d**2*e**2*log(d/e + x)/(d*e**3 + e**4*x) + 2*a*c*d**2*e**2/(d*e**3 + e**4*x) + 2*a*c*d*e**3*x*log(d/e + x)/(d*e**3 + e**4*x) - 2*c**2*d**4*log(d/e + x)/(d*e**3 + e**4*x) - 4*c**2*d**4/(d*e**3 + e**4*x) - 2*c**2*d**3*e*x*log(d/e + x)/(d*e**3 + e**4*x) - 2*c**2*d**3*e*x/(d*e**3 + e**4*x) + c**2*d**2*e**2*x**2/(d*e**3 + e**4*x), Eq(m, -4)), (a**2*e*log(d/e + x) - 2*a*c*d**2*log(d/e + x)/e + 2*a*c*d*x + c**2*d**4*log(d/e + x)/e**3 - c**2*d**3*x/e**2 + c**2*d**2*x**2/(2*e), Eq(m, -3)), (a**2*d**3*e**4*m**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 9*a**2*d**3*e**4*m*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 20*a**2*d**3*e**4*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 3*a**2*d**2*e**5*m**2*x*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 27*a**2*d**2*e**5*m*x*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 60*a**2*d**2*e**5*x*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 3*a**2*d*e**6*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 27*a**2*d*e**6*m*x**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 60*a**2*d*e**6*x**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + a**2*e**7*m**2*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 9*a**2*e**7*m*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 20*a**2*e**7*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) - 2*a*c*d**5*e**2*m*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) - 10*a*c*d**5*e**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 2*a*c*d**4*e**3*m**2*x*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 10*a*c*d**4*e**3*m*x*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 6*a*c*d**3*e**4*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 42*a*c*d**3*e**4*m*x**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 60*a*c*d**3*e**4*x**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 6*a*c*d**2*e**5*m**2*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 46*a*c*d**2*e**5*m*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 80*a*c*d**2*e**5*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 2*a*c*d*e**6*m**2*x**4*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 16*a*c*d*e**6*m*x**4*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 30*a*c*d*e**6*x**4*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 2*c**2*d**7*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) - 2*c**2*d**6*e*m*x*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + c**2*d**5*e**2*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + c**2*d**5*e**2*m*x**2*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 3*c**2*d**4*e**3*m**2*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 15*c**2*d**4*e**3*m*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 20*c**2*d**4*e**3*x**3*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 3*c**2*d**3*e**4*m**2*x**4*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 19*c**2*d**3*e**4*m*x**4*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 30*c**2*d**3*e**4*x**4*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + c**2*d**2*e**5*m**2*x**5*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 7*c**2*d**2*e**5*m*x**5*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3) + 12*c**2*d**2*e**5*x**5*(d + e*x)**m/(e**3*m**3 + 12*e**3*m**2 + 47*e**3*m + 60*e**3), True))","A",0
2086,1,556,0,1.341867," ","integrate((e*x+d)**m*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\begin{cases} \frac{c d^{2} d^{m} x^{2}}{2} & \text{for}\: e = 0 \\- \frac{a e^{2}}{d e^{2} + e^{3} x} + \frac{c d^{2} \log{\left(\frac{d}{e} + x \right)}}{d e^{2} + e^{3} x} + \frac{c d^{2}}{d e^{2} + e^{3} x} + \frac{c d e x \log{\left(\frac{d}{e} + x \right)}}{d e^{2} + e^{3} x} & \text{for}\: m = -3 \\a \log{\left(\frac{d}{e} + x \right)} - \frac{c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{c d x}{e} & \text{for}\: m = -2 \\\frac{a d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{3 a d^{2} e^{2} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{2 a d e^{3} m x \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{6 a d e^{3} x \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{a e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{3 a e^{4} x^{2} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} - \frac{c d^{4} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{c d^{3} e m x \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{2 c d^{2} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{3 c d^{2} e^{2} x^{2} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{c d e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} + \frac{2 c d e^{3} x^{3} \left(d + e x\right)^{m}}{e^{2} m^{2} + 5 e^{2} m + 6 e^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*d**2*d**m*x**2/2, Eq(e, 0)), (-a*e**2/(d*e**2 + e**3*x) + c*d**2*log(d/e + x)/(d*e**2 + e**3*x) + c*d**2/(d*e**2 + e**3*x) + c*d*e*x*log(d/e + x)/(d*e**2 + e**3*x), Eq(m, -3)), (a*log(d/e + x) - c*d**2*log(d/e + x)/e**2 + c*d*x/e, Eq(m, -2)), (a*d**2*e**2*m*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + 3*a*d**2*e**2*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + 2*a*d*e**3*m*x*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + 6*a*d*e**3*x*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + a*e**4*m*x**2*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + 3*a*e**4*x**2*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) - c*d**4*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + c*d**3*e*m*x*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + 2*c*d**2*e**2*m*x**2*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + 3*c*d**2*e**2*x**2*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + c*d*e**3*m*x**3*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2) + 2*c*d*e**3*x**3*(d + e*x)**m/(e**2*m**2 + 5*e**2*m + 6*e**2), True))","A",0
2087,0,0,0,0.000000," ","integrate((e*x+d)**m/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(d + e x\right) \left(a e + c d x\right)}\, dx"," ",0,"Integral((d + e*x)**m/((d + e*x)*(a*e + c*d*x)), x)","F",0
2088,0,0,0,0.000000," ","integrate((e*x+d)**m/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**2,x)","\int \frac{\left(d + e x\right)^{m}}{\left(d + e x\right)^{2} \left(a e + c d x\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**m/((d + e*x)**2*(a*e + c*d*x)**2), x)","F",0
2089,0,0,0,0.000000," ","integrate((e*x+d)**m/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3,x)","\int \frac{\left(d + e x\right)^{m}}{\left(d + e x\right)^{3} \left(a e + c d x\right)^{3}}\, dx"," ",0,"Integral((d + e*x)**m/((d + e*x)**3*(a*e + c*d*x)**3), x)","F",0
2090,-2,0,0,0.000000," ","integrate((e*x+d)**m/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2091,-1,0,0,0.000000," ","integrate((e*x+d)**m*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2092,-1,0,0,0.000000," ","integrate((e*x+d)**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2093,-1,0,0,0.000000," ","integrate((e*x+d)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2094,0,0,0,0.000000," ","integrate((e*x+d)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p,x)","\int \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{p} \left(d + e x\right)\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**p*(d + e*x), x)","F",0
2095,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p,x)","\int \left(a d e + c d e x^{2} + x \left(a e^{2} + c d^{2}\right)\right)^{p}\, dx"," ",0,"Integral((a*d*e + c*d*e*x**2 + x*(a*e**2 + c*d**2))**p, x)","F",0
2096,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{p}}{d + e x}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**p/(d + e*x), x)","F",0
2097,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p/(e*x+d)**2,x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**p/(d + e*x)**2, x)","F",0
2098,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2099,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p/((e*x+d)**(2*p)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2100,-1,0,0,0.000000," ","integrate((e*x+d)**(-1-2*p)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2101,-1,0,0,0.000000," ","integrate((e*x+d)**(-2-2*p)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2102,-1,0,0,0.000000," ","integrate((e*x+d)**(-3-2*p)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2103,-1,0,0,0.000000," ","integrate((e*x+d)**(-4-2*p)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2104,-1,0,0,0.000000," ","integrate((e*x+d)**(-5-2*p)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2105,-2,0,0,0.000000," ","integrate((e*x+d)**m/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
2106,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**p/((e*x+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2107,1,146,0,0.098065," ","integrate((e*x+d)**4*(c*x**2+b*x+a),x)","a d^{4} x + \frac{c e^{4} x^{7}}{7} + x^{6} \left(\frac{b e^{4}}{6} + \frac{2 c d e^{3}}{3}\right) + x^{5} \left(\frac{a e^{4}}{5} + \frac{4 b d e^{3}}{5} + \frac{6 c d^{2} e^{2}}{5}\right) + x^{4} \left(a d e^{3} + \frac{3 b d^{2} e^{2}}{2} + c d^{3} e\right) + x^{3} \left(2 a d^{2} e^{2} + \frac{4 b d^{3} e}{3} + \frac{c d^{4}}{3}\right) + x^{2} \left(2 a d^{3} e + \frac{b d^{4}}{2}\right)"," ",0,"a*d**4*x + c*e**4*x**7/7 + x**6*(b*e**4/6 + 2*c*d*e**3/3) + x**5*(a*e**4/5 + 4*b*d*e**3/5 + 6*c*d**2*e**2/5) + x**4*(a*d*e**3 + 3*b*d**2*e**2/2 + c*d**3*e) + x**3*(2*a*d**2*e**2 + 4*b*d**3*e/3 + c*d**4/3) + x**2*(2*a*d**3*e + b*d**4/2)","B",0
2108,1,110,0,0.095310," ","integrate((e*x+d)**3*(c*x**2+b*x+a),x)","a d^{3} x + \frac{c e^{3} x^{6}}{6} + x^{5} \left(\frac{b e^{3}}{5} + \frac{3 c d e^{2}}{5}\right) + x^{4} \left(\frac{a e^{3}}{4} + \frac{3 b d e^{2}}{4} + \frac{3 c d^{2} e}{4}\right) + x^{3} \left(a d e^{2} + b d^{2} e + \frac{c d^{3}}{3}\right) + x^{2} \left(\frac{3 a d^{2} e}{2} + \frac{b d^{3}}{2}\right)"," ",0,"a*d**3*x + c*e**3*x**6/6 + x**5*(b*e**3/5 + 3*c*d*e**2/5) + x**4*(a*e**3/4 + 3*b*d*e**2/4 + 3*c*d**2*e/4) + x**3*(a*d*e**2 + b*d**2*e + c*d**3/3) + x**2*(3*a*d**2*e/2 + b*d**3/2)","A",0
2109,1,73,0,0.113725," ","integrate((e*x+d)**2*(c*x**2+b*x+a),x)","a d^{2} x + \frac{c e^{2} x^{5}}{5} + x^{4} \left(\frac{b e^{2}}{4} + \frac{c d e}{2}\right) + x^{3} \left(\frac{a e^{2}}{3} + \frac{2 b d e}{3} + \frac{c d^{2}}{3}\right) + x^{2} \left(a d e + \frac{b d^{2}}{2}\right)"," ",0,"a*d**2*x + c*e**2*x**5/5 + x**4*(b*e**2/4 + c*d*e/2) + x**3*(a*e**2/3 + 2*b*d*e/3 + c*d**2/3) + x**2*(a*d*e + b*d**2/2)","A",0
2110,1,39,0,0.069514," ","integrate((e*x+d)*(c*x**2+b*x+a),x)","a d x + \frac{c e x^{4}}{4} + x^{3} \left(\frac{b e}{3} + \frac{c d}{3}\right) + x^{2} \left(\frac{a e}{2} + \frac{b d}{2}\right)"," ",0,"a*d*x + c*e*x**4/4 + x**3*(b*e/3 + c*d/3) + x**2*(a*e/2 + b*d/2)","A",0
2111,1,15,0,0.061017," ","integrate(c*x**2+b*x+a,x)","a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3}"," ",0,"a*x + b*x**2/2 + c*x**3/3","A",0
2112,1,44,0,0.213507," ","integrate((c*x**2+b*x+a)/(e*x+d),x)","\frac{c x^{2}}{2 e} + x \left(\frac{b}{e} - \frac{c d}{e^{2}}\right) + \frac{\left(a e^{2} - b d e + c d^{2}\right) \log{\left(d + e x \right)}}{e^{3}}"," ",0,"c*x**2/(2*e) + x*(b/e - c*d/e**2) + (a*e**2 - b*d*e + c*d**2)*log(d + e*x)/e**3","A",0
2113,1,49,0,0.334570," ","integrate((c*x**2+b*x+a)/(e*x+d)**2,x)","\frac{c x}{e^{2}} + \frac{- a e^{2} + b d e - c d^{2}}{d e^{3} + e^{4} x} + \frac{\left(b e - 2 c d\right) \log{\left(d + e x \right)}}{e^{3}}"," ",0,"c*x/e**2 + (-a*e**2 + b*d*e - c*d**2)/(d*e**3 + e**4*x) + (b*e - 2*c*d)*log(d + e*x)/e**3","A",0
2114,1,68,0,0.546108," ","integrate((c*x**2+b*x+a)/(e*x+d)**3,x)","\frac{c \log{\left(d + e x \right)}}{e^{3}} + \frac{- a e^{2} - b d e + 3 c d^{2} + x \left(- 2 b e^{2} + 4 c d e\right)}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}}"," ",0,"c*log(d + e*x)/e**3 + (-a*e**2 - b*d*e + 3*c*d**2 + x*(-2*b*e**2 + 4*c*d*e))/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2)","A",0
2115,1,82,0,0.886893," ","integrate((c*x**2+b*x+a)/(e*x+d)**4,x)","\frac{- 2 a e^{2} - b d e - 2 c d^{2} - 6 c e^{2} x^{2} + x \left(- 3 b e^{2} - 6 c d e\right)}{6 d^{3} e^{3} + 18 d^{2} e^{4} x + 18 d e^{5} x^{2} + 6 e^{6} x^{3}}"," ",0,"(-2*a*e**2 - b*d*e - 2*c*d**2 - 6*c*e**2*x**2 + x*(-3*b*e**2 - 6*c*d*e))/(6*d**3*e**3 + 18*d**2*e**4*x + 18*d*e**5*x**2 + 6*e**6*x**3)","A",0
2116,1,92,0,1.422824," ","integrate((c*x**2+b*x+a)/(e*x+d)**5,x)","\frac{- 3 a e^{2} - b d e - c d^{2} - 6 c e^{2} x^{2} + x \left(- 4 b e^{2} - 4 c d e\right)}{12 d^{4} e^{3} + 48 d^{3} e^{4} x + 72 d^{2} e^{5} x^{2} + 48 d e^{6} x^{3} + 12 e^{7} x^{4}}"," ",0,"(-3*a*e**2 - b*d*e - c*d**2 - 6*c*e**2*x**2 + x*(-4*b*e**2 - 4*c*d*e))/(12*d**4*e**3 + 48*d**3*e**4*x + 72*d**2*e**5*x**2 + 48*d*e**6*x**3 + 12*e**7*x**4)","A",0
2117,1,107,0,2.174113," ","integrate((c*x**2+b*x+a)/(e*x+d)**6,x)","\frac{- 12 a e^{2} - 3 b d e - 2 c d^{2} - 20 c e^{2} x^{2} + x \left(- 15 b e^{2} - 10 c d e\right)}{60 d^{5} e^{3} + 300 d^{4} e^{4} x + 600 d^{3} e^{5} x^{2} + 600 d^{2} e^{6} x^{3} + 300 d e^{7} x^{4} + 60 e^{8} x^{5}}"," ",0,"(-12*a*e**2 - 3*b*d*e - 2*c*d**2 - 20*c*e**2*x**2 + x*(-15*b*e**2 - 10*c*d*e))/(60*d**5*e**3 + 300*d**4*e**4*x + 600*d**3*e**5*x**2 + 600*d**2*e**6*x**3 + 300*d*e**7*x**4 + 60*e**8*x**5)","A",0
2118,1,337,0,0.125292," ","integrate((e*x+d)**4*(c*x**2+b*x+a)**2,x)","a^{2} d^{4} x + \frac{c^{2} e^{4} x^{9}}{9} + x^{8} \left(\frac{b c e^{4}}{4} + \frac{c^{2} d e^{3}}{2}\right) + x^{7} \left(\frac{2 a c e^{4}}{7} + \frac{b^{2} e^{4}}{7} + \frac{8 b c d e^{3}}{7} + \frac{6 c^{2} d^{2} e^{2}}{7}\right) + x^{6} \left(\frac{a b e^{4}}{3} + \frac{4 a c d e^{3}}{3} + \frac{2 b^{2} d e^{3}}{3} + 2 b c d^{2} e^{2} + \frac{2 c^{2} d^{3} e}{3}\right) + x^{5} \left(\frac{a^{2} e^{4}}{5} + \frac{8 a b d e^{3}}{5} + \frac{12 a c d^{2} e^{2}}{5} + \frac{6 b^{2} d^{2} e^{2}}{5} + \frac{8 b c d^{3} e}{5} + \frac{c^{2} d^{4}}{5}\right) + x^{4} \left(a^{2} d e^{3} + 3 a b d^{2} e^{2} + 2 a c d^{3} e + b^{2} d^{3} e + \frac{b c d^{4}}{2}\right) + x^{3} \left(2 a^{2} d^{2} e^{2} + \frac{8 a b d^{3} e}{3} + \frac{2 a c d^{4}}{3} + \frac{b^{2} d^{4}}{3}\right) + x^{2} \left(2 a^{2} d^{3} e + a b d^{4}\right)"," ",0,"a**2*d**4*x + c**2*e**4*x**9/9 + x**8*(b*c*e**4/4 + c**2*d*e**3/2) + x**7*(2*a*c*e**4/7 + b**2*e**4/7 + 8*b*c*d*e**3/7 + 6*c**2*d**2*e**2/7) + x**6*(a*b*e**4/3 + 4*a*c*d*e**3/3 + 2*b**2*d*e**3/3 + 2*b*c*d**2*e**2 + 2*c**2*d**3*e/3) + x**5*(a**2*e**4/5 + 8*a*b*d*e**3/5 + 12*a*c*d**2*e**2/5 + 6*b**2*d**2*e**2/5 + 8*b*c*d**3*e/5 + c**2*d**4/5) + x**4*(a**2*d*e**3 + 3*a*b*d**2*e**2 + 2*a*c*d**3*e + b**2*d**3*e + b*c*d**4/2) + x**3*(2*a**2*d**2*e**2 + 8*a*b*d**3*e/3 + 2*a*c*d**4/3 + b**2*d**4/3) + x**2*(2*a**2*d**3*e + a*b*d**4)","B",0
2119,1,260,0,0.113025," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**2,x)","a^{2} d^{3} x + \frac{c^{2} e^{3} x^{8}}{8} + x^{7} \left(\frac{2 b c e^{3}}{7} + \frac{3 c^{2} d e^{2}}{7}\right) + x^{6} \left(\frac{a c e^{3}}{3} + \frac{b^{2} e^{3}}{6} + b c d e^{2} + \frac{c^{2} d^{2} e}{2}\right) + x^{5} \left(\frac{2 a b e^{3}}{5} + \frac{6 a c d e^{2}}{5} + \frac{3 b^{2} d e^{2}}{5} + \frac{6 b c d^{2} e}{5} + \frac{c^{2} d^{3}}{5}\right) + x^{4} \left(\frac{a^{2} e^{3}}{4} + \frac{3 a b d e^{2}}{2} + \frac{3 a c d^{2} e}{2} + \frac{3 b^{2} d^{2} e}{4} + \frac{b c d^{3}}{2}\right) + x^{3} \left(a^{2} d e^{2} + 2 a b d^{2} e + \frac{2 a c d^{3}}{3} + \frac{b^{2} d^{3}}{3}\right) + x^{2} \left(\frac{3 a^{2} d^{2} e}{2} + a b d^{3}\right)"," ",0,"a**2*d**3*x + c**2*e**3*x**8/8 + x**7*(2*b*c*e**3/7 + 3*c**2*d*e**2/7) + x**6*(a*c*e**3/3 + b**2*e**3/6 + b*c*d*e**2 + c**2*d**2*e/2) + x**5*(2*a*b*e**3/5 + 6*a*c*d*e**2/5 + 3*b**2*d*e**2/5 + 6*b*c*d**2*e/5 + c**2*d**3/5) + x**4*(a**2*e**3/4 + 3*a*b*d*e**2/2 + 3*a*c*d**2*e/2 + 3*b**2*d**2*e/4 + b*c*d**3/2) + x**3*(a**2*d*e**2 + 2*a*b*d**2*e + 2*a*c*d**3/3 + b**2*d**3/3) + x**2*(3*a**2*d**2*e/2 + a*b*d**3)","A",0
2120,1,173,0,0.101977," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**2,x)","a^{2} d^{2} x + \frac{c^{2} e^{2} x^{7}}{7} + x^{6} \left(\frac{b c e^{2}}{3} + \frac{c^{2} d e}{3}\right) + x^{5} \left(\frac{2 a c e^{2}}{5} + \frac{b^{2} e^{2}}{5} + \frac{4 b c d e}{5} + \frac{c^{2} d^{2}}{5}\right) + x^{4} \left(\frac{a b e^{2}}{2} + a c d e + \frac{b^{2} d e}{2} + \frac{b c d^{2}}{2}\right) + x^{3} \left(\frac{a^{2} e^{2}}{3} + \frac{4 a b d e}{3} + \frac{2 a c d^{2}}{3} + \frac{b^{2} d^{2}}{3}\right) + x^{2} \left(a^{2} d e + a b d^{2}\right)"," ",0,"a**2*d**2*x + c**2*e**2*x**7/7 + x**6*(b*c*e**2/3 + c**2*d*e/3) + x**5*(2*a*c*e**2/5 + b**2*e**2/5 + 4*b*c*d*e/5 + c**2*d**2/5) + x**4*(a*b*e**2/2 + a*c*d*e + b**2*d*e/2 + b*c*d**2/2) + x**3*(a**2*e**2/3 + 4*a*b*d*e/3 + 2*a*c*d**2/3 + b**2*d**2/3) + x**2*(a**2*d*e + a*b*d**2)","A",0
2121,1,100,0,0.088029," ","integrate((e*x+d)*(c*x**2+b*x+a)**2,x)","a^{2} d x + \frac{c^{2} e x^{6}}{6} + x^{5} \left(\frac{2 b c e}{5} + \frac{c^{2} d}{5}\right) + x^{4} \left(\frac{a c e}{2} + \frac{b^{2} e}{4} + \frac{b c d}{2}\right) + x^{3} \left(\frac{2 a b e}{3} + \frac{2 a c d}{3} + \frac{b^{2} d}{3}\right) + x^{2} \left(\frac{a^{2} e}{2} + a b d\right)"," ",0,"a**2*d*x + c**2*e*x**6/6 + x**5*(2*b*c*e/5 + c**2*d/5) + x**4*(a*c*e/2 + b**2*e/4 + b*c*d/2) + x**3*(2*a*b*e/3 + 2*a*c*d/3 + b**2*d/3) + x**2*(a**2*e/2 + a*b*d)","A",0
2122,1,42,0,0.072976," ","integrate((c*x**2+b*x+a)**2,x)","a^{2} x + a b x^{2} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5} + x^{3} \left(\frac{2 a c}{3} + \frac{b^{2}}{3}\right)"," ",0,"a**2*x + a*b*x**2 + b*c*x**4/2 + c**2*x**5/5 + x**3*(2*a*c/3 + b**2/3)","A",0
2123,1,143,0,0.470050," ","integrate((c*x**2+b*x+a)**2/(e*x+d),x)","\frac{c^{2} x^{4}}{4 e} + x^{3} \left(\frac{2 b c}{3 e} - \frac{c^{2} d}{3 e^{2}}\right) + x^{2} \left(\frac{a c}{e} + \frac{b^{2}}{2 e} - \frac{b c d}{e^{2}} + \frac{c^{2} d^{2}}{2 e^{3}}\right) + x \left(\frac{2 a b}{e} - \frac{2 a c d}{e^{2}} - \frac{b^{2} d}{e^{2}} + \frac{2 b c d^{2}}{e^{3}} - \frac{c^{2} d^{3}}{e^{4}}\right) + \frac{\left(a e^{2} - b d e + c d^{2}\right)^{2} \log{\left(d + e x \right)}}{e^{5}}"," ",0,"c**2*x**4/(4*e) + x**3*(2*b*c/(3*e) - c**2*d/(3*e**2)) + x**2*(a*c/e + b**2/(2*e) - b*c*d/e**2 + c**2*d**2/(2*e**3)) + x*(2*a*b/e - 2*a*c*d/e**2 - b**2*d/e**2 + 2*b*c*d**2/e**3 - c**2*d**3/e**4) + (a*e**2 - b*d*e + c*d**2)**2*log(d + e*x)/e**5","A",0
2124,1,170,0,0.987721," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**2,x)","\frac{c^{2} x^{3}}{3 e^{2}} + x^{2} \left(\frac{b c}{e^{2}} - \frac{c^{2} d}{e^{3}}\right) + x \left(\frac{2 a c}{e^{2}} + \frac{b^{2}}{e^{2}} - \frac{4 b c d}{e^{3}} + \frac{3 c^{2} d^{2}}{e^{4}}\right) + \frac{- a^{2} e^{4} + 2 a b d e^{3} - 2 a c d^{2} e^{2} - b^{2} d^{2} e^{2} + 2 b c d^{3} e - c^{2} d^{4}}{d e^{5} + e^{6} x} + \frac{2 \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) \log{\left(d + e x \right)}}{e^{5}}"," ",0,"c**2*x**3/(3*e**2) + x**2*(b*c/e**2 - c**2*d/e**3) + x*(2*a*c/e**2 + b**2/e**2 - 4*b*c*d/e**3 + 3*c**2*d**2/e**4) + (-a**2*e**4 + 2*a*b*d*e**3 - 2*a*c*d**2*e**2 - b**2*d**2*e**2 + 2*b*c*d**3*e - c**2*d**4)/(d*e**5 + e**6*x) + 2*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)*log(d + e*x)/e**5","A",0
2125,1,211,0,2.925236," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**3,x)","\frac{c^{2} x^{2}}{2 e^{3}} + x \left(\frac{2 b c}{e^{3}} - \frac{3 c^{2} d}{e^{4}}\right) + \frac{- a^{2} e^{4} - 2 a b d e^{3} + 6 a c d^{2} e^{2} + 3 b^{2} d^{2} e^{2} - 10 b c d^{3} e + 7 c^{2} d^{4} + x \left(- 4 a b e^{4} + 8 a c d e^{3} + 4 b^{2} d e^{3} - 12 b c d^{2} e^{2} + 8 c^{2} d^{3} e\right)}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{\left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{5}}"," ",0,"c**2*x**2/(2*e**3) + x*(2*b*c/e**3 - 3*c**2*d/e**4) + (-a**2*e**4 - 2*a*b*d*e**3 + 6*a*c*d**2*e**2 + 3*b**2*d**2*e**2 - 10*b*c*d**3*e + 7*c**2*d**4 + x*(-4*a*b*e**4 + 8*a*c*d*e**3 + 4*b**2*d*e**3 - 12*b*c*d**2*e**2 + 8*c**2*d**3*e))/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + (2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2)*log(d + e*x)/e**5","A",0
2126,1,218,0,7.853700," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**4,x)","\frac{c^{2} x}{e^{4}} + \frac{2 c \left(b e - 2 c d\right) \log{\left(d + e x \right)}}{e^{5}} + \frac{- a^{2} e^{4} - a b d e^{3} - 2 a c d^{2} e^{2} - b^{2} d^{2} e^{2} + 11 b c d^{3} e - 13 c^{2} d^{4} + x^{2} \left(- 6 a c e^{4} - 3 b^{2} e^{4} + 18 b c d e^{3} - 18 c^{2} d^{2} e^{2}\right) + x \left(- 3 a b e^{4} - 6 a c d e^{3} - 3 b^{2} d e^{3} + 27 b c d^{2} e^{2} - 30 c^{2} d^{3} e\right)}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}}"," ",0,"c**2*x/e**4 + 2*c*(b*e - 2*c*d)*log(d + e*x)/e**5 + (-a**2*e**4 - a*b*d*e**3 - 2*a*c*d**2*e**2 - b**2*d**2*e**2 + 11*b*c*d**3*e - 13*c**2*d**4 + x**2*(-6*a*c*e**4 - 3*b**2*e**4 + 18*b*c*d*e**3 - 18*c**2*d**2*e**2) + x*(-3*a*b*e**4 - 6*a*c*d*e**3 - 3*b**2*d*e**3 + 27*b*c*d**2*e**2 - 30*c**2*d**3*e))/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3)","A",0
2127,1,238,0,17.423999," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**5,x)","\frac{c^{2} \log{\left(d + e x \right)}}{e^{5}} + \frac{- 3 a^{2} e^{4} - 2 a b d e^{3} - 2 a c d^{2} e^{2} - b^{2} d^{2} e^{2} - 6 b c d^{3} e + 25 c^{2} d^{4} + x^{3} \left(- 24 b c e^{4} + 48 c^{2} d e^{3}\right) + x^{2} \left(- 12 a c e^{4} - 6 b^{2} e^{4} - 36 b c d e^{3} + 108 c^{2} d^{2} e^{2}\right) + x \left(- 8 a b e^{4} - 8 a c d e^{3} - 4 b^{2} d e^{3} - 24 b c d^{2} e^{2} + 88 c^{2} d^{3} e\right)}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}}"," ",0,"c**2*log(d + e*x)/e**5 + (-3*a**2*e**4 - 2*a*b*d*e**3 - 2*a*c*d**2*e**2 - b**2*d**2*e**2 - 6*b*c*d**3*e + 25*c**2*d**4 + x**3*(-24*b*c*e**4 + 48*c**2*d*e**3) + x**2*(-12*a*c*e**4 - 6*b**2*e**4 - 36*b*c*d*e**3 + 108*c**2*d**2*e**2) + x*(-8*a*b*e**4 - 8*a*c*d*e**3 - 4*b**2*d*e**3 - 24*b*c*d**2*e**2 + 88*c**2*d**3*e))/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4)","A",0
2128,1,253,0,34.873499," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**6,x)","\frac{- 6 a^{2} e^{4} - 3 a b d e^{3} - 2 a c d^{2} e^{2} - b^{2} d^{2} e^{2} - 3 b c d^{3} e - 6 c^{2} d^{4} - 30 c^{2} e^{4} x^{4} + x^{3} \left(- 30 b c e^{4} - 60 c^{2} d e^{3}\right) + x^{2} \left(- 20 a c e^{4} - 10 b^{2} e^{4} - 30 b c d e^{3} - 60 c^{2} d^{2} e^{2}\right) + x \left(- 15 a b e^{4} - 10 a c d e^{3} - 5 b^{2} d e^{3} - 15 b c d^{2} e^{2} - 30 c^{2} d^{3} e\right)}{30 d^{5} e^{5} + 150 d^{4} e^{6} x + 300 d^{3} e^{7} x^{2} + 300 d^{2} e^{8} x^{3} + 150 d e^{9} x^{4} + 30 e^{10} x^{5}}"," ",0,"(-6*a**2*e**4 - 3*a*b*d*e**3 - 2*a*c*d**2*e**2 - b**2*d**2*e**2 - 3*b*c*d**3*e - 6*c**2*d**4 - 30*c**2*e**4*x**4 + x**3*(-30*b*c*e**4 - 60*c**2*d*e**3) + x**2*(-20*a*c*e**4 - 10*b**2*e**4 - 30*b*c*d*e**3 - 60*c**2*d**2*e**2) + x*(-15*a*b*e**4 - 10*a*c*d*e**3 - 5*b**2*d*e**3 - 15*b*c*d**2*e**2 - 30*c**2*d**3*e))/(30*d**5*e**5 + 150*d**4*e**6*x + 300*d**3*e**7*x**2 + 300*d**2*e**8*x**3 + 150*d*e**9*x**4 + 30*e**10*x**5)","A",0
2129,1,265,0,73.578864," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**7,x)","\frac{- 10 a^{2} e^{4} - 4 a b d e^{3} - 2 a c d^{2} e^{2} - b^{2} d^{2} e^{2} - 2 b c d^{3} e - 2 c^{2} d^{4} - 30 c^{2} e^{4} x^{4} + x^{3} \left(- 40 b c e^{4} - 40 c^{2} d e^{3}\right) + x^{2} \left(- 30 a c e^{4} - 15 b^{2} e^{4} - 30 b c d e^{3} - 30 c^{2} d^{2} e^{2}\right) + x \left(- 24 a b e^{4} - 12 a c d e^{3} - 6 b^{2} d e^{3} - 12 b c d^{2} e^{2} - 12 c^{2} d^{3} e\right)}{60 d^{6} e^{5} + 360 d^{5} e^{6} x + 900 d^{4} e^{7} x^{2} + 1200 d^{3} e^{8} x^{3} + 900 d^{2} e^{9} x^{4} + 360 d e^{10} x^{5} + 60 e^{11} x^{6}}"," ",0,"(-10*a**2*e**4 - 4*a*b*d*e**3 - 2*a*c*d**2*e**2 - b**2*d**2*e**2 - 2*b*c*d**3*e - 2*c**2*d**4 - 30*c**2*e**4*x**4 + x**3*(-40*b*c*e**4 - 40*c**2*d*e**3) + x**2*(-30*a*c*e**4 - 15*b**2*e**4 - 30*b*c*d*e**3 - 30*c**2*d**2*e**2) + x*(-24*a*b*e**4 - 12*a*c*d*e**3 - 6*b**2*d*e**3 - 12*b*c*d**2*e**2 - 12*c**2*d**3*e))/(60*d**6*e**5 + 360*d**5*e**6*x + 900*d**4*e**7*x**2 + 1200*d**3*e**8*x**3 + 900*d**2*e**9*x**4 + 360*d*e**10*x**5 + 60*e**11*x**6)","A",0
2130,1,279,0,168.161535," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**8,x)","\frac{- 30 a^{2} e^{4} - 10 a b d e^{3} - 4 a c d^{2} e^{2} - 2 b^{2} d^{2} e^{2} - 3 b c d^{3} e - 2 c^{2} d^{4} - 70 c^{2} e^{4} x^{4} + x^{3} \left(- 105 b c e^{4} - 70 c^{2} d e^{3}\right) + x^{2} \left(- 84 a c e^{4} - 42 b^{2} e^{4} - 63 b c d e^{3} - 42 c^{2} d^{2} e^{2}\right) + x \left(- 70 a b e^{4} - 28 a c d e^{3} - 14 b^{2} d e^{3} - 21 b c d^{2} e^{2} - 14 c^{2} d^{3} e\right)}{210 d^{7} e^{5} + 1470 d^{6} e^{6} x + 4410 d^{5} e^{7} x^{2} + 7350 d^{4} e^{8} x^{3} + 7350 d^{3} e^{9} x^{4} + 4410 d^{2} e^{10} x^{5} + 1470 d e^{11} x^{6} + 210 e^{12} x^{7}}"," ",0,"(-30*a**2*e**4 - 10*a*b*d*e**3 - 4*a*c*d**2*e**2 - 2*b**2*d**2*e**2 - 3*b*c*d**3*e - 2*c**2*d**4 - 70*c**2*e**4*x**4 + x**3*(-105*b*c*e**4 - 70*c**2*d*e**3) + x**2*(-84*a*c*e**4 - 42*b**2*e**4 - 63*b*c*d*e**3 - 42*c**2*d**2*e**2) + x*(-70*a*b*e**4 - 28*a*c*d*e**3 - 14*b**2*d*e**3 - 21*b*c*d**2*e**2 - 14*c**2*d**3*e))/(210*d**7*e**5 + 1470*d**6*e**6*x + 4410*d**5*e**7*x**2 + 7350*d**4*e**8*x**3 + 7350*d**3*e**9*x**4 + 4410*d**2*e**10*x**5 + 1470*d*e**11*x**6 + 210*e**12*x**7)","A",0
2131,1,620,0,0.160443," ","integrate((e*x+d)**4*(c*x**2+b*x+a)**3,x)","a^{3} d^{4} x + \frac{c^{3} e^{4} x^{11}}{11} + x^{10} \left(\frac{3 b c^{2} e^{4}}{10} + \frac{2 c^{3} d e^{3}}{5}\right) + x^{9} \left(\frac{a c^{2} e^{4}}{3} + \frac{b^{2} c e^{4}}{3} + \frac{4 b c^{2} d e^{3}}{3} + \frac{2 c^{3} d^{2} e^{2}}{3}\right) + x^{8} \left(\frac{3 a b c e^{4}}{4} + \frac{3 a c^{2} d e^{3}}{2} + \frac{b^{3} e^{4}}{8} + \frac{3 b^{2} c d e^{3}}{2} + \frac{9 b c^{2} d^{2} e^{2}}{4} + \frac{c^{3} d^{3} e}{2}\right) + x^{7} \left(\frac{3 a^{2} c e^{4}}{7} + \frac{3 a b^{2} e^{4}}{7} + \frac{24 a b c d e^{3}}{7} + \frac{18 a c^{2} d^{2} e^{2}}{7} + \frac{4 b^{3} d e^{3}}{7} + \frac{18 b^{2} c d^{2} e^{2}}{7} + \frac{12 b c^{2} d^{3} e}{7} + \frac{c^{3} d^{4}}{7}\right) + x^{6} \left(\frac{a^{2} b e^{4}}{2} + 2 a^{2} c d e^{3} + 2 a b^{2} d e^{3} + 6 a b c d^{2} e^{2} + 2 a c^{2} d^{3} e + b^{3} d^{2} e^{2} + 2 b^{2} c d^{3} e + \frac{b c^{2} d^{4}}{2}\right) + x^{5} \left(\frac{a^{3} e^{4}}{5} + \frac{12 a^{2} b d e^{3}}{5} + \frac{18 a^{2} c d^{2} e^{2}}{5} + \frac{18 a b^{2} d^{2} e^{2}}{5} + \frac{24 a b c d^{3} e}{5} + \frac{3 a c^{2} d^{4}}{5} + \frac{4 b^{3} d^{3} e}{5} + \frac{3 b^{2} c d^{4}}{5}\right) + x^{4} \left(a^{3} d e^{3} + \frac{9 a^{2} b d^{2} e^{2}}{2} + 3 a^{2} c d^{3} e + 3 a b^{2} d^{3} e + \frac{3 a b c d^{4}}{2} + \frac{b^{3} d^{4}}{4}\right) + x^{3} \left(2 a^{3} d^{2} e^{2} + 4 a^{2} b d^{3} e + a^{2} c d^{4} + a b^{2} d^{4}\right) + x^{2} \left(2 a^{3} d^{3} e + \frac{3 a^{2} b d^{4}}{2}\right)"," ",0,"a**3*d**4*x + c**3*e**4*x**11/11 + x**10*(3*b*c**2*e**4/10 + 2*c**3*d*e**3/5) + x**9*(a*c**2*e**4/3 + b**2*c*e**4/3 + 4*b*c**2*d*e**3/3 + 2*c**3*d**2*e**2/3) + x**8*(3*a*b*c*e**4/4 + 3*a*c**2*d*e**3/2 + b**3*e**4/8 + 3*b**2*c*d*e**3/2 + 9*b*c**2*d**2*e**2/4 + c**3*d**3*e/2) + x**7*(3*a**2*c*e**4/7 + 3*a*b**2*e**4/7 + 24*a*b*c*d*e**3/7 + 18*a*c**2*d**2*e**2/7 + 4*b**3*d*e**3/7 + 18*b**2*c*d**2*e**2/7 + 12*b*c**2*d**3*e/7 + c**3*d**4/7) + x**6*(a**2*b*e**4/2 + 2*a**2*c*d*e**3 + 2*a*b**2*d*e**3 + 6*a*b*c*d**2*e**2 + 2*a*c**2*d**3*e + b**3*d**2*e**2 + 2*b**2*c*d**3*e + b*c**2*d**4/2) + x**5*(a**3*e**4/5 + 12*a**2*b*d*e**3/5 + 18*a**2*c*d**2*e**2/5 + 18*a*b**2*d**2*e**2/5 + 24*a*b*c*d**3*e/5 + 3*a*c**2*d**4/5 + 4*b**3*d**3*e/5 + 3*b**2*c*d**4/5) + x**4*(a**3*d*e**3 + 9*a**2*b*d**2*e**2/2 + 3*a**2*c*d**3*e + 3*a*b**2*d**3*e + 3*a*b*c*d**4/2 + b**3*d**4/4) + x**3*(2*a**3*d**2*e**2 + 4*a**2*b*d**3*e + a**2*c*d**4 + a*b**2*d**4) + x**2*(2*a**3*d**3*e + 3*a**2*b*d**4/2)","B",0
2132,1,484,0,0.141299," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**3,x)","a^{3} d^{3} x + \frac{c^{3} e^{3} x^{10}}{10} + x^{9} \left(\frac{b c^{2} e^{3}}{3} + \frac{c^{3} d e^{2}}{3}\right) + x^{8} \left(\frac{3 a c^{2} e^{3}}{8} + \frac{3 b^{2} c e^{3}}{8} + \frac{9 b c^{2} d e^{2}}{8} + \frac{3 c^{3} d^{2} e}{8}\right) + x^{7} \left(\frac{6 a b c e^{3}}{7} + \frac{9 a c^{2} d e^{2}}{7} + \frac{b^{3} e^{3}}{7} + \frac{9 b^{2} c d e^{2}}{7} + \frac{9 b c^{2} d^{2} e}{7} + \frac{c^{3} d^{3}}{7}\right) + x^{6} \left(\frac{a^{2} c e^{3}}{2} + \frac{a b^{2} e^{3}}{2} + 3 a b c d e^{2} + \frac{3 a c^{2} d^{2} e}{2} + \frac{b^{3} d e^{2}}{2} + \frac{3 b^{2} c d^{2} e}{2} + \frac{b c^{2} d^{3}}{2}\right) + x^{5} \left(\frac{3 a^{2} b e^{3}}{5} + \frac{9 a^{2} c d e^{2}}{5} + \frac{9 a b^{2} d e^{2}}{5} + \frac{18 a b c d^{2} e}{5} + \frac{3 a c^{2} d^{3}}{5} + \frac{3 b^{3} d^{2} e}{5} + \frac{3 b^{2} c d^{3}}{5}\right) + x^{4} \left(\frac{a^{3} e^{3}}{4} + \frac{9 a^{2} b d e^{2}}{4} + \frac{9 a^{2} c d^{2} e}{4} + \frac{9 a b^{2} d^{2} e}{4} + \frac{3 a b c d^{3}}{2} + \frac{b^{3} d^{3}}{4}\right) + x^{3} \left(a^{3} d e^{2} + 3 a^{2} b d^{2} e + a^{2} c d^{3} + a b^{2} d^{3}\right) + x^{2} \left(\frac{3 a^{3} d^{2} e}{2} + \frac{3 a^{2} b d^{3}}{2}\right)"," ",0,"a**3*d**3*x + c**3*e**3*x**10/10 + x**9*(b*c**2*e**3/3 + c**3*d*e**2/3) + x**8*(3*a*c**2*e**3/8 + 3*b**2*c*e**3/8 + 9*b*c**2*d*e**2/8 + 3*c**3*d**2*e/8) + x**7*(6*a*b*c*e**3/7 + 9*a*c**2*d*e**2/7 + b**3*e**3/7 + 9*b**2*c*d*e**2/7 + 9*b*c**2*d**2*e/7 + c**3*d**3/7) + x**6*(a**2*c*e**3/2 + a*b**2*e**3/2 + 3*a*b*c*d*e**2 + 3*a*c**2*d**2*e/2 + b**3*d*e**2/2 + 3*b**2*c*d**2*e/2 + b*c**2*d**3/2) + x**5*(3*a**2*b*e**3/5 + 9*a**2*c*d*e**2/5 + 9*a*b**2*d*e**2/5 + 18*a*b*c*d**2*e/5 + 3*a*c**2*d**3/5 + 3*b**3*d**2*e/5 + 3*b**2*c*d**3/5) + x**4*(a**3*e**3/4 + 9*a**2*b*d*e**2/4 + 9*a**2*c*d**2*e/4 + 9*a*b**2*d**2*e/4 + 3*a*b*c*d**3/2 + b**3*d**3/4) + x**3*(a**3*d*e**2 + 3*a**2*b*d**2*e + a**2*c*d**3 + a*b**2*d**3) + x**2*(3*a**3*d**2*e/2 + 3*a**2*b*d**3/2)","A",0
2133,1,332,0,0.120448," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**3,x)","a^{3} d^{2} x + \frac{c^{3} e^{2} x^{9}}{9} + x^{8} \left(\frac{3 b c^{2} e^{2}}{8} + \frac{c^{3} d e}{4}\right) + x^{7} \left(\frac{3 a c^{2} e^{2}}{7} + \frac{3 b^{2} c e^{2}}{7} + \frac{6 b c^{2} d e}{7} + \frac{c^{3} d^{2}}{7}\right) + x^{6} \left(a b c e^{2} + a c^{2} d e + \frac{b^{3} e^{2}}{6} + b^{2} c d e + \frac{b c^{2} d^{2}}{2}\right) + x^{5} \left(\frac{3 a^{2} c e^{2}}{5} + \frac{3 a b^{2} e^{2}}{5} + \frac{12 a b c d e}{5} + \frac{3 a c^{2} d^{2}}{5} + \frac{2 b^{3} d e}{5} + \frac{3 b^{2} c d^{2}}{5}\right) + x^{4} \left(\frac{3 a^{2} b e^{2}}{4} + \frac{3 a^{2} c d e}{2} + \frac{3 a b^{2} d e}{2} + \frac{3 a b c d^{2}}{2} + \frac{b^{3} d^{2}}{4}\right) + x^{3} \left(\frac{a^{3} e^{2}}{3} + 2 a^{2} b d e + a^{2} c d^{2} + a b^{2} d^{2}\right) + x^{2} \left(a^{3} d e + \frac{3 a^{2} b d^{2}}{2}\right)"," ",0,"a**3*d**2*x + c**3*e**2*x**9/9 + x**8*(3*b*c**2*e**2/8 + c**3*d*e/4) + x**7*(3*a*c**2*e**2/7 + 3*b**2*c*e**2/7 + 6*b*c**2*d*e/7 + c**3*d**2/7) + x**6*(a*b*c*e**2 + a*c**2*d*e + b**3*e**2/6 + b**2*c*d*e + b*c**2*d**2/2) + x**5*(3*a**2*c*e**2/5 + 3*a*b**2*e**2/5 + 12*a*b*c*d*e/5 + 3*a*c**2*d**2/5 + 2*b**3*d*e/5 + 3*b**2*c*d**2/5) + x**4*(3*a**2*b*e**2/4 + 3*a**2*c*d*e/2 + 3*a*b**2*d*e/2 + 3*a*b*c*d**2/2 + b**3*d**2/4) + x**3*(a**3*e**2/3 + 2*a**2*b*d*e + a**2*c*d**2 + a*b**2*d**2) + x**2*(a**3*d*e + 3*a**2*b*d**2/2)","A",0
2134,1,190,0,0.105341," ","integrate((e*x+d)*(c*x**2+b*x+a)**3,x)","a^{3} d x + \frac{c^{3} e x^{8}}{8} + x^{7} \left(\frac{3 b c^{2} e}{7} + \frac{c^{3} d}{7}\right) + x^{6} \left(\frac{a c^{2} e}{2} + \frac{b^{2} c e}{2} + \frac{b c^{2} d}{2}\right) + x^{5} \left(\frac{6 a b c e}{5} + \frac{3 a c^{2} d}{5} + \frac{b^{3} e}{5} + \frac{3 b^{2} c d}{5}\right) + x^{4} \left(\frac{3 a^{2} c e}{4} + \frac{3 a b^{2} e}{4} + \frac{3 a b c d}{2} + \frac{b^{3} d}{4}\right) + x^{3} \left(a^{2} b e + a^{2} c d + a b^{2} d\right) + x^{2} \left(\frac{a^{3} e}{2} + \frac{3 a^{2} b d}{2}\right)"," ",0,"a**3*d*x + c**3*e*x**8/8 + x**7*(3*b*c**2*e/7 + c**3*d/7) + x**6*(a*c**2*e/2 + b**2*c*e/2 + b*c**2*d/2) + x**5*(6*a*b*c*e/5 + 3*a*c**2*d/5 + b**3*e/5 + 3*b**2*c*d/5) + x**4*(3*a**2*c*e/4 + 3*a*b**2*e/4 + 3*a*b*c*d/2 + b**3*d/4) + x**3*(a**2*b*e + a**2*c*d + a*b**2*d) + x**2*(a**3*e/2 + 3*a**2*b*d/2)","A",0
2135,1,85,0,0.080431," ","integrate((c*x**2+b*x+a)**3,x)","a^{3} x + \frac{3 a^{2} b x^{2}}{2} + \frac{b c^{2} x^{6}}{2} + \frac{c^{3} x^{7}}{7} + x^{5} \left(\frac{3 a c^{2}}{5} + \frac{3 b^{2} c}{5}\right) + x^{4} \left(\frac{3 a b c}{2} + \frac{b^{3}}{4}\right) + x^{3} \left(a^{2} c + a b^{2}\right)"," ",0,"a**3*x + 3*a**2*b*x**2/2 + b*c**2*x**6/2 + c**3*x**7/7 + x**5*(3*a*c**2/5 + 3*b**2*c/5) + x**4*(3*a*b*c/2 + b**3/4) + x**3*(a**2*c + a*b**2)","A",0
2136,1,384,0,0.870957," ","integrate((c*x**2+b*x+a)**3/(e*x+d),x)","\frac{c^{3} x^{6}}{6 e} + x^{5} \left(\frac{3 b c^{2}}{5 e} - \frac{c^{3} d}{5 e^{2}}\right) + x^{4} \left(\frac{3 a c^{2}}{4 e} + \frac{3 b^{2} c}{4 e} - \frac{3 b c^{2} d}{4 e^{2}} + \frac{c^{3} d^{2}}{4 e^{3}}\right) + x^{3} \left(\frac{2 a b c}{e} - \frac{a c^{2} d}{e^{2}} + \frac{b^{3}}{3 e} - \frac{b^{2} c d}{e^{2}} + \frac{b c^{2} d^{2}}{e^{3}} - \frac{c^{3} d^{3}}{3 e^{4}}\right) + x^{2} \left(\frac{3 a^{2} c}{2 e} + \frac{3 a b^{2}}{2 e} - \frac{3 a b c d}{e^{2}} + \frac{3 a c^{2} d^{2}}{2 e^{3}} - \frac{b^{3} d}{2 e^{2}} + \frac{3 b^{2} c d^{2}}{2 e^{3}} - \frac{3 b c^{2} d^{3}}{2 e^{4}} + \frac{c^{3} d^{4}}{2 e^{5}}\right) + x \left(\frac{3 a^{2} b}{e} - \frac{3 a^{2} c d}{e^{2}} - \frac{3 a b^{2} d}{e^{2}} + \frac{6 a b c d^{2}}{e^{3}} - \frac{3 a c^{2} d^{3}}{e^{4}} + \frac{b^{3} d^{2}}{e^{3}} - \frac{3 b^{2} c d^{3}}{e^{4}} + \frac{3 b c^{2} d^{4}}{e^{5}} - \frac{c^{3} d^{5}}{e^{6}}\right) + \frac{\left(a e^{2} - b d e + c d^{2}\right)^{3} \log{\left(d + e x \right)}}{e^{7}}"," ",0,"c**3*x**6/(6*e) + x**5*(3*b*c**2/(5*e) - c**3*d/(5*e**2)) + x**4*(3*a*c**2/(4*e) + 3*b**2*c/(4*e) - 3*b*c**2*d/(4*e**2) + c**3*d**2/(4*e**3)) + x**3*(2*a*b*c/e - a*c**2*d/e**2 + b**3/(3*e) - b**2*c*d/e**2 + b*c**2*d**2/e**3 - c**3*d**3/(3*e**4)) + x**2*(3*a**2*c/(2*e) + 3*a*b**2/(2*e) - 3*a*b*c*d/e**2 + 3*a*c**2*d**2/(2*e**3) - b**3*d/(2*e**2) + 3*b**2*c*d**2/(2*e**3) - 3*b*c**2*d**3/(2*e**4) + c**3*d**4/(2*e**5)) + x*(3*a**2*b/e - 3*a**2*c*d/e**2 - 3*a*b**2*d/e**2 + 6*a*b*c*d**2/e**3 - 3*a*c**2*d**3/e**4 + b**3*d**2/e**3 - 3*b**2*c*d**3/e**4 + 3*b*c**2*d**4/e**5 - c**3*d**5/e**6) + (a*e**2 - b*d*e + c*d**2)**3*log(d + e*x)/e**7","A",0
2137,1,411,0,2.183654," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**2,x)","\frac{c^{3} x^{5}}{5 e^{2}} + x^{4} \left(\frac{3 b c^{2}}{4 e^{2}} - \frac{c^{3} d}{2 e^{3}}\right) + x^{3} \left(\frac{a c^{2}}{e^{2}} + \frac{b^{2} c}{e^{2}} - \frac{2 b c^{2} d}{e^{3}} + \frac{c^{3} d^{2}}{e^{4}}\right) + x^{2} \left(\frac{3 a b c}{e^{2}} - \frac{3 a c^{2} d}{e^{3}} + \frac{b^{3}}{2 e^{2}} - \frac{3 b^{2} c d}{e^{3}} + \frac{9 b c^{2} d^{2}}{2 e^{4}} - \frac{2 c^{3} d^{3}}{e^{5}}\right) + x \left(\frac{3 a^{2} c}{e^{2}} + \frac{3 a b^{2}}{e^{2}} - \frac{12 a b c d}{e^{3}} + \frac{9 a c^{2} d^{2}}{e^{4}} - \frac{2 b^{3} d}{e^{3}} + \frac{9 b^{2} c d^{2}}{e^{4}} - \frac{12 b c^{2} d^{3}}{e^{5}} + \frac{5 c^{3} d^{4}}{e^{6}}\right) + \frac{- a^{3} e^{6} + 3 a^{2} b d e^{5} - 3 a^{2} c d^{2} e^{4} - 3 a b^{2} d^{2} e^{4} + 6 a b c d^{3} e^{3} - 3 a c^{2} d^{4} e^{2} + b^{3} d^{3} e^{3} - 3 b^{2} c d^{4} e^{2} + 3 b c^{2} d^{5} e - c^{3} d^{6}}{d e^{7} + e^{8} x} + \frac{3 \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right)^{2} \log{\left(d + e x \right)}}{e^{7}}"," ",0,"c**3*x**5/(5*e**2) + x**4*(3*b*c**2/(4*e**2) - c**3*d/(2*e**3)) + x**3*(a*c**2/e**2 + b**2*c/e**2 - 2*b*c**2*d/e**3 + c**3*d**2/e**4) + x**2*(3*a*b*c/e**2 - 3*a*c**2*d/e**3 + b**3/(2*e**2) - 3*b**2*c*d/e**3 + 9*b*c**2*d**2/(2*e**4) - 2*c**3*d**3/e**5) + x*(3*a**2*c/e**2 + 3*a*b**2/e**2 - 12*a*b*c*d/e**3 + 9*a*c**2*d**2/e**4 - 2*b**3*d/e**3 + 9*b**2*c*d**2/e**4 - 12*b*c**2*d**3/e**5 + 5*c**3*d**4/e**6) + (-a**3*e**6 + 3*a**2*b*d*e**5 - 3*a**2*c*d**2*e**4 - 3*a*b**2*d**2*e**4 + 6*a*b*c*d**3*e**3 - 3*a*c**2*d**4*e**2 + b**3*d**3*e**3 - 3*b**2*c*d**4*e**2 + 3*b*c**2*d**5*e - c**3*d**6)/(d*e**7 + e**8*x) + 3*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)**2*log(d + e*x)/e**7","A",0
2138,1,466,0,8.604393," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**3,x)","\frac{c^{3} x^{4}}{4 e^{3}} + x^{3} \left(\frac{b c^{2}}{e^{3}} - \frac{c^{3} d}{e^{4}}\right) + x^{2} \left(\frac{3 a c^{2}}{2 e^{3}} + \frac{3 b^{2} c}{2 e^{3}} - \frac{9 b c^{2} d}{2 e^{4}} + \frac{3 c^{3} d^{2}}{e^{5}}\right) + x \left(\frac{6 a b c}{e^{3}} - \frac{9 a c^{2} d}{e^{4}} + \frac{b^{3}}{e^{3}} - \frac{9 b^{2} c d}{e^{4}} + \frac{18 b c^{2} d^{2}}{e^{5}} - \frac{10 c^{3} d^{3}}{e^{6}}\right) + \frac{- a^{3} e^{6} - 3 a^{2} b d e^{5} + 9 a^{2} c d^{2} e^{4} + 9 a b^{2} d^{2} e^{4} - 30 a b c d^{3} e^{3} + 21 a c^{2} d^{4} e^{2} - 5 b^{3} d^{3} e^{3} + 21 b^{2} c d^{4} e^{2} - 27 b c^{2} d^{5} e + 11 c^{3} d^{6} + x \left(- 6 a^{2} b e^{6} + 12 a^{2} c d e^{5} + 12 a b^{2} d e^{5} - 36 a b c d^{2} e^{4} + 24 a c^{2} d^{3} e^{3} - 6 b^{3} d^{2} e^{4} + 24 b^{2} c d^{3} e^{3} - 30 b c^{2} d^{4} e^{2} + 12 c^{3} d^{5} e\right)}{2 d^{2} e^{7} + 4 d e^{8} x + 2 e^{9} x^{2}} + \frac{3 \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{7}}"," ",0,"c**3*x**4/(4*e**3) + x**3*(b*c**2/e**3 - c**3*d/e**4) + x**2*(3*a*c**2/(2*e**3) + 3*b**2*c/(2*e**3) - 9*b*c**2*d/(2*e**4) + 3*c**3*d**2/e**5) + x*(6*a*b*c/e**3 - 9*a*c**2*d/e**4 + b**3/e**3 - 9*b**2*c*d/e**4 + 18*b*c**2*d**2/e**5 - 10*c**3*d**3/e**6) + (-a**3*e**6 - 3*a**2*b*d*e**5 + 9*a**2*c*d**2*e**4 + 9*a*b**2*d**2*e**4 - 30*a*b*c*d**3*e**3 + 21*a*c**2*d**4*e**2 - 5*b**3*d**3*e**3 + 21*b**2*c*d**4*e**2 - 27*b*c**2*d**5*e + 11*c**3*d**6 + x*(-6*a**2*b*e**6 + 12*a**2*c*d*e**5 + 12*a*b**2*d*e**5 - 36*a*b*c*d**2*e**4 + 24*a*c**2*d**3*e**3 - 6*b**3*d**2*e**4 + 24*b**2*c*d**3*e**3 - 30*b*c**2*d**4*e**2 + 12*c**3*d**5*e))/(2*d**2*e**7 + 4*d*e**8*x + 2*e**9*x**2) + 3*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)*log(d + e*x)/e**7","A",0
2139,1,502,0,30.614030," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**4,x)","\frac{c^{3} x^{3}}{3 e^{4}} + x^{2} \left(\frac{3 b c^{2}}{2 e^{4}} - \frac{2 c^{3} d}{e^{5}}\right) + x \left(\frac{3 a c^{2}}{e^{4}} + \frac{3 b^{2} c}{e^{4}} - \frac{12 b c^{2} d}{e^{5}} + \frac{10 c^{3} d^{2}}{e^{6}}\right) + \frac{- 2 a^{3} e^{6} - 3 a^{2} b d e^{5} - 6 a^{2} c d^{2} e^{4} - 6 a b^{2} d^{2} e^{4} + 66 a b c d^{3} e^{3} - 78 a c^{2} d^{4} e^{2} + 11 b^{3} d^{3} e^{3} - 78 b^{2} c d^{4} e^{2} + 141 b c^{2} d^{5} e - 74 c^{3} d^{6} + x^{2} \left(- 18 a^{2} c e^{6} - 18 a b^{2} e^{6} + 108 a b c d e^{5} - 108 a c^{2} d^{2} e^{4} + 18 b^{3} d e^{5} - 108 b^{2} c d^{2} e^{4} + 180 b c^{2} d^{3} e^{3} - 90 c^{3} d^{4} e^{2}\right) + x \left(- 9 a^{2} b e^{6} - 18 a^{2} c d e^{5} - 18 a b^{2} d e^{5} + 162 a b c d^{2} e^{4} - 180 a c^{2} d^{3} e^{3} + 27 b^{3} d^{2} e^{4} - 180 b^{2} c d^{3} e^{3} + 315 b c^{2} d^{4} e^{2} - 162 c^{3} d^{5} e\right)}{6 d^{3} e^{7} + 18 d^{2} e^{8} x + 18 d e^{9} x^{2} + 6 e^{10} x^{3}} + \frac{\left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{7}}"," ",0,"c**3*x**3/(3*e**4) + x**2*(3*b*c**2/(2*e**4) - 2*c**3*d/e**5) + x*(3*a*c**2/e**4 + 3*b**2*c/e**4 - 12*b*c**2*d/e**5 + 10*c**3*d**2/e**6) + (-2*a**3*e**6 - 3*a**2*b*d*e**5 - 6*a**2*c*d**2*e**4 - 6*a*b**2*d**2*e**4 + 66*a*b*c*d**3*e**3 - 78*a*c**2*d**4*e**2 + 11*b**3*d**3*e**3 - 78*b**2*c*d**4*e**2 + 141*b*c**2*d**5*e - 74*c**3*d**6 + x**2*(-18*a**2*c*e**6 - 18*a*b**2*e**6 + 108*a*b*c*d*e**5 - 108*a*c**2*d**2*e**4 + 18*b**3*d*e**5 - 108*b**2*c*d**2*e**4 + 180*b*c**2*d**3*e**3 - 90*c**3*d**4*e**2) + x*(-9*a**2*b*e**6 - 18*a**2*c*d*e**5 - 18*a*b**2*d*e**5 + 162*a*b*c*d**2*e**4 - 180*a*c**2*d**3*e**3 + 27*b**3*d**2*e**4 - 180*b**2*c*d**3*e**3 + 315*b*c**2*d**4*e**2 - 162*c**3*d**5*e))/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + (b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2)*log(d + e*x)/e**7","B",0
2140,1,520,0,108.826218," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**5,x)","\frac{c^{3} x^{2}}{2 e^{5}} + \frac{3 c \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{7}} + x \left(\frac{3 b c^{2}}{e^{5}} - \frac{5 c^{3} d}{e^{6}}\right) + \frac{- a^{3} e^{6} - a^{2} b d e^{5} - a^{2} c d^{2} e^{4} - a b^{2} d^{2} e^{4} - 6 a b c d^{3} e^{3} + 25 a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} + 25 b^{2} c d^{4} e^{2} - 77 b c^{2} d^{5} e + 57 c^{3} d^{6} + x^{3} \left(- 24 a b c e^{6} + 48 a c^{2} d e^{5} - 4 b^{3} e^{6} + 48 b^{2} c d e^{5} - 120 b c^{2} d^{2} e^{4} + 80 c^{3} d^{3} e^{3}\right) + x^{2} \left(- 6 a^{2} c e^{6} - 6 a b^{2} e^{6} - 36 a b c d e^{5} + 108 a c^{2} d^{2} e^{4} - 6 b^{3} d e^{5} + 108 b^{2} c d^{2} e^{4} - 300 b c^{2} d^{3} e^{3} + 210 c^{3} d^{4} e^{2}\right) + x \left(- 4 a^{2} b e^{6} - 4 a^{2} c d e^{5} - 4 a b^{2} d e^{5} - 24 a b c d^{2} e^{4} + 88 a c^{2} d^{3} e^{3} - 4 b^{3} d^{2} e^{4} + 88 b^{2} c d^{3} e^{3} - 260 b c^{2} d^{4} e^{2} + 188 c^{3} d^{5} e\right)}{4 d^{4} e^{7} + 16 d^{3} e^{8} x + 24 d^{2} e^{9} x^{2} + 16 d e^{10} x^{3} + 4 e^{11} x^{4}}"," ",0,"c**3*x**2/(2*e**5) + 3*c*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)*log(d + e*x)/e**7 + x*(3*b*c**2/e**5 - 5*c**3*d/e**6) + (-a**3*e**6 - a**2*b*d*e**5 - a**2*c*d**2*e**4 - a*b**2*d**2*e**4 - 6*a*b*c*d**3*e**3 + 25*a*c**2*d**4*e**2 - b**3*d**3*e**3 + 25*b**2*c*d**4*e**2 - 77*b*c**2*d**5*e + 57*c**3*d**6 + x**3*(-24*a*b*c*e**6 + 48*a*c**2*d*e**5 - 4*b**3*e**6 + 48*b**2*c*d*e**5 - 120*b*c**2*d**2*e**4 + 80*c**3*d**3*e**3) + x**2*(-6*a**2*c*e**6 - 6*a*b**2*e**6 - 36*a*b*c*d*e**5 + 108*a*c**2*d**2*e**4 - 6*b**3*d*e**5 + 108*b**2*c*d**2*e**4 - 300*b*c**2*d**3*e**3 + 210*c**3*d**4*e**2) + x*(-4*a**2*b*e**6 - 4*a**2*c*d*e**5 - 4*a*b**2*d*e**5 - 24*a*b*c*d**2*e**4 + 88*a*c**2*d**3*e**3 - 4*b**3*d**2*e**4 + 88*b**2*c*d**3*e**3 - 260*b*c**2*d**4*e**2 + 188*c**3*d**5*e))/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4)","B",0
2141,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2142,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2143,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2144,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2145,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2146,1,998,0,0.210312," ","integrate((e*x+d)**4*(c*x**2+b*x+a)**4,x)","a^{4} d^{4} x + \frac{c^{4} e^{4} x^{13}}{13} + x^{12} \left(\frac{b c^{3} e^{4}}{3} + \frac{c^{4} d e^{3}}{3}\right) + x^{11} \left(\frac{4 a c^{3} e^{4}}{11} + \frac{6 b^{2} c^{2} e^{4}}{11} + \frac{16 b c^{3} d e^{3}}{11} + \frac{6 c^{4} d^{2} e^{2}}{11}\right) + x^{10} \left(\frac{6 a b c^{2} e^{4}}{5} + \frac{8 a c^{3} d e^{3}}{5} + \frac{2 b^{3} c e^{4}}{5} + \frac{12 b^{2} c^{2} d e^{3}}{5} + \frac{12 b c^{3} d^{2} e^{2}}{5} + \frac{2 c^{4} d^{3} e}{5}\right) + x^{9} \left(\frac{2 a^{2} c^{2} e^{4}}{3} + \frac{4 a b^{2} c e^{4}}{3} + \frac{16 a b c^{2} d e^{3}}{3} + \frac{8 a c^{3} d^{2} e^{2}}{3} + \frac{b^{4} e^{4}}{9} + \frac{16 b^{3} c d e^{3}}{9} + 4 b^{2} c^{2} d^{2} e^{2} + \frac{16 b c^{3} d^{3} e}{9} + \frac{c^{4} d^{4}}{9}\right) + x^{8} \left(\frac{3 a^{2} b c e^{4}}{2} + 3 a^{2} c^{2} d e^{3} + \frac{a b^{3} e^{4}}{2} + 6 a b^{2} c d e^{3} + 9 a b c^{2} d^{2} e^{2} + 2 a c^{3} d^{3} e + \frac{b^{4} d e^{3}}{2} + 3 b^{3} c d^{2} e^{2} + 3 b^{2} c^{2} d^{3} e + \frac{b c^{3} d^{4}}{2}\right) + x^{7} \left(\frac{4 a^{3} c e^{4}}{7} + \frac{6 a^{2} b^{2} e^{4}}{7} + \frac{48 a^{2} b c d e^{3}}{7} + \frac{36 a^{2} c^{2} d^{2} e^{2}}{7} + \frac{16 a b^{3} d e^{3}}{7} + \frac{72 a b^{2} c d^{2} e^{2}}{7} + \frac{48 a b c^{2} d^{3} e}{7} + \frac{4 a c^{3} d^{4}}{7} + \frac{6 b^{4} d^{2} e^{2}}{7} + \frac{16 b^{3} c d^{3} e}{7} + \frac{6 b^{2} c^{2} d^{4}}{7}\right) + x^{6} \left(\frac{2 a^{3} b e^{4}}{3} + \frac{8 a^{3} c d e^{3}}{3} + 4 a^{2} b^{2} d e^{3} + 12 a^{2} b c d^{2} e^{2} + 4 a^{2} c^{2} d^{3} e + 4 a b^{3} d^{2} e^{2} + 8 a b^{2} c d^{3} e + 2 a b c^{2} d^{4} + \frac{2 b^{4} d^{3} e}{3} + \frac{2 b^{3} c d^{4}}{3}\right) + x^{5} \left(\frac{a^{4} e^{4}}{5} + \frac{16 a^{3} b d e^{3}}{5} + \frac{24 a^{3} c d^{2} e^{2}}{5} + \frac{36 a^{2} b^{2} d^{2} e^{2}}{5} + \frac{48 a^{2} b c d^{3} e}{5} + \frac{6 a^{2} c^{2} d^{4}}{5} + \frac{16 a b^{3} d^{3} e}{5} + \frac{12 a b^{2} c d^{4}}{5} + \frac{b^{4} d^{4}}{5}\right) + x^{4} \left(a^{4} d e^{3} + 6 a^{3} b d^{2} e^{2} + 4 a^{3} c d^{3} e + 6 a^{2} b^{2} d^{3} e + 3 a^{2} b c d^{4} + a b^{3} d^{4}\right) + x^{3} \left(2 a^{4} d^{2} e^{2} + \frac{16 a^{3} b d^{3} e}{3} + \frac{4 a^{3} c d^{4}}{3} + 2 a^{2} b^{2} d^{4}\right) + x^{2} \left(2 a^{4} d^{3} e + 2 a^{3} b d^{4}\right)"," ",0,"a**4*d**4*x + c**4*e**4*x**13/13 + x**12*(b*c**3*e**4/3 + c**4*d*e**3/3) + x**11*(4*a*c**3*e**4/11 + 6*b**2*c**2*e**4/11 + 16*b*c**3*d*e**3/11 + 6*c**4*d**2*e**2/11) + x**10*(6*a*b*c**2*e**4/5 + 8*a*c**3*d*e**3/5 + 2*b**3*c*e**4/5 + 12*b**2*c**2*d*e**3/5 + 12*b*c**3*d**2*e**2/5 + 2*c**4*d**3*e/5) + x**9*(2*a**2*c**2*e**4/3 + 4*a*b**2*c*e**4/3 + 16*a*b*c**2*d*e**3/3 + 8*a*c**3*d**2*e**2/3 + b**4*e**4/9 + 16*b**3*c*d*e**3/9 + 4*b**2*c**2*d**2*e**2 + 16*b*c**3*d**3*e/9 + c**4*d**4/9) + x**8*(3*a**2*b*c*e**4/2 + 3*a**2*c**2*d*e**3 + a*b**3*e**4/2 + 6*a*b**2*c*d*e**3 + 9*a*b*c**2*d**2*e**2 + 2*a*c**3*d**3*e + b**4*d*e**3/2 + 3*b**3*c*d**2*e**2 + 3*b**2*c**2*d**3*e + b*c**3*d**4/2) + x**7*(4*a**3*c*e**4/7 + 6*a**2*b**2*e**4/7 + 48*a**2*b*c*d*e**3/7 + 36*a**2*c**2*d**2*e**2/7 + 16*a*b**3*d*e**3/7 + 72*a*b**2*c*d**2*e**2/7 + 48*a*b*c**2*d**3*e/7 + 4*a*c**3*d**4/7 + 6*b**4*d**2*e**2/7 + 16*b**3*c*d**3*e/7 + 6*b**2*c**2*d**4/7) + x**6*(2*a**3*b*e**4/3 + 8*a**3*c*d*e**3/3 + 4*a**2*b**2*d*e**3 + 12*a**2*b*c*d**2*e**2 + 4*a**2*c**2*d**3*e + 4*a*b**3*d**2*e**2 + 8*a*b**2*c*d**3*e + 2*a*b*c**2*d**4 + 2*b**4*d**3*e/3 + 2*b**3*c*d**4/3) + x**5*(a**4*e**4/5 + 16*a**3*b*d*e**3/5 + 24*a**3*c*d**2*e**2/5 + 36*a**2*b**2*d**2*e**2/5 + 48*a**2*b*c*d**3*e/5 + 6*a**2*c**2*d**4/5 + 16*a*b**3*d**3*e/5 + 12*a*b**2*c*d**4/5 + b**4*d**4/5) + x**4*(a**4*d*e**3 + 6*a**3*b*d**2*e**2 + 4*a**3*c*d**3*e + 6*a**2*b**2*d**3*e + 3*a**2*b*c*d**4 + a*b**3*d**4) + x**3*(2*a**4*d**2*e**2 + 16*a**3*b*d**3*e/3 + 4*a**3*c*d**4/3 + 2*a**2*b**2*d**4) + x**2*(2*a**4*d**3*e + 2*a**3*b*d**4)","B",0
2147,1,777,0,0.175893," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**4,x)","a^{4} d^{3} x + \frac{c^{4} e^{3} x^{12}}{12} + x^{11} \left(\frac{4 b c^{3} e^{3}}{11} + \frac{3 c^{4} d e^{2}}{11}\right) + x^{10} \left(\frac{2 a c^{3} e^{3}}{5} + \frac{3 b^{2} c^{2} e^{3}}{5} + \frac{6 b c^{3} d e^{2}}{5} + \frac{3 c^{4} d^{2} e}{10}\right) + x^{9} \left(\frac{4 a b c^{2} e^{3}}{3} + \frac{4 a c^{3} d e^{2}}{3} + \frac{4 b^{3} c e^{3}}{9} + 2 b^{2} c^{2} d e^{2} + \frac{4 b c^{3} d^{2} e}{3} + \frac{c^{4} d^{3}}{9}\right) + x^{8} \left(\frac{3 a^{2} c^{2} e^{3}}{4} + \frac{3 a b^{2} c e^{3}}{2} + \frac{9 a b c^{2} d e^{2}}{2} + \frac{3 a c^{3} d^{2} e}{2} + \frac{b^{4} e^{3}}{8} + \frac{3 b^{3} c d e^{2}}{2} + \frac{9 b^{2} c^{2} d^{2} e}{4} + \frac{b c^{3} d^{3}}{2}\right) + x^{7} \left(\frac{12 a^{2} b c e^{3}}{7} + \frac{18 a^{2} c^{2} d e^{2}}{7} + \frac{4 a b^{3} e^{3}}{7} + \frac{36 a b^{2} c d e^{2}}{7} + \frac{36 a b c^{2} d^{2} e}{7} + \frac{4 a c^{3} d^{3}}{7} + \frac{3 b^{4} d e^{2}}{7} + \frac{12 b^{3} c d^{2} e}{7} + \frac{6 b^{2} c^{2} d^{3}}{7}\right) + x^{6} \left(\frac{2 a^{3} c e^{3}}{3} + a^{2} b^{2} e^{3} + 6 a^{2} b c d e^{2} + 3 a^{2} c^{2} d^{2} e + 2 a b^{3} d e^{2} + 6 a b^{2} c d^{2} e + 2 a b c^{2} d^{3} + \frac{b^{4} d^{2} e}{2} + \frac{2 b^{3} c d^{3}}{3}\right) + x^{5} \left(\frac{4 a^{3} b e^{3}}{5} + \frac{12 a^{3} c d e^{2}}{5} + \frac{18 a^{2} b^{2} d e^{2}}{5} + \frac{36 a^{2} b c d^{2} e}{5} + \frac{6 a^{2} c^{2} d^{3}}{5} + \frac{12 a b^{3} d^{2} e}{5} + \frac{12 a b^{2} c d^{3}}{5} + \frac{b^{4} d^{3}}{5}\right) + x^{4} \left(\frac{a^{4} e^{3}}{4} + 3 a^{3} b d e^{2} + 3 a^{3} c d^{2} e + \frac{9 a^{2} b^{2} d^{2} e}{2} + 3 a^{2} b c d^{3} + a b^{3} d^{3}\right) + x^{3} \left(a^{4} d e^{2} + 4 a^{3} b d^{2} e + \frac{4 a^{3} c d^{3}}{3} + 2 a^{2} b^{2} d^{3}\right) + x^{2} \left(\frac{3 a^{4} d^{2} e}{2} + 2 a^{3} b d^{3}\right)"," ",0,"a**4*d**3*x + c**4*e**3*x**12/12 + x**11*(4*b*c**3*e**3/11 + 3*c**4*d*e**2/11) + x**10*(2*a*c**3*e**3/5 + 3*b**2*c**2*e**3/5 + 6*b*c**3*d*e**2/5 + 3*c**4*d**2*e/10) + x**9*(4*a*b*c**2*e**3/3 + 4*a*c**3*d*e**2/3 + 4*b**3*c*e**3/9 + 2*b**2*c**2*d*e**2 + 4*b*c**3*d**2*e/3 + c**4*d**3/9) + x**8*(3*a**2*c**2*e**3/4 + 3*a*b**2*c*e**3/2 + 9*a*b*c**2*d*e**2/2 + 3*a*c**3*d**2*e/2 + b**4*e**3/8 + 3*b**3*c*d*e**2/2 + 9*b**2*c**2*d**2*e/4 + b*c**3*d**3/2) + x**7*(12*a**2*b*c*e**3/7 + 18*a**2*c**2*d*e**2/7 + 4*a*b**3*e**3/7 + 36*a*b**2*c*d*e**2/7 + 36*a*b*c**2*d**2*e/7 + 4*a*c**3*d**3/7 + 3*b**4*d*e**2/7 + 12*b**3*c*d**2*e/7 + 6*b**2*c**2*d**3/7) + x**6*(2*a**3*c*e**3/3 + a**2*b**2*e**3 + 6*a**2*b*c*d*e**2 + 3*a**2*c**2*d**2*e + 2*a*b**3*d*e**2 + 6*a*b**2*c*d**2*e + 2*a*b*c**2*d**3 + b**4*d**2*e/2 + 2*b**3*c*d**3/3) + x**5*(4*a**3*b*e**3/5 + 12*a**3*c*d*e**2/5 + 18*a**2*b**2*d*e**2/5 + 36*a**2*b*c*d**2*e/5 + 6*a**2*c**2*d**3/5 + 12*a*b**3*d**2*e/5 + 12*a*b**2*c*d**3/5 + b**4*d**3/5) + x**4*(a**4*e**3/4 + 3*a**3*b*d*e**2 + 3*a**3*c*d**2*e + 9*a**2*b**2*d**2*e/2 + 3*a**2*b*c*d**3 + a*b**3*d**3) + x**3*(a**4*d*e**2 + 4*a**3*b*d**2*e + 4*a**3*c*d**3/3 + 2*a**2*b**2*d**3) + x**2*(3*a**4*d**2*e/2 + 2*a**3*b*d**3)","A",0
2148,1,537,0,0.153869," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**4,x)","a^{4} d^{2} x + \frac{c^{4} e^{2} x^{11}}{11} + x^{10} \left(\frac{2 b c^{3} e^{2}}{5} + \frac{c^{4} d e}{5}\right) + x^{9} \left(\frac{4 a c^{3} e^{2}}{9} + \frac{2 b^{2} c^{2} e^{2}}{3} + \frac{8 b c^{3} d e}{9} + \frac{c^{4} d^{2}}{9}\right) + x^{8} \left(\frac{3 a b c^{2} e^{2}}{2} + a c^{3} d e + \frac{b^{3} c e^{2}}{2} + \frac{3 b^{2} c^{2} d e}{2} + \frac{b c^{3} d^{2}}{2}\right) + x^{7} \left(\frac{6 a^{2} c^{2} e^{2}}{7} + \frac{12 a b^{2} c e^{2}}{7} + \frac{24 a b c^{2} d e}{7} + \frac{4 a c^{3} d^{2}}{7} + \frac{b^{4} e^{2}}{7} + \frac{8 b^{3} c d e}{7} + \frac{6 b^{2} c^{2} d^{2}}{7}\right) + x^{6} \left(2 a^{2} b c e^{2} + 2 a^{2} c^{2} d e + \frac{2 a b^{3} e^{2}}{3} + 4 a b^{2} c d e + 2 a b c^{2} d^{2} + \frac{b^{4} d e}{3} + \frac{2 b^{3} c d^{2}}{3}\right) + x^{5} \left(\frac{4 a^{3} c e^{2}}{5} + \frac{6 a^{2} b^{2} e^{2}}{5} + \frac{24 a^{2} b c d e}{5} + \frac{6 a^{2} c^{2} d^{2}}{5} + \frac{8 a b^{3} d e}{5} + \frac{12 a b^{2} c d^{2}}{5} + \frac{b^{4} d^{2}}{5}\right) + x^{4} \left(a^{3} b e^{2} + 2 a^{3} c d e + 3 a^{2} b^{2} d e + 3 a^{2} b c d^{2} + a b^{3} d^{2}\right) + x^{3} \left(\frac{a^{4} e^{2}}{3} + \frac{8 a^{3} b d e}{3} + \frac{4 a^{3} c d^{2}}{3} + 2 a^{2} b^{2} d^{2}\right) + x^{2} \left(a^{4} d e + 2 a^{3} b d^{2}\right)"," ",0,"a**4*d**2*x + c**4*e**2*x**11/11 + x**10*(2*b*c**3*e**2/5 + c**4*d*e/5) + x**9*(4*a*c**3*e**2/9 + 2*b**2*c**2*e**2/3 + 8*b*c**3*d*e/9 + c**4*d**2/9) + x**8*(3*a*b*c**2*e**2/2 + a*c**3*d*e + b**3*c*e**2/2 + 3*b**2*c**2*d*e/2 + b*c**3*d**2/2) + x**7*(6*a**2*c**2*e**2/7 + 12*a*b**2*c*e**2/7 + 24*a*b*c**2*d*e/7 + 4*a*c**3*d**2/7 + b**4*e**2/7 + 8*b**3*c*d*e/7 + 6*b**2*c**2*d**2/7) + x**6*(2*a**2*b*c*e**2 + 2*a**2*c**2*d*e + 2*a*b**3*e**2/3 + 4*a*b**2*c*d*e + 2*a*b*c**2*d**2 + b**4*d*e/3 + 2*b**3*c*d**2/3) + x**5*(4*a**3*c*e**2/5 + 6*a**2*b**2*e**2/5 + 24*a**2*b*c*d*e/5 + 6*a**2*c**2*d**2/5 + 8*a*b**3*d*e/5 + 12*a*b**2*c*d**2/5 + b**4*d**2/5) + x**4*(a**3*b*e**2 + 2*a**3*c*d*e + 3*a**2*b**2*d*e + 3*a**2*b*c*d**2 + a*b**3*d**2) + x**3*(a**4*e**2/3 + 8*a**3*b*d*e/3 + 4*a**3*c*d**2/3 + 2*a**2*b**2*d**2) + x**2*(a**4*d*e + 2*a**3*b*d**2)","A",0
2149,1,313,0,0.128363," ","integrate((e*x+d)*(c*x**2+b*x+a)**4,x)","a^{4} d x + \frac{c^{4} e x^{10}}{10} + x^{9} \left(\frac{4 b c^{3} e}{9} + \frac{c^{4} d}{9}\right) + x^{8} \left(\frac{a c^{3} e}{2} + \frac{3 b^{2} c^{2} e}{4} + \frac{b c^{3} d}{2}\right) + x^{7} \left(\frac{12 a b c^{2} e}{7} + \frac{4 a c^{3} d}{7} + \frac{4 b^{3} c e}{7} + \frac{6 b^{2} c^{2} d}{7}\right) + x^{6} \left(a^{2} c^{2} e + 2 a b^{2} c e + 2 a b c^{2} d + \frac{b^{4} e}{6} + \frac{2 b^{3} c d}{3}\right) + x^{5} \left(\frac{12 a^{2} b c e}{5} + \frac{6 a^{2} c^{2} d}{5} + \frac{4 a b^{3} e}{5} + \frac{12 a b^{2} c d}{5} + \frac{b^{4} d}{5}\right) + x^{4} \left(a^{3} c e + \frac{3 a^{2} b^{2} e}{2} + 3 a^{2} b c d + a b^{3} d\right) + x^{3} \left(\frac{4 a^{3} b e}{3} + \frac{4 a^{3} c d}{3} + 2 a^{2} b^{2} d\right) + x^{2} \left(\frac{a^{4} e}{2} + 2 a^{3} b d\right)"," ",0,"a**4*d*x + c**4*e*x**10/10 + x**9*(4*b*c**3*e/9 + c**4*d/9) + x**8*(a*c**3*e/2 + 3*b**2*c**2*e/4 + b*c**3*d/2) + x**7*(12*a*b*c**2*e/7 + 4*a*c**3*d/7 + 4*b**3*c*e/7 + 6*b**2*c**2*d/7) + x**6*(a**2*c**2*e + 2*a*b**2*c*e + 2*a*b*c**2*d + b**4*e/6 + 2*b**3*c*d/3) + x**5*(12*a**2*b*c*e/5 + 6*a**2*c**2*d/5 + 4*a*b**3*e/5 + 12*a*b**2*c*d/5 + b**4*d/5) + x**4*(a**3*c*e + 3*a**2*b**2*e/2 + 3*a**2*b*c*d + a*b**3*d) + x**3*(4*a**3*b*e/3 + 4*a**3*c*d/3 + 2*a**2*b**2*d) + x**2*(a**4*e/2 + 2*a**3*b*d)","A",0
2150,1,141,0,0.091536," ","integrate((c*x**2+b*x+a)**4,x)","a^{4} x + 2 a^{3} b x^{2} + \frac{b c^{3} x^{8}}{2} + \frac{c^{4} x^{9}}{9} + x^{7} \left(\frac{4 a c^{3}}{7} + \frac{6 b^{2} c^{2}}{7}\right) + x^{6} \left(2 a b c^{2} + \frac{2 b^{3} c}{3}\right) + x^{5} \left(\frac{6 a^{2} c^{2}}{5} + \frac{12 a b^{2} c}{5} + \frac{b^{4}}{5}\right) + x^{4} \left(3 a^{2} b c + a b^{3}\right) + x^{3} \left(\frac{4 a^{3} c}{3} + 2 a^{2} b^{2}\right)"," ",0,"a**4*x + 2*a**3*b*x**2 + b*c**3*x**8/2 + c**4*x**9/9 + x**7*(4*a*c**3/7 + 6*b**2*c**2/7) + x**6*(2*a*b*c**2 + 2*b**3*c/3) + x**5*(6*a**2*c**2/5 + 12*a*b**2*c/5 + b**4/5) + x**4*(3*a**2*b*c + a*b**3) + x**3*(4*a**3*c/3 + 2*a**2*b**2)","A",0
2151,1,808,0,1.542040," ","integrate((c*x**2+b*x+a)**4/(e*x+d),x)","\frac{c^{4} x^{8}}{8 e} + x^{7} \left(\frac{4 b c^{3}}{7 e} - \frac{c^{4} d}{7 e^{2}}\right) + x^{6} \left(\frac{2 a c^{3}}{3 e} + \frac{b^{2} c^{2}}{e} - \frac{2 b c^{3} d}{3 e^{2}} + \frac{c^{4} d^{2}}{6 e^{3}}\right) + x^{5} \left(\frac{12 a b c^{2}}{5 e} - \frac{4 a c^{3} d}{5 e^{2}} + \frac{4 b^{3} c}{5 e} - \frac{6 b^{2} c^{2} d}{5 e^{2}} + \frac{4 b c^{3} d^{2}}{5 e^{3}} - \frac{c^{4} d^{3}}{5 e^{4}}\right) + x^{4} \left(\frac{3 a^{2} c^{2}}{2 e} + \frac{3 a b^{2} c}{e} - \frac{3 a b c^{2} d}{e^{2}} + \frac{a c^{3} d^{2}}{e^{3}} + \frac{b^{4}}{4 e} - \frac{b^{3} c d}{e^{2}} + \frac{3 b^{2} c^{2} d^{2}}{2 e^{3}} - \frac{b c^{3} d^{3}}{e^{4}} + \frac{c^{4} d^{4}}{4 e^{5}}\right) + x^{3} \left(\frac{4 a^{2} b c}{e} - \frac{2 a^{2} c^{2} d}{e^{2}} + \frac{4 a b^{3}}{3 e} - \frac{4 a b^{2} c d}{e^{2}} + \frac{4 a b c^{2} d^{2}}{e^{3}} - \frac{4 a c^{3} d^{3}}{3 e^{4}} - \frac{b^{4} d}{3 e^{2}} + \frac{4 b^{3} c d^{2}}{3 e^{3}} - \frac{2 b^{2} c^{2} d^{3}}{e^{4}} + \frac{4 b c^{3} d^{4}}{3 e^{5}} - \frac{c^{4} d^{5}}{3 e^{6}}\right) + x^{2} \left(\frac{2 a^{3} c}{e} + \frac{3 a^{2} b^{2}}{e} - \frac{6 a^{2} b c d}{e^{2}} + \frac{3 a^{2} c^{2} d^{2}}{e^{3}} - \frac{2 a b^{3} d}{e^{2}} + \frac{6 a b^{2} c d^{2}}{e^{3}} - \frac{6 a b c^{2} d^{3}}{e^{4}} + \frac{2 a c^{3} d^{4}}{e^{5}} + \frac{b^{4} d^{2}}{2 e^{3}} - \frac{2 b^{3} c d^{3}}{e^{4}} + \frac{3 b^{2} c^{2} d^{4}}{e^{5}} - \frac{2 b c^{3} d^{5}}{e^{6}} + \frac{c^{4} d^{6}}{2 e^{7}}\right) + x \left(\frac{4 a^{3} b}{e} - \frac{4 a^{3} c d}{e^{2}} - \frac{6 a^{2} b^{2} d}{e^{2}} + \frac{12 a^{2} b c d^{2}}{e^{3}} - \frac{6 a^{2} c^{2} d^{3}}{e^{4}} + \frac{4 a b^{3} d^{2}}{e^{3}} - \frac{12 a b^{2} c d^{3}}{e^{4}} + \frac{12 a b c^{2} d^{4}}{e^{5}} - \frac{4 a c^{3} d^{5}}{e^{6}} - \frac{b^{4} d^{3}}{e^{4}} + \frac{4 b^{3} c d^{4}}{e^{5}} - \frac{6 b^{2} c^{2} d^{5}}{e^{6}} + \frac{4 b c^{3} d^{6}}{e^{7}} - \frac{c^{4} d^{7}}{e^{8}}\right) + \frac{\left(a e^{2} - b d e + c d^{2}\right)^{4} \log{\left(d + e x \right)}}{e^{9}}"," ",0,"c**4*x**8/(8*e) + x**7*(4*b*c**3/(7*e) - c**4*d/(7*e**2)) + x**6*(2*a*c**3/(3*e) + b**2*c**2/e - 2*b*c**3*d/(3*e**2) + c**4*d**2/(6*e**3)) + x**5*(12*a*b*c**2/(5*e) - 4*a*c**3*d/(5*e**2) + 4*b**3*c/(5*e) - 6*b**2*c**2*d/(5*e**2) + 4*b*c**3*d**2/(5*e**3) - c**4*d**3/(5*e**4)) + x**4*(3*a**2*c**2/(2*e) + 3*a*b**2*c/e - 3*a*b*c**2*d/e**2 + a*c**3*d**2/e**3 + b**4/(4*e) - b**3*c*d/e**2 + 3*b**2*c**2*d**2/(2*e**3) - b*c**3*d**3/e**4 + c**4*d**4/(4*e**5)) + x**3*(4*a**2*b*c/e - 2*a**2*c**2*d/e**2 + 4*a*b**3/(3*e) - 4*a*b**2*c*d/e**2 + 4*a*b*c**2*d**2/e**3 - 4*a*c**3*d**3/(3*e**4) - b**4*d/(3*e**2) + 4*b**3*c*d**2/(3*e**3) - 2*b**2*c**2*d**3/e**4 + 4*b*c**3*d**4/(3*e**5) - c**4*d**5/(3*e**6)) + x**2*(2*a**3*c/e + 3*a**2*b**2/e - 6*a**2*b*c*d/e**2 + 3*a**2*c**2*d**2/e**3 - 2*a*b**3*d/e**2 + 6*a*b**2*c*d**2/e**3 - 6*a*b*c**2*d**3/e**4 + 2*a*c**3*d**4/e**5 + b**4*d**2/(2*e**3) - 2*b**3*c*d**3/e**4 + 3*b**2*c**2*d**4/e**5 - 2*b*c**3*d**5/e**6 + c**4*d**6/(2*e**7)) + x*(4*a**3*b/e - 4*a**3*c*d/e**2 - 6*a**2*b**2*d/e**2 + 12*a**2*b*c*d**2/e**3 - 6*a**2*c**2*d**3/e**4 + 4*a*b**3*d**2/e**3 - 12*a*b**2*c*d**3/e**4 + 12*a*b*c**2*d**4/e**5 - 4*a*c**3*d**5/e**6 - b**4*d**3/e**4 + 4*b**3*c*d**4/e**5 - 6*b**2*c**2*d**5/e**6 + 4*b*c**3*d**6/e**7 - c**4*d**7/e**8) + (a*e**2 - b*d*e + c*d**2)**4*log(d + e*x)/e**9","A",0
2152,1,847,0,4.545151," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**2,x)","\frac{c^{4} x^{7}}{7 e^{2}} + x^{6} \left(\frac{2 b c^{3}}{3 e^{2}} - \frac{c^{4} d}{3 e^{3}}\right) + x^{5} \left(\frac{4 a c^{3}}{5 e^{2}} + \frac{6 b^{2} c^{2}}{5 e^{2}} - \frac{8 b c^{3} d}{5 e^{3}} + \frac{3 c^{4} d^{2}}{5 e^{4}}\right) + x^{4} \left(\frac{3 a b c^{2}}{e^{2}} - \frac{2 a c^{3} d}{e^{3}} + \frac{b^{3} c}{e^{2}} - \frac{3 b^{2} c^{2} d}{e^{3}} + \frac{3 b c^{3} d^{2}}{e^{4}} - \frac{c^{4} d^{3}}{e^{5}}\right) + x^{3} \left(\frac{2 a^{2} c^{2}}{e^{2}} + \frac{4 a b^{2} c}{e^{2}} - \frac{8 a b c^{2} d}{e^{3}} + \frac{4 a c^{3} d^{2}}{e^{4}} + \frac{b^{4}}{3 e^{2}} - \frac{8 b^{3} c d}{3 e^{3}} + \frac{6 b^{2} c^{2} d^{2}}{e^{4}} - \frac{16 b c^{3} d^{3}}{3 e^{5}} + \frac{5 c^{4} d^{4}}{3 e^{6}}\right) + x^{2} \left(\frac{6 a^{2} b c}{e^{2}} - \frac{6 a^{2} c^{2} d}{e^{3}} + \frac{2 a b^{3}}{e^{2}} - \frac{12 a b^{2} c d}{e^{3}} + \frac{18 a b c^{2} d^{2}}{e^{4}} - \frac{8 a c^{3} d^{3}}{e^{5}} - \frac{b^{4} d}{e^{3}} + \frac{6 b^{3} c d^{2}}{e^{4}} - \frac{12 b^{2} c^{2} d^{3}}{e^{5}} + \frac{10 b c^{3} d^{4}}{e^{6}} - \frac{3 c^{4} d^{5}}{e^{7}}\right) + x \left(\frac{4 a^{3} c}{e^{2}} + \frac{6 a^{2} b^{2}}{e^{2}} - \frac{24 a^{2} b c d}{e^{3}} + \frac{18 a^{2} c^{2} d^{2}}{e^{4}} - \frac{8 a b^{3} d}{e^{3}} + \frac{36 a b^{2} c d^{2}}{e^{4}} - \frac{48 a b c^{2} d^{3}}{e^{5}} + \frac{20 a c^{3} d^{4}}{e^{6}} + \frac{3 b^{4} d^{2}}{e^{4}} - \frac{16 b^{3} c d^{3}}{e^{5}} + \frac{30 b^{2} c^{2} d^{4}}{e^{6}} - \frac{24 b c^{3} d^{5}}{e^{7}} + \frac{7 c^{4} d^{6}}{e^{8}}\right) + \frac{- a^{4} e^{8} + 4 a^{3} b d e^{7} - 4 a^{3} c d^{2} e^{6} - 6 a^{2} b^{2} d^{2} e^{6} + 12 a^{2} b c d^{3} e^{5} - 6 a^{2} c^{2} d^{4} e^{4} + 4 a b^{3} d^{3} e^{5} - 12 a b^{2} c d^{4} e^{4} + 12 a b c^{2} d^{5} e^{3} - 4 a c^{3} d^{6} e^{2} - b^{4} d^{4} e^{4} + 4 b^{3} c d^{5} e^{3} - 6 b^{2} c^{2} d^{6} e^{2} + 4 b c^{3} d^{7} e - c^{4} d^{8}}{d e^{9} + e^{10} x} + \frac{4 \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right)^{3} \log{\left(d + e x \right)}}{e^{9}}"," ",0,"c**4*x**7/(7*e**2) + x**6*(2*b*c**3/(3*e**2) - c**4*d/(3*e**3)) + x**5*(4*a*c**3/(5*e**2) + 6*b**2*c**2/(5*e**2) - 8*b*c**3*d/(5*e**3) + 3*c**4*d**2/(5*e**4)) + x**4*(3*a*b*c**2/e**2 - 2*a*c**3*d/e**3 + b**3*c/e**2 - 3*b**2*c**2*d/e**3 + 3*b*c**3*d**2/e**4 - c**4*d**3/e**5) + x**3*(2*a**2*c**2/e**2 + 4*a*b**2*c/e**2 - 8*a*b*c**2*d/e**3 + 4*a*c**3*d**2/e**4 + b**4/(3*e**2) - 8*b**3*c*d/(3*e**3) + 6*b**2*c**2*d**2/e**4 - 16*b*c**3*d**3/(3*e**5) + 5*c**4*d**4/(3*e**6)) + x**2*(6*a**2*b*c/e**2 - 6*a**2*c**2*d/e**3 + 2*a*b**3/e**2 - 12*a*b**2*c*d/e**3 + 18*a*b*c**2*d**2/e**4 - 8*a*c**3*d**3/e**5 - b**4*d/e**3 + 6*b**3*c*d**2/e**4 - 12*b**2*c**2*d**3/e**5 + 10*b*c**3*d**4/e**6 - 3*c**4*d**5/e**7) + x*(4*a**3*c/e**2 + 6*a**2*b**2/e**2 - 24*a**2*b*c*d/e**3 + 18*a**2*c**2*d**2/e**4 - 8*a*b**3*d/e**3 + 36*a*b**2*c*d**2/e**4 - 48*a*b*c**2*d**3/e**5 + 20*a*c**3*d**4/e**6 + 3*b**4*d**2/e**4 - 16*b**3*c*d**3/e**5 + 30*b**2*c**2*d**4/e**6 - 24*b*c**3*d**5/e**7 + 7*c**4*d**6/e**8) + (-a**4*e**8 + 4*a**3*b*d*e**7 - 4*a**3*c*d**2*e**6 - 6*a**2*b**2*d**2*e**6 + 12*a**2*b*c*d**3*e**5 - 6*a**2*c**2*d**4*e**4 + 4*a*b**3*d**3*e**5 - 12*a*b**2*c*d**4*e**4 + 12*a*b*c**2*d**5*e**3 - 4*a*c**3*d**6*e**2 - b**4*d**4*e**4 + 4*b**3*c*d**5*e**3 - 6*b**2*c**2*d**6*e**2 + 4*b*c**3*d**7*e - c**4*d**8)/(d*e**9 + e**10*x) + 4*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)**3*log(d + e*x)/e**9","B",0
2153,1,906,0,19.578714," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**3,x)","\frac{c^{4} x^{6}}{6 e^{3}} + x^{5} \left(\frac{4 b c^{3}}{5 e^{3}} - \frac{3 c^{4} d}{5 e^{4}}\right) + x^{4} \left(\frac{a c^{3}}{e^{3}} + \frac{3 b^{2} c^{2}}{2 e^{3}} - \frac{3 b c^{3} d}{e^{4}} + \frac{3 c^{4} d^{2}}{2 e^{5}}\right) + x^{3} \left(\frac{4 a b c^{2}}{e^{3}} - \frac{4 a c^{3} d}{e^{4}} + \frac{4 b^{3} c}{3 e^{3}} - \frac{6 b^{2} c^{2} d}{e^{4}} + \frac{8 b c^{3} d^{2}}{e^{5}} - \frac{10 c^{4} d^{3}}{3 e^{6}}\right) + x^{2} \left(\frac{3 a^{2} c^{2}}{e^{3}} + \frac{6 a b^{2} c}{e^{3}} - \frac{18 a b c^{2} d}{e^{4}} + \frac{12 a c^{3} d^{2}}{e^{5}} + \frac{b^{4}}{2 e^{3}} - \frac{6 b^{3} c d}{e^{4}} + \frac{18 b^{2} c^{2} d^{2}}{e^{5}} - \frac{20 b c^{3} d^{3}}{e^{6}} + \frac{15 c^{4} d^{4}}{2 e^{7}}\right) + x \left(\frac{12 a^{2} b c}{e^{3}} - \frac{18 a^{2} c^{2} d}{e^{4}} + \frac{4 a b^{3}}{e^{3}} - \frac{36 a b^{2} c d}{e^{4}} + \frac{72 a b c^{2} d^{2}}{e^{5}} - \frac{40 a c^{3} d^{3}}{e^{6}} - \frac{3 b^{4} d}{e^{4}} + \frac{24 b^{3} c d^{2}}{e^{5}} - \frac{60 b^{2} c^{2} d^{3}}{e^{6}} + \frac{60 b c^{3} d^{4}}{e^{7}} - \frac{21 c^{4} d^{5}}{e^{8}}\right) + \frac{- a^{4} e^{8} - 4 a^{3} b d e^{7} + 12 a^{3} c d^{2} e^{6} + 18 a^{2} b^{2} d^{2} e^{6} - 60 a^{2} b c d^{3} e^{5} + 42 a^{2} c^{2} d^{4} e^{4} - 20 a b^{3} d^{3} e^{5} + 84 a b^{2} c d^{4} e^{4} - 108 a b c^{2} d^{5} e^{3} + 44 a c^{3} d^{6} e^{2} + 7 b^{4} d^{4} e^{4} - 36 b^{3} c d^{5} e^{3} + 66 b^{2} c^{2} d^{6} e^{2} - 52 b c^{3} d^{7} e + 15 c^{4} d^{8} + x \left(- 8 a^{3} b e^{8} + 16 a^{3} c d e^{7} + 24 a^{2} b^{2} d e^{7} - 72 a^{2} b c d^{2} e^{6} + 48 a^{2} c^{2} d^{3} e^{5} - 24 a b^{3} d^{2} e^{6} + 96 a b^{2} c d^{3} e^{5} - 120 a b c^{2} d^{4} e^{4} + 48 a c^{3} d^{5} e^{3} + 8 b^{4} d^{3} e^{5} - 40 b^{3} c d^{4} e^{4} + 72 b^{2} c^{2} d^{5} e^{3} - 56 b c^{3} d^{6} e^{2} + 16 c^{4} d^{7} e\right)}{2 d^{2} e^{9} + 4 d e^{10} x + 2 e^{11} x^{2}} + \frac{2 \left(a e^{2} - b d e + c d^{2}\right)^{2} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{9}}"," ",0,"c**4*x**6/(6*e**3) + x**5*(4*b*c**3/(5*e**3) - 3*c**4*d/(5*e**4)) + x**4*(a*c**3/e**3 + 3*b**2*c**2/(2*e**3) - 3*b*c**3*d/e**4 + 3*c**4*d**2/(2*e**5)) + x**3*(4*a*b*c**2/e**3 - 4*a*c**3*d/e**4 + 4*b**3*c/(3*e**3) - 6*b**2*c**2*d/e**4 + 8*b*c**3*d**2/e**5 - 10*c**4*d**3/(3*e**6)) + x**2*(3*a**2*c**2/e**3 + 6*a*b**2*c/e**3 - 18*a*b*c**2*d/e**4 + 12*a*c**3*d**2/e**5 + b**4/(2*e**3) - 6*b**3*c*d/e**4 + 18*b**2*c**2*d**2/e**5 - 20*b*c**3*d**3/e**6 + 15*c**4*d**4/(2*e**7)) + x*(12*a**2*b*c/e**3 - 18*a**2*c**2*d/e**4 + 4*a*b**3/e**3 - 36*a*b**2*c*d/e**4 + 72*a*b*c**2*d**2/e**5 - 40*a*c**3*d**3/e**6 - 3*b**4*d/e**4 + 24*b**3*c*d**2/e**5 - 60*b**2*c**2*d**3/e**6 + 60*b*c**3*d**4/e**7 - 21*c**4*d**5/e**8) + (-a**4*e**8 - 4*a**3*b*d*e**7 + 12*a**3*c*d**2*e**6 + 18*a**2*b**2*d**2*e**6 - 60*a**2*b*c*d**3*e**5 + 42*a**2*c**2*d**4*e**4 - 20*a*b**3*d**3*e**5 + 84*a*b**2*c*d**4*e**4 - 108*a*b*c**2*d**5*e**3 + 44*a*c**3*d**6*e**2 + 7*b**4*d**4*e**4 - 36*b**3*c*d**5*e**3 + 66*b**2*c**2*d**6*e**2 - 52*b*c**3*d**7*e + 15*c**4*d**8 + x*(-8*a**3*b*e**8 + 16*a**3*c*d*e**7 + 24*a**2*b**2*d*e**7 - 72*a**2*b*c*d**2*e**6 + 48*a**2*c**2*d**3*e**5 - 24*a*b**3*d**2*e**6 + 96*a*b**2*c*d**3*e**5 - 120*a*b*c**2*d**4*e**4 + 48*a*c**3*d**5*e**3 + 8*b**4*d**3*e**5 - 40*b**3*c*d**4*e**4 + 72*b**2*c**2*d**5*e**3 - 56*b*c**3*d**6*e**2 + 16*c**4*d**7*e))/(2*d**2*e**9 + 4*d*e**10*x + 2*e**11*x**2) + 2*(a*e**2 - b*d*e + c*d**2)**2*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2)*log(d + e*x)/e**9","B",0
2154,1,944,0,97.983485," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**4,x)","\frac{c^{4} x^{5}}{5 e^{4}} + x^{4} \left(\frac{b c^{3}}{e^{4}} - \frac{c^{4} d}{e^{5}}\right) + x^{3} \left(\frac{4 a c^{3}}{3 e^{4}} + \frac{2 b^{2} c^{2}}{e^{4}} - \frac{16 b c^{3} d}{3 e^{5}} + \frac{10 c^{4} d^{2}}{3 e^{6}}\right) + x^{2} \left(\frac{6 a b c^{2}}{e^{4}} - \frac{8 a c^{3} d}{e^{5}} + \frac{2 b^{3} c}{e^{4}} - \frac{12 b^{2} c^{2} d}{e^{5}} + \frac{20 b c^{3} d^{2}}{e^{6}} - \frac{10 c^{4} d^{3}}{e^{7}}\right) + x \left(\frac{6 a^{2} c^{2}}{e^{4}} + \frac{12 a b^{2} c}{e^{4}} - \frac{48 a b c^{2} d}{e^{5}} + \frac{40 a c^{3} d^{2}}{e^{6}} + \frac{b^{4}}{e^{4}} - \frac{16 b^{3} c d}{e^{5}} + \frac{60 b^{2} c^{2} d^{2}}{e^{6}} - \frac{80 b c^{3} d^{3}}{e^{7}} + \frac{35 c^{4} d^{4}}{e^{8}}\right) + \frac{- a^{4} e^{8} - 2 a^{3} b d e^{7} - 4 a^{3} c d^{2} e^{6} - 6 a^{2} b^{2} d^{2} e^{6} + 66 a^{2} b c d^{3} e^{5} - 78 a^{2} c^{2} d^{4} e^{4} + 22 a b^{3} d^{3} e^{5} - 156 a b^{2} c d^{4} e^{4} + 282 a b c^{2} d^{5} e^{3} - 148 a c^{3} d^{6} e^{2} - 13 b^{4} d^{4} e^{4} + 94 b^{3} c d^{5} e^{3} - 222 b^{2} c^{2} d^{6} e^{2} + 214 b c^{3} d^{7} e - 73 c^{4} d^{8} + x^{2} \left(- 12 a^{3} c e^{8} - 18 a^{2} b^{2} e^{8} + 108 a^{2} b c d e^{7} - 108 a^{2} c^{2} d^{2} e^{6} + 36 a b^{3} d e^{7} - 216 a b^{2} c d^{2} e^{6} + 360 a b c^{2} d^{3} e^{5} - 180 a c^{3} d^{4} e^{4} - 18 b^{4} d^{2} e^{6} + 120 b^{3} c d^{3} e^{5} - 270 b^{2} c^{2} d^{4} e^{4} + 252 b c^{3} d^{5} e^{3} - 84 c^{4} d^{6} e^{2}\right) + x \left(- 6 a^{3} b e^{8} - 12 a^{3} c d e^{7} - 18 a^{2} b^{2} d e^{7} + 162 a^{2} b c d^{2} e^{6} - 180 a^{2} c^{2} d^{3} e^{5} + 54 a b^{3} d^{2} e^{6} - 360 a b^{2} c d^{3} e^{5} + 630 a b c^{2} d^{4} e^{4} - 324 a c^{3} d^{5} e^{3} - 30 b^{4} d^{3} e^{5} + 210 b^{3} c d^{4} e^{4} - 486 b^{2} c^{2} d^{5} e^{3} + 462 b c^{3} d^{6} e^{2} - 156 c^{4} d^{7} e\right)}{3 d^{3} e^{9} + 9 d^{2} e^{10} x + 9 d e^{11} x^{2} + 3 e^{12} x^{3}} + \frac{4 \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{9}}"," ",0,"c**4*x**5/(5*e**4) + x**4*(b*c**3/e**4 - c**4*d/e**5) + x**3*(4*a*c**3/(3*e**4) + 2*b**2*c**2/e**4 - 16*b*c**3*d/(3*e**5) + 10*c**4*d**2/(3*e**6)) + x**2*(6*a*b*c**2/e**4 - 8*a*c**3*d/e**5 + 2*b**3*c/e**4 - 12*b**2*c**2*d/e**5 + 20*b*c**3*d**2/e**6 - 10*c**4*d**3/e**7) + x*(6*a**2*c**2/e**4 + 12*a*b**2*c/e**4 - 48*a*b*c**2*d/e**5 + 40*a*c**3*d**2/e**6 + b**4/e**4 - 16*b**3*c*d/e**5 + 60*b**2*c**2*d**2/e**6 - 80*b*c**3*d**3/e**7 + 35*c**4*d**4/e**8) + (-a**4*e**8 - 2*a**3*b*d*e**7 - 4*a**3*c*d**2*e**6 - 6*a**2*b**2*d**2*e**6 + 66*a**2*b*c*d**3*e**5 - 78*a**2*c**2*d**4*e**4 + 22*a*b**3*d**3*e**5 - 156*a*b**2*c*d**4*e**4 + 282*a*b*c**2*d**5*e**3 - 148*a*c**3*d**6*e**2 - 13*b**4*d**4*e**4 + 94*b**3*c*d**5*e**3 - 222*b**2*c**2*d**6*e**2 + 214*b*c**3*d**7*e - 73*c**4*d**8 + x**2*(-12*a**3*c*e**8 - 18*a**2*b**2*e**8 + 108*a**2*b*c*d*e**7 - 108*a**2*c**2*d**2*e**6 + 36*a*b**3*d*e**7 - 216*a*b**2*c*d**2*e**6 + 360*a*b*c**2*d**3*e**5 - 180*a*c**3*d**4*e**4 - 18*b**4*d**2*e**6 + 120*b**3*c*d**3*e**5 - 270*b**2*c**2*d**4*e**4 + 252*b*c**3*d**5*e**3 - 84*c**4*d**6*e**2) + x*(-6*a**3*b*e**8 - 12*a**3*c*d*e**7 - 18*a**2*b**2*d*e**7 + 162*a**2*b*c*d**2*e**6 - 180*a**2*c**2*d**3*e**5 + 54*a*b**3*d**2*e**6 - 360*a*b**2*c*d**3*e**5 + 630*a*b*c**2*d**4*e**4 - 324*a*c**3*d**5*e**3 - 30*b**4*d**3*e**5 + 210*b**3*c*d**4*e**4 - 486*b**2*c**2*d**5*e**3 + 462*b*c**3*d**6*e**2 - 156*c**4*d**7*e))/(3*d**3*e**9 + 9*d**2*e**10*x + 9*d*e**11*x**2 + 3*e**12*x**3) + 4*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2)*log(d + e*x)/e**9","B",0
2155,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2156,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2157,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2158,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2159,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2160,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2161,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2162,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**4/(e*x+d)**12,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2163,1,26,0,0.066576," ","integrate(x**4*(x**2-4*x+3)**2,x)","\frac{x^{9}}{9} - x^{8} + \frac{22 x^{7}}{7} - 4 x^{6} + \frac{9 x^{5}}{5}"," ",0,"x**9/9 - x**8 + 22*x**7/7 - 4*x**6 + 9*x**5/5","A",0
2164,1,31,0,0.064674," ","integrate(x**3*(x**2-4*x+3)**2,x)","\frac{x^{8}}{8} - \frac{8 x^{7}}{7} + \frac{11 x^{6}}{3} - \frac{24 x^{5}}{5} + \frac{9 x^{4}}{4}"," ",0,"x**8/8 - 8*x**7/7 + 11*x**6/3 - 24*x**5/5 + 9*x**4/4","A",0
2165,1,27,0,0.065198," ","integrate(x**2*(x**2-4*x+3)**2,x)","\frac{x^{7}}{7} - \frac{4 x^{6}}{3} + \frac{22 x^{5}}{5} - 6 x^{4} + 3 x^{3}"," ",0,"x**7/7 - 4*x**6/3 + 22*x**5/5 - 6*x**4 + 3*x**3","A",0
2166,1,29,0,0.065744," ","integrate(x*(x**2-4*x+3)**2,x)","\frac{x^{6}}{6} - \frac{8 x^{5}}{5} + \frac{11 x^{4}}{2} - 8 x^{3} + \frac{9 x^{2}}{2}"," ",0,"x**6/6 - 8*x**5/5 + 11*x**4/2 - 8*x**3 + 9*x**2/2","A",0
2167,1,24,0,0.063427," ","integrate((x**2-4*x+3)**2,x)","\frac{x^{5}}{5} - 2 x^{4} + \frac{22 x^{3}}{3} - 12 x^{2} + 9 x"," ",0,"x**5/5 - 2*x**4 + 22*x**3/3 - 12*x**2 + 9*x","A",0
2168,1,24,0,0.089702," ","integrate((x**2-4*x+3)**2/x,x)","\frac{x^{4}}{4} - \frac{8 x^{3}}{3} + 11 x^{2} - 24 x + 9 \log{\left(x \right)}"," ",0,"x**4/4 - 8*x**3/3 + 11*x**2 - 24*x + 9*log(x)","A",0
2169,1,20,0,0.092344," ","integrate((x**2-4*x+3)**2/x**2,x)","\frac{x^{3}}{3} - 4 x^{2} + 22 x - 24 \log{\left(x \right)} - \frac{9}{x}"," ",0,"x**3/3 - 4*x**2 + 22*x - 24*log(x) - 9/x","A",0
2170,1,22,0,0.099952," ","integrate((x**2-4*x+3)**2/x**3,x)","\frac{x^{2}}{2} - 8 x + 22 \log{\left(x \right)} + \frac{48 x - 9}{2 x^{2}}"," ",0,"x**2/2 - 8*x + 22*log(x) + (48*x - 9)/(2*x**2)","A",0
2171,1,19,0,0.102627," ","integrate((x**2-4*x+3)**2/x**4,x)","x - 8 \log{\left(x \right)} + \frac{- 22 x^{2} + 12 x - 3}{x^{3}}"," ",0,"x - 8*log(x) + (-22*x**2 + 12*x - 3)/x**3","A",0
2172,1,22,0,0.112522," ","integrate((x**2-4*x+3)**2/x**5,x)","\log{\left(x \right)} + \frac{32 x^{3} - 44 x^{2} + 32 x - 9}{4 x^{4}}"," ",0,"log(x) + (32*x**3 - 44*x**2 + 32*x - 9)/(4*x**4)","A",0
2173,1,24,0,0.109406," ","integrate((x**2-4*x+3)**2/x**6,x)","\frac{- 15 x^{4} + 60 x^{3} - 110 x^{2} + 90 x - 27}{15 x^{5}}"," ",0,"(-15*x**4 + 60*x**3 - 110*x**2 + 90*x - 27)/(15*x**5)","A",0
2174,1,24,0,0.113767," ","integrate((x**2-4*x+3)**2/x**7,x)","\frac{- 15 x^{4} + 80 x^{3} - 165 x^{2} + 144 x - 45}{30 x^{6}}"," ",0,"(-15*x**4 + 80*x**3 - 165*x**2 + 144*x - 45)/(30*x**6)","A",0
2175,1,10,0,0.079157," ","integrate((x**2+2*x+2)/(2+x),x)","\frac{x^{2}}{2} + 2 \log{\left(x + 2 \right)}"," ",0,"x**2/2 + 2*log(x + 2)","A",0
2176,1,14,0,0.082206," ","integrate((x**2+4*x+5)/(-2+x),x)","\frac{x^{2}}{2} + 6 x + 17 \log{\left(x - 2 \right)}"," ",0,"x**2/2 + 6*x + 17*log(x - 2)","A",0
2177,1,15,0,0.096662," ","integrate((x**2+2*x+2)/(1+x)**3,x)","\log{\left(x + 1 \right)} - \frac{1}{2 x^{2} + 4 x + 2}"," ",0,"log(x + 1) - 1/(2*x**2 + 4*x + 2)","A",0
2178,1,15,0,0.097498," ","integrate((2*x**2+3*x+3)/(1+x)**3,x)","\frac{x}{x^{2} + 2 x + 1} + 2 \log{\left(x + 1 \right)}"," ",0,"x/(x**2 + 2*x + 1) + 2*log(x + 1)","A",0
2179,1,8,0,0.078767," ","integrate((x**2+x+1)/x,x)","\frac{x^{2}}{2} + x + \log{\left(x \right)}"," ",0,"x**2/2 + x + log(x)","A",0
2180,1,8,0,0.111985," ","integrate((x**2+6*x+9)/x**2,x)","x + 6 \log{\left(x \right)} - \frac{9}{x}"," ",0,"x + 6*log(x) - 9/x","A",0
2181,1,15,0,0.101274," ","integrate((x**2+2*x+1)/x**4,x)","\frac{- 3 x^{2} - 3 x - 1}{3 x^{3}}"," ",0,"(-3*x**2 - 3*x - 1)/(3*x**3)","A",0
2182,1,1556,0,8.471882," ","integrate((e*x+d)**4/(c*x**2+b*x+a),x)","x^{2} \left(- \frac{b e^{4}}{2 c^{2}} + \frac{2 d e^{3}}{c}\right) + x \left(- \frac{a e^{4}}{c^{2}} + \frac{b^{2} e^{4}}{c^{3}} - \frac{4 b d e^{3}}{c^{2}} + \frac{6 d^{2} e^{2}}{c}\right) + \left(\frac{e \left(b e - 2 c d\right) \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{4}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 3 a^{2} b c e^{4} + 8 a^{2} c^{2} d e^{3} + a b^{3} e^{4} - 4 a b^{2} c d e^{3} + 6 a b c^{2} d^{2} e^{2} + 4 a c^{4} \left(\frac{e \left(b e - 2 c d\right) \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{4}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right) - 8 a c^{3} d^{3} e - b^{2} c^{3} \left(\frac{e \left(b e - 2 c d\right) \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{4}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right) + b c^{3} d^{4}}{2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}} \right)} + \left(\frac{e \left(b e - 2 c d\right) \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{4}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 3 a^{2} b c e^{4} + 8 a^{2} c^{2} d e^{3} + a b^{3} e^{4} - 4 a b^{2} c d e^{3} + 6 a b c^{2} d^{2} e^{2} + 4 a c^{4} \left(\frac{e \left(b e - 2 c d\right) \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{4}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right) - 8 a c^{3} d^{3} e - b^{2} c^{3} \left(\frac{e \left(b e - 2 c d\right) \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{4}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right) + b c^{3} d^{4}}{2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}} \right)} + \frac{e^{4} x^{3}}{3 c}"," ",0,"x**2*(-b*e**4/(2*c**2) + 2*d*e**3/c) + x*(-a*e**4/c**2 + b**2*e**4/c**3 - 4*b*d*e**3/c**2 + 6*d**2*e**2/c) + (e*(b*e - 2*c*d)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**4) - sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)/(2*c**4*(4*a*c - b**2)))*log(x + (-3*a**2*b*c*e**4 + 8*a**2*c**2*d*e**3 + a*b**3*e**4 - 4*a*b**2*c*d*e**3 + 6*a*b*c**2*d**2*e**2 + 4*a*c**4*(e*(b*e - 2*c*d)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**4) - sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)/(2*c**4*(4*a*c - b**2))) - 8*a*c**3*d**3*e - b**2*c**3*(e*(b*e - 2*c*d)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**4) - sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)/(2*c**4*(4*a*c - b**2))) + b*c**3*d**4)/(2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)) + (e*(b*e - 2*c*d)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**4) + sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)/(2*c**4*(4*a*c - b**2)))*log(x + (-3*a**2*b*c*e**4 + 8*a**2*c**2*d*e**3 + a*b**3*e**4 - 4*a*b**2*c*d*e**3 + 6*a*b*c**2*d**2*e**2 + 4*a*c**4*(e*(b*e - 2*c*d)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**4) + sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)/(2*c**4*(4*a*c - b**2))) - 8*a*c**3*d**3*e - b**2*c**3*(e*(b*e - 2*c*d)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**4) + sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)/(2*c**4*(4*a*c - b**2))) + b*c**3*d**4)/(2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)) + e**4*x**3/(3*c)","B",0
2183,1,892,0,4.309119," ","integrate((e*x+d)**3/(c*x**2+b*x+a),x)","x \left(- \frac{b e^{3}}{c^{2}} + \frac{3 d e^{2}}{c}\right) + \left(- \frac{e \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{2 c^{3}} - \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{2 a^{2} c e^{3} - a b^{2} e^{3} + 3 a b c d e^{2} + 4 a c^{3} \left(- \frac{e \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{2 c^{3}} - \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)}\right) - 6 a c^{2} d^{2} e - b^{2} c^{2} \left(- \frac{e \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{2 c^{3}} - \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)}\right) + b c^{2} d^{3}}{3 a b c e^{3} - 6 a c^{2} d e^{2} - b^{3} e^{3} + 3 b^{2} c d e^{2} - 3 b c^{2} d^{2} e + 2 c^{3} d^{3}} \right)} + \left(- \frac{e \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{2 c^{3}} + \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{2 a^{2} c e^{3} - a b^{2} e^{3} + 3 a b c d e^{2} + 4 a c^{3} \left(- \frac{e \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{2 c^{3}} + \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)}\right) - 6 a c^{2} d^{2} e - b^{2} c^{2} \left(- \frac{e \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{2 c^{3}} + \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)}\right) + b c^{2} d^{3}}{3 a b c e^{3} - 6 a c^{2} d e^{2} - b^{3} e^{3} + 3 b^{2} c d e^{2} - 3 b c^{2} d^{2} e + 2 c^{3} d^{3}} \right)} + \frac{e^{3} x^{2}}{2 c}"," ",0,"x*(-b*e**3/c**2 + 3*d*e**2/c) + (-e*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/(2*c**3) - sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(2*c**3*(4*a*c - b**2)))*log(x + (2*a**2*c*e**3 - a*b**2*e**3 + 3*a*b*c*d*e**2 + 4*a*c**3*(-e*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/(2*c**3) - sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(2*c**3*(4*a*c - b**2))) - 6*a*c**2*d**2*e - b**2*c**2*(-e*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/(2*c**3) - sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(2*c**3*(4*a*c - b**2))) + b*c**2*d**3)/(3*a*b*c*e**3 - 6*a*c**2*d*e**2 - b**3*e**3 + 3*b**2*c*d*e**2 - 3*b*c**2*d**2*e + 2*c**3*d**3)) + (-e*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/(2*c**3) + sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(2*c**3*(4*a*c - b**2)))*log(x + (2*a**2*c*e**3 - a*b**2*e**3 + 3*a*b*c*d*e**2 + 4*a*c**3*(-e*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/(2*c**3) + sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(2*c**3*(4*a*c - b**2))) - 6*a*c**2*d**2*e - b**2*c**2*(-e*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/(2*c**3) + sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(2*c**3*(4*a*c - b**2))) + b*c**2*d**3)/(3*a*b*c*e**3 - 6*a*c**2*d*e**2 - b**3*e**3 + 3*b**2*c*d*e**2 - 3*b*c**2*d**2*e + 2*c**3*d**3)) + e**3*x**2/(2*c)","B",0
2184,1,588,0,2.062867," ","integrate((e*x+d)**2/(c*x**2+b*x+a),x)","\left(- \frac{e \left(b e - 2 c d\right)}{2 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- a b e^{2} - 4 a c^{2} \left(- \frac{e \left(b e - 2 c d\right)}{2 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) + 4 a c d e + b^{2} c \left(- \frac{e \left(b e - 2 c d\right)}{2 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) - b c d^{2}}{2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}} \right)} + \left(- \frac{e \left(b e - 2 c d\right)}{2 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- a b e^{2} - 4 a c^{2} \left(- \frac{e \left(b e - 2 c d\right)}{2 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) + 4 a c d e + b^{2} c \left(- \frac{e \left(b e - 2 c d\right)}{2 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) - b c d^{2}}{2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}} \right)} + \frac{e^{2} x}{c}"," ",0,"(-e*(b*e - 2*c*d)/(2*c**2) - sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2)))*log(x + (-a*b*e**2 - 4*a*c**2*(-e*(b*e - 2*c*d)/(2*c**2) - sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2))) + 4*a*c*d*e + b**2*c*(-e*(b*e - 2*c*d)/(2*c**2) - sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2))) - b*c*d**2)/(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)) + (-e*(b*e - 2*c*d)/(2*c**2) + sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2)))*log(x + (-a*b*e**2 - 4*a*c**2*(-e*(b*e - 2*c*d)/(2*c**2) + sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2))) + 4*a*c*d*e + b**2*c*(-e*(b*e - 2*c*d)/(2*c**2) + sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2))) - b*c*d**2)/(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)) + e**2*x/c","B",0
2185,1,280,0,0.790663," ","integrate((e*x+d)/(c*x**2+b*x+a),x)","\left(\frac{e}{2 c} - \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 4 a c \left(\frac{e}{2 c} - \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) + 2 a e + b^{2} \left(\frac{e}{2 c} - \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) - b d}{b e - 2 c d} \right)} + \left(\frac{e}{2 c} + \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 4 a c \left(\frac{e}{2 c} + \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) + 2 a e + b^{2} \left(\frac{e}{2 c} + \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) - b d}{b e - 2 c d} \right)}"," ",0,"(e/(2*c) - sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2)))*log(x + (-4*a*c*(e/(2*c) - sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2))) + 2*a*e + b**2*(e/(2*c) - sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2))) - b*d)/(b*e - 2*c*d)) + (e/(2*c) + sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2)))*log(x + (-4*a*c*(e/(2*c) + sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2))) + 2*a*e + b**2*(e/(2*c) + sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2))) - b*d)/(b*e - 2*c*d))","B",0
2186,1,124,0,0.217553," ","integrate(1/(c*x**2+b*x+a),x)","- \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{- 4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} + b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 c} \right)} + \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} - b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 c} \right)}"," ",0,"-sqrt(-1/(4*a*c - b**2))*log(x + (-4*a*c*sqrt(-1/(4*a*c - b**2)) + b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*c)) + sqrt(-1/(4*a*c - b**2))*log(x + (4*a*c*sqrt(-1/(4*a*c - b**2)) - b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*c))","B",0
2187,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2188,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2189,-1,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2190,1,2671,0,33.524261," ","integrate((e*x+d)**5/(c*x**2+b*x+a)**2,x)","x \left(- \frac{2 b e^{5}}{c^{3}} + \frac{5 d e^{4}}{c^{2}}\right) + \left(- \frac{e^{3} \left(2 a c e^{2} - 3 b^{2} e^{2} + 10 b c d e - 10 c^{2} d^{2}\right)}{2 c^{4}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 20 a b^{2} c e^{4} + 20 a b c^{2} d e^{3} - 20 a c^{3} d^{2} e^{2} + 3 b^{4} e^{4} - 4 b^{3} c d e^{3} + 2 b^{2} c^{2} d^{2} e^{2} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{16 a^{3} c^{2} e^{5} - 17 a^{2} b^{2} c e^{5} + 50 a^{2} b c^{2} d e^{4} + 16 a^{2} c^{5} \left(- \frac{e^{3} \left(2 a c e^{2} - 3 b^{2} e^{2} + 10 b c d e - 10 c^{2} d^{2}\right)}{2 c^{4}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 20 a b^{2} c e^{4} + 20 a b c^{2} d e^{3} - 20 a c^{3} d^{2} e^{2} + 3 b^{4} e^{4} - 4 b^{3} c d e^{3} + 2 b^{2} c^{2} d^{2} e^{2} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - 80 a^{2} c^{3} d^{2} e^{3} + 3 a b^{4} e^{5} - 10 a b^{3} c d e^{4} - 8 a b^{2} c^{4} \left(- \frac{e^{3} \left(2 a c e^{2} - 3 b^{2} e^{2} + 10 b c d e - 10 c^{2} d^{2}\right)}{2 c^{4}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 20 a b^{2} c e^{4} + 20 a b c^{2} d e^{3} - 20 a c^{3} d^{2} e^{2} + 3 b^{4} e^{4} - 4 b^{3} c d e^{3} + 2 b^{2} c^{2} d^{2} e^{2} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 10 a b^{2} c^{2} d^{2} e^{3} + 20 a b c^{3} d^{3} e^{2} + b^{4} c^{3} \left(- \frac{e^{3} \left(2 a c e^{2} - 3 b^{2} e^{2} + 10 b c d e - 10 c^{2} d^{2}\right)}{2 c^{4}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 20 a b^{2} c e^{4} + 20 a b c^{2} d e^{3} - 20 a c^{3} d^{2} e^{2} + 3 b^{4} e^{4} - 4 b^{3} c d e^{3} + 2 b^{2} c^{2} d^{2} e^{2} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - 5 b^{2} c^{3} d^{4} e + 2 b c^{4} d^{5}}{30 a^{2} b c^{2} e^{5} - 60 a^{2} c^{3} d e^{4} - 20 a b^{3} c e^{5} + 60 a b^{2} c^{2} d e^{4} - 60 a b c^{3} d^{2} e^{3} + 40 a c^{4} d^{3} e^{2} + 3 b^{5} e^{5} - 10 b^{4} c d e^{4} + 10 b^{3} c^{2} d^{2} e^{3} - 10 b c^{4} d^{4} e + 4 c^{5} d^{5}} \right)} + \left(- \frac{e^{3} \left(2 a c e^{2} - 3 b^{2} e^{2} + 10 b c d e - 10 c^{2} d^{2}\right)}{2 c^{4}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 20 a b^{2} c e^{4} + 20 a b c^{2} d e^{3} - 20 a c^{3} d^{2} e^{2} + 3 b^{4} e^{4} - 4 b^{3} c d e^{3} + 2 b^{2} c^{2} d^{2} e^{2} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{16 a^{3} c^{2} e^{5} - 17 a^{2} b^{2} c e^{5} + 50 a^{2} b c^{2} d e^{4} + 16 a^{2} c^{5} \left(- \frac{e^{3} \left(2 a c e^{2} - 3 b^{2} e^{2} + 10 b c d e - 10 c^{2} d^{2}\right)}{2 c^{4}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 20 a b^{2} c e^{4} + 20 a b c^{2} d e^{3} - 20 a c^{3} d^{2} e^{2} + 3 b^{4} e^{4} - 4 b^{3} c d e^{3} + 2 b^{2} c^{2} d^{2} e^{2} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - 80 a^{2} c^{3} d^{2} e^{3} + 3 a b^{4} e^{5} - 10 a b^{3} c d e^{4} - 8 a b^{2} c^{4} \left(- \frac{e^{3} \left(2 a c e^{2} - 3 b^{2} e^{2} + 10 b c d e - 10 c^{2} d^{2}\right)}{2 c^{4}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 20 a b^{2} c e^{4} + 20 a b c^{2} d e^{3} - 20 a c^{3} d^{2} e^{2} + 3 b^{4} e^{4} - 4 b^{3} c d e^{3} + 2 b^{2} c^{2} d^{2} e^{2} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 10 a b^{2} c^{2} d^{2} e^{3} + 20 a b c^{3} d^{3} e^{2} + b^{4} c^{3} \left(- \frac{e^{3} \left(2 a c e^{2} - 3 b^{2} e^{2} + 10 b c d e - 10 c^{2} d^{2}\right)}{2 c^{4}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 20 a b^{2} c e^{4} + 20 a b c^{2} d e^{3} - 20 a c^{3} d^{2} e^{2} + 3 b^{4} e^{4} - 4 b^{3} c d e^{3} + 2 b^{2} c^{2} d^{2} e^{2} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - 5 b^{2} c^{3} d^{4} e + 2 b c^{4} d^{5}}{30 a^{2} b c^{2} e^{5} - 60 a^{2} c^{3} d e^{4} - 20 a b^{3} c e^{5} + 60 a b^{2} c^{2} d e^{4} - 60 a b c^{3} d^{2} e^{3} + 40 a c^{4} d^{3} e^{2} + 3 b^{5} e^{5} - 10 b^{4} c d e^{4} + 10 b^{3} c^{2} d^{2} e^{3} - 10 b c^{4} d^{4} e + 4 c^{5} d^{5}} \right)} + \frac{- 2 a^{3} c^{2} e^{5} + 4 a^{2} b^{2} c e^{5} - 15 a^{2} b c^{2} d e^{4} + 20 a^{2} c^{3} d^{2} e^{3} - a b^{4} e^{5} + 5 a b^{3} c d e^{4} - 10 a b^{2} c^{2} d^{2} e^{3} + 10 a b c^{3} d^{3} e^{2} - 10 a c^{4} d^{4} e + b c^{4} d^{5} + x \left(- 5 a^{2} b c^{2} e^{5} + 10 a^{2} c^{3} d e^{4} + 5 a b^{3} c e^{5} - 20 a b^{2} c^{2} d e^{4} + 30 a b c^{3} d^{2} e^{3} - 20 a c^{4} d^{3} e^{2} - b^{5} e^{5} + 5 b^{4} c d e^{4} - 10 b^{3} c^{2} d^{2} e^{3} + 10 b^{2} c^{3} d^{3} e^{2} - 5 b c^{4} d^{4} e + 2 c^{5} d^{5}\right)}{4 a^{2} c^{5} - a b^{2} c^{4} + x^{2} \left(4 a c^{6} - b^{2} c^{5}\right) + x \left(4 a b c^{5} - b^{3} c^{4}\right)} + \frac{e^{5} x^{2}}{2 c^{2}}"," ",0,"x*(-2*b*e**5/c**3 + 5*d*e**4/c**2) + (-e**3*(2*a*c*e**2 - 3*b**2*e**2 + 10*b*c*d*e - 10*c**2*d**2)/(2*c**4) - sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 20*a*b**2*c*e**4 + 20*a*b*c**2*d*e**3 - 20*a*c**3*d**2*e**2 + 3*b**4*e**4 - 4*b**3*c*d*e**3 + 2*b**2*c**2*d**2*e**2 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (16*a**3*c**2*e**5 - 17*a**2*b**2*c*e**5 + 50*a**2*b*c**2*d*e**4 + 16*a**2*c**5*(-e**3*(2*a*c*e**2 - 3*b**2*e**2 + 10*b*c*d*e - 10*c**2*d**2)/(2*c**4) - sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 20*a*b**2*c*e**4 + 20*a*b*c**2*d*e**3 - 20*a*c**3*d**2*e**2 + 3*b**4*e**4 - 4*b**3*c*d*e**3 + 2*b**2*c**2*d**2*e**2 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - 80*a**2*c**3*d**2*e**3 + 3*a*b**4*e**5 - 10*a*b**3*c*d*e**4 - 8*a*b**2*c**4*(-e**3*(2*a*c*e**2 - 3*b**2*e**2 + 10*b*c*d*e - 10*c**2*d**2)/(2*c**4) - sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 20*a*b**2*c*e**4 + 20*a*b*c**2*d*e**3 - 20*a*c**3*d**2*e**2 + 3*b**4*e**4 - 4*b**3*c*d*e**3 + 2*b**2*c**2*d**2*e**2 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 10*a*b**2*c**2*d**2*e**3 + 20*a*b*c**3*d**3*e**2 + b**4*c**3*(-e**3*(2*a*c*e**2 - 3*b**2*e**2 + 10*b*c*d*e - 10*c**2*d**2)/(2*c**4) - sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 20*a*b**2*c*e**4 + 20*a*b*c**2*d*e**3 - 20*a*c**3*d**2*e**2 + 3*b**4*e**4 - 4*b**3*c*d*e**3 + 2*b**2*c**2*d**2*e**2 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - 5*b**2*c**3*d**4*e + 2*b*c**4*d**5)/(30*a**2*b*c**2*e**5 - 60*a**2*c**3*d*e**4 - 20*a*b**3*c*e**5 + 60*a*b**2*c**2*d*e**4 - 60*a*b*c**3*d**2*e**3 + 40*a*c**4*d**3*e**2 + 3*b**5*e**5 - 10*b**4*c*d*e**4 + 10*b**3*c**2*d**2*e**3 - 10*b*c**4*d**4*e + 4*c**5*d**5)) + (-e**3*(2*a*c*e**2 - 3*b**2*e**2 + 10*b*c*d*e - 10*c**2*d**2)/(2*c**4) + sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 20*a*b**2*c*e**4 + 20*a*b*c**2*d*e**3 - 20*a*c**3*d**2*e**2 + 3*b**4*e**4 - 4*b**3*c*d*e**3 + 2*b**2*c**2*d**2*e**2 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (16*a**3*c**2*e**5 - 17*a**2*b**2*c*e**5 + 50*a**2*b*c**2*d*e**4 + 16*a**2*c**5*(-e**3*(2*a*c*e**2 - 3*b**2*e**2 + 10*b*c*d*e - 10*c**2*d**2)/(2*c**4) + sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 20*a*b**2*c*e**4 + 20*a*b*c**2*d*e**3 - 20*a*c**3*d**2*e**2 + 3*b**4*e**4 - 4*b**3*c*d*e**3 + 2*b**2*c**2*d**2*e**2 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - 80*a**2*c**3*d**2*e**3 + 3*a*b**4*e**5 - 10*a*b**3*c*d*e**4 - 8*a*b**2*c**4*(-e**3*(2*a*c*e**2 - 3*b**2*e**2 + 10*b*c*d*e - 10*c**2*d**2)/(2*c**4) + sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 20*a*b**2*c*e**4 + 20*a*b*c**2*d*e**3 - 20*a*c**3*d**2*e**2 + 3*b**4*e**4 - 4*b**3*c*d*e**3 + 2*b**2*c**2*d**2*e**2 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 10*a*b**2*c**2*d**2*e**3 + 20*a*b*c**3*d**3*e**2 + b**4*c**3*(-e**3*(2*a*c*e**2 - 3*b**2*e**2 + 10*b*c*d*e - 10*c**2*d**2)/(2*c**4) + sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 20*a*b**2*c*e**4 + 20*a*b*c**2*d*e**3 - 20*a*c**3*d**2*e**2 + 3*b**4*e**4 - 4*b**3*c*d*e**3 + 2*b**2*c**2*d**2*e**2 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - 5*b**2*c**3*d**4*e + 2*b*c**4*d**5)/(30*a**2*b*c**2*e**5 - 60*a**2*c**3*d*e**4 - 20*a*b**3*c*e**5 + 60*a*b**2*c**2*d*e**4 - 60*a*b*c**3*d**2*e**3 + 40*a*c**4*d**3*e**2 + 3*b**5*e**5 - 10*b**4*c*d*e**4 + 10*b**3*c**2*d**2*e**3 - 10*b*c**4*d**4*e + 4*c**5*d**5)) + (-2*a**3*c**2*e**5 + 4*a**2*b**2*c*e**5 - 15*a**2*b*c**2*d*e**4 + 20*a**2*c**3*d**2*e**3 - a*b**4*e**5 + 5*a*b**3*c*d*e**4 - 10*a*b**2*c**2*d**2*e**3 + 10*a*b*c**3*d**3*e**2 - 10*a*c**4*d**4*e + b*c**4*d**5 + x*(-5*a**2*b*c**2*e**5 + 10*a**2*c**3*d*e**4 + 5*a*b**3*c*e**5 - 20*a*b**2*c**2*d*e**4 + 30*a*b*c**3*d**2*e**3 - 20*a*c**4*d**3*e**2 - b**5*e**5 + 5*b**4*c*d*e**4 - 10*b**3*c**2*d**2*e**3 + 10*b**2*c**3*d**3*e**2 - 5*b*c**4*d**4*e + 2*c**5*d**5))/(4*a**2*c**5 - a*b**2*c**4 + x**2*(4*a*c**6 - b**2*c**5) + x*(4*a*b*c**5 - b**3*c**4)) + e**5*x**2/(2*c**2)","B",0
2191,1,1924,0,17.090720," ","integrate((e*x+d)**4/(c*x**2+b*x+a)**2,x)","\left(- \frac{e^{3} \left(b e - 2 c d\right)}{c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} e^{4} - 6 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 2 b^{3} c d e^{3} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 10 a^{2} b c e^{4} - 16 a^{2} c^{4} \left(- \frac{e^{3} \left(b e - 2 c d\right)}{c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} e^{4} - 6 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 2 b^{3} c d e^{3} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 32 a^{2} c^{2} d e^{3} + 2 a b^{3} e^{4} + 8 a b^{2} c^{3} \left(- \frac{e^{3} \left(b e - 2 c d\right)}{c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} e^{4} - 6 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 2 b^{3} c d e^{3} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - 4 a b^{2} c d e^{3} - 12 a b c^{2} d^{2} e^{2} - b^{4} c^{2} \left(- \frac{e^{3} \left(b e - 2 c d\right)}{c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} e^{4} - 6 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 2 b^{3} c d e^{3} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 4 b^{2} c^{2} d^{3} e - 2 b c^{3} d^{4}}{12 a^{2} c^{2} e^{4} - 12 a b^{2} c e^{4} + 24 a b c^{2} d e^{3} - 24 a c^{3} d^{2} e^{2} + 2 b^{4} e^{4} - 4 b^{3} c d e^{3} + 8 b c^{3} d^{3} e - 4 c^{4} d^{4}} \right)} + \left(- \frac{e^{3} \left(b e - 2 c d\right)}{c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} e^{4} - 6 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 2 b^{3} c d e^{3} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 10 a^{2} b c e^{4} - 16 a^{2} c^{4} \left(- \frac{e^{3} \left(b e - 2 c d\right)}{c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} e^{4} - 6 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 2 b^{3} c d e^{3} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 32 a^{2} c^{2} d e^{3} + 2 a b^{3} e^{4} + 8 a b^{2} c^{3} \left(- \frac{e^{3} \left(b e - 2 c d\right)}{c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} e^{4} - 6 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 2 b^{3} c d e^{3} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - 4 a b^{2} c d e^{3} - 12 a b c^{2} d^{2} e^{2} - b^{4} c^{2} \left(- \frac{e^{3} \left(b e - 2 c d\right)}{c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} e^{4} - 6 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 2 b^{3} c d e^{3} + 4 b c^{3} d^{3} e - 2 c^{4} d^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 4 b^{2} c^{2} d^{3} e - 2 b c^{3} d^{4}}{12 a^{2} c^{2} e^{4} - 12 a b^{2} c e^{4} + 24 a b c^{2} d e^{3} - 24 a c^{3} d^{2} e^{2} + 2 b^{4} e^{4} - 4 b^{3} c d e^{3} + 8 b c^{3} d^{3} e - 4 c^{4} d^{4}} \right)} + \frac{- 3 a^{2} b c e^{4} + 8 a^{2} c^{2} d e^{3} + a b^{3} e^{4} - 4 a b^{2} c d e^{3} + 6 a b c^{2} d^{2} e^{2} - 8 a c^{3} d^{3} e + b c^{3} d^{4} + x \left(2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}\right)}{4 a^{2} c^{4} - a b^{2} c^{3} + x^{2} \left(4 a c^{5} - b^{2} c^{4}\right) + x \left(4 a b c^{4} - b^{3} c^{3}\right)} + \frac{e^{4} x}{c^{2}}"," ",0,"(-e**3*(b*e - 2*c*d)/c**3 - sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2*e**4 - 6*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 2*b**3*c*d*e**3 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-10*a**2*b*c*e**4 - 16*a**2*c**4*(-e**3*(b*e - 2*c*d)/c**3 - sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2*e**4 - 6*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 2*b**3*c*d*e**3 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 32*a**2*c**2*d*e**3 + 2*a*b**3*e**4 + 8*a*b**2*c**3*(-e**3*(b*e - 2*c*d)/c**3 - sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2*e**4 - 6*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 2*b**3*c*d*e**3 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - 4*a*b**2*c*d*e**3 - 12*a*b*c**2*d**2*e**2 - b**4*c**2*(-e**3*(b*e - 2*c*d)/c**3 - sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2*e**4 - 6*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 2*b**3*c*d*e**3 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 4*b**2*c**2*d**3*e - 2*b*c**3*d**4)/(12*a**2*c**2*e**4 - 12*a*b**2*c*e**4 + 24*a*b*c**2*d*e**3 - 24*a*c**3*d**2*e**2 + 2*b**4*e**4 - 4*b**3*c*d*e**3 + 8*b*c**3*d**3*e - 4*c**4*d**4)) + (-e**3*(b*e - 2*c*d)/c**3 + sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2*e**4 - 6*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 2*b**3*c*d*e**3 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-10*a**2*b*c*e**4 - 16*a**2*c**4*(-e**3*(b*e - 2*c*d)/c**3 + sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2*e**4 - 6*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 2*b**3*c*d*e**3 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 32*a**2*c**2*d*e**3 + 2*a*b**3*e**4 + 8*a*b**2*c**3*(-e**3*(b*e - 2*c*d)/c**3 + sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2*e**4 - 6*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 2*b**3*c*d*e**3 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - 4*a*b**2*c*d*e**3 - 12*a*b*c**2*d**2*e**2 - b**4*c**2*(-e**3*(b*e - 2*c*d)/c**3 + sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2*e**4 - 6*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 2*b**3*c*d*e**3 + 4*b*c**3*d**3*e - 2*c**4*d**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 4*b**2*c**2*d**3*e - 2*b*c**3*d**4)/(12*a**2*c**2*e**4 - 12*a*b**2*c*e**4 + 24*a*b*c**2*d*e**3 - 24*a*c**3*d**2*e**2 + 2*b**4*e**4 - 4*b**3*c*d*e**3 + 8*b*c**3*d**3*e - 4*c**4*d**4)) + (-3*a**2*b*c*e**4 + 8*a**2*c**2*d*e**3 + a*b**3*e**4 - 4*a*b**2*c*d*e**3 + 6*a*b*c**2*d**2*e**2 - 8*a*c**3*d**3*e + b*c**3*d**4 + x*(2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4))/(4*a**2*c**4 - a*b**2*c**3 + x**2*(4*a*c**5 - b**2*c**4) + x*(4*a*b*c**4 - b**3*c**3)) + e**4*x/c**2","B",0
2192,1,1238,0,6.719428," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**2,x)","\left(\frac{e^{3}}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 16 a^{2} c^{3} \left(\frac{e^{3}}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 8 a^{2} c e^{3} + 8 a b^{2} c^{2} \left(\frac{e^{3}}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - a b^{2} e^{3} - 6 a b c d e^{2} - b^{4} c \left(\frac{e^{3}}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 3 b^{2} c d^{2} e - 2 b c^{2} d^{3}}{6 a b c e^{3} - 12 a c^{2} d e^{2} - b^{3} e^{3} + 6 b c^{2} d^{2} e - 4 c^{3} d^{3}} \right)} + \left(\frac{e^{3}}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 16 a^{2} c^{3} \left(\frac{e^{3}}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 8 a^{2} c e^{3} + 8 a b^{2} c^{2} \left(\frac{e^{3}}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - a b^{2} e^{3} - 6 a b c d e^{2} - b^{4} c \left(\frac{e^{3}}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 3 b^{2} c d^{2} e - 2 b c^{2} d^{3}}{6 a b c e^{3} - 12 a c^{2} d e^{2} - b^{3} e^{3} + 6 b c^{2} d^{2} e - 4 c^{3} d^{3}} \right)} + \frac{2 a^{2} c e^{3} - a b^{2} e^{3} + 3 a b c d e^{2} - 6 a c^{2} d^{2} e + b c^{2} d^{3} + x \left(3 a b c e^{3} - 6 a c^{2} d e^{2} - b^{3} e^{3} + 3 b^{2} c d e^{2} - 3 b c^{2} d^{2} e + 2 c^{3} d^{3}\right)}{4 a^{2} c^{3} - a b^{2} c^{2} + x^{2} \left(4 a c^{4} - b^{2} c^{3}\right) + x \left(4 a b c^{3} - b^{3} c^{2}\right)}"," ",0,"(e**3/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-16*a**2*c**3*(e**3/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 8*a**2*c*e**3 + 8*a*b**2*c**2*(e**3/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - a*b**2*e**3 - 6*a*b*c*d*e**2 - b**4*c*(e**3/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 3*b**2*c*d**2*e - 2*b*c**2*d**3)/(6*a*b*c*e**3 - 12*a*c**2*d*e**2 - b**3*e**3 + 6*b*c**2*d**2*e - 4*c**3*d**3)) + (e**3/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-16*a**2*c**3*(e**3/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 8*a**2*c*e**3 + 8*a*b**2*c**2*(e**3/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - a*b**2*e**3 - 6*a*b*c*d*e**2 - b**4*c*(e**3/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 3*b**2*c*d**2*e - 2*b*c**2*d**3)/(6*a*b*c*e**3 - 12*a*c**2*d*e**2 - b**3*e**3 + 6*b*c**2*d**2*e - 4*c**3*d**3)) + (2*a**2*c*e**3 - a*b**2*e**3 + 3*a*b*c*d*e**2 - 6*a*c**2*d**2*e + b*c**2*d**3 + x*(3*a*b*c*e**3 - 6*a*c**2*d*e**2 - b**3*e**3 + 3*b**2*c*d*e**2 - 3*b*c**2*d**2*e + 2*c**3*d**3))/(4*a**2*c**3 - a*b**2*c**2 + x**2*(4*a*c**4 - b**2*c**3) + x*(4*a*b*c**3 - b**3*c**2))","B",0
2193,1,517,0,1.793955," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**2,x)","- 2 \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) \log{\left(x + \frac{- 32 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) + 16 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) + 2 a b e^{2} - 2 b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) - 2 b^{2} d e + 2 b c d^{2}}{4 a c e^{2} - 4 b c d e + 4 c^{2} d^{2}} \right)} + 2 \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) \log{\left(x + \frac{32 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) - 16 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) + 2 a b e^{2} + 2 b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) - 2 b^{2} d e + 2 b c d^{2}}{4 a c e^{2} - 4 b c d e + 4 c^{2} d^{2}} \right)} + \frac{a b e^{2} - 4 a c d e + b c d^{2} + x \left(- 2 a c e^{2} + b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{4 a^{2} c^{2} - a b^{2} c + x^{2} \left(4 a c^{3} - b^{2} c^{2}\right) + x \left(4 a b c^{2} - b^{3} c\right)}"," ",0,"-2*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2)*log(x + (-32*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) + 16*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) + 2*a*b*e**2 - 2*b**4*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) - 2*b**2*d*e + 2*b*c*d**2)/(4*a*c*e**2 - 4*b*c*d*e + 4*c**2*d**2)) + 2*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2)*log(x + (32*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) - 16*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) + 2*a*b*e**2 + 2*b**4*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) - 2*b**2*d*e + 2*b*c*d**2)/(4*a*c*e**2 - 4*b*c*d*e + 4*c**2*d**2)) + (a*b*e**2 - 4*a*c*d*e + b*c*d**2 + x*(-2*a*c*e**2 + b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2))/(4*a**2*c**2 - a*b**2*c + x**2*(4*a*c**3 - b**2*c**2) + x*(4*a*b*c**2 - b**3*c))","B",0
2194,1,359,0,0.985915," ","integrate((e*x+d)/(c*x**2+b*x+a)**2,x)","\sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) \log{\left(x + \frac{- 16 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + 8 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) - b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + b^{2} e - 2 b c d}{2 b c e - 4 c^{2} d} \right)} - \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) \log{\left(x + \frac{16 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) - 8 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + b^{2} e - 2 b c d}{2 b c e - 4 c^{2} d} \right)} + \frac{- 2 a e + b d + x \left(- b e + 2 c d\right)}{4 a^{2} c - a b^{2} + x^{2} \left(4 a c^{2} - b^{2} c\right) + x \left(4 a b c - b^{3}\right)}"," ",0,"sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d)*log(x + (-16*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + 8*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) - b**4*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + b**2*e - 2*b*c*d)/(2*b*c*e - 4*c**2*d)) - sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d)*log(x + (16*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) - 8*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + b**4*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + b**2*e - 2*b*c*d)/(2*b*c*e - 4*c**2*d)) + (-2*a*e + b*d + x*(-b*e + 2*c*d))/(4*a**2*c - a*b**2 + x**2*(4*a*c**2 - b**2*c) + x*(4*a*b*c - b**3))","B",0
2195,1,265,0,0.577532," ","integrate(1/(c*x**2+b*x+a)**2,x)","- 2 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{- 32 a^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 16 a b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 2 b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 b c}{4 c^{2}} \right)} + 2 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{32 a^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 16 a b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 b c}{4 c^{2}} \right)} + \frac{b + 2 c x}{4 a^{2} c - a b^{2} + x^{2} \left(4 a c^{2} - b^{2} c\right) + x \left(4 a b c - b^{3}\right)}"," ",0,"-2*c*sqrt(-1/(4*a*c - b**2)**3)*log(x + (-32*a**2*c**3*sqrt(-1/(4*a*c - b**2)**3) + 16*a*b**2*c**2*sqrt(-1/(4*a*c - b**2)**3) - 2*b**4*c*sqrt(-1/(4*a*c - b**2)**3) + 2*b*c)/(4*c**2)) + 2*c*sqrt(-1/(4*a*c - b**2)**3)*log(x + (32*a**2*c**3*sqrt(-1/(4*a*c - b**2)**3) - 16*a*b**2*c**2*sqrt(-1/(4*a*c - b**2)**3) + 2*b**4*c*sqrt(-1/(4*a*c - b**2)**3) + 2*b*c)/(4*c**2)) + (b + 2*c*x)/(4*a**2*c - a*b**2 + x**2*(4*a*c**2 - b**2*c) + x*(4*a*b*c - b**3))","B",0
2196,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2197,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2198,-1,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2199,1,1875,0,5.769597," ","integrate(x**7/(c*x**2+b*x+a)**3,x)","- \frac{3 b x}{c^{4}} + \left(- \frac{3 b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(70 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 21 a b^{4} c - 2 b^{6}\right)}{2 c^{5} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} - \frac{3 \left(a c - 2 b^{2}\right)}{2 c^{5}}\right) \log{\left(x + \frac{96 a^{4} c^{3} - 159 a^{3} b^{2} c^{2} + 64 a^{3} c^{7} \left(- \frac{3 b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(70 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 21 a b^{4} c - 2 b^{6}\right)}{2 c^{5} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} - \frac{3 \left(a c - 2 b^{2}\right)}{2 c^{5}}\right) + 57 a^{2} b^{4} c - 48 a^{2} b^{2} c^{6} \left(- \frac{3 b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(70 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 21 a b^{4} c - 2 b^{6}\right)}{2 c^{5} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} - \frac{3 \left(a c - 2 b^{2}\right)}{2 c^{5}}\right) - 6 a b^{6} + 12 a b^{4} c^{5} \left(- \frac{3 b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(70 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 21 a b^{4} c - 2 b^{6}\right)}{2 c^{5} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} - \frac{3 \left(a c - 2 b^{2}\right)}{2 c^{5}}\right) - b^{6} c^{4} \left(- \frac{3 b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(70 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 21 a b^{4} c - 2 b^{6}\right)}{2 c^{5} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} - \frac{3 \left(a c - 2 b^{2}\right)}{2 c^{5}}\right)}{210 a^{3} b c^{3} - 210 a^{2} b^{3} c^{2} + 63 a b^{5} c - 6 b^{7}} \right)} + \left(\frac{3 b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(70 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 21 a b^{4} c - 2 b^{6}\right)}{2 c^{5} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} - \frac{3 \left(a c - 2 b^{2}\right)}{2 c^{5}}\right) \log{\left(x + \frac{96 a^{4} c^{3} - 159 a^{3} b^{2} c^{2} + 64 a^{3} c^{7} \left(\frac{3 b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(70 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 21 a b^{4} c - 2 b^{6}\right)}{2 c^{5} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} - \frac{3 \left(a c - 2 b^{2}\right)}{2 c^{5}}\right) + 57 a^{2} b^{4} c - 48 a^{2} b^{2} c^{6} \left(\frac{3 b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(70 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 21 a b^{4} c - 2 b^{6}\right)}{2 c^{5} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} - \frac{3 \left(a c - 2 b^{2}\right)}{2 c^{5}}\right) - 6 a b^{6} + 12 a b^{4} c^{5} \left(\frac{3 b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(70 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 21 a b^{4} c - 2 b^{6}\right)}{2 c^{5} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} - \frac{3 \left(a c - 2 b^{2}\right)}{2 c^{5}}\right) - b^{6} c^{4} \left(\frac{3 b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(70 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 21 a b^{4} c - 2 b^{6}\right)}{2 c^{5} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} - \frac{3 \left(a c - 2 b^{2}\right)}{2 c^{5}}\right)}{210 a^{3} b c^{3} - 210 a^{2} b^{3} c^{2} + 63 a b^{5} c - 6 b^{7}} \right)} + \frac{- 40 a^{5} c^{3} + 115 a^{4} b^{2} c^{2} - 55 a^{3} b^{4} c + 7 a^{2} b^{6} + x^{3} \left(- 126 a^{3} b c^{4} + 182 a^{2} b^{3} c^{3} - 70 a b^{5} c^{2} + 8 b^{7} c\right) + x^{2} \left(- 48 a^{4} c^{4} + 27 a^{3} b^{2} c^{3} + 94 a^{2} b^{4} c^{2} - 53 a b^{6} c + 7 b^{8}\right) + x \left(- 146 a^{4} b c^{3} + 272 a^{3} b^{3} c^{2} - 116 a^{2} b^{5} c + 14 a b^{7}\right)}{32 a^{4} c^{7} - 16 a^{3} b^{2} c^{6} + 2 a^{2} b^{4} c^{5} + x^{4} \left(32 a^{2} c^{9} - 16 a b^{2} c^{8} + 2 b^{4} c^{7}\right) + x^{3} \left(64 a^{2} b c^{8} - 32 a b^{3} c^{7} + 4 b^{5} c^{6}\right) + x^{2} \left(64 a^{3} c^{8} - 12 a b^{4} c^{6} + 2 b^{6} c^{5}\right) + x \left(64 a^{3} b c^{7} - 32 a^{2} b^{3} c^{6} + 4 a b^{5} c^{5}\right)} + \frac{x^{2}}{2 c^{3}}"," ",0,"-3*b*x/c**4 + (-3*b*sqrt(-(4*a*c - b**2)**5)*(70*a**3*c**3 - 70*a**2*b**2*c**2 + 21*a*b**4*c - 2*b**6)/(2*c**5*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) - 3*(a*c - 2*b**2)/(2*c**5))*log(x + (96*a**4*c**3 - 159*a**3*b**2*c**2 + 64*a**3*c**7*(-3*b*sqrt(-(4*a*c - b**2)**5)*(70*a**3*c**3 - 70*a**2*b**2*c**2 + 21*a*b**4*c - 2*b**6)/(2*c**5*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) - 3*(a*c - 2*b**2)/(2*c**5)) + 57*a**2*b**4*c - 48*a**2*b**2*c**6*(-3*b*sqrt(-(4*a*c - b**2)**5)*(70*a**3*c**3 - 70*a**2*b**2*c**2 + 21*a*b**4*c - 2*b**6)/(2*c**5*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) - 3*(a*c - 2*b**2)/(2*c**5)) - 6*a*b**6 + 12*a*b**4*c**5*(-3*b*sqrt(-(4*a*c - b**2)**5)*(70*a**3*c**3 - 70*a**2*b**2*c**2 + 21*a*b**4*c - 2*b**6)/(2*c**5*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) - 3*(a*c - 2*b**2)/(2*c**5)) - b**6*c**4*(-3*b*sqrt(-(4*a*c - b**2)**5)*(70*a**3*c**3 - 70*a**2*b**2*c**2 + 21*a*b**4*c - 2*b**6)/(2*c**5*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) - 3*(a*c - 2*b**2)/(2*c**5)))/(210*a**3*b*c**3 - 210*a**2*b**3*c**2 + 63*a*b**5*c - 6*b**7)) + (3*b*sqrt(-(4*a*c - b**2)**5)*(70*a**3*c**3 - 70*a**2*b**2*c**2 + 21*a*b**4*c - 2*b**6)/(2*c**5*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) - 3*(a*c - 2*b**2)/(2*c**5))*log(x + (96*a**4*c**3 - 159*a**3*b**2*c**2 + 64*a**3*c**7*(3*b*sqrt(-(4*a*c - b**2)**5)*(70*a**3*c**3 - 70*a**2*b**2*c**2 + 21*a*b**4*c - 2*b**6)/(2*c**5*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) - 3*(a*c - 2*b**2)/(2*c**5)) + 57*a**2*b**4*c - 48*a**2*b**2*c**6*(3*b*sqrt(-(4*a*c - b**2)**5)*(70*a**3*c**3 - 70*a**2*b**2*c**2 + 21*a*b**4*c - 2*b**6)/(2*c**5*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) - 3*(a*c - 2*b**2)/(2*c**5)) - 6*a*b**6 + 12*a*b**4*c**5*(3*b*sqrt(-(4*a*c - b**2)**5)*(70*a**3*c**3 - 70*a**2*b**2*c**2 + 21*a*b**4*c - 2*b**6)/(2*c**5*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) - 3*(a*c - 2*b**2)/(2*c**5)) - b**6*c**4*(3*b*sqrt(-(4*a*c - b**2)**5)*(70*a**3*c**3 - 70*a**2*b**2*c**2 + 21*a*b**4*c - 2*b**6)/(2*c**5*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) - 3*(a*c - 2*b**2)/(2*c**5)))/(210*a**3*b*c**3 - 210*a**2*b**3*c**2 + 63*a*b**5*c - 6*b**7)) + (-40*a**5*c**3 + 115*a**4*b**2*c**2 - 55*a**3*b**4*c + 7*a**2*b**6 + x**3*(-126*a**3*b*c**4 + 182*a**2*b**3*c**3 - 70*a*b**5*c**2 + 8*b**7*c) + x**2*(-48*a**4*c**4 + 27*a**3*b**2*c**3 + 94*a**2*b**4*c**2 - 53*a*b**6*c + 7*b**8) + x*(-146*a**4*b*c**3 + 272*a**3*b**3*c**2 - 116*a**2*b**5*c + 14*a*b**7))/(32*a**4*c**7 - 16*a**3*b**2*c**6 + 2*a**2*b**4*c**5 + x**4*(32*a**2*c**9 - 16*a*b**2*c**8 + 2*b**4*c**7) + x**3*(64*a**2*b*c**8 - 32*a*b**3*c**7 + 4*b**5*c**6) + x**2*(64*a**3*c**8 - 12*a*b**4*c**6 + 2*b**6*c**5) + x*(64*a**3*b*c**7 - 32*a**2*b**3*c**6 + 4*a*b**5*c**5)) + x**2/(2*c**3)","B",0
2200,1,1714,0,4.307137," ","integrate(x**6/(c*x**2+b*x+a)**3,x)","\left(- \frac{3 b}{2 c^{4}} - \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) \log{\left(x + \frac{- 66 a^{3} b c^{2} - 64 a^{3} c^{6} \left(- \frac{3 b}{2 c^{4}} - \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + 27 a^{2} b^{3} c + 48 a^{2} b^{2} c^{5} \left(- \frac{3 b}{2 c^{4}} - \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) - 3 a b^{5} - 12 a b^{4} c^{4} \left(- \frac{3 b}{2 c^{4}} - \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + b^{6} c^{3} \left(- \frac{3 b}{2 c^{4}} - \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right)}{60 a^{3} c^{3} - 90 a^{2} b^{2} c^{2} + 30 a b^{4} c - 3 b^{6}} \right)} + \left(- \frac{3 b}{2 c^{4}} + \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) \log{\left(x + \frac{- 66 a^{3} b c^{2} - 64 a^{3} c^{6} \left(- \frac{3 b}{2 c^{4}} + \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + 27 a^{2} b^{3} c + 48 a^{2} b^{2} c^{5} \left(- \frac{3 b}{2 c^{4}} + \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) - 3 a b^{5} - 12 a b^{4} c^{4} \left(- \frac{3 b}{2 c^{4}} + \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + b^{6} c^{3} \left(- \frac{3 b}{2 c^{4}} + \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right)}{60 a^{3} c^{3} - 90 a^{2} b^{2} c^{2} + 30 a b^{4} c - 3 b^{6}} \right)} + \frac{- 58 a^{4} b c^{2} + 36 a^{3} b^{3} c - 5 a^{2} b^{5} + x^{3} \left(36 a^{3} c^{4} - 102 a^{2} b^{2} c^{3} + 48 a b^{4} c^{2} - 6 b^{6} c\right) + x^{2} \left(- 42 a^{3} b c^{3} - 41 a^{2} b^{3} c^{2} + 34 a b^{5} c - 5 b^{7}\right) + x \left(28 a^{4} c^{3} - 142 a^{3} b^{2} c^{2} + 76 a^{2} b^{4} c - 10 a b^{6}\right)}{32 a^{4} c^{6} - 16 a^{3} b^{2} c^{5} + 2 a^{2} b^{4} c^{4} + x^{4} \left(32 a^{2} c^{8} - 16 a b^{2} c^{7} + 2 b^{4} c^{6}\right) + x^{3} \left(64 a^{2} b c^{7} - 32 a b^{3} c^{6} + 4 b^{5} c^{5}\right) + x^{2} \left(64 a^{3} c^{7} - 12 a b^{4} c^{5} + 2 b^{6} c^{4}\right) + x \left(64 a^{3} b c^{6} - 32 a^{2} b^{3} c^{5} + 4 a b^{5} c^{4}\right)} + \frac{x}{c^{3}}"," ",0,"(-3*b/(2*c**4) - 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)))*log(x + (-66*a**3*b*c**2 - 64*a**3*c**6*(-3*b/(2*c**4) - 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + 27*a**2*b**3*c + 48*a**2*b**2*c**5*(-3*b/(2*c**4) - 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) - 3*a*b**5 - 12*a*b**4*c**4*(-3*b/(2*c**4) - 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + b**6*c**3*(-3*b/(2*c**4) - 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))))/(60*a**3*c**3 - 90*a**2*b**2*c**2 + 30*a*b**4*c - 3*b**6)) + (-3*b/(2*c**4) + 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)))*log(x + (-66*a**3*b*c**2 - 64*a**3*c**6*(-3*b/(2*c**4) + 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + 27*a**2*b**3*c + 48*a**2*b**2*c**5*(-3*b/(2*c**4) + 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) - 3*a*b**5 - 12*a*b**4*c**4*(-3*b/(2*c**4) + 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + b**6*c**3*(-3*b/(2*c**4) + 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))))/(60*a**3*c**3 - 90*a**2*b**2*c**2 + 30*a*b**4*c - 3*b**6)) + (-58*a**4*b*c**2 + 36*a**3*b**3*c - 5*a**2*b**5 + x**3*(36*a**3*c**4 - 102*a**2*b**2*c**3 + 48*a*b**4*c**2 - 6*b**6*c) + x**2*(-42*a**3*b*c**3 - 41*a**2*b**3*c**2 + 34*a*b**5*c - 5*b**7) + x*(28*a**4*c**3 - 142*a**3*b**2*c**2 + 76*a**2*b**4*c - 10*a*b**6))/(32*a**4*c**6 - 16*a**3*b**2*c**5 + 2*a**2*b**4*c**4 + x**4*(32*a**2*c**8 - 16*a*b**2*c**7 + 2*b**4*c**6) + x**3*(64*a**2*b*c**7 - 32*a*b**3*c**6 + 4*b**5*c**5) + x**2*(64*a**3*c**7 - 12*a*b**4*c**5 + 2*b**6*c**4) + x*(64*a**3*b*c**6 - 32*a**2*b**3*c**5 + 4*a*b**5*c**4)) + x/c**3","B",0
2201,1,3403,0,119.895644," ","integrate((e*x+d)**5/(c*x**2+b*x+a)**3,x)","\left(\frac{e^{5}}{2 c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 10 a b^{2} c e^{4} - 20 a b c^{2} d e^{3} + 20 a c^{3} d^{2} e^{2} + b^{4} e^{4} + 2 b^{3} c d e^{3} + 4 b^{2} c^{2} d^{2} e^{2} - 12 b c^{3} d^{3} e + 6 c^{4} d^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) \log{\left(x + \frac{- 64 a^{3} c^{5} \left(\frac{e^{5}}{2 c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 10 a b^{2} c e^{4} - 20 a b c^{2} d e^{3} + 20 a c^{3} d^{2} e^{2} + b^{4} e^{4} + 2 b^{3} c d e^{3} + 4 b^{2} c^{2} d^{2} e^{2} - 12 b c^{3} d^{3} e + 6 c^{4} d^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + 32 a^{3} c^{2} e^{5} + 48 a^{2} b^{2} c^{4} \left(\frac{e^{5}}{2 c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 10 a b^{2} c e^{4} - 20 a b c^{2} d e^{3} + 20 a c^{3} d^{2} e^{2} + b^{4} e^{4} + 2 b^{3} c d e^{3} + 4 b^{2} c^{2} d^{2} e^{2} - 12 b c^{3} d^{3} e + 6 c^{4} d^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) - 9 a^{2} b^{2} c e^{5} - 30 a^{2} b c^{2} d e^{4} - 12 a b^{4} c^{3} \left(\frac{e^{5}}{2 c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 10 a b^{2} c e^{4} - 20 a b c^{2} d e^{3} + 20 a c^{3} d^{2} e^{2} + b^{4} e^{4} + 2 b^{3} c d e^{3} + 4 b^{2} c^{2} d^{2} e^{2} - 12 b c^{3} d^{3} e + 6 c^{4} d^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + a b^{4} e^{5} + 30 a b^{2} c^{2} d^{2} e^{3} - 20 a b c^{3} d^{3} e^{2} + b^{6} c^{2} \left(\frac{e^{5}}{2 c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 10 a b^{2} c e^{4} - 20 a b c^{2} d e^{3} + 20 a c^{3} d^{2} e^{2} + b^{4} e^{4} + 2 b^{3} c d e^{3} + 4 b^{2} c^{2} d^{2} e^{2} - 12 b c^{3} d^{3} e + 6 c^{4} d^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) - 10 b^{3} c^{2} d^{3} e^{2} + 15 b^{2} c^{3} d^{4} e - 6 b c^{4} d^{5}}{30 a^{2} b c^{2} e^{5} - 60 a^{2} c^{3} d e^{4} - 10 a b^{3} c e^{5} + 60 a b c^{3} d^{2} e^{3} - 40 a c^{4} d^{3} e^{2} + b^{5} e^{5} - 20 b^{2} c^{3} d^{3} e^{2} + 30 b c^{4} d^{4} e - 12 c^{5} d^{5}} \right)} + \left(\frac{e^{5}}{2 c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 10 a b^{2} c e^{4} - 20 a b c^{2} d e^{3} + 20 a c^{3} d^{2} e^{2} + b^{4} e^{4} + 2 b^{3} c d e^{3} + 4 b^{2} c^{2} d^{2} e^{2} - 12 b c^{3} d^{3} e + 6 c^{4} d^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) \log{\left(x + \frac{- 64 a^{3} c^{5} \left(\frac{e^{5}}{2 c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 10 a b^{2} c e^{4} - 20 a b c^{2} d e^{3} + 20 a c^{3} d^{2} e^{2} + b^{4} e^{4} + 2 b^{3} c d e^{3} + 4 b^{2} c^{2} d^{2} e^{2} - 12 b c^{3} d^{3} e + 6 c^{4} d^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + 32 a^{3} c^{2} e^{5} + 48 a^{2} b^{2} c^{4} \left(\frac{e^{5}}{2 c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 10 a b^{2} c e^{4} - 20 a b c^{2} d e^{3} + 20 a c^{3} d^{2} e^{2} + b^{4} e^{4} + 2 b^{3} c d e^{3} + 4 b^{2} c^{2} d^{2} e^{2} - 12 b c^{3} d^{3} e + 6 c^{4} d^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) - 9 a^{2} b^{2} c e^{5} - 30 a^{2} b c^{2} d e^{4} - 12 a b^{4} c^{3} \left(\frac{e^{5}}{2 c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 10 a b^{2} c e^{4} - 20 a b c^{2} d e^{3} + 20 a c^{3} d^{2} e^{2} + b^{4} e^{4} + 2 b^{3} c d e^{3} + 4 b^{2} c^{2} d^{2} e^{2} - 12 b c^{3} d^{3} e + 6 c^{4} d^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + a b^{4} e^{5} + 30 a b^{2} c^{2} d^{2} e^{3} - 20 a b c^{3} d^{3} e^{2} + b^{6} c^{2} \left(\frac{e^{5}}{2 c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(b e - 2 c d\right) \left(30 a^{2} c^{2} e^{4} - 10 a b^{2} c e^{4} - 20 a b c^{2} d e^{3} + 20 a c^{3} d^{2} e^{2} + b^{4} e^{4} + 2 b^{3} c d e^{3} + 4 b^{2} c^{2} d^{2} e^{2} - 12 b c^{3} d^{3} e + 6 c^{4} d^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) - 10 b^{3} c^{2} d^{3} e^{2} + 15 b^{2} c^{3} d^{4} e - 6 b c^{4} d^{5}}{30 a^{2} b c^{2} e^{5} - 60 a^{2} c^{3} d e^{4} - 10 a b^{3} c e^{5} + 60 a b c^{3} d^{2} e^{3} - 40 a c^{4} d^{3} e^{2} + b^{5} e^{5} - 20 b^{2} c^{3} d^{3} e^{2} + 30 b c^{4} d^{4} e - 12 c^{5} d^{5}} \right)} + \frac{24 a^{4} c^{2} e^{5} - 21 a^{3} b^{2} c e^{5} + 50 a^{3} b c^{2} d e^{4} - 80 a^{3} c^{3} d^{2} e^{3} + 3 a^{2} b^{4} e^{5} - 5 a^{2} b^{3} c d e^{4} - 10 a^{2} b^{2} c^{2} d^{2} e^{3} + 60 a^{2} b c^{3} d^{3} e^{2} - 40 a^{2} c^{4} d^{4} e - 5 a b^{2} c^{3} d^{4} e + 10 a b c^{4} d^{5} - b^{3} c^{3} d^{5} + x^{3} \left(50 a^{2} b c^{3} e^{5} - 100 a^{2} c^{4} d e^{4} - 30 a b^{3} c^{2} e^{5} + 80 a b^{2} c^{3} d e^{4} - 60 a b c^{4} d^{2} e^{3} + 40 a c^{5} d^{3} e^{2} + 4 b^{5} c e^{5} - 10 b^{4} c^{2} d e^{4} + 20 b^{2} c^{4} d^{3} e^{2} - 30 b c^{5} d^{4} e + 12 c^{6} d^{5}\right) + x^{2} \left(32 a^{3} c^{3} e^{5} + 11 a^{2} b^{2} c^{2} e^{5} + 10 a^{2} b c^{3} d e^{4} - 160 a^{2} c^{4} d^{2} e^{3} - 19 a b^{4} c e^{5} + 40 a b^{3} c^{2} d e^{4} - 10 a b^{2} c^{3} d^{2} e^{3} + 60 a b c^{4} d^{3} e^{2} + 3 b^{6} e^{5} - 5 b^{5} c d e^{4} - 10 b^{4} c^{2} d^{2} e^{3} + 30 b^{3} c^{3} d^{3} e^{2} - 45 b^{2} c^{4} d^{4} e + 18 b c^{5} d^{5}\right) + x \left(62 a^{3} b c^{2} e^{5} - 60 a^{3} c^{3} d e^{4} - 44 a^{2} b^{3} c e^{5} + 100 a^{2} b^{2} c^{2} d e^{4} - 100 a^{2} b c^{3} d^{2} e^{3} - 40 a^{2} c^{4} d^{3} e^{2} + 6 a b^{5} e^{5} - 10 a b^{4} c d e^{4} - 20 a b^{3} c^{2} d^{2} e^{3} + 100 a b^{2} c^{3} d^{3} e^{2} - 50 a b c^{4} d^{4} e + 20 a c^{5} d^{5} - 10 b^{3} c^{3} d^{4} e + 4 b^{2} c^{4} d^{5}\right)}{32 a^{4} c^{5} - 16 a^{3} b^{2} c^{4} + 2 a^{2} b^{4} c^{3} + x^{4} \left(32 a^{2} c^{7} - 16 a b^{2} c^{6} + 2 b^{4} c^{5}\right) + x^{3} \left(64 a^{2} b c^{6} - 32 a b^{3} c^{5} + 4 b^{5} c^{4}\right) + x^{2} \left(64 a^{3} c^{6} - 12 a b^{4} c^{4} + 2 b^{6} c^{3}\right) + x \left(64 a^{3} b c^{5} - 32 a^{2} b^{3} c^{4} + 4 a b^{5} c^{3}\right)}"," ",0,"(e**5/(2*c**3) - sqrt(-(4*a*c - b**2)**5)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 10*a*b**2*c*e**4 - 20*a*b*c**2*d*e**3 + 20*a*c**3*d**2*e**2 + b**4*e**4 + 2*b**3*c*d*e**3 + 4*b**2*c**2*d**2*e**2 - 12*b*c**3*d**3*e + 6*c**4*d**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)))*log(x + (-64*a**3*c**5*(e**5/(2*c**3) - sqrt(-(4*a*c - b**2)**5)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 10*a*b**2*c*e**4 - 20*a*b*c**2*d*e**3 + 20*a*c**3*d**2*e**2 + b**4*e**4 + 2*b**3*c*d*e**3 + 4*b**2*c**2*d**2*e**2 - 12*b*c**3*d**3*e + 6*c**4*d**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + 32*a**3*c**2*e**5 + 48*a**2*b**2*c**4*(e**5/(2*c**3) - sqrt(-(4*a*c - b**2)**5)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 10*a*b**2*c*e**4 - 20*a*b*c**2*d*e**3 + 20*a*c**3*d**2*e**2 + b**4*e**4 + 2*b**3*c*d*e**3 + 4*b**2*c**2*d**2*e**2 - 12*b*c**3*d**3*e + 6*c**4*d**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) - 9*a**2*b**2*c*e**5 - 30*a**2*b*c**2*d*e**4 - 12*a*b**4*c**3*(e**5/(2*c**3) - sqrt(-(4*a*c - b**2)**5)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 10*a*b**2*c*e**4 - 20*a*b*c**2*d*e**3 + 20*a*c**3*d**2*e**2 + b**4*e**4 + 2*b**3*c*d*e**3 + 4*b**2*c**2*d**2*e**2 - 12*b*c**3*d**3*e + 6*c**4*d**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + a*b**4*e**5 + 30*a*b**2*c**2*d**2*e**3 - 20*a*b*c**3*d**3*e**2 + b**6*c**2*(e**5/(2*c**3) - sqrt(-(4*a*c - b**2)**5)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 10*a*b**2*c*e**4 - 20*a*b*c**2*d*e**3 + 20*a*c**3*d**2*e**2 + b**4*e**4 + 2*b**3*c*d*e**3 + 4*b**2*c**2*d**2*e**2 - 12*b*c**3*d**3*e + 6*c**4*d**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) - 10*b**3*c**2*d**3*e**2 + 15*b**2*c**3*d**4*e - 6*b*c**4*d**5)/(30*a**2*b*c**2*e**5 - 60*a**2*c**3*d*e**4 - 10*a*b**3*c*e**5 + 60*a*b*c**3*d**2*e**3 - 40*a*c**4*d**3*e**2 + b**5*e**5 - 20*b**2*c**3*d**3*e**2 + 30*b*c**4*d**4*e - 12*c**5*d**5)) + (e**5/(2*c**3) + sqrt(-(4*a*c - b**2)**5)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 10*a*b**2*c*e**4 - 20*a*b*c**2*d*e**3 + 20*a*c**3*d**2*e**2 + b**4*e**4 + 2*b**3*c*d*e**3 + 4*b**2*c**2*d**2*e**2 - 12*b*c**3*d**3*e + 6*c**4*d**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)))*log(x + (-64*a**3*c**5*(e**5/(2*c**3) + sqrt(-(4*a*c - b**2)**5)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 10*a*b**2*c*e**4 - 20*a*b*c**2*d*e**3 + 20*a*c**3*d**2*e**2 + b**4*e**4 + 2*b**3*c*d*e**3 + 4*b**2*c**2*d**2*e**2 - 12*b*c**3*d**3*e + 6*c**4*d**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + 32*a**3*c**2*e**5 + 48*a**2*b**2*c**4*(e**5/(2*c**3) + sqrt(-(4*a*c - b**2)**5)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 10*a*b**2*c*e**4 - 20*a*b*c**2*d*e**3 + 20*a*c**3*d**2*e**2 + b**4*e**4 + 2*b**3*c*d*e**3 + 4*b**2*c**2*d**2*e**2 - 12*b*c**3*d**3*e + 6*c**4*d**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) - 9*a**2*b**2*c*e**5 - 30*a**2*b*c**2*d*e**4 - 12*a*b**4*c**3*(e**5/(2*c**3) + sqrt(-(4*a*c - b**2)**5)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 10*a*b**2*c*e**4 - 20*a*b*c**2*d*e**3 + 20*a*c**3*d**2*e**2 + b**4*e**4 + 2*b**3*c*d*e**3 + 4*b**2*c**2*d**2*e**2 - 12*b*c**3*d**3*e + 6*c**4*d**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + a*b**4*e**5 + 30*a*b**2*c**2*d**2*e**3 - 20*a*b*c**3*d**3*e**2 + b**6*c**2*(e**5/(2*c**3) + sqrt(-(4*a*c - b**2)**5)*(b*e - 2*c*d)*(30*a**2*c**2*e**4 - 10*a*b**2*c*e**4 - 20*a*b*c**2*d*e**3 + 20*a*c**3*d**2*e**2 + b**4*e**4 + 2*b**3*c*d*e**3 + 4*b**2*c**2*d**2*e**2 - 12*b*c**3*d**3*e + 6*c**4*d**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) - 10*b**3*c**2*d**3*e**2 + 15*b**2*c**3*d**4*e - 6*b*c**4*d**5)/(30*a**2*b*c**2*e**5 - 60*a**2*c**3*d*e**4 - 10*a*b**3*c*e**5 + 60*a*b*c**3*d**2*e**3 - 40*a*c**4*d**3*e**2 + b**5*e**5 - 20*b**2*c**3*d**3*e**2 + 30*b*c**4*d**4*e - 12*c**5*d**5)) + (24*a**4*c**2*e**5 - 21*a**3*b**2*c*e**5 + 50*a**3*b*c**2*d*e**4 - 80*a**3*c**3*d**2*e**3 + 3*a**2*b**4*e**5 - 5*a**2*b**3*c*d*e**4 - 10*a**2*b**2*c**2*d**2*e**3 + 60*a**2*b*c**3*d**3*e**2 - 40*a**2*c**4*d**4*e - 5*a*b**2*c**3*d**4*e + 10*a*b*c**4*d**5 - b**3*c**3*d**5 + x**3*(50*a**2*b*c**3*e**5 - 100*a**2*c**4*d*e**4 - 30*a*b**3*c**2*e**5 + 80*a*b**2*c**3*d*e**4 - 60*a*b*c**4*d**2*e**3 + 40*a*c**5*d**3*e**2 + 4*b**5*c*e**5 - 10*b**4*c**2*d*e**4 + 20*b**2*c**4*d**3*e**2 - 30*b*c**5*d**4*e + 12*c**6*d**5) + x**2*(32*a**3*c**3*e**5 + 11*a**2*b**2*c**2*e**5 + 10*a**2*b*c**3*d*e**4 - 160*a**2*c**4*d**2*e**3 - 19*a*b**4*c*e**5 + 40*a*b**3*c**2*d*e**4 - 10*a*b**2*c**3*d**2*e**3 + 60*a*b*c**4*d**3*e**2 + 3*b**6*e**5 - 5*b**5*c*d*e**4 - 10*b**4*c**2*d**2*e**3 + 30*b**3*c**3*d**3*e**2 - 45*b**2*c**4*d**4*e + 18*b*c**5*d**5) + x*(62*a**3*b*c**2*e**5 - 60*a**3*c**3*d*e**4 - 44*a**2*b**3*c*e**5 + 100*a**2*b**2*c**2*d*e**4 - 100*a**2*b*c**3*d**2*e**3 - 40*a**2*c**4*d**3*e**2 + 6*a*b**5*e**5 - 10*a*b**4*c*d*e**4 - 20*a*b**3*c**2*d**2*e**3 + 100*a*b**2*c**3*d**3*e**2 - 50*a*b*c**4*d**4*e + 20*a*c**5*d**5 - 10*b**3*c**3*d**4*e + 4*b**2*c**4*d**5))/(32*a**4*c**5 - 16*a**3*b**2*c**4 + 2*a**2*b**4*c**3 + x**4*(32*a**2*c**7 - 16*a*b**2*c**6 + 2*b**4*c**5) + x**3*(64*a**2*b*c**6 - 32*a*b**3*c**5 + 4*b**5*c**4) + x**2*(64*a**3*c**6 - 12*a*b**4*c**4 + 2*b**6*c**3) + x*(64*a**3*b*c**5 - 32*a**2*b**3*c**4 + 4*a*b**5*c**3))","B",0
2202,1,1355,0,32.628980," ","integrate((e*x+d)**4/(c*x**2+b*x+a)**3,x)","- 6 \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} \log{\left(x + \frac{- 384 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} + 288 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} + 6 a^{2} b e^{4} - 72 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} - 12 a b^{2} d e^{3} + 12 a b c d^{2} e^{2} + 6 b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} + 6 b^{3} d^{2} e^{2} - 12 b^{2} c d^{3} e + 6 b c^{2} d^{4}}{12 a^{2} c e^{4} - 24 a b c d e^{3} + 24 a c^{2} d^{2} e^{2} + 12 b^{2} c d^{2} e^{2} - 24 b c^{2} d^{3} e + 12 c^{3} d^{4}} \right)} + 6 \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} \log{\left(x + \frac{384 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} - 288 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} + 6 a^{2} b e^{4} + 72 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} - 12 a b^{2} d e^{3} + 12 a b c d^{2} e^{2} - 6 b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} + 6 b^{3} d^{2} e^{2} - 12 b^{2} c d^{3} e + 6 b c^{2} d^{4}}{12 a^{2} c e^{4} - 24 a b c d e^{3} + 24 a c^{2} d^{2} e^{2} + 12 b^{2} c d^{2} e^{2} - 24 b c^{2} d^{3} e + 12 c^{3} d^{4}} \right)} + \frac{10 a^{3} b c e^{4} - 32 a^{3} c^{2} d e^{3} - a^{2} b^{3} e^{4} - 4 a^{2} b^{2} c d e^{3} + 36 a^{2} b c^{2} d^{2} e^{2} - 32 a^{2} c^{3} d^{3} e - 4 a b^{2} c^{2} d^{3} e + 10 a b c^{3} d^{4} - b^{3} c^{2} d^{4} + x^{3} \left(- 20 a^{2} c^{3} e^{4} + 16 a b^{2} c^{2} e^{4} - 24 a b c^{3} d e^{3} + 24 a c^{4} d^{2} e^{2} - 2 b^{4} c e^{4} + 12 b^{2} c^{3} d^{2} e^{2} - 24 b c^{4} d^{3} e + 12 c^{5} d^{4}\right) + x^{2} \left(2 a^{2} b c^{2} e^{4} - 64 a^{2} c^{3} d e^{3} + 8 a b^{3} c e^{4} - 4 a b^{2} c^{2} d e^{3} + 36 a b c^{3} d^{2} e^{2} - b^{5} e^{4} - 4 b^{4} c d e^{3} + 18 b^{3} c^{2} d^{2} e^{2} - 36 b^{2} c^{3} d^{3} e + 18 b c^{4} d^{4}\right) + x \left(- 12 a^{3} c^{2} e^{4} + 20 a^{2} b^{2} c e^{4} - 40 a^{2} b c^{2} d e^{3} - 24 a^{2} c^{3} d^{2} e^{2} - 2 a b^{4} e^{4} - 8 a b^{3} c d e^{3} + 60 a b^{2} c^{2} d^{2} e^{2} - 40 a b c^{3} d^{3} e + 20 a c^{4} d^{4} - 8 b^{3} c^{2} d^{3} e + 4 b^{2} c^{3} d^{4}\right)}{32 a^{4} c^{4} - 16 a^{3} b^{2} c^{3} + 2 a^{2} b^{4} c^{2} + x^{4} \left(32 a^{2} c^{6} - 16 a b^{2} c^{5} + 2 b^{4} c^{4}\right) + x^{3} \left(64 a^{2} b c^{5} - 32 a b^{3} c^{4} + 4 b^{5} c^{3}\right) + x^{2} \left(64 a^{3} c^{5} - 12 a b^{4} c^{3} + 2 b^{6} c^{2}\right) + x \left(64 a^{3} b c^{4} - 32 a^{2} b^{3} c^{3} + 4 a b^{5} c^{2}\right)}"," ",0,"-6*sqrt(-1/(4*a*c - b**2)**5)*(a*e**2 - b*d*e + c*d**2)**2*log(x + (-384*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(a*e**2 - b*d*e + c*d**2)**2 + 288*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(a*e**2 - b*d*e + c*d**2)**2 + 6*a**2*b*e**4 - 72*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(a*e**2 - b*d*e + c*d**2)**2 - 12*a*b**2*d*e**3 + 12*a*b*c*d**2*e**2 + 6*b**6*sqrt(-1/(4*a*c - b**2)**5)*(a*e**2 - b*d*e + c*d**2)**2 + 6*b**3*d**2*e**2 - 12*b**2*c*d**3*e + 6*b*c**2*d**4)/(12*a**2*c*e**4 - 24*a*b*c*d*e**3 + 24*a*c**2*d**2*e**2 + 12*b**2*c*d**2*e**2 - 24*b*c**2*d**3*e + 12*c**3*d**4)) + 6*sqrt(-1/(4*a*c - b**2)**5)*(a*e**2 - b*d*e + c*d**2)**2*log(x + (384*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(a*e**2 - b*d*e + c*d**2)**2 - 288*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(a*e**2 - b*d*e + c*d**2)**2 + 6*a**2*b*e**4 + 72*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(a*e**2 - b*d*e + c*d**2)**2 - 12*a*b**2*d*e**3 + 12*a*b*c*d**2*e**2 - 6*b**6*sqrt(-1/(4*a*c - b**2)**5)*(a*e**2 - b*d*e + c*d**2)**2 + 6*b**3*d**2*e**2 - 12*b**2*c*d**3*e + 6*b*c**2*d**4)/(12*a**2*c*e**4 - 24*a*b*c*d*e**3 + 24*a*c**2*d**2*e**2 + 12*b**2*c*d**2*e**2 - 24*b*c**2*d**3*e + 12*c**3*d**4)) + (10*a**3*b*c*e**4 - 32*a**3*c**2*d*e**3 - a**2*b**3*e**4 - 4*a**2*b**2*c*d*e**3 + 36*a**2*b*c**2*d**2*e**2 - 32*a**2*c**3*d**3*e - 4*a*b**2*c**2*d**3*e + 10*a*b*c**3*d**4 - b**3*c**2*d**4 + x**3*(-20*a**2*c**3*e**4 + 16*a*b**2*c**2*e**4 - 24*a*b*c**3*d*e**3 + 24*a*c**4*d**2*e**2 - 2*b**4*c*e**4 + 12*b**2*c**3*d**2*e**2 - 24*b*c**4*d**3*e + 12*c**5*d**4) + x**2*(2*a**2*b*c**2*e**4 - 64*a**2*c**3*d*e**3 + 8*a*b**3*c*e**4 - 4*a*b**2*c**2*d*e**3 + 36*a*b*c**3*d**2*e**2 - b**5*e**4 - 4*b**4*c*d*e**3 + 18*b**3*c**2*d**2*e**2 - 36*b**2*c**3*d**3*e + 18*b*c**4*d**4) + x*(-12*a**3*c**2*e**4 + 20*a**2*b**2*c*e**4 - 40*a**2*b*c**2*d*e**3 - 24*a**2*c**3*d**2*e**2 - 2*a*b**4*e**4 - 8*a*b**3*c*d*e**3 + 60*a*b**2*c**2*d**2*e**2 - 40*a*b*c**3*d**3*e + 20*a*c**4*d**4 - 8*b**3*c**2*d**3*e + 4*b**2*c**3*d**4))/(32*a**4*c**4 - 16*a**3*b**2*c**3 + 2*a**2*b**4*c**2 + x**4*(32*a**2*c**6 - 16*a*b**2*c**5 + 2*b**4*c**4) + x**3*(64*a**2*b*c**5 - 32*a*b**3*c**4 + 4*b**5*c**3) + x**2*(64*a**3*c**5 - 12*a*b**4*c**3 + 2*b**6*c**2) + x*(64*a**3*b*c**4 - 32*a**2*b**3*c**3 + 4*a*b**5*c**2))","B",0
2203,1,1180,0,10.905394," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**3,x)","3 \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) \log{\left(x + \frac{- 192 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) + 144 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) - 36 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) + 3 a b^{2} e^{3} - 6 a b c d e^{2} + 3 b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) - 3 b^{3} d e^{2} + 9 b^{2} c d^{2} e - 6 b c^{2} d^{3}}{6 a b c e^{3} - 12 a c^{2} d e^{2} - 6 b^{2} c d e^{2} + 18 b c^{2} d^{2} e - 12 c^{3} d^{3}} \right)} - 3 \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) \log{\left(x + \frac{192 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) - 144 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) + 36 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) + 3 a b^{2} e^{3} - 6 a b c d e^{2} - 3 b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) - 3 b^{3} d e^{2} + 9 b^{2} c d^{2} e - 6 b c^{2} d^{3}}{6 a b c e^{3} - 12 a c^{2} d e^{2} - 6 b^{2} c d e^{2} + 18 b c^{2} d^{2} e - 12 c^{3} d^{3}} \right)} + \frac{- 8 a^{3} c e^{3} - a^{2} b^{2} e^{3} + 18 a^{2} b c d e^{2} - 24 a^{2} c^{2} d^{2} e - 3 a b^{2} c d^{2} e + 10 a b c^{2} d^{3} - b^{3} c d^{3} + x^{3} \left(- 6 a b c^{2} e^{3} + 12 a c^{3} d e^{2} + 6 b^{2} c^{2} d e^{2} - 18 b c^{3} d^{2} e + 12 c^{4} d^{3}\right) + x^{2} \left(- 16 a^{2} c^{2} e^{3} - a b^{2} c e^{3} + 18 a b c^{2} d e^{2} - b^{4} e^{3} + 9 b^{3} c d e^{2} - 27 b^{2} c^{2} d^{2} e + 18 b c^{3} d^{3}\right) + x \left(- 10 a^{2} b c e^{3} - 12 a^{2} c^{2} d e^{2} - 2 a b^{3} e^{3} + 30 a b^{2} c d e^{2} - 30 a b c^{2} d^{2} e + 20 a c^{3} d^{3} - 6 b^{3} c d^{2} e + 4 b^{2} c^{2} d^{3}\right)}{32 a^{4} c^{3} - 16 a^{3} b^{2} c^{2} + 2 a^{2} b^{4} c + x^{4} \left(32 a^{2} c^{5} - 16 a b^{2} c^{4} + 2 b^{4} c^{3}\right) + x^{3} \left(64 a^{2} b c^{4} - 32 a b^{3} c^{3} + 4 b^{5} c^{2}\right) + x^{2} \left(64 a^{3} c^{4} - 12 a b^{4} c^{2} + 2 b^{6} c\right) + x \left(64 a^{3} b c^{3} - 32 a^{2} b^{3} c^{2} + 4 a b^{5} c\right)}"," ",0,"3*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)*log(x + (-192*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2) + 144*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2) - 36*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2) + 3*a*b**2*e**3 - 6*a*b*c*d*e**2 + 3*b**6*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2) - 3*b**3*d*e**2 + 9*b**2*c*d**2*e - 6*b*c**2*d**3)/(6*a*b*c*e**3 - 12*a*c**2*d*e**2 - 6*b**2*c*d*e**2 + 18*b*c**2*d**2*e - 12*c**3*d**3)) - 3*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)*log(x + (192*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2) - 144*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2) + 36*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2) + 3*a*b**2*e**3 - 6*a*b*c*d*e**2 - 3*b**6*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2) - 3*b**3*d*e**2 + 9*b**2*c*d**2*e - 6*b*c**2*d**3)/(6*a*b*c*e**3 - 12*a*c**2*d*e**2 - 6*b**2*c*d*e**2 + 18*b*c**2*d**2*e - 12*c**3*d**3)) + (-8*a**3*c*e**3 - a**2*b**2*e**3 + 18*a**2*b*c*d*e**2 - 24*a**2*c**2*d**2*e - 3*a*b**2*c*d**2*e + 10*a*b*c**2*d**3 - b**3*c*d**3 + x**3*(-6*a*b*c**2*e**3 + 12*a*c**3*d*e**2 + 6*b**2*c**2*d*e**2 - 18*b*c**3*d**2*e + 12*c**4*d**3) + x**2*(-16*a**2*c**2*e**3 - a*b**2*c*e**3 + 18*a*b*c**2*d*e**2 - b**4*e**3 + 9*b**3*c*d*e**2 - 27*b**2*c**2*d**2*e + 18*b*c**3*d**3) + x*(-10*a**2*b*c*e**3 - 12*a**2*c**2*d*e**2 - 2*a*b**3*e**3 + 30*a*b**2*c*d*e**2 - 30*a*b*c**2*d**2*e + 20*a*c**3*d**3 - 6*b**3*c*d**2*e + 4*b**2*c**2*d**3))/(32*a**4*c**3 - 16*a**3*b**2*c**2 + 2*a**2*b**4*c + x**4*(32*a**2*c**5 - 16*a*b**2*c**4 + 2*b**4*c**3) + x**3*(64*a**2*b*c**4 - 32*a*b**3*c**3 + 4*b**5*c**2) + x**2*(64*a**3*c**4 - 12*a*b**4*c**2 + 2*b**6*c) + x*(64*a**3*b*c**3 - 32*a**2*b**3*c**2 + 4*a*b**5*c))","B",0
2204,1,1052,0,3.705809," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**3,x)","- \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) \log{\left(x + \frac{- 64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) + 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) - 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) + 2 a b c e^{2} + b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) + b^{3} e^{2} - 6 b^{2} c d e + 6 b c^{2} d^{2}}{4 a c^{2} e^{2} + 2 b^{2} c e^{2} - 12 b c^{2} d e + 12 c^{3} d^{2}} \right)} + \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) \log{\left(x + \frac{64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) - 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) + 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) + 2 a b c e^{2} - b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) + b^{3} e^{2} - 6 b^{2} c d e + 6 b c^{2} d^{2}}{4 a c^{2} e^{2} + 2 b^{2} c e^{2} - 12 b c^{2} d e + 12 c^{3} d^{2}} \right)} + \frac{6 a^{2} b e^{2} - 16 a^{2} c d e - 2 a b^{2} d e + 10 a b c d^{2} - b^{3} d^{2} + x^{3} \left(4 a c^{2} e^{2} + 2 b^{2} c e^{2} - 12 b c^{2} d e + 12 c^{3} d^{2}\right) + x^{2} \left(6 a b c e^{2} + 3 b^{3} e^{2} - 18 b^{2} c d e + 18 b c^{2} d^{2}\right) + x \left(- 4 a^{2} c e^{2} + 10 a b^{2} e^{2} - 20 a b c d e + 20 a c^{2} d^{2} - 4 b^{3} d e + 4 b^{2} c d^{2}\right)}{32 a^{4} c^{2} - 16 a^{3} b^{2} c + 2 a^{2} b^{4} + x^{4} \left(32 a^{2} c^{4} - 16 a b^{2} c^{3} + 2 b^{4} c^{2}\right) + x^{3} \left(64 a^{2} b c^{3} - 32 a b^{3} c^{2} + 4 b^{5} c\right) + x^{2} \left(64 a^{3} c^{3} - 12 a b^{4} c + 2 b^{6}\right) + x \left(64 a^{3} b c^{2} - 32 a^{2} b^{3} c + 4 a b^{5}\right)}"," ",0,"-sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2)*log(x + (-64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2) + 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2) - 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2) + 2*a*b*c*e**2 + b**6*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2) + b**3*e**2 - 6*b**2*c*d*e + 6*b*c**2*d**2)/(4*a*c**2*e**2 + 2*b**2*c*e**2 - 12*b*c**2*d*e + 12*c**3*d**2)) + sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2)*log(x + (64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2) - 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2) + 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2) + 2*a*b*c*e**2 - b**6*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2) + b**3*e**2 - 6*b**2*c*d*e + 6*b*c**2*d**2)/(4*a*c**2*e**2 + 2*b**2*c*e**2 - 12*b*c**2*d*e + 12*c**3*d**2)) + (6*a**2*b*e**2 - 16*a**2*c*d*e - 2*a*b**2*d*e + 10*a*b*c*d**2 - b**3*d**2 + x**3*(4*a*c**2*e**2 + 2*b**2*c*e**2 - 12*b*c**2*d*e + 12*c**3*d**2) + x**2*(6*a*b*c*e**2 + 3*b**3*e**2 - 18*b**2*c*d*e + 18*b*c**2*d**2) + x*(-4*a**2*c*e**2 + 10*a*b**2*e**2 - 20*a*b*c*d*e + 20*a*c**2*d**2 - 4*b**3*d*e + 4*b**2*c*d**2))/(32*a**4*c**2 - 16*a**3*b**2*c + 2*a**2*b**4 + x**4*(32*a**2*c**4 - 16*a*b**2*c**3 + 2*b**4*c**2) + x**3*(64*a**2*b*c**3 - 32*a*b**3*c**2 + 4*b**5*c) + x**2*(64*a**3*c**3 - 12*a*b**4*c + 2*b**6) + x*(64*a**3*b*c**2 - 32*a**2*b**3*c + 4*a*b**5))","B",0
2205,1,651,0,1.839071," ","integrate((e*x+d)/(c*x**2+b*x+a)**3,x)","3 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \log{\left(x + \frac{- 192 a^{3} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) + 144 a^{2} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) - 36 a b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) + 3 b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) + 3 b^{2} c e - 6 b c^{2} d}{6 b c^{2} e - 12 c^{3} d} \right)} - 3 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) \log{\left(x + \frac{192 a^{3} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) - 144 a^{2} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) + 36 a b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) - 3 b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b e - 2 c d\right) + 3 b^{2} c e - 6 b c^{2} d}{6 b c^{2} e - 12 c^{3} d} \right)} + \frac{- 8 a^{2} c e - a b^{2} e + 10 a b c d - b^{3} d + x^{3} \left(- 6 b c^{2} e + 12 c^{3} d\right) + x^{2} \left(- 9 b^{2} c e + 18 b c^{2} d\right) + x \left(- 10 a b c e + 20 a c^{2} d - 2 b^{3} e + 4 b^{2} c d\right)}{32 a^{4} c^{2} - 16 a^{3} b^{2} c + 2 a^{2} b^{4} + x^{4} \left(32 a^{2} c^{4} - 16 a b^{2} c^{3} + 2 b^{4} c^{2}\right) + x^{3} \left(64 a^{2} b c^{3} - 32 a b^{3} c^{2} + 4 b^{5} c\right) + x^{2} \left(64 a^{3} c^{3} - 12 a b^{4} c + 2 b^{6}\right) + x \left(64 a^{3} b c^{2} - 32 a^{2} b^{3} c + 4 a b^{5}\right)}"," ",0,"3*c*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*log(x + (-192*a**3*c**4*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d) + 144*a**2*b**2*c**3*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d) - 36*a*b**4*c**2*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d) + 3*b**6*c*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d) + 3*b**2*c*e - 6*b*c**2*d)/(6*b*c**2*e - 12*c**3*d)) - 3*c*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d)*log(x + (192*a**3*c**4*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d) - 144*a**2*b**2*c**3*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d) + 36*a*b**4*c**2*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d) - 3*b**6*c*sqrt(-1/(4*a*c - b**2)**5)*(b*e - 2*c*d) + 3*b**2*c*e - 6*b*c**2*d)/(6*b*c**2*e - 12*c**3*d)) + (-8*a**2*c*e - a*b**2*e + 10*a*b*c*d - b**3*d + x**3*(-6*b*c**2*e + 12*c**3*d) + x**2*(-9*b**2*c*e + 18*b*c**2*d) + x*(-10*a*b*c*e + 20*a*c**2*d - 2*b**3*e + 4*b**2*c*d))/(32*a**4*c**2 - 16*a**3*b**2*c + 2*a**2*b**4 + x**4*(32*a**2*c**4 - 16*a*b**2*c**3 + 2*b**4*c**2) + x**3*(64*a**2*b*c**3 - 32*a*b**3*c**2 + 4*b**5*c) + x**2*(64*a**3*c**3 - 12*a*b**4*c + 2*b**6) + x*(64*a**3*b*c**2 - 32*a**2*b**3*c + 4*a*b**5))","B",0
2206,1,474,0,1.131953," ","integrate(1/(c*x**2+b*x+a)**3,x)","- 6 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{- 384 a^{3} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 288 a^{2} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 72 a b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 b c^{2}}{12 c^{3}} \right)} + 6 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{384 a^{3} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 288 a^{2} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 72 a b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 6 b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 b c^{2}}{12 c^{3}} \right)} + \frac{10 a b c - b^{3} + 18 b c^{2} x^{2} + 12 c^{3} x^{3} + x \left(20 a c^{2} + 4 b^{2} c\right)}{32 a^{4} c^{2} - 16 a^{3} b^{2} c + 2 a^{2} b^{4} + x^{4} \left(32 a^{2} c^{4} - 16 a b^{2} c^{3} + 2 b^{4} c^{2}\right) + x^{3} \left(64 a^{2} b c^{3} - 32 a b^{3} c^{2} + 4 b^{5} c\right) + x^{2} \left(64 a^{3} c^{3} - 12 a b^{4} c + 2 b^{6}\right) + x \left(64 a^{3} b c^{2} - 32 a^{2} b^{3} c + 4 a b^{5}\right)}"," ",0,"-6*c**2*sqrt(-1/(4*a*c - b**2)**5)*log(x + (-384*a**3*c**5*sqrt(-1/(4*a*c - b**2)**5) + 288*a**2*b**2*c**4*sqrt(-1/(4*a*c - b**2)**5) - 72*a*b**4*c**3*sqrt(-1/(4*a*c - b**2)**5) + 6*b**6*c**2*sqrt(-1/(4*a*c - b**2)**5) + 6*b*c**2)/(12*c**3)) + 6*c**2*sqrt(-1/(4*a*c - b**2)**5)*log(x + (384*a**3*c**5*sqrt(-1/(4*a*c - b**2)**5) - 288*a**2*b**2*c**4*sqrt(-1/(4*a*c - b**2)**5) + 72*a*b**4*c**3*sqrt(-1/(4*a*c - b**2)**5) - 6*b**6*c**2*sqrt(-1/(4*a*c - b**2)**5) + 6*b*c**2)/(12*c**3)) + (10*a*b*c - b**3 + 18*b*c**2*x**2 + 12*c**3*x**3 + x*(20*a*c**2 + 4*b**2*c))/(32*a**4*c**2 - 16*a**3*b**2*c + 2*a**2*b**4 + x**4*(32*a**2*c**4 - 16*a*b**2*c**3 + 2*b**4*c**2) + x**3*(64*a**2*b*c**3 - 32*a*b**3*c**2 + 4*b**5*c) + x**2*(64*a**3*c**3 - 12*a*b**4*c + 2*b**6) + x*(64*a**3*b*c**2 - 32*a**2*b**3*c + 4*a*b**5))","B",0
2207,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2208,-1,0,0,0.000000," ","integrate(1/x**2/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2209,-1,0,0,0.000000," ","integrate(1/x**3/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2210,1,2769,0,11.229334," ","integrate(x**8/(c*x**2+b*x+a)**4,x)","\left(- \frac{2 b}{c^{5}} - \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right) \log{\left(x + \frac{- 372 a^{4} b c^{3} - 256 a^{4} c^{8} \left(- \frac{2 b}{c^{5}} - \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right) + 232 a^{3} b^{3} c^{2} + 256 a^{3} b^{2} c^{7} \left(- \frac{2 b}{c^{5}} - \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right) - 52 a^{2} b^{5} c - 96 a^{2} b^{4} c^{6} \left(- \frac{2 b}{c^{5}} - \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right) + 4 a b^{7} + 16 a b^{6} c^{5} \left(- \frac{2 b}{c^{5}} - \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right) - b^{8} c^{4} \left(- \frac{2 b}{c^{5}} - \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right)}{280 a^{4} c^{4} - 560 a^{3} b^{2} c^{3} + 280 a^{2} b^{4} c^{2} - 56 a b^{6} c + 4 b^{8}} \right)} + \left(- \frac{2 b}{c^{5}} + \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right) \log{\left(x + \frac{- 372 a^{4} b c^{3} - 256 a^{4} c^{8} \left(- \frac{2 b}{c^{5}} + \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right) + 232 a^{3} b^{3} c^{2} + 256 a^{3} b^{2} c^{7} \left(- \frac{2 b}{c^{5}} + \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right) - 52 a^{2} b^{5} c - 96 a^{2} b^{4} c^{6} \left(- \frac{2 b}{c^{5}} + \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right) + 4 a b^{7} + 16 a b^{6} c^{5} \left(- \frac{2 b}{c^{5}} + \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right) - b^{8} c^{4} \left(- \frac{2 b}{c^{5}} + \frac{2 \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(70 a^{4} c^{4} - 140 a^{3} b^{2} c^{3} + 70 a^{2} b^{4} c^{2} - 14 a b^{6} c + b^{8}\right)}{c^{5} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)}\right)}{280 a^{4} c^{4} - 560 a^{3} b^{2} c^{3} + 280 a^{2} b^{4} c^{2} - 56 a b^{6} c + 4 b^{8}} \right)} + \frac{- 590 a^{6} b c^{3} + 535 a^{5} b^{3} c^{2} - 147 a^{4} b^{5} c + 13 a^{3} b^{7} + x^{5} \left(348 a^{4} c^{6} - 1272 a^{3} b^{2} c^{5} + 876 a^{2} b^{4} c^{4} - 216 a b^{6} c^{3} + 18 b^{8} c^{2}\right) + x^{4} \left(- 282 a^{4} b c^{5} - 1356 a^{3} b^{3} c^{4} + 1254 a^{2} b^{5} c^{3} - 342 a b^{7} c^{2} + 30 b^{9} c\right) + x^{3} \left(544 a^{5} c^{5} - 3234 a^{4} b^{2} c^{4} + 1788 a^{3} b^{4} c^{3} - 68 a^{2} b^{6} c^{2} - 96 a b^{8} c + 13 b^{10}\right) + x^{2} \left(- 912 a^{5} b c^{4} - 1161 a^{4} b^{3} c^{3} + 1458 a^{3} b^{5} c^{2} - 429 a^{2} b^{7} c + 39 a b^{9}\right) + x \left(228 a^{6} c^{4} - 2082 a^{5} b^{2} c^{3} + 1701 a^{4} b^{4} c^{2} - 450 a^{3} b^{6} c + 39 a^{2} b^{8}\right)}{192 a^{6} c^{8} - 144 a^{5} b^{2} c^{7} + 36 a^{4} b^{4} c^{6} - 3 a^{3} b^{6} c^{5} + x^{6} \left(192 a^{3} c^{11} - 144 a^{2} b^{2} c^{10} + 36 a b^{4} c^{9} - 3 b^{6} c^{8}\right) + x^{5} \left(576 a^{3} b c^{10} - 432 a^{2} b^{3} c^{9} + 108 a b^{5} c^{8} - 9 b^{7} c^{7}\right) + x^{4} \left(576 a^{4} c^{10} + 144 a^{3} b^{2} c^{9} - 324 a^{2} b^{4} c^{8} + 99 a b^{6} c^{7} - 9 b^{8} c^{6}\right) + x^{3} \left(1152 a^{4} b c^{9} - 672 a^{3} b^{3} c^{8} + 72 a^{2} b^{5} c^{7} + 18 a b^{7} c^{6} - 3 b^{9} c^{5}\right) + x^{2} \left(576 a^{5} c^{9} + 144 a^{4} b^{2} c^{8} - 324 a^{3} b^{4} c^{7} + 99 a^{2} b^{6} c^{6} - 9 a b^{8} c^{5}\right) + x \left(576 a^{5} b c^{8} - 432 a^{4} b^{3} c^{7} + 108 a^{3} b^{5} c^{6} - 9 a^{2} b^{7} c^{5}\right)} + \frac{x}{c^{4}}"," ",0,"(-2*b/c**5 - 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)))*log(x + (-372*a**4*b*c**3 - 256*a**4*c**8*(-2*b/c**5 - 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14))) + 232*a**3*b**3*c**2 + 256*a**3*b**2*c**7*(-2*b/c**5 - 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14))) - 52*a**2*b**5*c - 96*a**2*b**4*c**6*(-2*b/c**5 - 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14))) + 4*a*b**7 + 16*a*b**6*c**5*(-2*b/c**5 - 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14))) - b**8*c**4*(-2*b/c**5 - 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14))))/(280*a**4*c**4 - 560*a**3*b**2*c**3 + 280*a**2*b**4*c**2 - 56*a*b**6*c + 4*b**8)) + (-2*b/c**5 + 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)))*log(x + (-372*a**4*b*c**3 - 256*a**4*c**8*(-2*b/c**5 + 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14))) + 232*a**3*b**3*c**2 + 256*a**3*b**2*c**7*(-2*b/c**5 + 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14))) - 52*a**2*b**5*c - 96*a**2*b**4*c**6*(-2*b/c**5 + 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14))) + 4*a*b**7 + 16*a*b**6*c**5*(-2*b/c**5 + 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14))) - b**8*c**4*(-2*b/c**5 + 2*sqrt(-(4*a*c - b**2)**7)*(70*a**4*c**4 - 140*a**3*b**2*c**3 + 70*a**2*b**4*c**2 - 14*a*b**6*c + b**8)/(c**5*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14))))/(280*a**4*c**4 - 560*a**3*b**2*c**3 + 280*a**2*b**4*c**2 - 56*a*b**6*c + 4*b**8)) + (-590*a**6*b*c**3 + 535*a**5*b**3*c**2 - 147*a**4*b**5*c + 13*a**3*b**7 + x**5*(348*a**4*c**6 - 1272*a**3*b**2*c**5 + 876*a**2*b**4*c**4 - 216*a*b**6*c**3 + 18*b**8*c**2) + x**4*(-282*a**4*b*c**5 - 1356*a**3*b**3*c**4 + 1254*a**2*b**5*c**3 - 342*a*b**7*c**2 + 30*b**9*c) + x**3*(544*a**5*c**5 - 3234*a**4*b**2*c**4 + 1788*a**3*b**4*c**3 - 68*a**2*b**6*c**2 - 96*a*b**8*c + 13*b**10) + x**2*(-912*a**5*b*c**4 - 1161*a**4*b**3*c**3 + 1458*a**3*b**5*c**2 - 429*a**2*b**7*c + 39*a*b**9) + x*(228*a**6*c**4 - 2082*a**5*b**2*c**3 + 1701*a**4*b**4*c**2 - 450*a**3*b**6*c + 39*a**2*b**8))/(192*a**6*c**8 - 144*a**5*b**2*c**7 + 36*a**4*b**4*c**6 - 3*a**3*b**6*c**5 + x**6*(192*a**3*c**11 - 144*a**2*b**2*c**10 + 36*a*b**4*c**9 - 3*b**6*c**8) + x**5*(576*a**3*b*c**10 - 432*a**2*b**3*c**9 + 108*a*b**5*c**8 - 9*b**7*c**7) + x**4*(576*a**4*c**10 + 144*a**3*b**2*c**9 - 324*a**2*b**4*c**8 + 99*a*b**6*c**7 - 9*b**8*c**6) + x**3*(1152*a**4*b*c**9 - 672*a**3*b**3*c**8 + 72*a**2*b**5*c**7 + 18*a*b**7*c**6 - 3*b**9*c**5) + x**2*(576*a**5*c**9 + 144*a**4*b**2*c**8 - 324*a**3*b**4*c**7 + 99*a**2*b**6*c**6 - 9*a*b**8*c**5) + x*(576*a**5*b*c**8 - 432*a**4*b**3*c**7 + 108*a**3*b**5*c**6 - 9*a**2*b**7*c**5)) + x/c**4","B",0
2211,1,2565,0,8.249072," ","integrate(x**7/(c*x**2+b*x+a)**4,x)","\left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right) \log{\left(x + \frac{- 256 a^{4} c^{7} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right) + 128 a^{4} c^{3} + 256 a^{3} b^{2} c^{6} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right) - 58 a^{3} b^{2} c^{2} - 96 a^{2} b^{4} c^{5} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right) + 13 a^{2} b^{4} c + 16 a b^{6} c^{4} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right) - a b^{6} - b^{8} c^{3} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right)}{140 a^{3} b c^{3} - 70 a^{2} b^{3} c^{2} + 14 a b^{5} c - b^{7}} \right)} + \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right) \log{\left(x + \frac{- 256 a^{4} c^{7} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right) + 128 a^{4} c^{3} + 256 a^{3} b^{2} c^{6} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right) - 58 a^{3} b^{2} c^{2} - 96 a^{2} b^{4} c^{5} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right) + 13 a^{2} b^{4} c + 16 a b^{6} c^{4} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right) - a b^{6} - b^{8} c^{3} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{7}} \left(140 a^{3} c^{3} - 70 a^{2} b^{2} c^{2} + 14 a b^{4} c - b^{6}\right)}{2 c^{4} \left(16384 a^{7} c^{7} - 28672 a^{6} b^{2} c^{6} + 21504 a^{5} b^{4} c^{5} - 8960 a^{4} b^{6} c^{4} + 2240 a^{3} b^{8} c^{3} - 336 a^{2} b^{10} c^{2} + 28 a b^{12} c - b^{14}\right)} + \frac{1}{2 c^{4}}\right)}{140 a^{3} b c^{3} - 70 a^{2} b^{3} c^{2} + 14 a b^{5} c - b^{7}} \right)} + \frac{352 a^{6} c^{3} - 438 a^{5} b^{2} c^{2} + 124 a^{4} b^{4} c - 11 a^{3} b^{6} + x^{5} \left(924 a^{3} b c^{5} - 798 a^{2} b^{3} c^{4} + 210 a b^{5} c^{3} - 18 b^{7} c^{2}\right) + x^{4} \left(576 a^{4} c^{5} + 726 a^{3} b^{2} c^{4} - 1023 a^{2} b^{4} c^{3} + 300 a b^{6} c^{2} - 27 b^{8} c\right) + x^{3} \left(2272 a^{4} b c^{4} - 1698 a^{3} b^{3} c^{3} + 117 a^{2} b^{5} c^{2} + 76 a b^{7} c - 11 b^{9}\right) + x^{2} \left(864 a^{5} c^{4} + 456 a^{4} b^{2} c^{3} - 1143 a^{3} b^{4} c^{2} + 357 a^{2} b^{6} c - 33 a b^{8}\right) + x \left(1284 a^{5} b c^{3} - 1380 a^{4} b^{3} c^{2} + 378 a^{3} b^{5} c - 33 a^{2} b^{7}\right)}{384 a^{6} c^{7} - 288 a^{5} b^{2} c^{6} + 72 a^{4} b^{4} c^{5} - 6 a^{3} b^{6} c^{4} + x^{6} \left(384 a^{3} c^{10} - 288 a^{2} b^{2} c^{9} + 72 a b^{4} c^{8} - 6 b^{6} c^{7}\right) + x^{5} \left(1152 a^{3} b c^{9} - 864 a^{2} b^{3} c^{8} + 216 a b^{5} c^{7} - 18 b^{7} c^{6}\right) + x^{4} \left(1152 a^{4} c^{9} + 288 a^{3} b^{2} c^{8} - 648 a^{2} b^{4} c^{7} + 198 a b^{6} c^{6} - 18 b^{8} c^{5}\right) + x^{3} \left(2304 a^{4} b c^{8} - 1344 a^{3} b^{3} c^{7} + 144 a^{2} b^{5} c^{6} + 36 a b^{7} c^{5} - 6 b^{9} c^{4}\right) + x^{2} \left(1152 a^{5} c^{8} + 288 a^{4} b^{2} c^{7} - 648 a^{3} b^{4} c^{6} + 198 a^{2} b^{6} c^{5} - 18 a b^{8} c^{4}\right) + x \left(1152 a^{5} b c^{7} - 864 a^{4} b^{3} c^{6} + 216 a^{3} b^{5} c^{5} - 18 a^{2} b^{7} c^{4}\right)}"," ",0,"(-b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4))*log(x + (-256*a**4*c**7*(-b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4)) + 128*a**4*c**3 + 256*a**3*b**2*c**6*(-b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4)) - 58*a**3*b**2*c**2 - 96*a**2*b**4*c**5*(-b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4)) + 13*a**2*b**4*c + 16*a*b**6*c**4*(-b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4)) - a*b**6 - b**8*c**3*(-b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4)))/(140*a**3*b*c**3 - 70*a**2*b**3*c**2 + 14*a*b**5*c - b**7)) + (b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4))*log(x + (-256*a**4*c**7*(b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4)) + 128*a**4*c**3 + 256*a**3*b**2*c**6*(b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4)) - 58*a**3*b**2*c**2 - 96*a**2*b**4*c**5*(b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4)) + 13*a**2*b**4*c + 16*a*b**6*c**4*(b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4)) - a*b**6 - b**8*c**3*(b*sqrt(-(4*a*c - b**2)**7)*(140*a**3*c**3 - 70*a**2*b**2*c**2 + 14*a*b**4*c - b**6)/(2*c**4*(16384*a**7*c**7 - 28672*a**6*b**2*c**6 + 21504*a**5*b**4*c**5 - 8960*a**4*b**6*c**4 + 2240*a**3*b**8*c**3 - 336*a**2*b**10*c**2 + 28*a*b**12*c - b**14)) + 1/(2*c**4)))/(140*a**3*b*c**3 - 70*a**2*b**3*c**2 + 14*a*b**5*c - b**7)) + (352*a**6*c**3 - 438*a**5*b**2*c**2 + 124*a**4*b**4*c - 11*a**3*b**6 + x**5*(924*a**3*b*c**5 - 798*a**2*b**3*c**4 + 210*a*b**5*c**3 - 18*b**7*c**2) + x**4*(576*a**4*c**5 + 726*a**3*b**2*c**4 - 1023*a**2*b**4*c**3 + 300*a*b**6*c**2 - 27*b**8*c) + x**3*(2272*a**4*b*c**4 - 1698*a**3*b**3*c**3 + 117*a**2*b**5*c**2 + 76*a*b**7*c - 11*b**9) + x**2*(864*a**5*c**4 + 456*a**4*b**2*c**3 - 1143*a**3*b**4*c**2 + 357*a**2*b**6*c - 33*a*b**8) + x*(1284*a**5*b*c**3 - 1380*a**4*b**3*c**2 + 378*a**3*b**5*c - 33*a**2*b**7))/(384*a**6*c**7 - 288*a**5*b**2*c**6 + 72*a**4*b**4*c**5 - 6*a**3*b**6*c**4 + x**6*(384*a**3*c**10 - 288*a**2*b**2*c**9 + 72*a*b**4*c**8 - 6*b**6*c**7) + x**5*(1152*a**3*b*c**9 - 864*a**2*b**3*c**8 + 216*a*b**5*c**7 - 18*b**7*c**6) + x**4*(1152*a**4*c**9 + 288*a**3*b**2*c**8 - 648*a**2*b**4*c**7 + 198*a*b**6*c**6 - 18*b**8*c**5) + x**3*(2304*a**4*b*c**8 - 1344*a**3*b**3*c**7 + 144*a**2*b**5*c**6 + 36*a*b**7*c**5 - 6*b**9*c**4) + x**2*(1152*a**5*c**8 + 288*a**4*b**2*c**7 - 648*a**3*b**4*c**6 + 198*a**2*b**6*c**5 - 18*a*b**8*c**4) + x*(1152*a**5*b*c**7 - 864*a**4*b**3*c**6 + 216*a**3*b**5*c**5 - 18*a**2*b**7*c**4))","B",0
2212,1,938,0,3.480115," ","integrate(x**6/(c*x**2+b*x+a)**4,x)","- 20 a^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \log{\left(x + \frac{- 5120 a^{7} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 5120 a^{6} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 1920 a^{5} b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 320 a^{4} b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 20 a^{3} b^{8} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 20 a^{3} b}{40 a^{3} c} \right)} + 20 a^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \log{\left(x + \frac{5120 a^{7} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 5120 a^{6} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 1920 a^{5} b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 320 a^{4} b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 20 a^{3} b^{8} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 20 a^{3} b}{40 a^{3} c} \right)} + \frac{66 a^{5} b c^{2} - 13 a^{4} b^{3} c + a^{3} b^{5} + x^{5} \left(- 132 a^{3} c^{5} + 144 a^{2} b^{2} c^{4} - 36 a b^{4} c^{3} + 3 b^{6} c^{2}\right) + x^{4} \left(- 42 a^{3} b c^{4} + 144 a^{2} b^{3} c^{3} - 36 a b^{5} c^{2} + 3 b^{7} c\right) + x^{3} \left(- 160 a^{4} c^{4} + 286 a^{3} b^{2} c^{3} - 12 a^{2} b^{4} c^{2} - 7 a b^{6} c + b^{8}\right) + x^{2} \left(48 a^{4} b c^{3} + 159 a^{3} b^{3} c^{2} - 36 a^{2} b^{5} c + 3 a b^{7}\right) + x \left(- 60 a^{5} c^{3} + 198 a^{4} b^{2} c^{2} - 39 a^{3} b^{4} c + 3 a^{2} b^{6}\right)}{192 a^{6} c^{6} - 144 a^{5} b^{2} c^{5} + 36 a^{4} b^{4} c^{4} - 3 a^{3} b^{6} c^{3} + x^{6} \left(192 a^{3} c^{9} - 144 a^{2} b^{2} c^{8} + 36 a b^{4} c^{7} - 3 b^{6} c^{6}\right) + x^{5} \left(576 a^{3} b c^{8} - 432 a^{2} b^{3} c^{7} + 108 a b^{5} c^{6} - 9 b^{7} c^{5}\right) + x^{4} \left(576 a^{4} c^{8} + 144 a^{3} b^{2} c^{7} - 324 a^{2} b^{4} c^{6} + 99 a b^{6} c^{5} - 9 b^{8} c^{4}\right) + x^{3} \left(1152 a^{4} b c^{7} - 672 a^{3} b^{3} c^{6} + 72 a^{2} b^{5} c^{5} + 18 a b^{7} c^{4} - 3 b^{9} c^{3}\right) + x^{2} \left(576 a^{5} c^{7} + 144 a^{4} b^{2} c^{6} - 324 a^{3} b^{4} c^{5} + 99 a^{2} b^{6} c^{4} - 9 a b^{8} c^{3}\right) + x \left(576 a^{5} b c^{6} - 432 a^{4} b^{3} c^{5} + 108 a^{3} b^{5} c^{4} - 9 a^{2} b^{7} c^{3}\right)}"," ",0,"-20*a**3*sqrt(-1/(4*a*c - b**2)**7)*log(x + (-5120*a**7*c**4*sqrt(-1/(4*a*c - b**2)**7) + 5120*a**6*b**2*c**3*sqrt(-1/(4*a*c - b**2)**7) - 1920*a**5*b**4*c**2*sqrt(-1/(4*a*c - b**2)**7) + 320*a**4*b**6*c*sqrt(-1/(4*a*c - b**2)**7) - 20*a**3*b**8*sqrt(-1/(4*a*c - b**2)**7) + 20*a**3*b)/(40*a**3*c)) + 20*a**3*sqrt(-1/(4*a*c - b**2)**7)*log(x + (5120*a**7*c**4*sqrt(-1/(4*a*c - b**2)**7) - 5120*a**6*b**2*c**3*sqrt(-1/(4*a*c - b**2)**7) + 1920*a**5*b**4*c**2*sqrt(-1/(4*a*c - b**2)**7) - 320*a**4*b**6*c*sqrt(-1/(4*a*c - b**2)**7) + 20*a**3*b**8*sqrt(-1/(4*a*c - b**2)**7) + 20*a**3*b)/(40*a**3*c)) + (66*a**5*b*c**2 - 13*a**4*b**3*c + a**3*b**5 + x**5*(-132*a**3*c**5 + 144*a**2*b**2*c**4 - 36*a*b**4*c**3 + 3*b**6*c**2) + x**4*(-42*a**3*b*c**4 + 144*a**2*b**3*c**3 - 36*a*b**5*c**2 + 3*b**7*c) + x**3*(-160*a**4*c**4 + 286*a**3*b**2*c**3 - 12*a**2*b**4*c**2 - 7*a*b**6*c + b**8) + x**2*(48*a**4*b*c**3 + 159*a**3*b**3*c**2 - 36*a**2*b**5*c + 3*a*b**7) + x*(-60*a**5*c**3 + 198*a**4*b**2*c**2 - 39*a**3*b**4*c + 3*a**2*b**6))/(192*a**6*c**6 - 144*a**5*b**2*c**5 + 36*a**4*b**4*c**4 - 3*a**3*b**6*c**3 + x**6*(192*a**3*c**9 - 144*a**2*b**2*c**8 + 36*a*b**4*c**7 - 3*b**6*c**6) + x**5*(576*a**3*b*c**8 - 432*a**2*b**3*c**7 + 108*a*b**5*c**6 - 9*b**7*c**5) + x**4*(576*a**4*c**8 + 144*a**3*b**2*c**7 - 324*a**2*b**4*c**6 + 99*a*b**6*c**5 - 9*b**8*c**4) + x**3*(1152*a**4*b*c**7 - 672*a**3*b**3*c**6 + 72*a**2*b**5*c**5 + 18*a*b**7*c**4 - 3*b**9*c**3) + x**2*(576*a**5*c**7 + 144*a**4*b**2*c**6 - 324*a**3*b**4*c**5 + 99*a**2*b**6*c**4 - 9*a*b**8*c**3) + x*(576*a**5*b*c**6 - 432*a**4*b**3*c**5 + 108*a**3*b**5*c**4 - 9*a**2*b**7*c**3))","B",0
2213,1,898,0,2.627633," ","integrate(x**5/(c*x**2+b*x+a)**4,x)","10 a^{2} b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \log{\left(x + \frac{- 2560 a^{6} b c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 2560 a^{5} b^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 960 a^{4} b^{5} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 160 a^{3} b^{7} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 10 a^{2} b^{9} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 10 a^{2} b^{2}}{20 a^{2} b c} \right)} - 10 a^{2} b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \log{\left(x + \frac{2560 a^{6} b c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 2560 a^{5} b^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 960 a^{4} b^{5} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 160 a^{3} b^{7} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 10 a^{2} b^{9} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 10 a^{2} b^{2}}{20 a^{2} b c} \right)} + \frac{- 64 a^{5} c^{2} - 18 a^{4} b^{2} c + a^{3} b^{4} - 60 a^{2} b c^{4} x^{5} + x^{4} \left(- 192 a^{3} c^{4} - 6 a^{2} b^{2} c^{3} - 36 a b^{4} c^{2} + 3 b^{6} c\right) + x^{3} \left(- 224 a^{3} b c^{3} - 62 a^{2} b^{3} c^{2} - 12 a b^{5} c + b^{7}\right) + x^{2} \left(- 192 a^{4} c^{3} - 96 a^{3} b^{2} c^{2} - 51 a^{2} b^{4} c + 3 a b^{6}\right) + x \left(- 132 a^{4} b c^{2} - 54 a^{3} b^{3} c + 3 a^{2} b^{5}\right)}{384 a^{6} c^{5} - 288 a^{5} b^{2} c^{4} + 72 a^{4} b^{4} c^{3} - 6 a^{3} b^{6} c^{2} + x^{6} \left(384 a^{3} c^{8} - 288 a^{2} b^{2} c^{7} + 72 a b^{4} c^{6} - 6 b^{6} c^{5}\right) + x^{5} \left(1152 a^{3} b c^{7} - 864 a^{2} b^{3} c^{6} + 216 a b^{5} c^{5} - 18 b^{7} c^{4}\right) + x^{4} \left(1152 a^{4} c^{7} + 288 a^{3} b^{2} c^{6} - 648 a^{2} b^{4} c^{5} + 198 a b^{6} c^{4} - 18 b^{8} c^{3}\right) + x^{3} \left(2304 a^{4} b c^{6} - 1344 a^{3} b^{3} c^{5} + 144 a^{2} b^{5} c^{4} + 36 a b^{7} c^{3} - 6 b^{9} c^{2}\right) + x^{2} \left(1152 a^{5} c^{6} + 288 a^{4} b^{2} c^{5} - 648 a^{3} b^{4} c^{4} + 198 a^{2} b^{6} c^{3} - 18 a b^{8} c^{2}\right) + x \left(1152 a^{5} b c^{5} - 864 a^{4} b^{3} c^{4} + 216 a^{3} b^{5} c^{3} - 18 a^{2} b^{7} c^{2}\right)}"," ",0,"10*a**2*b*sqrt(-1/(4*a*c - b**2)**7)*log(x + (-2560*a**6*b*c**4*sqrt(-1/(4*a*c - b**2)**7) + 2560*a**5*b**3*c**3*sqrt(-1/(4*a*c - b**2)**7) - 960*a**4*b**5*c**2*sqrt(-1/(4*a*c - b**2)**7) + 160*a**3*b**7*c*sqrt(-1/(4*a*c - b**2)**7) - 10*a**2*b**9*sqrt(-1/(4*a*c - b**2)**7) + 10*a**2*b**2)/(20*a**2*b*c)) - 10*a**2*b*sqrt(-1/(4*a*c - b**2)**7)*log(x + (2560*a**6*b*c**4*sqrt(-1/(4*a*c - b**2)**7) - 2560*a**5*b**3*c**3*sqrt(-1/(4*a*c - b**2)**7) + 960*a**4*b**5*c**2*sqrt(-1/(4*a*c - b**2)**7) - 160*a**3*b**7*c*sqrt(-1/(4*a*c - b**2)**7) + 10*a**2*b**9*sqrt(-1/(4*a*c - b**2)**7) + 10*a**2*b**2)/(20*a**2*b*c)) + (-64*a**5*c**2 - 18*a**4*b**2*c + a**3*b**4 - 60*a**2*b*c**4*x**5 + x**4*(-192*a**3*c**4 - 6*a**2*b**2*c**3 - 36*a*b**4*c**2 + 3*b**6*c) + x**3*(-224*a**3*b*c**3 - 62*a**2*b**3*c**2 - 12*a*b**5*c + b**7) + x**2*(-192*a**4*c**3 - 96*a**3*b**2*c**2 - 51*a**2*b**4*c + 3*a*b**6) + x*(-132*a**4*b*c**2 - 54*a**3*b**3*c + 3*a**2*b**5))/(384*a**6*c**5 - 288*a**5*b**2*c**4 + 72*a**4*b**4*c**3 - 6*a**3*b**6*c**2 + x**6*(384*a**3*c**8 - 288*a**2*b**2*c**7 + 72*a*b**4*c**6 - 6*b**6*c**5) + x**5*(1152*a**3*b*c**7 - 864*a**2*b**3*c**6 + 216*a*b**5*c**5 - 18*b**7*c**4) + x**4*(1152*a**4*c**7 + 288*a**3*b**2*c**6 - 648*a**2*b**4*c**5 + 198*a*b**6*c**4 - 18*b**8*c**3) + x**3*(2304*a**4*b*c**6 - 1344*a**3*b**3*c**5 + 144*a**2*b**5*c**4 + 36*a*b**7*c**3 - 6*b**9*c**2) + x**2*(1152*a**5*c**6 + 288*a**4*b**2*c**5 - 648*a**3*b**4*c**4 + 198*a**2*b**6*c**3 - 18*a*b**8*c**2) + x*(1152*a**5*b*c**5 - 864*a**4*b**3*c**4 + 216*a**3*b**5*c**3 - 18*a**2*b**7*c**2))","B",0
2214,1,2547,0,105.898821," ","integrate((e*x+d)**4/(c*x**2+b*x+a)**4,x)","- 4 \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) \log{\left(x + \frac{- 1024 a^{4} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 1024 a^{3} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) - 384 a^{2} b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 4 a^{2} b c e^{4} + 64 a b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 4 a b^{3} e^{4} - 24 a b^{2} c d e^{3} + 24 a b c^{2} d^{2} e^{2} - 4 b^{8} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) - 4 b^{4} d e^{3} + 24 b^{3} c d^{2} e^{2} - 40 b^{2} c^{2} d^{3} e + 20 b c^{3} d^{4}}{8 a^{2} c^{2} e^{4} + 8 a b^{2} c e^{4} - 48 a b c^{2} d e^{3} + 48 a c^{3} d^{2} e^{2} - 8 b^{3} c d e^{3} + 48 b^{2} c^{2} d^{2} e^{2} - 80 b c^{3} d^{3} e + 40 c^{4} d^{4}} \right)} + 4 \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) \log{\left(x + \frac{1024 a^{4} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) - 1024 a^{3} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 384 a^{2} b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 4 a^{2} b c e^{4} - 64 a b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 4 a b^{3} e^{4} - 24 a b^{2} c d e^{3} + 24 a b c^{2} d^{2} e^{2} + 4 b^{8} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) - 4 b^{4} d e^{3} + 24 b^{3} c d^{2} e^{2} - 40 b^{2} c^{2} d^{3} e + 20 b c^{3} d^{4}}{8 a^{2} c^{2} e^{4} + 8 a b^{2} c e^{4} - 48 a b c^{2} d e^{3} + 48 a c^{3} d^{2} e^{2} - 8 b^{3} c d e^{3} + 48 b^{2} c^{2} d^{2} e^{2} - 80 b c^{3} d^{3} e + 40 c^{4} d^{4}} \right)} + \frac{26 a^{4} b c e^{4} - 64 a^{4} c^{2} d e^{3} + a^{3} b^{3} e^{4} - 44 a^{3} b^{2} c d e^{3} + 156 a^{3} b c^{2} d^{2} e^{2} - 128 a^{3} c^{3} d^{3} e + 6 a^{2} b^{3} c d^{2} e^{2} - 36 a^{2} b^{2} c^{2} d^{3} e + 66 a^{2} b c^{3} d^{4} + 2 a b^{4} c d^{3} e - 13 a b^{3} c^{2} d^{4} + b^{5} c d^{4} + x^{5} \left(12 a^{2} c^{4} e^{4} + 12 a b^{2} c^{3} e^{4} - 72 a b c^{4} d e^{3} + 72 a c^{5} d^{2} e^{2} - 12 b^{3} c^{3} d e^{3} + 72 b^{2} c^{4} d^{2} e^{2} - 120 b c^{5} d^{3} e + 60 c^{6} d^{4}\right) + x^{4} \left(30 a^{2} b c^{3} e^{4} + 30 a b^{3} c^{2} e^{4} - 180 a b^{2} c^{3} d e^{3} + 180 a b c^{4} d^{2} e^{2} - 30 b^{4} c^{2} d e^{3} + 180 b^{3} c^{3} d^{2} e^{2} - 300 b^{2} c^{4} d^{3} e + 150 b c^{5} d^{4}\right) + x^{3} \left(- 32 a^{3} c^{3} e^{4} + 102 a^{2} b^{2} c^{2} e^{4} - 192 a^{2} b c^{3} d e^{3} + 192 a^{2} c^{4} d^{2} e^{2} + 10 a b^{4} c e^{4} - 164 a b^{3} c^{2} d e^{3} + 324 a b^{2} c^{3} d^{2} e^{2} - 320 a b c^{4} d^{3} e + 160 a c^{5} d^{4} + b^{6} e^{4} - 22 b^{5} c d e^{3} + 132 b^{4} c^{2} d^{2} e^{2} - 220 b^{3} c^{3} d^{3} e + 110 b^{2} c^{4} d^{4}\right) + x^{2} \left(48 a^{3} b c^{2} e^{4} - 192 a^{3} c^{3} d e^{3} + 51 a^{2} b^{3} c e^{4} - 144 a^{2} b^{2} c^{2} d e^{3} + 288 a^{2} b c^{3} d^{2} e^{2} + 3 a b^{5} e^{4} - 102 a b^{4} c d e^{3} + 306 a b^{3} c^{2} d^{2} e^{2} - 480 a b^{2} c^{3} d^{3} e + 240 a b c^{4} d^{4} + 18 b^{5} c d^{2} e^{2} - 30 b^{4} c^{2} d^{3} e + 15 b^{3} c^{3} d^{4}\right) + x \left(- 12 a^{4} c^{2} e^{4} + 66 a^{3} b^{2} c e^{4} - 120 a^{3} b c^{2} d e^{3} - 72 a^{3} c^{3} d^{2} e^{2} + 3 a^{2} b^{4} e^{4} - 120 a^{2} b^{3} c d e^{3} + 396 a^{2} b^{2} c^{2} d^{2} e^{2} - 264 a^{2} b c^{3} d^{3} e + 132 a^{2} c^{4} d^{4} + 18 a b^{4} c d^{2} e^{2} - 108 a b^{3} c^{2} d^{3} e + 54 a b^{2} c^{3} d^{4} + 6 b^{5} c d^{3} e - 3 b^{4} c^{2} d^{4}\right)}{192 a^{6} c^{4} - 144 a^{5} b^{2} c^{3} + 36 a^{4} b^{4} c^{2} - 3 a^{3} b^{6} c + x^{6} \left(192 a^{3} c^{7} - 144 a^{2} b^{2} c^{6} + 36 a b^{4} c^{5} - 3 b^{6} c^{4}\right) + x^{5} \left(576 a^{3} b c^{6} - 432 a^{2} b^{3} c^{5} + 108 a b^{5} c^{4} - 9 b^{7} c^{3}\right) + x^{4} \left(576 a^{4} c^{6} + 144 a^{3} b^{2} c^{5} - 324 a^{2} b^{4} c^{4} + 99 a b^{6} c^{3} - 9 b^{8} c^{2}\right) + x^{3} \left(1152 a^{4} b c^{5} - 672 a^{3} b^{3} c^{4} + 72 a^{2} b^{5} c^{3} + 18 a b^{7} c^{2} - 3 b^{9} c\right) + x^{2} \left(576 a^{5} c^{5} + 144 a^{4} b^{2} c^{4} - 324 a^{3} b^{4} c^{3} + 99 a^{2} b^{6} c^{2} - 9 a b^{8} c\right) + x \left(576 a^{5} b c^{4} - 432 a^{4} b^{3} c^{3} + 108 a^{3} b^{5} c^{2} - 9 a^{2} b^{7} c\right)}"," ",0,"-4*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)*log(x + (-1024*a**4*c**4*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 1024*a**3*b**2*c**3*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) - 384*a**2*b**4*c**2*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 4*a**2*b*c*e**4 + 64*a*b**6*c*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 4*a*b**3*e**4 - 24*a*b**2*c*d*e**3 + 24*a*b*c**2*d**2*e**2 - 4*b**8*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) - 4*b**4*d*e**3 + 24*b**3*c*d**2*e**2 - 40*b**2*c**2*d**3*e + 20*b*c**3*d**4)/(8*a**2*c**2*e**4 + 8*a*b**2*c*e**4 - 48*a*b*c**2*d*e**3 + 48*a*c**3*d**2*e**2 - 8*b**3*c*d*e**3 + 48*b**2*c**2*d**2*e**2 - 80*b*c**3*d**3*e + 40*c**4*d**4)) + 4*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)*log(x + (1024*a**4*c**4*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) - 1024*a**3*b**2*c**3*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 384*a**2*b**4*c**2*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 4*a**2*b*c*e**4 - 64*a*b**6*c*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 4*a*b**3*e**4 - 24*a*b**2*c*d*e**3 + 24*a*b*c**2*d**2*e**2 + 4*b**8*sqrt(-1/(4*a*c - b**2)**7)*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) - 4*b**4*d*e**3 + 24*b**3*c*d**2*e**2 - 40*b**2*c**2*d**3*e + 20*b*c**3*d**4)/(8*a**2*c**2*e**4 + 8*a*b**2*c*e**4 - 48*a*b*c**2*d*e**3 + 48*a*c**3*d**2*e**2 - 8*b**3*c*d*e**3 + 48*b**2*c**2*d**2*e**2 - 80*b*c**3*d**3*e + 40*c**4*d**4)) + (26*a**4*b*c*e**4 - 64*a**4*c**2*d*e**3 + a**3*b**3*e**4 - 44*a**3*b**2*c*d*e**3 + 156*a**3*b*c**2*d**2*e**2 - 128*a**3*c**3*d**3*e + 6*a**2*b**3*c*d**2*e**2 - 36*a**2*b**2*c**2*d**3*e + 66*a**2*b*c**3*d**4 + 2*a*b**4*c*d**3*e - 13*a*b**3*c**2*d**4 + b**5*c*d**4 + x**5*(12*a**2*c**4*e**4 + 12*a*b**2*c**3*e**4 - 72*a*b*c**4*d*e**3 + 72*a*c**5*d**2*e**2 - 12*b**3*c**3*d*e**3 + 72*b**2*c**4*d**2*e**2 - 120*b*c**5*d**3*e + 60*c**6*d**4) + x**4*(30*a**2*b*c**3*e**4 + 30*a*b**3*c**2*e**4 - 180*a*b**2*c**3*d*e**3 + 180*a*b*c**4*d**2*e**2 - 30*b**4*c**2*d*e**3 + 180*b**3*c**3*d**2*e**2 - 300*b**2*c**4*d**3*e + 150*b*c**5*d**4) + x**3*(-32*a**3*c**3*e**4 + 102*a**2*b**2*c**2*e**4 - 192*a**2*b*c**3*d*e**3 + 192*a**2*c**4*d**2*e**2 + 10*a*b**4*c*e**4 - 164*a*b**3*c**2*d*e**3 + 324*a*b**2*c**3*d**2*e**2 - 320*a*b*c**4*d**3*e + 160*a*c**5*d**4 + b**6*e**4 - 22*b**5*c*d*e**3 + 132*b**4*c**2*d**2*e**2 - 220*b**3*c**3*d**3*e + 110*b**2*c**4*d**4) + x**2*(48*a**3*b*c**2*e**4 - 192*a**3*c**3*d*e**3 + 51*a**2*b**3*c*e**4 - 144*a**2*b**2*c**2*d*e**3 + 288*a**2*b*c**3*d**2*e**2 + 3*a*b**5*e**4 - 102*a*b**4*c*d*e**3 + 306*a*b**3*c**2*d**2*e**2 - 480*a*b**2*c**3*d**3*e + 240*a*b*c**4*d**4 + 18*b**5*c*d**2*e**2 - 30*b**4*c**2*d**3*e + 15*b**3*c**3*d**4) + x*(-12*a**4*c**2*e**4 + 66*a**3*b**2*c*e**4 - 120*a**3*b*c**2*d*e**3 - 72*a**3*c**3*d**2*e**2 + 3*a**2*b**4*e**4 - 120*a**2*b**3*c*d*e**3 + 396*a**2*b**2*c**2*d**2*e**2 - 264*a**2*b*c**3*d**3*e + 132*a**2*c**4*d**4 + 18*a*b**4*c*d**2*e**2 - 108*a*b**3*c**2*d**3*e + 54*a*b**2*c**3*d**4 + 6*b**5*c*d**3*e - 3*b**4*c**2*d**4))/(192*a**6*c**4 - 144*a**5*b**2*c**3 + 36*a**4*b**4*c**2 - 3*a**3*b**6*c + x**6*(192*a**3*c**7 - 144*a**2*b**2*c**6 + 36*a*b**4*c**5 - 3*b**6*c**4) + x**5*(576*a**3*b*c**6 - 432*a**2*b**3*c**5 + 108*a*b**5*c**4 - 9*b**7*c**3) + x**4*(576*a**4*c**6 + 144*a**3*b**2*c**5 - 324*a**2*b**4*c**4 + 99*a*b**6*c**3 - 9*b**8*c**2) + x**3*(1152*a**4*b*c**5 - 672*a**3*b**3*c**4 + 72*a**2*b**5*c**3 + 18*a*b**7*c**2 - 3*b**9*c) + x**2*(576*a**5*c**5 + 144*a**4*b**2*c**4 - 324*a**3*b**4*c**3 + 99*a**2*b**6*c**2 - 9*a*b**8*c) + x*(576*a**5*b*c**4 - 432*a**4*b**3*c**3 + 108*a**3*b**5*c**2 - 9*a**2*b**7*c))","B",0
2215,1,2057,0,23.756879," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**4,x)","\sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) \log{\left(x + \frac{- 256 a^{4} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) + 256 a^{3} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) - 96 a^{2} b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) + 16 a b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) + 6 a b^{2} c e^{3} - 12 a b c^{2} d e^{2} - b^{8} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) + b^{4} e^{3} - 12 b^{3} c d e^{2} + 30 b^{2} c^{2} d^{2} e - 20 b c^{3} d^{3}}{12 a b c^{2} e^{3} - 24 a c^{3} d e^{2} + 2 b^{3} c e^{3} - 24 b^{2} c^{2} d e^{2} + 60 b c^{3} d^{2} e - 40 c^{4} d^{3}} \right)} - \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) \log{\left(x + \frac{256 a^{4} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) - 256 a^{3} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) + 96 a^{2} b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) - 16 a b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) + 6 a b^{2} c e^{3} - 12 a b c^{2} d e^{2} + b^{8} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) + b^{4} e^{3} - 12 b^{3} c d e^{2} + 30 b^{2} c^{2} d^{2} e - 20 b c^{3} d^{3}}{12 a b c^{2} e^{3} - 24 a c^{3} d e^{2} + 2 b^{3} c e^{3} - 24 b^{2} c^{2} d e^{2} + 60 b c^{3} d^{2} e - 40 c^{4} d^{3}} \right)} + \frac{- 32 a^{4} c e^{3} - 22 a^{3} b^{2} e^{3} + 156 a^{3} b c d e^{2} - 192 a^{3} c^{2} d^{2} e + 6 a^{2} b^{3} d e^{2} - 54 a^{2} b^{2} c d^{2} e + 132 a^{2} b c^{2} d^{3} + 3 a b^{4} d^{2} e - 26 a b^{3} c d^{3} + 2 b^{5} d^{3} + x^{5} \left(- 36 a b c^{3} e^{3} + 72 a c^{4} d e^{2} - 6 b^{3} c^{2} e^{3} + 72 b^{2} c^{3} d e^{2} - 180 b c^{4} d^{2} e + 120 c^{5} d^{3}\right) + x^{4} \left(- 90 a b^{2} c^{2} e^{3} + 180 a b c^{3} d e^{2} - 15 b^{4} c e^{3} + 180 b^{3} c^{2} d e^{2} - 450 b^{2} c^{3} d^{2} e + 300 b c^{4} d^{3}\right) + x^{3} \left(- 96 a^{2} b c^{2} e^{3} + 192 a^{2} c^{3} d e^{2} - 82 a b^{3} c e^{3} + 324 a b^{2} c^{2} d e^{2} - 480 a b c^{3} d^{2} e + 320 a c^{4} d^{3} - 11 b^{5} e^{3} + 132 b^{4} c d e^{2} - 330 b^{3} c^{2} d^{2} e + 220 b^{2} c^{3} d^{3}\right) + x^{2} \left(- 96 a^{3} c^{2} e^{3} - 72 a^{2} b^{2} c e^{3} + 288 a^{2} b c^{2} d e^{2} - 51 a b^{4} e^{3} + 306 a b^{3} c d e^{2} - 720 a b^{2} c^{2} d^{2} e + 480 a b c^{3} d^{3} + 18 b^{5} d e^{2} - 45 b^{4} c d^{2} e + 30 b^{3} c^{2} d^{3}\right) + x \left(- 60 a^{3} b c e^{3} - 72 a^{3} c^{2} d e^{2} - 60 a^{2} b^{3} e^{3} + 396 a^{2} b^{2} c d e^{2} - 396 a^{2} b c^{2} d^{2} e + 264 a^{2} c^{3} d^{3} + 18 a b^{4} d e^{2} - 162 a b^{3} c d^{2} e + 108 a b^{2} c^{2} d^{3} + 9 b^{5} d^{2} e - 6 b^{4} c d^{3}\right)}{384 a^{6} c^{3} - 288 a^{5} b^{2} c^{2} + 72 a^{4} b^{4} c - 6 a^{3} b^{6} + x^{6} \left(384 a^{3} c^{6} - 288 a^{2} b^{2} c^{5} + 72 a b^{4} c^{4} - 6 b^{6} c^{3}\right) + x^{5} \left(1152 a^{3} b c^{5} - 864 a^{2} b^{3} c^{4} + 216 a b^{5} c^{3} - 18 b^{7} c^{2}\right) + x^{4} \left(1152 a^{4} c^{5} + 288 a^{3} b^{2} c^{4} - 648 a^{2} b^{4} c^{3} + 198 a b^{6} c^{2} - 18 b^{8} c\right) + x^{3} \left(2304 a^{4} b c^{4} - 1344 a^{3} b^{3} c^{3} + 144 a^{2} b^{5} c^{2} + 36 a b^{7} c - 6 b^{9}\right) + x^{2} \left(1152 a^{5} c^{4} + 288 a^{4} b^{2} c^{3} - 648 a^{3} b^{4} c^{2} + 198 a^{2} b^{6} c - 18 a b^{8}\right) + x \left(1152 a^{5} b c^{3} - 864 a^{4} b^{3} c^{2} + 216 a^{3} b^{5} c - 18 a^{2} b^{7}\right)}"," ",0,"sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2)*log(x + (-256*a**4*c**4*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2) + 256*a**3*b**2*c**3*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2) - 96*a**2*b**4*c**2*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2) + 16*a*b**6*c*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2) + 6*a*b**2*c*e**3 - 12*a*b*c**2*d*e**2 - b**8*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2) + b**4*e**3 - 12*b**3*c*d*e**2 + 30*b**2*c**2*d**2*e - 20*b*c**3*d**3)/(12*a*b*c**2*e**3 - 24*a*c**3*d*e**2 + 2*b**3*c*e**3 - 24*b**2*c**2*d*e**2 + 60*b*c**3*d**2*e - 40*c**4*d**3)) - sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2)*log(x + (256*a**4*c**4*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2) - 256*a**3*b**2*c**3*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2) + 96*a**2*b**4*c**2*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2) - 16*a*b**6*c*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2) + 6*a*b**2*c*e**3 - 12*a*b*c**2*d*e**2 + b**8*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2) + b**4*e**3 - 12*b**3*c*d*e**2 + 30*b**2*c**2*d**2*e - 20*b*c**3*d**3)/(12*a*b*c**2*e**3 - 24*a*c**3*d*e**2 + 2*b**3*c*e**3 - 24*b**2*c**2*d*e**2 + 60*b*c**3*d**2*e - 40*c**4*d**3)) + (-32*a**4*c*e**3 - 22*a**3*b**2*e**3 + 156*a**3*b*c*d*e**2 - 192*a**3*c**2*d**2*e + 6*a**2*b**3*d*e**2 - 54*a**2*b**2*c*d**2*e + 132*a**2*b*c**2*d**3 + 3*a*b**4*d**2*e - 26*a*b**3*c*d**3 + 2*b**5*d**3 + x**5*(-36*a*b*c**3*e**3 + 72*a*c**4*d*e**2 - 6*b**3*c**2*e**3 + 72*b**2*c**3*d*e**2 - 180*b*c**4*d**2*e + 120*c**5*d**3) + x**4*(-90*a*b**2*c**2*e**3 + 180*a*b*c**3*d*e**2 - 15*b**4*c*e**3 + 180*b**3*c**2*d*e**2 - 450*b**2*c**3*d**2*e + 300*b*c**4*d**3) + x**3*(-96*a**2*b*c**2*e**3 + 192*a**2*c**3*d*e**2 - 82*a*b**3*c*e**3 + 324*a*b**2*c**2*d*e**2 - 480*a*b*c**3*d**2*e + 320*a*c**4*d**3 - 11*b**5*e**3 + 132*b**4*c*d*e**2 - 330*b**3*c**2*d**2*e + 220*b**2*c**3*d**3) + x**2*(-96*a**3*c**2*e**3 - 72*a**2*b**2*c*e**3 + 288*a**2*b*c**2*d*e**2 - 51*a*b**4*e**3 + 306*a*b**3*c*d*e**2 - 720*a*b**2*c**2*d**2*e + 480*a*b*c**3*d**3 + 18*b**5*d*e**2 - 45*b**4*c*d**2*e + 30*b**3*c**2*d**3) + x*(-60*a**3*b*c*e**3 - 72*a**3*c**2*d*e**2 - 60*a**2*b**3*e**3 + 396*a**2*b**2*c*d*e**2 - 396*a**2*b*c**2*d**2*e + 264*a**2*c**3*d**3 + 18*a*b**4*d*e**2 - 162*a*b**3*c*d**2*e + 108*a*b**2*c**2*d**3 + 9*b**5*d**2*e - 6*b**4*c*d**3))/(384*a**6*c**3 - 288*a**5*b**2*c**2 + 72*a**4*b**4*c - 6*a**3*b**6 + x**6*(384*a**3*c**6 - 288*a**2*b**2*c**5 + 72*a*b**4*c**4 - 6*b**6*c**3) + x**5*(1152*a**3*b*c**5 - 864*a**2*b**3*c**4 + 216*a*b**5*c**3 - 18*b**7*c**2) + x**4*(1152*a**4*c**5 + 288*a**3*b**2*c**4 - 648*a**2*b**4*c**3 + 198*a*b**6*c**2 - 18*b**8*c) + x**3*(2304*a**4*b*c**4 - 1344*a**3*b**3*c**3 + 144*a**2*b**5*c**2 + 36*a*b**7*c - 6*b**9) + x**2*(1152*a**5*c**4 + 288*a**4*b**2*c**3 - 648*a**3*b**4*c**2 + 198*a**2*b**6*c - 18*a*b**8) + x*(1152*a**5*b*c**3 - 864*a**4*b**3*c**2 + 216*a**3*b**5*c - 18*a**2*b**7))","B",0
2216,1,1635,0,7.089795," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**4,x)","- 4 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) \log{\left(x + \frac{- 1024 a^{4} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 1024 a^{3} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) - 384 a^{2} b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 64 a b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 4 a b c^{2} e^{2} - 4 b^{8} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 4 b^{3} c e^{2} - 20 b^{2} c^{2} d e + 20 b c^{3} d^{2}}{8 a c^{3} e^{2} + 8 b^{2} c^{2} e^{2} - 40 b c^{3} d e + 40 c^{4} d^{2}} \right)} + 4 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) \log{\left(x + \frac{1024 a^{4} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) - 1024 a^{3} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 384 a^{2} b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) - 64 a b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 4 a b c^{2} e^{2} + 4 b^{8} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) + 4 b^{3} c e^{2} - 20 b^{2} c^{2} d e + 20 b c^{3} d^{2}}{8 a c^{3} e^{2} + 8 b^{2} c^{2} e^{2} - 40 b c^{3} d e + 40 c^{4} d^{2}} \right)} + \frac{26 a^{3} b c e^{2} - 64 a^{3} c^{2} d e + a^{2} b^{3} e^{2} - 18 a^{2} b^{2} c d e + 66 a^{2} b c^{2} d^{2} + a b^{4} d e - 13 a b^{3} c d^{2} + b^{5} d^{2} + x^{5} \left(12 a c^{4} e^{2} + 12 b^{2} c^{3} e^{2} - 60 b c^{4} d e + 60 c^{5} d^{2}\right) + x^{4} \left(30 a b c^{3} e^{2} + 30 b^{3} c^{2} e^{2} - 150 b^{2} c^{3} d e + 150 b c^{4} d^{2}\right) + x^{3} \left(32 a^{2} c^{3} e^{2} + 54 a b^{2} c^{2} e^{2} - 160 a b c^{3} d e + 160 a c^{4} d^{2} + 22 b^{4} c e^{2} - 110 b^{3} c^{2} d e + 110 b^{2} c^{3} d^{2}\right) + x^{2} \left(48 a^{2} b c^{2} e^{2} + 51 a b^{3} c e^{2} - 240 a b^{2} c^{2} d e + 240 a b c^{3} d^{2} + 3 b^{5} e^{2} - 15 b^{4} c d e + 15 b^{3} c^{2} d^{2}\right) + x \left(- 12 a^{3} c^{2} e^{2} + 66 a^{2} b^{2} c e^{2} - 132 a^{2} b c^{2} d e + 132 a^{2} c^{3} d^{2} + 3 a b^{4} e^{2} - 54 a b^{3} c d e + 54 a b^{2} c^{2} d^{2} + 3 b^{5} d e - 3 b^{4} c d^{2}\right)}{192 a^{6} c^{3} - 144 a^{5} b^{2} c^{2} + 36 a^{4} b^{4} c - 3 a^{3} b^{6} + x^{6} \left(192 a^{3} c^{6} - 144 a^{2} b^{2} c^{5} + 36 a b^{4} c^{4} - 3 b^{6} c^{3}\right) + x^{5} \left(576 a^{3} b c^{5} - 432 a^{2} b^{3} c^{4} + 108 a b^{5} c^{3} - 9 b^{7} c^{2}\right) + x^{4} \left(576 a^{4} c^{5} + 144 a^{3} b^{2} c^{4} - 324 a^{2} b^{4} c^{3} + 99 a b^{6} c^{2} - 9 b^{8} c\right) + x^{3} \left(1152 a^{4} b c^{4} - 672 a^{3} b^{3} c^{3} + 72 a^{2} b^{5} c^{2} + 18 a b^{7} c - 3 b^{9}\right) + x^{2} \left(576 a^{5} c^{4} + 144 a^{4} b^{2} c^{3} - 324 a^{3} b^{4} c^{2} + 99 a^{2} b^{6} c - 9 a b^{8}\right) + x \left(576 a^{5} b c^{3} - 432 a^{4} b^{3} c^{2} + 108 a^{3} b^{5} c - 9 a^{2} b^{7}\right)}"," ",0,"-4*c*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)*log(x + (-1024*a**4*c**5*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 1024*a**3*b**2*c**4*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) - 384*a**2*b**4*c**3*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 64*a*b**6*c**2*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 4*a*b*c**2*e**2 - 4*b**8*c*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 4*b**3*c*e**2 - 20*b**2*c**2*d*e + 20*b*c**3*d**2)/(8*a*c**3*e**2 + 8*b**2*c**2*e**2 - 40*b*c**3*d*e + 40*c**4*d**2)) + 4*c*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)*log(x + (1024*a**4*c**5*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) - 1024*a**3*b**2*c**4*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 384*a**2*b**4*c**3*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) - 64*a*b**6*c**2*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 4*a*b*c**2*e**2 + 4*b**8*c*sqrt(-1/(4*a*c - b**2)**7)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2) + 4*b**3*c*e**2 - 20*b**2*c**2*d*e + 20*b*c**3*d**2)/(8*a*c**3*e**2 + 8*b**2*c**2*e**2 - 40*b*c**3*d*e + 40*c**4*d**2)) + (26*a**3*b*c*e**2 - 64*a**3*c**2*d*e + a**2*b**3*e**2 - 18*a**2*b**2*c*d*e + 66*a**2*b*c**2*d**2 + a*b**4*d*e - 13*a*b**3*c*d**2 + b**5*d**2 + x**5*(12*a*c**4*e**2 + 12*b**2*c**3*e**2 - 60*b*c**4*d*e + 60*c**5*d**2) + x**4*(30*a*b*c**3*e**2 + 30*b**3*c**2*e**2 - 150*b**2*c**3*d*e + 150*b*c**4*d**2) + x**3*(32*a**2*c**3*e**2 + 54*a*b**2*c**2*e**2 - 160*a*b*c**3*d*e + 160*a*c**4*d**2 + 22*b**4*c*e**2 - 110*b**3*c**2*d*e + 110*b**2*c**3*d**2) + x**2*(48*a**2*b*c**2*e**2 + 51*a*b**3*c*e**2 - 240*a*b**2*c**2*d*e + 240*a*b*c**3*d**2 + 3*b**5*e**2 - 15*b**4*c*d*e + 15*b**3*c**2*d**2) + x*(-12*a**3*c**2*e**2 + 66*a**2*b**2*c*e**2 - 132*a**2*b*c**2*d*e + 132*a**2*c**3*d**2 + 3*a*b**4*e**2 - 54*a*b**3*c*d*e + 54*a*b**2*c**2*d**2 + 3*b**5*d*e - 3*b**4*c*d**2))/(192*a**6*c**3 - 144*a**5*b**2*c**2 + 36*a**4*b**4*c - 3*a**3*b**6 + x**6*(192*a**3*c**6 - 144*a**2*b**2*c**5 + 36*a*b**4*c**4 - 3*b**6*c**3) + x**5*(576*a**3*b*c**5 - 432*a**2*b**3*c**4 + 108*a*b**5*c**3 - 9*b**7*c**2) + x**4*(576*a**4*c**5 + 144*a**3*b**2*c**4 - 324*a**2*b**4*c**3 + 99*a*b**6*c**2 - 9*b**8*c) + x**3*(1152*a**4*b*c**4 - 672*a**3*b**3*c**3 + 72*a**2*b**5*c**2 + 18*a*b**7*c - 3*b**9) + x**2*(576*a**5*c**4 + 144*a**4*b**2*c**3 - 324*a**3*b**4*c**2 + 99*a**2*b**6*c - 9*a*b**8) + x*(576*a**5*b*c**3 - 432*a**4*b**3*c**2 + 108*a**3*b**5*c - 9*a**2*b**7))","B",0
2217,1,1062,0,3.406335," ","integrate((e*x+d)/(c*x**2+b*x+a)**4,x)","10 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \log{\left(x + \frac{- 2560 a^{4} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) + 2560 a^{3} b^{2} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) - 960 a^{2} b^{4} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) + 160 a b^{6} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) - 10 b^{8} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) + 10 b^{2} c^{2} e - 20 b c^{3} d}{20 b c^{3} e - 40 c^{4} d} \right)} - 10 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) \log{\left(x + \frac{2560 a^{4} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) - 2560 a^{3} b^{2} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) + 960 a^{2} b^{4} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) - 160 a b^{6} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) + 10 b^{8} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(b e - 2 c d\right) + 10 b^{2} c^{2} e - 20 b c^{3} d}{20 b c^{3} e - 40 c^{4} d} \right)} + \frac{- 64 a^{3} c^{2} e - 18 a^{2} b^{2} c e + 132 a^{2} b c^{2} d + a b^{4} e - 26 a b^{3} c d + 2 b^{5} d + x^{5} \left(- 60 b c^{4} e + 120 c^{5} d\right) + x^{4} \left(- 150 b^{2} c^{3} e + 300 b c^{4} d\right) + x^{3} \left(- 160 a b c^{3} e + 320 a c^{4} d - 110 b^{3} c^{2} e + 220 b^{2} c^{3} d\right) + x^{2} \left(- 240 a b^{2} c^{2} e + 480 a b c^{3} d - 15 b^{4} c e + 30 b^{3} c^{2} d\right) + x \left(- 132 a^{2} b c^{2} e + 264 a^{2} c^{3} d - 54 a b^{3} c e + 108 a b^{2} c^{2} d + 3 b^{5} e - 6 b^{4} c d\right)}{384 a^{6} c^{3} - 288 a^{5} b^{2} c^{2} + 72 a^{4} b^{4} c - 6 a^{3} b^{6} + x^{6} \left(384 a^{3} c^{6} - 288 a^{2} b^{2} c^{5} + 72 a b^{4} c^{4} - 6 b^{6} c^{3}\right) + x^{5} \left(1152 a^{3} b c^{5} - 864 a^{2} b^{3} c^{4} + 216 a b^{5} c^{3} - 18 b^{7} c^{2}\right) + x^{4} \left(1152 a^{4} c^{5} + 288 a^{3} b^{2} c^{4} - 648 a^{2} b^{4} c^{3} + 198 a b^{6} c^{2} - 18 b^{8} c\right) + x^{3} \left(2304 a^{4} b c^{4} - 1344 a^{3} b^{3} c^{3} + 144 a^{2} b^{5} c^{2} + 36 a b^{7} c - 6 b^{9}\right) + x^{2} \left(1152 a^{5} c^{4} + 288 a^{4} b^{2} c^{3} - 648 a^{3} b^{4} c^{2} + 198 a^{2} b^{6} c - 18 a b^{8}\right) + x \left(1152 a^{5} b c^{3} - 864 a^{4} b^{3} c^{2} + 216 a^{3} b^{5} c - 18 a^{2} b^{7}\right)}"," ",0,"10*c**2*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*log(x + (-2560*a**4*c**6*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d) + 2560*a**3*b**2*c**5*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d) - 960*a**2*b**4*c**4*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d) + 160*a*b**6*c**3*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d) - 10*b**8*c**2*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d) + 10*b**2*c**2*e - 20*b*c**3*d)/(20*b*c**3*e - 40*c**4*d)) - 10*c**2*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d)*log(x + (2560*a**4*c**6*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d) - 2560*a**3*b**2*c**5*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d) + 960*a**2*b**4*c**4*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d) - 160*a*b**6*c**3*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d) + 10*b**8*c**2*sqrt(-1/(4*a*c - b**2)**7)*(b*e - 2*c*d) + 10*b**2*c**2*e - 20*b*c**3*d)/(20*b*c**3*e - 40*c**4*d)) + (-64*a**3*c**2*e - 18*a**2*b**2*c*e + 132*a**2*b*c**2*d + a*b**4*e - 26*a*b**3*c*d + 2*b**5*d + x**5*(-60*b*c**4*e + 120*c**5*d) + x**4*(-150*b**2*c**3*e + 300*b*c**4*d) + x**3*(-160*a*b*c**3*e + 320*a*c**4*d - 110*b**3*c**2*e + 220*b**2*c**3*d) + x**2*(-240*a*b**2*c**2*e + 480*a*b*c**3*d - 15*b**4*c*e + 30*b**3*c**2*d) + x*(-132*a**2*b*c**2*e + 264*a**2*c**3*d - 54*a*b**3*c*e + 108*a*b**2*c**2*d + 3*b**5*e - 6*b**4*c*d))/(384*a**6*c**3 - 288*a**5*b**2*c**2 + 72*a**4*b**4*c - 6*a**3*b**6 + x**6*(384*a**3*c**6 - 288*a**2*b**2*c**5 + 72*a*b**4*c**4 - 6*b**6*c**3) + x**5*(1152*a**3*b*c**5 - 864*a**2*b**3*c**4 + 216*a*b**5*c**3 - 18*b**7*c**2) + x**4*(1152*a**4*c**5 + 288*a**3*b**2*c**4 - 648*a**2*b**4*c**3 + 198*a*b**6*c**2 - 18*b**8*c) + x**3*(2304*a**4*b*c**4 - 1344*a**3*b**3*c**3 + 144*a**2*b**5*c**2 + 36*a*b**7*c - 6*b**9) + x**2*(1152*a**5*c**4 + 288*a**4*b**2*c**3 - 648*a**3*b**4*c**2 + 198*a**2*b**6*c - 18*a*b**8) + x*(1152*a**5*b*c**3 - 864*a**4*b**3*c**2 + 216*a**3*b**5*c - 18*a**2*b**7))","B",0
2218,1,777,0,1.855019," ","integrate(1/(c*x**2+b*x+a)**4,x)","- 20 c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \log{\left(x + \frac{- 5120 a^{4} c^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 5120 a^{3} b^{2} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 1920 a^{2} b^{4} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 320 a b^{6} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 20 b^{8} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 20 b c^{3}}{40 c^{4}} \right)} + 20 c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \log{\left(x + \frac{5120 a^{4} c^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 5120 a^{3} b^{2} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 1920 a^{2} b^{4} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} - 320 a b^{6} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 20 b^{8} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} + 20 b c^{3}}{40 c^{4}} \right)} + \frac{66 a^{2} b c^{2} - 13 a b^{3} c + b^{5} + 150 b c^{4} x^{4} + 60 c^{5} x^{5} + x^{3} \left(160 a c^{4} + 110 b^{2} c^{3}\right) + x^{2} \left(240 a b c^{3} + 15 b^{3} c^{2}\right) + x \left(132 a^{2} c^{3} + 54 a b^{2} c^{2} - 3 b^{4} c\right)}{192 a^{6} c^{3} - 144 a^{5} b^{2} c^{2} + 36 a^{4} b^{4} c - 3 a^{3} b^{6} + x^{6} \left(192 a^{3} c^{6} - 144 a^{2} b^{2} c^{5} + 36 a b^{4} c^{4} - 3 b^{6} c^{3}\right) + x^{5} \left(576 a^{3} b c^{5} - 432 a^{2} b^{3} c^{4} + 108 a b^{5} c^{3} - 9 b^{7} c^{2}\right) + x^{4} \left(576 a^{4} c^{5} + 144 a^{3} b^{2} c^{4} - 324 a^{2} b^{4} c^{3} + 99 a b^{6} c^{2} - 9 b^{8} c\right) + x^{3} \left(1152 a^{4} b c^{4} - 672 a^{3} b^{3} c^{3} + 72 a^{2} b^{5} c^{2} + 18 a b^{7} c - 3 b^{9}\right) + x^{2} \left(576 a^{5} c^{4} + 144 a^{4} b^{2} c^{3} - 324 a^{3} b^{4} c^{2} + 99 a^{2} b^{6} c - 9 a b^{8}\right) + x \left(576 a^{5} b c^{3} - 432 a^{4} b^{3} c^{2} + 108 a^{3} b^{5} c - 9 a^{2} b^{7}\right)}"," ",0,"-20*c**3*sqrt(-1/(4*a*c - b**2)**7)*log(x + (-5120*a**4*c**7*sqrt(-1/(4*a*c - b**2)**7) + 5120*a**3*b**2*c**6*sqrt(-1/(4*a*c - b**2)**7) - 1920*a**2*b**4*c**5*sqrt(-1/(4*a*c - b**2)**7) + 320*a*b**6*c**4*sqrt(-1/(4*a*c - b**2)**7) - 20*b**8*c**3*sqrt(-1/(4*a*c - b**2)**7) + 20*b*c**3)/(40*c**4)) + 20*c**3*sqrt(-1/(4*a*c - b**2)**7)*log(x + (5120*a**4*c**7*sqrt(-1/(4*a*c - b**2)**7) - 5120*a**3*b**2*c**6*sqrt(-1/(4*a*c - b**2)**7) + 1920*a**2*b**4*c**5*sqrt(-1/(4*a*c - b**2)**7) - 320*a*b**6*c**4*sqrt(-1/(4*a*c - b**2)**7) + 20*b**8*c**3*sqrt(-1/(4*a*c - b**2)**7) + 20*b*c**3)/(40*c**4)) + (66*a**2*b*c**2 - 13*a*b**3*c + b**5 + 150*b*c**4*x**4 + 60*c**5*x**5 + x**3*(160*a*c**4 + 110*b**2*c**3) + x**2*(240*a*b*c**3 + 15*b**3*c**2) + x*(132*a**2*c**3 + 54*a*b**2*c**2 - 3*b**4*c))/(192*a**6*c**3 - 144*a**5*b**2*c**2 + 36*a**4*b**4*c - 3*a**3*b**6 + x**6*(192*a**3*c**6 - 144*a**2*b**2*c**5 + 36*a*b**4*c**4 - 3*b**6*c**3) + x**5*(576*a**3*b*c**5 - 432*a**2*b**3*c**4 + 108*a*b**5*c**3 - 9*b**7*c**2) + x**4*(576*a**4*c**5 + 144*a**3*b**2*c**4 - 324*a**2*b**4*c**3 + 99*a*b**6*c**2 - 9*b**8*c) + x**3*(1152*a**4*b*c**4 - 672*a**3*b**3*c**3 + 72*a**2*b**5*c**2 + 18*a*b**7*c - 3*b**9) + x**2*(576*a**5*c**4 + 144*a**4*b**2*c**3 - 324*a**3*b**4*c**2 + 99*a**2*b**6*c - 9*a*b**8) + x*(576*a**5*b*c**3 - 432*a**4*b**3*c**2 + 108*a**3*b**5*c - 9*a**2*b**7))","B",0
2219,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2220,-1,0,0,0.000000," ","integrate(1/x**2/(c*x**2+b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2221,-1,0,0,0.000000," ","integrate((e*x+d)**5/(c*x**2+b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2222,-1,0,0,0.000000," ","integrate((e*x+d)**4/(c*x**2+b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2223,1,2994,0,49.081882," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**5,x)","5 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) \log{\left(x + \frac{- 5120 a^{5} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) + 6400 a^{4} b^{2} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) - 3200 a^{3} b^{4} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) + 800 a^{2} b^{6} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) - 100 a b^{8} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) + 15 a b^{2} c^{2} e^{3} - 30 a b c^{3} d e^{2} + 5 b^{10} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) + 5 b^{4} c e^{3} - 45 b^{3} c^{2} d e^{2} + 105 b^{2} c^{3} d^{2} e - 70 b c^{4} d^{3}}{30 a b c^{3} e^{3} - 60 a c^{4} d e^{2} + 10 b^{3} c^{2} e^{3} - 90 b^{2} c^{3} d e^{2} + 210 b c^{4} d^{2} e - 140 c^{5} d^{3}} \right)} - 5 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) \log{\left(x + \frac{5120 a^{5} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) - 6400 a^{4} b^{2} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) + 3200 a^{3} b^{4} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) - 800 a^{2} b^{6} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) + 100 a b^{8} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) + 15 a b^{2} c^{2} e^{3} - 30 a b c^{3} d e^{2} - 5 b^{10} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) + 5 b^{4} c e^{3} - 45 b^{3} c^{2} d e^{2} + 105 b^{2} c^{3} d^{2} e - 70 b c^{4} d^{3}}{30 a b c^{3} e^{3} - 60 a c^{4} d e^{2} + 10 b^{3} c^{2} e^{3} - 90 b^{2} c^{3} d e^{2} + 210 b c^{4} d^{2} e - 140 c^{5} d^{3}} \right)} + \frac{- 128 a^{5} c^{2} e^{3} - 166 a^{4} b^{2} c e^{3} + 972 a^{4} b c^{2} d e^{2} - 1152 a^{4} c^{3} d^{2} e - 3 a^{3} b^{4} e^{3} + 84 a^{3} b^{3} c d e^{2} - 522 a^{3} b^{2} c^{2} d^{2} e + 1116 a^{3} b c^{3} d^{3} - 3 a^{2} b^{5} d e^{2} + 57 a^{2} b^{4} c d^{2} e - 326 a^{2} b^{3} c^{2} d^{3} - 3 a b^{6} d^{2} e + 50 a b^{5} c d^{3} - 3 b^{7} d^{3} + x^{7} \left(- 180 a b c^{5} e^{3} + 360 a c^{6} d e^{2} - 60 b^{3} c^{4} e^{3} + 540 b^{2} c^{5} d e^{2} - 1260 b c^{6} d^{2} e + 840 c^{7} d^{3}\right) + x^{6} \left(- 630 a b^{2} c^{4} e^{3} + 1260 a b c^{5} d e^{2} - 210 b^{4} c^{3} e^{3} + 1890 b^{3} c^{4} d e^{2} - 4410 b^{2} c^{5} d^{2} e + 2940 b c^{6} d^{3}\right) + x^{5} \left(- 660 a^{2} b c^{4} e^{3} + 1320 a^{2} c^{5} d e^{2} - 1000 a b^{3} c^{3} e^{3} + 3540 a b^{2} c^{4} d e^{2} - 4620 a b c^{5} d^{2} e + 3080 a c^{6} d^{3} - 260 b^{5} c^{2} e^{3} + 2340 b^{4} c^{3} d e^{2} - 5460 b^{3} c^{4} d^{2} e + 3640 b^{2} c^{5} d^{3}\right) + x^{4} \left(- 1650 a^{2} b^{2} c^{3} e^{3} + 3300 a^{2} b c^{4} d e^{2} - 925 a b^{4} c^{2} e^{3} + 5700 a b^{3} c^{3} d e^{2} - 11550 a b^{2} c^{4} d^{2} e + 7700 a b c^{5} d^{3} - 125 b^{6} c e^{3} + 1125 b^{5} c^{2} d e^{2} - 2625 b^{4} c^{3} d^{2} e + 1750 b^{3} c^{4} d^{3}\right) + x^{3} \left(- 876 a^{3} b c^{3} e^{3} + 1752 a^{3} c^{4} d e^{2} - 1504 a^{2} b^{3} c^{2} e^{3} + 5052 a^{2} b^{2} c^{3} d e^{2} - 6132 a^{2} b c^{4} d^{2} e + 4088 a^{2} c^{5} d^{3} - 440 a b^{5} c e^{3} + 3708 a b^{4} c^{2} d e^{2} - 8484 a b^{3} c^{3} d^{2} e + 5656 a b^{2} c^{4} d^{3} - 12 b^{7} e^{3} + 108 b^{6} c d e^{2} - 252 b^{5} c^{2} d^{2} e + 168 b^{4} c^{3} d^{3}\right) + x^{2} \left(- 512 a^{4} c^{3} e^{3} - 802 a^{3} b^{2} c^{2} e^{3} + 2628 a^{3} b c^{3} d e^{2} - 798 a^{2} b^{4} c e^{3} + 4278 a^{2} b^{3} c^{2} d e^{2} - 9198 a^{2} b^{2} c^{3} d^{2} e + 6132 a^{2} b c^{4} d^{3} - 18 a b^{6} e^{3} + 492 a b^{5} c d e^{2} - 1176 a b^{4} c^{2} d^{2} e + 784 a b^{3} c^{3} d^{3} - 18 b^{7} d e^{2} + 42 b^{6} c d^{2} e - 28 b^{5} c^{2} d^{3}\right) + x \left(- 332 a^{4} b c^{2} e^{3} - 360 a^{4} c^{3} d e^{2} - 604 a^{3} b^{3} c e^{3} + 3348 a^{3} b^{2} c^{2} d e^{2} - 3348 a^{3} b c^{3} d^{2} e + 2232 a^{3} c^{4} d^{3} - 12 a^{2} b^{5} e^{3} + 336 a^{2} b^{4} c d e^{2} - 2088 a^{2} b^{3} c^{2} d^{2} e + 1392 a^{2} b^{2} c^{3} d^{3} - 12 a b^{6} d e^{2} + 228 a b^{5} c d^{2} e - 152 a b^{4} c^{2} d^{3} - 12 b^{7} d^{2} e + 8 b^{6} c d^{3}\right)}{3072 a^{8} c^{4} - 3072 a^{7} b^{2} c^{3} + 1152 a^{6} b^{4} c^{2} - 192 a^{5} b^{6} c + 12 a^{4} b^{8} + x^{8} \left(3072 a^{4} c^{8} - 3072 a^{3} b^{2} c^{7} + 1152 a^{2} b^{4} c^{6} - 192 a b^{6} c^{5} + 12 b^{8} c^{4}\right) + x^{7} \left(12288 a^{4} b c^{7} - 12288 a^{3} b^{3} c^{6} + 4608 a^{2} b^{5} c^{5} - 768 a b^{7} c^{4} + 48 b^{9} c^{3}\right) + x^{6} \left(12288 a^{5} c^{7} + 6144 a^{4} b^{2} c^{6} - 13824 a^{3} b^{4} c^{5} + 6144 a^{2} b^{6} c^{4} - 1104 a b^{8} c^{3} + 72 b^{10} c^{2}\right) + x^{5} \left(36864 a^{5} b c^{6} - 24576 a^{4} b^{3} c^{5} + 1536 a^{3} b^{5} c^{4} + 2304 a^{2} b^{7} c^{3} - 624 a b^{9} c^{2} + 48 b^{11} c\right) + x^{4} \left(18432 a^{6} c^{6} + 18432 a^{5} b^{2} c^{5} - 26880 a^{4} b^{4} c^{4} + 9600 a^{3} b^{6} c^{3} - 1080 a^{2} b^{8} c^{2} - 48 a b^{10} c + 12 b^{12}\right) + x^{3} \left(36864 a^{6} b c^{5} - 24576 a^{5} b^{3} c^{4} + 1536 a^{4} b^{5} c^{3} + 2304 a^{3} b^{7} c^{2} - 624 a^{2} b^{9} c + 48 a b^{11}\right) + x^{2} \left(12288 a^{7} c^{5} + 6144 a^{6} b^{2} c^{4} - 13824 a^{5} b^{4} c^{3} + 6144 a^{4} b^{6} c^{2} - 1104 a^{3} b^{8} c + 72 a^{2} b^{10}\right) + x \left(12288 a^{7} b c^{4} - 12288 a^{6} b^{3} c^{3} + 4608 a^{5} b^{5} c^{2} - 768 a^{4} b^{7} c + 48 a^{3} b^{9}\right)}"," ",0,"5*c*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2)*log(x + (-5120*a**5*c**6*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) + 6400*a**4*b**2*c**5*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) - 3200*a**3*b**4*c**4*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) + 800*a**2*b**6*c**3*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) - 100*a*b**8*c**2*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) + 15*a*b**2*c**2*e**3 - 30*a*b*c**3*d*e**2 + 5*b**10*c*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) + 5*b**4*c*e**3 - 45*b**3*c**2*d*e**2 + 105*b**2*c**3*d**2*e - 70*b*c**4*d**3)/(30*a*b*c**3*e**3 - 60*a*c**4*d*e**2 + 10*b**3*c**2*e**3 - 90*b**2*c**3*d*e**2 + 210*b*c**4*d**2*e - 140*c**5*d**3)) - 5*c*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2)*log(x + (5120*a**5*c**6*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) - 6400*a**4*b**2*c**5*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) + 3200*a**3*b**4*c**4*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) - 800*a**2*b**6*c**3*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) + 100*a*b**8*c**2*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) + 15*a*b**2*c**2*e**3 - 30*a*b*c**3*d*e**2 - 5*b**10*c*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2) + 5*b**4*c*e**3 - 45*b**3*c**2*d*e**2 + 105*b**2*c**3*d**2*e - 70*b*c**4*d**3)/(30*a*b*c**3*e**3 - 60*a*c**4*d*e**2 + 10*b**3*c**2*e**3 - 90*b**2*c**3*d*e**2 + 210*b*c**4*d**2*e - 140*c**5*d**3)) + (-128*a**5*c**2*e**3 - 166*a**4*b**2*c*e**3 + 972*a**4*b*c**2*d*e**2 - 1152*a**4*c**3*d**2*e - 3*a**3*b**4*e**3 + 84*a**3*b**3*c*d*e**2 - 522*a**3*b**2*c**2*d**2*e + 1116*a**3*b*c**3*d**3 - 3*a**2*b**5*d*e**2 + 57*a**2*b**4*c*d**2*e - 326*a**2*b**3*c**2*d**3 - 3*a*b**6*d**2*e + 50*a*b**5*c*d**3 - 3*b**7*d**3 + x**7*(-180*a*b*c**5*e**3 + 360*a*c**6*d*e**2 - 60*b**3*c**4*e**3 + 540*b**2*c**5*d*e**2 - 1260*b*c**6*d**2*e + 840*c**7*d**3) + x**6*(-630*a*b**2*c**4*e**3 + 1260*a*b*c**5*d*e**2 - 210*b**4*c**3*e**3 + 1890*b**3*c**4*d*e**2 - 4410*b**2*c**5*d**2*e + 2940*b*c**6*d**3) + x**5*(-660*a**2*b*c**4*e**3 + 1320*a**2*c**5*d*e**2 - 1000*a*b**3*c**3*e**3 + 3540*a*b**2*c**4*d*e**2 - 4620*a*b*c**5*d**2*e + 3080*a*c**6*d**3 - 260*b**5*c**2*e**3 + 2340*b**4*c**3*d*e**2 - 5460*b**3*c**4*d**2*e + 3640*b**2*c**5*d**3) + x**4*(-1650*a**2*b**2*c**3*e**3 + 3300*a**2*b*c**4*d*e**2 - 925*a*b**4*c**2*e**3 + 5700*a*b**3*c**3*d*e**2 - 11550*a*b**2*c**4*d**2*e + 7700*a*b*c**5*d**3 - 125*b**6*c*e**3 + 1125*b**5*c**2*d*e**2 - 2625*b**4*c**3*d**2*e + 1750*b**3*c**4*d**3) + x**3*(-876*a**3*b*c**3*e**3 + 1752*a**3*c**4*d*e**2 - 1504*a**2*b**3*c**2*e**3 + 5052*a**2*b**2*c**3*d*e**2 - 6132*a**2*b*c**4*d**2*e + 4088*a**2*c**5*d**3 - 440*a*b**5*c*e**3 + 3708*a*b**4*c**2*d*e**2 - 8484*a*b**3*c**3*d**2*e + 5656*a*b**2*c**4*d**3 - 12*b**7*e**3 + 108*b**6*c*d*e**2 - 252*b**5*c**2*d**2*e + 168*b**4*c**3*d**3) + x**2*(-512*a**4*c**3*e**3 - 802*a**3*b**2*c**2*e**3 + 2628*a**3*b*c**3*d*e**2 - 798*a**2*b**4*c*e**3 + 4278*a**2*b**3*c**2*d*e**2 - 9198*a**2*b**2*c**3*d**2*e + 6132*a**2*b*c**4*d**3 - 18*a*b**6*e**3 + 492*a*b**5*c*d*e**2 - 1176*a*b**4*c**2*d**2*e + 784*a*b**3*c**3*d**3 - 18*b**7*d*e**2 + 42*b**6*c*d**2*e - 28*b**5*c**2*d**3) + x*(-332*a**4*b*c**2*e**3 - 360*a**4*c**3*d*e**2 - 604*a**3*b**3*c*e**3 + 3348*a**3*b**2*c**2*d*e**2 - 3348*a**3*b*c**3*d**2*e + 2232*a**3*c**4*d**3 - 12*a**2*b**5*e**3 + 336*a**2*b**4*c*d*e**2 - 2088*a**2*b**3*c**2*d**2*e + 1392*a**2*b**2*c**3*d**3 - 12*a*b**6*d*e**2 + 228*a*b**5*c*d**2*e - 152*a*b**4*c**2*d**3 - 12*b**7*d**2*e + 8*b**6*c*d**3))/(3072*a**8*c**4 - 3072*a**7*b**2*c**3 + 1152*a**6*b**4*c**2 - 192*a**5*b**6*c + 12*a**4*b**8 + x**8*(3072*a**4*c**8 - 3072*a**3*b**2*c**7 + 1152*a**2*b**4*c**6 - 192*a*b**6*c**5 + 12*b**8*c**4) + x**7*(12288*a**4*b*c**7 - 12288*a**3*b**3*c**6 + 4608*a**2*b**5*c**5 - 768*a*b**7*c**4 + 48*b**9*c**3) + x**6*(12288*a**5*c**7 + 6144*a**4*b**2*c**6 - 13824*a**3*b**4*c**5 + 6144*a**2*b**6*c**4 - 1104*a*b**8*c**3 + 72*b**10*c**2) + x**5*(36864*a**5*b*c**6 - 24576*a**4*b**3*c**5 + 1536*a**3*b**5*c**4 + 2304*a**2*b**7*c**3 - 624*a*b**9*c**2 + 48*b**11*c) + x**4*(18432*a**6*c**6 + 18432*a**5*b**2*c**5 - 26880*a**4*b**4*c**4 + 9600*a**3*b**6*c**3 - 1080*a**2*b**8*c**2 - 48*a*b**10*c + 12*b**12) + x**3*(36864*a**6*b*c**5 - 24576*a**5*b**3*c**4 + 1536*a**4*b**5*c**3 + 2304*a**3*b**7*c**2 - 624*a**2*b**9*c + 48*a*b**11) + x**2*(12288*a**7*c**5 + 6144*a**6*b**2*c**4 - 13824*a**5*b**4*c**3 + 6144*a**4*b**6*c**2 - 1104*a**3*b**8*c + 72*a**2*b**10) + x*(12288*a**7*b*c**4 - 12288*a**6*b**3*c**3 + 4608*a**5*b**5*c**2 - 768*a**4*b**7*c + 48*a**3*b**9))","B",0
2224,1,2407,0,13.807055," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**5,x)","- 5 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) \log{\left(x + \frac{- 5120 a^{5} c^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) + 6400 a^{4} b^{2} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) - 3200 a^{3} b^{4} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) + 800 a^{2} b^{6} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) - 100 a b^{8} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) + 10 a b c^{3} e^{2} + 5 b^{10} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) + 15 b^{3} c^{2} e^{2} - 70 b^{2} c^{3} d e + 70 b c^{4} d^{2}}{20 a c^{4} e^{2} + 30 b^{2} c^{3} e^{2} - 140 b c^{4} d e + 140 c^{5} d^{2}} \right)} + 5 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) \log{\left(x + \frac{5120 a^{5} c^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) - 6400 a^{4} b^{2} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) + 3200 a^{3} b^{4} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) - 800 a^{2} b^{6} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) + 100 a b^{8} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) + 10 a b c^{3} e^{2} - 5 b^{10} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) + 15 b^{3} c^{2} e^{2} - 70 b^{2} c^{3} d e + 70 b c^{4} d^{2}}{20 a c^{4} e^{2} + 30 b^{2} c^{3} e^{2} - 140 b c^{4} d e + 140 c^{5} d^{2}} \right)} + \frac{324 a^{4} b c^{2} e^{2} - 768 a^{4} c^{3} d e + 28 a^{3} b^{3} c e^{2} - 348 a^{3} b^{2} c^{2} d e + 1116 a^{3} b c^{3} d^{2} - a^{2} b^{5} e^{2} + 38 a^{2} b^{4} c d e - 326 a^{2} b^{3} c^{2} d^{2} - 2 a b^{6} d e + 50 a b^{5} c d^{2} - 3 b^{7} d^{2} + x^{7} \left(120 a c^{6} e^{2} + 180 b^{2} c^{5} e^{2} - 840 b c^{6} d e + 840 c^{7} d^{2}\right) + x^{6} \left(420 a b c^{5} e^{2} + 630 b^{3} c^{4} e^{2} - 2940 b^{2} c^{5} d e + 2940 b c^{6} d^{2}\right) + x^{5} \left(440 a^{2} c^{5} e^{2} + 1180 a b^{2} c^{4} e^{2} - 3080 a b c^{5} d e + 3080 a c^{6} d^{2} + 780 b^{4} c^{3} e^{2} - 3640 b^{3} c^{4} d e + 3640 b^{2} c^{5} d^{2}\right) + x^{4} \left(1100 a^{2} b c^{4} e^{2} + 1900 a b^{3} c^{3} e^{2} - 7700 a b^{2} c^{4} d e + 7700 a b c^{5} d^{2} + 375 b^{5} c^{2} e^{2} - 1750 b^{4} c^{3} d e + 1750 b^{3} c^{4} d^{2}\right) + x^{3} \left(584 a^{3} c^{4} e^{2} + 1684 a^{2} b^{2} c^{3} e^{2} - 4088 a^{2} b c^{4} d e + 4088 a^{2} c^{5} d^{2} + 1236 a b^{4} c^{2} e^{2} - 5656 a b^{3} c^{3} d e + 5656 a b^{2} c^{4} d^{2} + 36 b^{6} c e^{2} - 168 b^{5} c^{2} d e + 168 b^{4} c^{3} d^{2}\right) + x^{2} \left(876 a^{3} b c^{3} e^{2} + 1426 a^{2} b^{3} c^{2} e^{2} - 6132 a^{2} b^{2} c^{3} d e + 6132 a^{2} b c^{4} d^{2} + 164 a b^{5} c e^{2} - 784 a b^{4} c^{2} d e + 784 a b^{3} c^{3} d^{2} - 6 b^{7} e^{2} + 28 b^{6} c d e - 28 b^{5} c^{2} d^{2}\right) + x \left(- 120 a^{4} c^{3} e^{2} + 1116 a^{3} b^{2} c^{2} e^{2} - 2232 a^{3} b c^{3} d e + 2232 a^{3} c^{4} d^{2} + 112 a^{2} b^{4} c e^{2} - 1392 a^{2} b^{3} c^{2} d e + 1392 a^{2} b^{2} c^{3} d^{2} - 4 a b^{6} e^{2} + 152 a b^{5} c d e - 152 a b^{4} c^{2} d^{2} - 8 b^{7} d e + 8 b^{6} c d^{2}\right)}{3072 a^{8} c^{4} - 3072 a^{7} b^{2} c^{3} + 1152 a^{6} b^{4} c^{2} - 192 a^{5} b^{6} c + 12 a^{4} b^{8} + x^{8} \left(3072 a^{4} c^{8} - 3072 a^{3} b^{2} c^{7} + 1152 a^{2} b^{4} c^{6} - 192 a b^{6} c^{5} + 12 b^{8} c^{4}\right) + x^{7} \left(12288 a^{4} b c^{7} - 12288 a^{3} b^{3} c^{6} + 4608 a^{2} b^{5} c^{5} - 768 a b^{7} c^{4} + 48 b^{9} c^{3}\right) + x^{6} \left(12288 a^{5} c^{7} + 6144 a^{4} b^{2} c^{6} - 13824 a^{3} b^{4} c^{5} + 6144 a^{2} b^{6} c^{4} - 1104 a b^{8} c^{3} + 72 b^{10} c^{2}\right) + x^{5} \left(36864 a^{5} b c^{6} - 24576 a^{4} b^{3} c^{5} + 1536 a^{3} b^{5} c^{4} + 2304 a^{2} b^{7} c^{3} - 624 a b^{9} c^{2} + 48 b^{11} c\right) + x^{4} \left(18432 a^{6} c^{6} + 18432 a^{5} b^{2} c^{5} - 26880 a^{4} b^{4} c^{4} + 9600 a^{3} b^{6} c^{3} - 1080 a^{2} b^{8} c^{2} - 48 a b^{10} c + 12 b^{12}\right) + x^{3} \left(36864 a^{6} b c^{5} - 24576 a^{5} b^{3} c^{4} + 1536 a^{4} b^{5} c^{3} + 2304 a^{3} b^{7} c^{2} - 624 a^{2} b^{9} c + 48 a b^{11}\right) + x^{2} \left(12288 a^{7} c^{5} + 6144 a^{6} b^{2} c^{4} - 13824 a^{5} b^{4} c^{3} + 6144 a^{4} b^{6} c^{2} - 1104 a^{3} b^{8} c + 72 a^{2} b^{10}\right) + x \left(12288 a^{7} b c^{4} - 12288 a^{6} b^{3} c^{3} + 4608 a^{5} b^{5} c^{2} - 768 a^{4} b^{7} c + 48 a^{3} b^{9}\right)}"," ",0,"-5*c**2*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2)*log(x + (-5120*a**5*c**7*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) + 6400*a**4*b**2*c**6*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) - 3200*a**3*b**4*c**5*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) + 800*a**2*b**6*c**4*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) - 100*a*b**8*c**3*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) + 10*a*b*c**3*e**2 + 5*b**10*c**2*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) + 15*b**3*c**2*e**2 - 70*b**2*c**3*d*e + 70*b*c**4*d**2)/(20*a*c**4*e**2 + 30*b**2*c**3*e**2 - 140*b*c**4*d*e + 140*c**5*d**2)) + 5*c**2*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2)*log(x + (5120*a**5*c**7*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) - 6400*a**4*b**2*c**6*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) + 3200*a**3*b**4*c**5*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) - 800*a**2*b**6*c**4*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) + 100*a*b**8*c**3*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) + 10*a*b*c**3*e**2 - 5*b**10*c**2*sqrt(-1/(4*a*c - b**2)**9)*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2) + 15*b**3*c**2*e**2 - 70*b**2*c**3*d*e + 70*b*c**4*d**2)/(20*a*c**4*e**2 + 30*b**2*c**3*e**2 - 140*b*c**4*d*e + 140*c**5*d**2)) + (324*a**4*b*c**2*e**2 - 768*a**4*c**3*d*e + 28*a**3*b**3*c*e**2 - 348*a**3*b**2*c**2*d*e + 1116*a**3*b*c**3*d**2 - a**2*b**5*e**2 + 38*a**2*b**4*c*d*e - 326*a**2*b**3*c**2*d**2 - 2*a*b**6*d*e + 50*a*b**5*c*d**2 - 3*b**7*d**2 + x**7*(120*a*c**6*e**2 + 180*b**2*c**5*e**2 - 840*b*c**6*d*e + 840*c**7*d**2) + x**6*(420*a*b*c**5*e**2 + 630*b**3*c**4*e**2 - 2940*b**2*c**5*d*e + 2940*b*c**6*d**2) + x**5*(440*a**2*c**5*e**2 + 1180*a*b**2*c**4*e**2 - 3080*a*b*c**5*d*e + 3080*a*c**6*d**2 + 780*b**4*c**3*e**2 - 3640*b**3*c**4*d*e + 3640*b**2*c**5*d**2) + x**4*(1100*a**2*b*c**4*e**2 + 1900*a*b**3*c**3*e**2 - 7700*a*b**2*c**4*d*e + 7700*a*b*c**5*d**2 + 375*b**5*c**2*e**2 - 1750*b**4*c**3*d*e + 1750*b**3*c**4*d**2) + x**3*(584*a**3*c**4*e**2 + 1684*a**2*b**2*c**3*e**2 - 4088*a**2*b*c**4*d*e + 4088*a**2*c**5*d**2 + 1236*a*b**4*c**2*e**2 - 5656*a*b**3*c**3*d*e + 5656*a*b**2*c**4*d**2 + 36*b**6*c*e**2 - 168*b**5*c**2*d*e + 168*b**4*c**3*d**2) + x**2*(876*a**3*b*c**3*e**2 + 1426*a**2*b**3*c**2*e**2 - 6132*a**2*b**2*c**3*d*e + 6132*a**2*b*c**4*d**2 + 164*a*b**5*c*e**2 - 784*a*b**4*c**2*d*e + 784*a*b**3*c**3*d**2 - 6*b**7*e**2 + 28*b**6*c*d*e - 28*b**5*c**2*d**2) + x*(-120*a**4*c**3*e**2 + 1116*a**3*b**2*c**2*e**2 - 2232*a**3*b*c**3*d*e + 2232*a**3*c**4*d**2 + 112*a**2*b**4*c*e**2 - 1392*a**2*b**3*c**2*d*e + 1392*a**2*b**2*c**3*d**2 - 4*a*b**6*e**2 + 152*a*b**5*c*d*e - 152*a*b**4*c**2*d**2 - 8*b**7*d*e + 8*b**6*c*d**2))/(3072*a**8*c**4 - 3072*a**7*b**2*c**3 + 1152*a**6*b**4*c**2 - 192*a**5*b**6*c + 12*a**4*b**8 + x**8*(3072*a**4*c**8 - 3072*a**3*b**2*c**7 + 1152*a**2*b**4*c**6 - 192*a*b**6*c**5 + 12*b**8*c**4) + x**7*(12288*a**4*b*c**7 - 12288*a**3*b**3*c**6 + 4608*a**2*b**5*c**5 - 768*a*b**7*c**4 + 48*b**9*c**3) + x**6*(12288*a**5*c**7 + 6144*a**4*b**2*c**6 - 13824*a**3*b**4*c**5 + 6144*a**2*b**6*c**4 - 1104*a*b**8*c**3 + 72*b**10*c**2) + x**5*(36864*a**5*b*c**6 - 24576*a**4*b**3*c**5 + 1536*a**3*b**5*c**4 + 2304*a**2*b**7*c**3 - 624*a*b**9*c**2 + 48*b**11*c) + x**4*(18432*a**6*c**6 + 18432*a**5*b**2*c**5 - 26880*a**4*b**4*c**4 + 9600*a**3*b**6*c**3 - 1080*a**2*b**8*c**2 - 48*a*b**10*c + 12*b**12) + x**3*(36864*a**6*b*c**5 - 24576*a**5*b**3*c**4 + 1536*a**4*b**5*c**3 + 2304*a**3*b**7*c**2 - 624*a**2*b**9*c + 48*a*b**11) + x**2*(12288*a**7*c**5 + 6144*a**6*b**2*c**4 - 13824*a**5*b**4*c**3 + 6144*a**4*b**6*c**2 - 1104*a**3*b**8*c + 72*a**2*b**10) + x*(12288*a**7*b*c**4 - 12288*a**6*b**3*c**3 + 4608*a**5*b**5*c**2 - 768*a**4*b**7*c + 48*a**3*b**9))","B",0
2225,1,1564,0,5.283991," ","integrate((e*x+d)/(c*x**2+b*x+a)**5,x)","35 c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \log{\left(x + \frac{- 35840 a^{5} c^{8} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) + 44800 a^{4} b^{2} c^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) - 22400 a^{3} b^{4} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) + 5600 a^{2} b^{6} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) - 700 a b^{8} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) + 35 b^{10} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) + 35 b^{2} c^{3} e - 70 b c^{4} d}{70 b c^{4} e - 140 c^{5} d} \right)} - 35 c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) \log{\left(x + \frac{35840 a^{5} c^{8} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) - 44800 a^{4} b^{2} c^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) + 22400 a^{3} b^{4} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) - 5600 a^{2} b^{6} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) + 700 a b^{8} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) - 35 b^{10} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \left(b e - 2 c d\right) + 35 b^{2} c^{3} e - 70 b c^{4} d}{70 b c^{4} e - 140 c^{5} d} \right)} + \frac{- 384 a^{4} c^{3} e - 174 a^{3} b^{2} c^{2} e + 1116 a^{3} b c^{3} d + 19 a^{2} b^{4} c e - 326 a^{2} b^{3} c^{2} d - a b^{6} e + 50 a b^{5} c d - 3 b^{7} d + x^{7} \left(- 420 b c^{6} e + 840 c^{7} d\right) + x^{6} \left(- 1470 b^{2} c^{5} e + 2940 b c^{6} d\right) + x^{5} \left(- 1540 a b c^{5} e + 3080 a c^{6} d - 1820 b^{3} c^{4} e + 3640 b^{2} c^{5} d\right) + x^{4} \left(- 3850 a b^{2} c^{4} e + 7700 a b c^{5} d - 875 b^{4} c^{3} e + 1750 b^{3} c^{4} d\right) + x^{3} \left(- 2044 a^{2} b c^{4} e + 4088 a^{2} c^{5} d - 2828 a b^{3} c^{3} e + 5656 a b^{2} c^{4} d - 84 b^{5} c^{2} e + 168 b^{4} c^{3} d\right) + x^{2} \left(- 3066 a^{2} b^{2} c^{3} e + 6132 a^{2} b c^{4} d - 392 a b^{4} c^{2} e + 784 a b^{3} c^{3} d + 14 b^{6} c e - 28 b^{5} c^{2} d\right) + x \left(- 1116 a^{3} b c^{3} e + 2232 a^{3} c^{4} d - 696 a^{2} b^{3} c^{2} e + 1392 a^{2} b^{2} c^{3} d + 76 a b^{5} c e - 152 a b^{4} c^{2} d - 4 b^{7} e + 8 b^{6} c d\right)}{3072 a^{8} c^{4} - 3072 a^{7} b^{2} c^{3} + 1152 a^{6} b^{4} c^{2} - 192 a^{5} b^{6} c + 12 a^{4} b^{8} + x^{8} \left(3072 a^{4} c^{8} - 3072 a^{3} b^{2} c^{7} + 1152 a^{2} b^{4} c^{6} - 192 a b^{6} c^{5} + 12 b^{8} c^{4}\right) + x^{7} \left(12288 a^{4} b c^{7} - 12288 a^{3} b^{3} c^{6} + 4608 a^{2} b^{5} c^{5} - 768 a b^{7} c^{4} + 48 b^{9} c^{3}\right) + x^{6} \left(12288 a^{5} c^{7} + 6144 a^{4} b^{2} c^{6} - 13824 a^{3} b^{4} c^{5} + 6144 a^{2} b^{6} c^{4} - 1104 a b^{8} c^{3} + 72 b^{10} c^{2}\right) + x^{5} \left(36864 a^{5} b c^{6} - 24576 a^{4} b^{3} c^{5} + 1536 a^{3} b^{5} c^{4} + 2304 a^{2} b^{7} c^{3} - 624 a b^{9} c^{2} + 48 b^{11} c\right) + x^{4} \left(18432 a^{6} c^{6} + 18432 a^{5} b^{2} c^{5} - 26880 a^{4} b^{4} c^{4} + 9600 a^{3} b^{6} c^{3} - 1080 a^{2} b^{8} c^{2} - 48 a b^{10} c + 12 b^{12}\right) + x^{3} \left(36864 a^{6} b c^{5} - 24576 a^{5} b^{3} c^{4} + 1536 a^{4} b^{5} c^{3} + 2304 a^{3} b^{7} c^{2} - 624 a^{2} b^{9} c + 48 a b^{11}\right) + x^{2} \left(12288 a^{7} c^{5} + 6144 a^{6} b^{2} c^{4} - 13824 a^{5} b^{4} c^{3} + 6144 a^{4} b^{6} c^{2} - 1104 a^{3} b^{8} c + 72 a^{2} b^{10}\right) + x \left(12288 a^{7} b c^{4} - 12288 a^{6} b^{3} c^{3} + 4608 a^{5} b^{5} c^{2} - 768 a^{4} b^{7} c + 48 a^{3} b^{9}\right)}"," ",0,"35*c**3*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*log(x + (-35840*a**5*c**8*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) + 44800*a**4*b**2*c**7*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) - 22400*a**3*b**4*c**6*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) + 5600*a**2*b**6*c**5*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) - 700*a*b**8*c**4*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) + 35*b**10*c**3*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) + 35*b**2*c**3*e - 70*b*c**4*d)/(70*b*c**4*e - 140*c**5*d)) - 35*c**3*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d)*log(x + (35840*a**5*c**8*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) - 44800*a**4*b**2*c**7*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) + 22400*a**3*b**4*c**6*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) - 5600*a**2*b**6*c**5*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) + 700*a*b**8*c**4*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) - 35*b**10*c**3*sqrt(-1/(4*a*c - b**2)**9)*(b*e - 2*c*d) + 35*b**2*c**3*e - 70*b*c**4*d)/(70*b*c**4*e - 140*c**5*d)) + (-384*a**4*c**3*e - 174*a**3*b**2*c**2*e + 1116*a**3*b*c**3*d + 19*a**2*b**4*c*e - 326*a**2*b**3*c**2*d - a*b**6*e + 50*a*b**5*c*d - 3*b**7*d + x**7*(-420*b*c**6*e + 840*c**7*d) + x**6*(-1470*b**2*c**5*e + 2940*b*c**6*d) + x**5*(-1540*a*b*c**5*e + 3080*a*c**6*d - 1820*b**3*c**4*e + 3640*b**2*c**5*d) + x**4*(-3850*a*b**2*c**4*e + 7700*a*b*c**5*d - 875*b**4*c**3*e + 1750*b**3*c**4*d) + x**3*(-2044*a**2*b*c**4*e + 4088*a**2*c**5*d - 2828*a*b**3*c**3*e + 5656*a*b**2*c**4*d - 84*b**5*c**2*e + 168*b**4*c**3*d) + x**2*(-3066*a**2*b**2*c**3*e + 6132*a**2*b*c**4*d - 392*a*b**4*c**2*e + 784*a*b**3*c**3*d + 14*b**6*c*e - 28*b**5*c**2*d) + x*(-1116*a**3*b*c**3*e + 2232*a**3*c**4*d - 696*a**2*b**3*c**2*e + 1392*a**2*b**2*c**3*d + 76*a*b**5*c*e - 152*a*b**4*c**2*d - 4*b**7*e + 8*b**6*c*d))/(3072*a**8*c**4 - 3072*a**7*b**2*c**3 + 1152*a**6*b**4*c**2 - 192*a**5*b**6*c + 12*a**4*b**8 + x**8*(3072*a**4*c**8 - 3072*a**3*b**2*c**7 + 1152*a**2*b**4*c**6 - 192*a*b**6*c**5 + 12*b**8*c**4) + x**7*(12288*a**4*b*c**7 - 12288*a**3*b**3*c**6 + 4608*a**2*b**5*c**5 - 768*a*b**7*c**4 + 48*b**9*c**3) + x**6*(12288*a**5*c**7 + 6144*a**4*b**2*c**6 - 13824*a**3*b**4*c**5 + 6144*a**2*b**6*c**4 - 1104*a*b**8*c**3 + 72*b**10*c**2) + x**5*(36864*a**5*b*c**6 - 24576*a**4*b**3*c**5 + 1536*a**3*b**5*c**4 + 2304*a**2*b**7*c**3 - 624*a*b**9*c**2 + 48*b**11*c) + x**4*(18432*a**6*c**6 + 18432*a**5*b**2*c**5 - 26880*a**4*b**4*c**4 + 9600*a**3*b**6*c**3 - 1080*a**2*b**8*c**2 - 48*a*b**10*c + 12*b**12) + x**3*(36864*a**6*b*c**5 - 24576*a**5*b**3*c**4 + 1536*a**4*b**5*c**3 + 2304*a**3*b**7*c**2 - 624*a**2*b**9*c + 48*a*b**11) + x**2*(12288*a**7*c**5 + 6144*a**6*b**2*c**4 - 13824*a**5*b**4*c**3 + 6144*a**4*b**6*c**2 - 1104*a**3*b**8*c + 72*a**2*b**10) + x*(12288*a**7*b*c**4 - 12288*a**6*b**3*c**3 + 4608*a**5*b**5*c**2 - 768*a**4*b**7*c + 48*a**3*b**9))","B",0
2226,1,1153,0,2.669807," ","integrate(1/(c*x**2+b*x+a)**5,x)","- 70 c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \log{\left(x + \frac{- 71680 a^{5} c^{9} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 89600 a^{4} b^{2} c^{8} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} - 44800 a^{3} b^{4} c^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 11200 a^{2} b^{6} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} - 1400 a b^{8} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 70 b^{10} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 70 b c^{4}}{140 c^{5}} \right)} + 70 c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} \log{\left(x + \frac{71680 a^{5} c^{9} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} - 89600 a^{4} b^{2} c^{8} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 44800 a^{3} b^{4} c^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} - 11200 a^{2} b^{6} c^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 1400 a b^{8} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} - 70 b^{10} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{9}}} + 70 b c^{4}}{140 c^{5}} \right)} + \frac{1116 a^{3} b c^{3} - 326 a^{2} b^{3} c^{2} + 50 a b^{5} c - 3 b^{7} + 2940 b c^{6} x^{6} + 840 c^{7} x^{7} + x^{5} \left(3080 a c^{6} + 3640 b^{2} c^{5}\right) + x^{4} \left(7700 a b c^{5} + 1750 b^{3} c^{4}\right) + x^{3} \left(4088 a^{2} c^{5} + 5656 a b^{2} c^{4} + 168 b^{4} c^{3}\right) + x^{2} \left(6132 a^{2} b c^{4} + 784 a b^{3} c^{3} - 28 b^{5} c^{2}\right) + x \left(2232 a^{3} c^{4} + 1392 a^{2} b^{2} c^{3} - 152 a b^{4} c^{2} + 8 b^{6} c\right)}{3072 a^{8} c^{4} - 3072 a^{7} b^{2} c^{3} + 1152 a^{6} b^{4} c^{2} - 192 a^{5} b^{6} c + 12 a^{4} b^{8} + x^{8} \left(3072 a^{4} c^{8} - 3072 a^{3} b^{2} c^{7} + 1152 a^{2} b^{4} c^{6} - 192 a b^{6} c^{5} + 12 b^{8} c^{4}\right) + x^{7} \left(12288 a^{4} b c^{7} - 12288 a^{3} b^{3} c^{6} + 4608 a^{2} b^{5} c^{5} - 768 a b^{7} c^{4} + 48 b^{9} c^{3}\right) + x^{6} \left(12288 a^{5} c^{7} + 6144 a^{4} b^{2} c^{6} - 13824 a^{3} b^{4} c^{5} + 6144 a^{2} b^{6} c^{4} - 1104 a b^{8} c^{3} + 72 b^{10} c^{2}\right) + x^{5} \left(36864 a^{5} b c^{6} - 24576 a^{4} b^{3} c^{5} + 1536 a^{3} b^{5} c^{4} + 2304 a^{2} b^{7} c^{3} - 624 a b^{9} c^{2} + 48 b^{11} c\right) + x^{4} \left(18432 a^{6} c^{6} + 18432 a^{5} b^{2} c^{5} - 26880 a^{4} b^{4} c^{4} + 9600 a^{3} b^{6} c^{3} - 1080 a^{2} b^{8} c^{2} - 48 a b^{10} c + 12 b^{12}\right) + x^{3} \left(36864 a^{6} b c^{5} - 24576 a^{5} b^{3} c^{4} + 1536 a^{4} b^{5} c^{3} + 2304 a^{3} b^{7} c^{2} - 624 a^{2} b^{9} c + 48 a b^{11}\right) + x^{2} \left(12288 a^{7} c^{5} + 6144 a^{6} b^{2} c^{4} - 13824 a^{5} b^{4} c^{3} + 6144 a^{4} b^{6} c^{2} - 1104 a^{3} b^{8} c + 72 a^{2} b^{10}\right) + x \left(12288 a^{7} b c^{4} - 12288 a^{6} b^{3} c^{3} + 4608 a^{5} b^{5} c^{2} - 768 a^{4} b^{7} c + 48 a^{3} b^{9}\right)}"," ",0,"-70*c**4*sqrt(-1/(4*a*c - b**2)**9)*log(x + (-71680*a**5*c**9*sqrt(-1/(4*a*c - b**2)**9) + 89600*a**4*b**2*c**8*sqrt(-1/(4*a*c - b**2)**9) - 44800*a**3*b**4*c**7*sqrt(-1/(4*a*c - b**2)**9) + 11200*a**2*b**6*c**6*sqrt(-1/(4*a*c - b**2)**9) - 1400*a*b**8*c**5*sqrt(-1/(4*a*c - b**2)**9) + 70*b**10*c**4*sqrt(-1/(4*a*c - b**2)**9) + 70*b*c**4)/(140*c**5)) + 70*c**4*sqrt(-1/(4*a*c - b**2)**9)*log(x + (71680*a**5*c**9*sqrt(-1/(4*a*c - b**2)**9) - 89600*a**4*b**2*c**8*sqrt(-1/(4*a*c - b**2)**9) + 44800*a**3*b**4*c**7*sqrt(-1/(4*a*c - b**2)**9) - 11200*a**2*b**6*c**6*sqrt(-1/(4*a*c - b**2)**9) + 1400*a*b**8*c**5*sqrt(-1/(4*a*c - b**2)**9) - 70*b**10*c**4*sqrt(-1/(4*a*c - b**2)**9) + 70*b*c**4)/(140*c**5)) + (1116*a**3*b*c**3 - 326*a**2*b**3*c**2 + 50*a*b**5*c - 3*b**7 + 2940*b*c**6*x**6 + 840*c**7*x**7 + x**5*(3080*a*c**6 + 3640*b**2*c**5) + x**4*(7700*a*b*c**5 + 1750*b**3*c**4) + x**3*(4088*a**2*c**5 + 5656*a*b**2*c**4 + 168*b**4*c**3) + x**2*(6132*a**2*b*c**4 + 784*a*b**3*c**3 - 28*b**5*c**2) + x*(2232*a**3*c**4 + 1392*a**2*b**2*c**3 - 152*a*b**4*c**2 + 8*b**6*c))/(3072*a**8*c**4 - 3072*a**7*b**2*c**3 + 1152*a**6*b**4*c**2 - 192*a**5*b**6*c + 12*a**4*b**8 + x**8*(3072*a**4*c**8 - 3072*a**3*b**2*c**7 + 1152*a**2*b**4*c**6 - 192*a*b**6*c**5 + 12*b**8*c**4) + x**7*(12288*a**4*b*c**7 - 12288*a**3*b**3*c**6 + 4608*a**2*b**5*c**5 - 768*a*b**7*c**4 + 48*b**9*c**3) + x**6*(12288*a**5*c**7 + 6144*a**4*b**2*c**6 - 13824*a**3*b**4*c**5 + 6144*a**2*b**6*c**4 - 1104*a*b**8*c**3 + 72*b**10*c**2) + x**5*(36864*a**5*b*c**6 - 24576*a**4*b**3*c**5 + 1536*a**3*b**5*c**4 + 2304*a**2*b**7*c**3 - 624*a*b**9*c**2 + 48*b**11*c) + x**4*(18432*a**6*c**6 + 18432*a**5*b**2*c**5 - 26880*a**4*b**4*c**4 + 9600*a**3*b**6*c**3 - 1080*a**2*b**8*c**2 - 48*a*b**10*c + 12*b**12) + x**3*(36864*a**6*b*c**5 - 24576*a**5*b**3*c**4 + 1536*a**4*b**5*c**3 + 2304*a**3*b**7*c**2 - 624*a**2*b**9*c + 48*a*b**11) + x**2*(12288*a**7*c**5 + 6144*a**6*b**2*c**4 - 13824*a**5*b**4*c**3 + 6144*a**4*b**6*c**2 - 1104*a**3*b**8*c + 72*a**2*b**10) + x*(12288*a**7*b*c**4 - 12288*a**6*b**3*c**3 + 4608*a**5*b**5*c**2 - 768*a**4*b**7*c + 48*a**3*b**9))","B",0
2227,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2228,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2229,1,90,0,0.251210," ","integrate(1/(1+2*x)/(5*x**2+3*x+2)**3,x)","\frac{45800 x^{3} + 79660 x^{2} + 53968 x + 28901}{2354450 x^{4} + 2825340 x^{3} + 2731162 x^{2} + 1130136 x + 376712} + \frac{32 \log{\left(x + \frac{1}{2} \right)}}{343} - \frac{16 \log{\left(x^{2} + \frac{3 x}{5} + \frac{2}{5} \right)}}{343} + \frac{125624 \sqrt{31} \operatorname{atan}{\left(\frac{10 \sqrt{31} x}{31} + \frac{3 \sqrt{31}}{31} \right)}}{10218313}"," ",0,"(45800*x**3 + 79660*x**2 + 53968*x + 28901)/(2354450*x**4 + 2825340*x**3 + 2731162*x**2 + 1130136*x + 376712) + 32*log(x + 1/2)/343 - 16*log(x**2 + 3*x/5 + 2/5)/343 + 125624*sqrt(31)*atan(10*sqrt(31)*x/31 + 3*sqrt(31)/31)/10218313","A",0
2230,1,102,0,0.274559," ","integrate(1/(1+2*x)**2/(5*x**2+3*x+2)**3,x)","\frac{- 2575800 x^{4} - 2683560 x^{3} - 2293598 x^{2} - 773110 x - 175969}{32962300 x^{5} + 56035910 x^{4} + 58013648 x^{3} + 34940038 x^{2} + 13184920 x + 2636984} + \frac{384 \log{\left(x + \frac{1}{2} \right)}}{2401} - \frac{192 \log{\left(x^{2} + \frac{3 x}{5} + \frac{2}{5} \right)}}{2401} - \frac{1065012 \sqrt{31} \operatorname{atan}{\left(\frac{10 \sqrt{31} x}{31} + \frac{3 \sqrt{31}}{31} \right)}}{71528191}"," ",0,"(-2575800*x**4 - 2683560*x**3 - 2293598*x**2 - 773110*x - 175969)/(32962300*x**5 + 56035910*x**4 + 58013648*x**3 + 34940038*x**2 + 13184920*x + 2636984) + 384*log(x + 1/2)/2401 - 192*log(x**2 + 3*x/5 + 2/5)/2401 - 1065012*sqrt(31)*atan(10*sqrt(31)*x/31 + 3*sqrt(31)/31)/71528191","A",0
2231,1,110,0,0.290811," ","integrate(1/(1+2*x)/(5*x**2+3*x+2)**4,x)","\frac{60969000 x^{5} + 127202700 x^{4} + 143405620 x^{3} + 105257844 x^{2} + 44933184 x + 13831165}{3831867375 x^{6} + 6897361275 x^{5} + 8736657615 x^{4} + 6345572373 x^{3} + 3494663046 x^{2} + 1103577804 x + 245239512} + \frac{128 \log{\left(x + \frac{1}{2} \right)}}{2401} - \frac{64 \log{\left(x^{2} + \frac{3 x}{5} + \frac{2}{5} \right)}}{2401} + \frac{19007376 \sqrt{31} \operatorname{atan}{\left(\frac{10 \sqrt{31} x}{31} + \frac{3 \sqrt{31}}{31} \right)}}{2217373921}"," ",0,"(60969000*x**5 + 127202700*x**4 + 143405620*x**3 + 105257844*x**2 + 44933184*x + 13831165)/(3831867375*x**6 + 6897361275*x**5 + 8736657615*x**4 + 6345572373*x**3 + 3494663046*x**2 + 1103577804*x + 245239512) + 128*log(x + 1/2)/2401 - 64*log(x**2 + 3*x/5 + 2/5)/2401 + 19007376*sqrt(31)*atan(10*sqrt(31)*x/31 + 3*sqrt(31)/31)/2217373921","A",0
2232,1,122,0,0.309710," ","integrate(1/(1+2*x)**2/(5*x**2+3*x+2)**4,x)","\frac{- 2550867000 x^{6} - 3957759600 x^{5} - 4525420710 x^{4} - 2788779072 x^{3} - 1299394083 x^{2} - 304894531 x - 38489903}{53646143250 x^{7} + 123386129475 x^{6} + 170594735535 x^{5} + 149994616527 x^{4} + 93344289255 x^{3} + 39912730578 x^{2} + 11158397796 x + 1716676584} + \frac{2048 \log{\left(x + \frac{1}{2} \right)}}{16807} - \frac{1024 \log{\left(x^{2} + \frac{3 x}{5} + \frac{2}{5} \right)}}{16807} - \frac{116056984 \sqrt{31} \operatorname{atan}{\left(\frac{10 \sqrt{31} x}{31} + \frac{3 \sqrt{31}}{31} \right)}}{15521617447}"," ",0,"(-2550867000*x**6 - 3957759600*x**5 - 4525420710*x**4 - 2788779072*x**3 - 1299394083*x**2 - 304894531*x - 38489903)/(53646143250*x**7 + 123386129475*x**6 + 170594735535*x**5 + 149994616527*x**4 + 93344289255*x**3 + 39912730578*x**2 + 11158397796*x + 1716676584) + 2048*log(x + 1/2)/16807 - 1024*log(x**2 + 3*x/5 + 2/5)/16807 - 116056984*sqrt(31)*atan(10*sqrt(31)*x/31 + 3*sqrt(31)/31)/15521617447","A",0
2233,1,44,0,0.120287," ","integrate((7-3*x)/(x**2+2*x-5),x)","- \left(\frac{3}{2} + \frac{5 \sqrt{6}}{6}\right) \log{\left(x + 1 + \sqrt{6} \right)} - \left(\frac{3}{2} - \frac{5 \sqrt{6}}{6}\right) \log{\left(x - \sqrt{6} + 1 \right)}"," ",0,"-(3/2 + 5*sqrt(6)/6)*log(x + 1 + sqrt(6)) - (3/2 - 5*sqrt(6)/6)*log(x - sqrt(6) + 1)","A",0
2234,1,41,0,0.143627," ","integrate(1/(-1+x)/(x**2+x+1),x)","\frac{\log{\left(x - 1 \right)}}{3} - \frac{\log{\left(x^{2} + x + 1 \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"log(x - 1)/3 - log(x**2 + x + 1)/6 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3","A",0
2235,1,177,0,0.866252," ","integrate(2*((a/b)**(1/n)-x*cos((-1+2*k)*pi/n))/((a/b)**(2/n)+x**2-2*(a/b)**(1/n)*x*cos((-1+2*k)*pi/n)),x)","- \left(- \sqrt{\left(\cos{\left(\frac{\pi \left(2 k - 1\right)}{n} \right)} - 1\right) \left(\cos{\left(\frac{\pi \left(2 k - 1\right)}{n} \right)} + 1\right)} + \cos{\left(\frac{2 \pi k}{n} - \frac{\pi}{n} \right)}\right) \log{\left(x - \left(\frac{a}{b}\right)^{\frac{1}{n}} \left(- \sqrt{\left(\cos{\left(\frac{\pi \left(2 k - 1\right)}{n} \right)} - 1\right) \left(\cos{\left(\frac{\pi \left(2 k - 1\right)}{n} \right)} + 1\right)} + \cos{\left(\frac{2 \pi k}{n} - \frac{\pi}{n} \right)}\right) \right)} - \left(\sqrt{\left(\cos{\left(\frac{\pi \left(2 k - 1\right)}{n} \right)} - 1\right) \left(\cos{\left(\frac{\pi \left(2 k - 1\right)}{n} \right)} + 1\right)} + \cos{\left(\frac{2 \pi k}{n} - \frac{\pi}{n} \right)}\right) \log{\left(x - \left(\frac{a}{b}\right)^{\frac{1}{n}} \left(\sqrt{\left(\cos{\left(\frac{\pi \left(2 k - 1\right)}{n} \right)} - 1\right) \left(\cos{\left(\frac{\pi \left(2 k - 1\right)}{n} \right)} + 1\right)} + \cos{\left(\frac{2 \pi k}{n} - \frac{\pi}{n} \right)}\right) \right)}"," ",0,"-(-sqrt((cos(pi*(2*k - 1)/n) - 1)*(cos(pi*(2*k - 1)/n) + 1)) + cos(2*pi*k/n - pi/n))*log(x - (a/b)**(1/n)*(-sqrt((cos(pi*(2*k - 1)/n) - 1)*(cos(pi*(2*k - 1)/n) + 1)) + cos(2*pi*k/n - pi/n))) - (sqrt((cos(pi*(2*k - 1)/n) - 1)*(cos(pi*(2*k - 1)/n) + 1)) + cos(2*pi*k/n - pi/n))*log(x - (a/b)**(1/n)*(sqrt((cos(pi*(2*k - 1)/n) - 1)*(cos(pi*(2*k - 1)/n) + 1)) + cos(2*pi*k/n - pi/n)))","A",0
2236,1,34,0,0.111837," ","integrate(x**4/(15*x**2+13*x+2),x)","\frac{x^{3}}{45} - \frac{13 x^{2}}{450} + \frac{139 x}{3375} + \frac{\log{\left(x + \frac{1}{5} \right)}}{4375} - \frac{16 \log{\left(x + \frac{2}{3} \right)}}{567}"," ",0,"x**3/45 - 13*x**2/450 + 139*x/3375 + log(x + 1/5)/4375 - 16*log(x + 2/3)/567","A",0
2237,1,27,0,0.113234," ","integrate(x**3/(15*x**2+13*x+2),x)","\frac{x^{2}}{30} - \frac{13 x}{225} - \frac{\log{\left(x + \frac{1}{5} \right)}}{875} + \frac{8 \log{\left(x + \frac{2}{3} \right)}}{189}"," ",0,"x**2/30 - 13*x/225 - log(x + 1/5)/875 + 8*log(x + 2/3)/189","A",0
2238,1,20,0,0.111130," ","integrate(x**2/(15*x**2+13*x+2),x)","\frac{x}{15} + \frac{\log{\left(x + \frac{1}{5} \right)}}{175} - \frac{4 \log{\left(x + \frac{2}{3} \right)}}{63}"," ",0,"x/15 + log(x + 1/5)/175 - 4*log(x + 2/3)/63","A",0
2239,1,17,0,0.104036," ","integrate(x/(15*x**2+13*x+2),x)","- \frac{\log{\left(x + \frac{1}{5} \right)}}{35} + \frac{2 \log{\left(x + \frac{2}{3} \right)}}{21}"," ",0,"-log(x + 1/5)/35 + 2*log(x + 2/3)/21","A",0
2240,1,15,0,0.103659," ","integrate(1/(15*x**2+13*x+2),x)","\frac{\log{\left(x + \frac{1}{5} \right)}}{7} - \frac{\log{\left(x + \frac{2}{3} \right)}}{7}"," ",0,"log(x + 1/5)/7 - log(x + 2/3)/7","A",0
2241,1,24,0,0.140800," ","integrate(1/x/(15*x**2+13*x+2),x)","\frac{\log{\left(x \right)}}{2} - \frac{5 \log{\left(x + \frac{1}{5} \right)}}{7} + \frac{3 \log{\left(x + \frac{2}{3} \right)}}{14}"," ",0,"log(x)/2 - 5*log(x + 1/5)/7 + 3*log(x + 2/3)/14","A",0
2242,1,31,0,0.157366," ","integrate(1/x**2/(15*x**2+13*x+2),x)","- \frac{13 \log{\left(x \right)}}{4} + \frac{25 \log{\left(x + \frac{1}{5} \right)}}{7} - \frac{9 \log{\left(x + \frac{2}{3} \right)}}{28} - \frac{1}{2 x}"," ",0,"-13*log(x)/4 + 25*log(x + 1/5)/7 - 9*log(x + 2/3)/28 - 1/(2*x)","A",0
2243,1,36,0,0.166842," ","integrate(1/x**3/(15*x**2+13*x+2),x)","\frac{139 \log{\left(x \right)}}{8} - \frac{125 \log{\left(x + \frac{1}{5} \right)}}{7} + \frac{27 \log{\left(x + \frac{2}{3} \right)}}{56} + \frac{13 x - 1}{4 x^{2}}"," ",0,"139*log(x)/8 - 125*log(x + 1/5)/7 + 27*log(x + 2/3)/56 + (13*x - 1)/(4*x**2)","A",0
2244,1,41,0,0.176082," ","integrate(1/x**4/(15*x**2+13*x+2),x)","- \frac{1417 \log{\left(x \right)}}{16} + \frac{625 \log{\left(x + \frac{1}{5} \right)}}{7} - \frac{81 \log{\left(x + \frac{2}{3} \right)}}{112} + \frac{- 417 x^{2} + 39 x - 4}{24 x^{3}}"," ",0,"-1417*log(x)/16 + 625*log(x + 1/5)/7 - 81*log(x + 2/3)/112 + (-417*x**2 + 39*x - 4)/(24*x**3)","A",0
2245,1,34,0,0.119209," ","integrate(x**5/(15*x**3+13*x**2+2*x),x)","\frac{x^{3}}{45} - \frac{13 x^{2}}{450} + \frac{139 x}{3375} + \frac{\log{\left(x + \frac{1}{5} \right)}}{4375} - \frac{16 \log{\left(x + \frac{2}{3} \right)}}{567}"," ",0,"x**3/45 - 13*x**2/450 + 139*x/3375 + log(x + 1/5)/4375 - 16*log(x + 2/3)/567","A",0
2246,1,27,0,0.117421," ","integrate(x**4/(15*x**3+13*x**2+2*x),x)","\frac{x^{2}}{30} - \frac{13 x}{225} - \frac{\log{\left(x + \frac{1}{5} \right)}}{875} + \frac{8 \log{\left(x + \frac{2}{3} \right)}}{189}"," ",0,"x**2/30 - 13*x/225 - log(x + 1/5)/875 + 8*log(x + 2/3)/189","A",0
2247,1,20,0,0.116751," ","integrate(x**3/(15*x**3+13*x**2+2*x),x)","\frac{x}{15} + \frac{\log{\left(x + \frac{1}{5} \right)}}{175} - \frac{4 \log{\left(x + \frac{2}{3} \right)}}{63}"," ",0,"x/15 + log(x + 1/5)/175 - 4*log(x + 2/3)/63","A",0
2248,1,17,0,0.107860," ","integrate(x**2/(15*x**3+13*x**2+2*x),x)","- \frac{\log{\left(x + \frac{1}{5} \right)}}{35} + \frac{2 \log{\left(x + \frac{2}{3} \right)}}{21}"," ",0,"-log(x + 1/5)/35 + 2*log(x + 2/3)/21","A",0
2249,1,15,0,0.109565," ","integrate(x/(15*x**3+13*x**2+2*x),x)","\frac{\log{\left(x + \frac{1}{5} \right)}}{7} - \frac{\log{\left(x + \frac{2}{3} \right)}}{7}"," ",0,"log(x + 1/5)/7 - log(x + 2/3)/7","A",0
2250,1,24,0,0.139525," ","integrate(1/(15*x**3+13*x**2+2*x),x)","\frac{\log{\left(x \right)}}{2} - \frac{5 \log{\left(x + \frac{1}{5} \right)}}{7} + \frac{3 \log{\left(x + \frac{2}{3} \right)}}{14}"," ",0,"log(x)/2 - 5*log(x + 1/5)/7 + 3*log(x + 2/3)/14","A",0
2251,1,31,0,0.156369," ","integrate(1/x/(15*x**3+13*x**2+2*x),x)","- \frac{13 \log{\left(x \right)}}{4} + \frac{25 \log{\left(x + \frac{1}{5} \right)}}{7} - \frac{9 \log{\left(x + \frac{2}{3} \right)}}{28} - \frac{1}{2 x}"," ",0,"-13*log(x)/4 + 25*log(x + 1/5)/7 - 9*log(x + 2/3)/28 - 1/(2*x)","A",0
2252,1,36,0,0.169251," ","integrate(1/x**2/(15*x**3+13*x**2+2*x),x)","\frac{139 \log{\left(x \right)}}{8} - \frac{125 \log{\left(x + \frac{1}{5} \right)}}{7} + \frac{27 \log{\left(x + \frac{2}{3} \right)}}{56} + \frac{13 x - 1}{4 x^{2}}"," ",0,"139*log(x)/8 - 125*log(x + 1/5)/7 + 27*log(x + 2/3)/56 + (13*x - 1)/(4*x**2)","A",0
2253,1,41,0,0.176364," ","integrate(1/x**3/(15*x**3+13*x**2+2*x),x)","- \frac{1417 \log{\left(x \right)}}{16} + \frac{625 \log{\left(x + \frac{1}{5} \right)}}{7} - \frac{81 \log{\left(x + \frac{2}{3} \right)}}{112} + \frac{- 417 x^{2} + 39 x - 4}{24 x^{3}}"," ",0,"-1417*log(x)/16 + 625*log(x + 1/5)/7 - 81*log(x + 2/3)/112 + (-417*x**2 + 39*x - 4)/(24*x**3)","A",0
2254,1,8,0,0.080789," ","integrate(x/(x**2+4*x+4),x)","\log{\left(x + 2 \right)} + \frac{2}{x + 2}"," ",0,"log(x + 2) + 2/(x + 2)","A",0
2255,1,20,0,0.104169," ","integrate(x/(x**2+2*x+5),x)","\frac{\log{\left(x^{2} + 2 x + 5 \right)}}{2} - \frac{\operatorname{atan}{\left(\frac{x}{2} + \frac{1}{2} \right)}}{2}"," ",0,"log(x**2 + 2*x + 5)/2 - atan(x/2 + 1/2)/2","A",0
2256,1,12,0,0.101760," ","integrate(x/(x**2-5*x+6),x)","3 \log{\left(x - 3 \right)} - 2 \log{\left(x - 2 \right)}"," ",0,"3*log(x - 3) - 2*log(x - 2)","A",0
2257,1,20,0,0.114298," ","integrate(x/(x**2+2*x+2)**2,x)","\frac{- x - 2}{2 x^{2} + 4 x + 4} - \frac{\operatorname{atan}{\left(x + 1 \right)}}{2}"," ",0,"(-x - 2)/(2*x**2 + 4*x + 4) - atan(x + 1)/2","A",0
2258,1,63,0,0.144465," ","integrate(x/(x**2+x+1)**3,x)","\frac{- 2 x^{3} - 3 x^{2} - 4 x - 3}{6 x^{4} + 12 x^{3} + 18 x^{2} + 12 x + 6} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"(-2*x**3 - 3*x**2 - 4*x - 3)/(6*x**4 + 12*x**3 + 18*x**2 + 12*x + 6) - 2*sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/9","A",0
2259,1,36,0,0.113059," ","integrate(x**2/(x**2+x+1),x)","x - \frac{\log{\left(x^{2} + x + 1 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"x - log(x**2 + x + 1)/2 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3","A",0
2260,1,12,0,0.104469," ","integrate(x**2/(x**2-3*x+2),x)","x + 4 \log{\left(x - 2 \right)} - \log{\left(x - 1 \right)}"," ",0,"x + 4*log(x - 2) - log(x - 1)","A",0
2261,1,17,0,0.105101," ","integrate(x**2/(x**2+x-6),x)","x + \frac{4 \log{\left(x - 2 \right)}}{5} - \frac{9 \log{\left(x + 3 \right)}}{5}"," ",0,"x + 4*log(x - 2)/5 - 9*log(x + 3)/5","A",0
2262,1,14,0,0.110418," ","integrate(x**2/(x**2+2*x+2)**2,x)","\operatorname{atan}{\left(x + 1 \right)} + \frac{1}{x^{2} + 2 x + 2}"," ",0,"atan(x + 1) + 1/(x**2 + 2*x + 2)","A",0
2263,1,19,0,0.106090," ","integrate(x**3/(x**2-3*x+2),x)","\frac{x^{2}}{2} + 3 x + 8 \log{\left(x - 2 \right)} - \log{\left(x - 1 \right)}"," ",0,"x**2/2 + 3*x + 8*log(x - 2) - log(x - 1)","A",0
2264,1,19,0,0.080719," ","integrate(x**3/(x**2+2*x+1),x)","\frac{x^{2}}{2} - 2 x + 3 \log{\left(x + 1 \right)} + \frac{1}{x + 1}"," ",0,"x**2/2 - 2*x + 3*log(x + 1) + 1/(x + 1)","A",0
2265,1,19,0,0.081596," ","integrate(x**3/(x**2-2*x+1),x)","\frac{x^{2}}{2} + 2 x + 3 \log{\left(x - 1 \right)} - \frac{1}{x - 1}"," ",0,"x**2/2 + 2*x + 3*log(x - 1) - 1/(x - 1)","A",0
2266,1,24,0,0.083869," ","integrate(x**4/(x**2+4*x+4),x)","\frac{x^{3}}{3} - 2 x^{2} + 12 x - 32 \log{\left(x + 2 \right)} - \frac{16}{x + 2}"," ",0,"x**3/3 - 2*x**2 + 12*x - 32*log(x + 2) - 16/(x + 2)","A",0
2267,1,37,0,0.140256," ","integrate(1/x/(x**2+x+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{2} + x + 1 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"log(x) - log(x**2 + x + 1)/2 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3","A",0
2268,1,326,0,3.543186," ","integrate((e*x+d)**(5/2)*(c*x**2+b*x+a),x)","\begin{cases} \frac{2 a d^{3} \sqrt{d + e x}}{7 e} + \frac{6 a d^{2} x \sqrt{d + e x}}{7} + \frac{6 a d e x^{2} \sqrt{d + e x}}{7} + \frac{2 a e^{2} x^{3} \sqrt{d + e x}}{7} - \frac{4 b d^{4} \sqrt{d + e x}}{63 e^{2}} + \frac{2 b d^{3} x \sqrt{d + e x}}{63 e} + \frac{10 b d^{2} x^{2} \sqrt{d + e x}}{21} + \frac{38 b d e x^{3} \sqrt{d + e x}}{63} + \frac{2 b e^{2} x^{4} \sqrt{d + e x}}{9} + \frac{16 c d^{5} \sqrt{d + e x}}{693 e^{3}} - \frac{8 c d^{4} x \sqrt{d + e x}}{693 e^{2}} + \frac{2 c d^{3} x^{2} \sqrt{d + e x}}{231 e} + \frac{226 c d^{2} x^{3} \sqrt{d + e x}}{693} + \frac{46 c d e x^{4} \sqrt{d + e x}}{99} + \frac{2 c e^{2} x^{5} \sqrt{d + e x}}{11} & \text{for}\: e \neq 0 \\d^{\frac{5}{2}} \left(a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*d**3*sqrt(d + e*x)/(7*e) + 6*a*d**2*x*sqrt(d + e*x)/7 + 6*a*d*e*x**2*sqrt(d + e*x)/7 + 2*a*e**2*x**3*sqrt(d + e*x)/7 - 4*b*d**4*sqrt(d + e*x)/(63*e**2) + 2*b*d**3*x*sqrt(d + e*x)/(63*e) + 10*b*d**2*x**2*sqrt(d + e*x)/21 + 38*b*d*e*x**3*sqrt(d + e*x)/63 + 2*b*e**2*x**4*sqrt(d + e*x)/9 + 16*c*d**5*sqrt(d + e*x)/(693*e**3) - 8*c*d**4*x*sqrt(d + e*x)/(693*e**2) + 2*c*d**3*x**2*sqrt(d + e*x)/(231*e) + 226*c*d**2*x**3*sqrt(d + e*x)/693 + 46*c*d*e*x**4*sqrt(d + e*x)/99 + 2*c*e**2*x**5*sqrt(d + e*x)/11, Ne(e, 0)), (d**(5/2)*(a*x + b*x**2/2 + c*x**3/3), True))","A",0
2269,1,230,0,10.366452," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x+a),x)","a d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{2 b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}}"," ",0,"a*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 2*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3","A",0
2270,1,71,0,3.034889," ","integrate((c*x**2+b*x+a)*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{c \left(d + e x\right)^{\frac{7}{2}}}{7 e^{2}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(b e - 2 c d\right)}{5 e^{2}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a e^{2} - b d e + c d^{2}\right)}{3 e^{2}}\right)}{e}"," ",0,"2*(c*(d + e*x)**(7/2)/(7*e**2) + (d + e*x)**(5/2)*(b*e - 2*c*d)/(5*e**2) + (d + e*x)**(3/2)*(a*e**2 - b*d*e + c*d**2)/(3*e**2))/e","A",0
2271,1,223,0,10.767626," ","integrate((c*x**2+b*x+a)/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a d}{\sqrt{d + e x}} - 2 a \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{2 b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{2 b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{2 c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}}}{e} & \text{for}\: e \neq 0 \\\frac{a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*d/sqrt(d + e*x) - 2*a*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 2*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 2*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 2*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2)/e, Ne(e, 0)), ((a*x + b*x**2/2 + c*x**3/3)/sqrt(d), True))","A",0
2272,1,70,0,13.066445," ","integrate((c*x**2+b*x+a)/(e*x+d)**(3/2),x)","\frac{2 c \left(d + e x\right)^{\frac{3}{2}}}{3 e^{3}} + \frac{\sqrt{d + e x} \left(2 b e - 4 c d\right)}{e^{3}} - \frac{2 \left(a e^{2} - b d e + c d^{2}\right)}{e^{3} \sqrt{d + e x}}"," ",0,"2*c*(d + e*x)**(3/2)/(3*e**3) + sqrt(d + e*x)*(2*b*e - 4*c*d)/e**3 - 2*(a*e**2 - b*d*e + c*d**2)/(e**3*sqrt(d + e*x))","A",0
2273,1,252,0,1.238907," ","integrate((c*x**2+b*x+a)/(e*x+d)**(5/2),x)","\begin{cases} - \frac{2 a e^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} - \frac{4 b d e}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} - \frac{6 b e^{2} x}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{16 c d^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{24 c d e x}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} + \frac{6 c e^{2} x^{2}}{3 d e^{3} \sqrt{d + e x} + 3 e^{4} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3}}{d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*e**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) - 4*b*d*e/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) - 6*b*e**2*x/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 16*c*d**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 24*c*d*e*x/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)) + 6*c*e**2*x**2/(3*d*e**3*sqrt(d + e*x) + 3*e**4*x*sqrt(d + e*x)), Ne(e, 0)), ((a*x + b*x**2/2 + c*x**3/3)/d**(5/2), True))","A",0
2274,1,376,0,2.846548," ","integrate((c*x**2+b*x+a)/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 a e^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{4 b d e}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{10 b e^{2} x}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{16 c d^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{40 c d e x}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} - \frac{30 c e^{2} x^{2}}{15 d^{2} e^{3} \sqrt{d + e x} + 30 d e^{4} x \sqrt{d + e x} + 15 e^{5} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a*e**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 4*b*d*e/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 10*b*e**2*x/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 16*c*d**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 40*c*d*e*x/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)) - 30*c*e**2*x**2/(15*d**2*e**3*sqrt(d + e*x) + 30*d*e**4*x*sqrt(d + e*x) + 15*e**5*x**2*sqrt(d + e*x)), Ne(e, 0)), ((a*x + b*x**2/2 + c*x**3/3)/d**(7/2), True))","A",0
2275,1,1129,0,41.426914," ","integrate((e*x+d)**(5/2)*(c*x**2+b*x+a)**2,x)","a^{2} d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 a^{2} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 a^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{4 a b d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{8 a b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{4 a b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{4 a c d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{8 a c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{4 a c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{2 b^{2} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{4 b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{4 b c d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{8 b c d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{4 b c \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{2 c^{2} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{4 c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}}"," ",0,"a**2*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a**2*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*a**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 4*a*b*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 8*a*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 4*a*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 4*a*c*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 8*a*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 4*a*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 2*b**2*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 4*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 4*b*c*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 8*b*c*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 4*b*c*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 2*c**2*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 4*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5","A",0
2276,1,654,0,24.739416," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x+a)**2,x)","a^{2} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{4 a b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{4 a b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{4 a c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{4 a c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{4 b c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{4 b c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 c^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{2 c^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}}"," ",0,"a**2*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 4*a*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 4*a*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 4*a*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 4*a*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 4*b*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 4*b*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*c**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 2*c**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5","A",0
2277,1,230,0,5.141635," ","integrate((c*x**2+b*x+a)**2*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{c^{2} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{4}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(2 b c e - 4 c^{2} d\right)}{9 e^{4}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right)}{7 e^{4}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(2 a b e^{3} - 4 a c d e^{2} - 2 b^{2} d e^{2} + 6 b c d^{2} e - 4 c^{2} d^{3}\right)}{5 e^{4}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{2} e^{4} - 2 a b d e^{3} + 2 a c d^{2} e^{2} + b^{2} d^{2} e^{2} - 2 b c d^{3} e + c^{2} d^{4}\right)}{3 e^{4}}\right)}{e}"," ",0,"2*(c**2*(d + e*x)**(11/2)/(11*e**4) + (d + e*x)**(9/2)*(2*b*c*e - 4*c**2*d)/(9*e**4) + (d + e*x)**(7/2)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2)/(7*e**4) + (d + e*x)**(5/2)*(2*a*b*e**3 - 4*a*c*d*e**2 - 2*b**2*d*e**2 + 6*b*c*d**2*e - 4*c**2*d**3)/(5*e**4) + (d + e*x)**(3/2)*(a**2*e**4 - 2*a*b*d*e**3 + 2*a*c*d**2*e**2 + b**2*d**2*e**2 - 2*b*c*d**3*e + c**2*d**4)/(3*e**4))/e","A",0
2278,1,644,0,67.248019," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{2} d}{\sqrt{d + e x}} - 2 a^{2} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{4 a b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{4 a b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{4 a c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{4 a c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{2 b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{4 b c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{4 b c \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{2 c^{2} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{2 c^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}}}{e} & \text{for}\: e \neq 0 \\\frac{a^{2} x + a b x^{2} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5} + \frac{x^{3} \left(2 a c + b^{2}\right)}{3}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**2*d/sqrt(d + e*x) - 2*a**2*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 4*a*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 4*a*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 4*a*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 4*a*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 2*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 4*b*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 4*b*c*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 2*c**2*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 2*c**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4)/e, Ne(e, 0)), ((a**2*x + a*b*x**2 + b*c*x**4/2 + c**2*x**5/5 + x**3*(2*a*c + b**2)/3)/sqrt(d), True))","A",0
2279,1,182,0,41.910098," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**(3/2),x)","\frac{2 c^{2} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{5}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(4 b c e - 8 c^{2} d\right)}{5 e^{5}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(4 a c e^{2} + 2 b^{2} e^{2} - 12 b c d e + 12 c^{2} d^{2}\right)}{3 e^{5}} + \frac{\sqrt{d + e x} \left(4 a b e^{3} - 8 a c d e^{2} - 4 b^{2} d e^{2} + 12 b c d^{2} e - 8 c^{2} d^{3}\right)}{e^{5}} - \frac{2 \left(a e^{2} - b d e + c d^{2}\right)^{2}}{e^{5} \sqrt{d + e x}}"," ",0,"2*c**2*(d + e*x)**(7/2)/(7*e**5) + (d + e*x)**(5/2)*(4*b*c*e - 8*c**2*d)/(5*e**5) + (d + e*x)**(3/2)*(4*a*c*e**2 + 2*b**2*e**2 - 12*b*c*d*e + 12*c**2*d**2)/(3*e**5) + sqrt(d + e*x)*(4*a*b*e**3 - 8*a*c*d*e**2 - 4*b**2*d*e**2 + 12*b*c*d**2*e - 8*c**2*d**3)/e**5 - 2*(a*e**2 - b*d*e + c*d**2)**2/(e**5*sqrt(d + e*x))","A",0
2280,1,160,0,66.240282," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**(5/2),x)","\frac{2 c^{2} \left(d + e x\right)^{\frac{5}{2}}}{5 e^{5}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(4 b c e - 8 c^{2} d\right)}{3 e^{5}} + \frac{\sqrt{d + e x} \left(4 a c e^{2} + 2 b^{2} e^{2} - 12 b c d e + 12 c^{2} d^{2}\right)}{e^{5}} - \frac{4 \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right)}{e^{5} \sqrt{d + e x}} - \frac{2 \left(a e^{2} - b d e + c d^{2}\right)^{2}}{3 e^{5} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"2*c**2*(d + e*x)**(5/2)/(5*e**5) + (d + e*x)**(3/2)*(4*b*c*e - 8*c**2*d)/(3*e**5) + sqrt(d + e*x)*(4*a*c*e**2 + 2*b**2*e**2 - 12*b*c*d*e + 12*c**2*d**2)/e**5 - 4*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)/(e**5*sqrt(d + e*x)) - 2*(a*e**2 - b*d*e + c*d**2)**2/(3*e**5*(d + e*x)**(3/2))","A",0
2281,1,1180,0,4.424287," ","integrate((c*x**2+b*x+a)**2/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 a^{2} e^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{8 a b d e^{3}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{20 a b e^{4} x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{32 a c d^{2} e^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{80 a c d e^{3} x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{60 a c e^{4} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{16 b^{2} d^{2} e^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{40 b^{2} d e^{3} x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{30 b^{2} e^{4} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{192 b c d^{3} e}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{480 b c d^{2} e^{2} x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{360 b c d e^{3} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{60 b c e^{4} x^{3}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{256 c^{2} d^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{640 c^{2} d^{3} e x}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{480 c^{2} d^{2} e^{2} x^{2}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} - \frac{80 c^{2} d e^{3} x^{3}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} + \frac{10 c^{2} e^{4} x^{4}}{15 d^{2} e^{5} \sqrt{d + e x} + 30 d e^{6} x \sqrt{d + e x} + 15 e^{7} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a^{2} x + a b x^{2} + \frac{2 a c x^{3}}{3} + \frac{b^{2} x^{3}}{3} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a**2*e**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 8*a*b*d*e**3/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 20*a*b*e**4*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 32*a*c*d**2*e**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 80*a*c*d*e**3*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 60*a*c*e**4*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 16*b**2*d**2*e**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 40*b**2*d*e**3*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 30*b**2*e**4*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 192*b*c*d**3*e/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 480*b*c*d**2*e**2*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 360*b*c*d*e**3*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 60*b*c*e**4*x**3/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 256*c**2*d**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 640*c**2*d**3*e*x/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 480*c**2*d**2*e**2*x**2/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) - 80*c**2*d*e**3*x**3/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)) + 10*c**2*e**4*x**4/(15*d**2*e**5*sqrt(d + e*x) + 30*d*e**6*x*sqrt(d + e*x) + 15*e**7*x**2*sqrt(d + e*x)), Ne(e, 0)), ((a**2*x + a*b*x**2 + 2*a*c*x**3/3 + b**2*x**3/3 + b*c*x**4/2 + c**2*x**5/5)/d**(7/2), True))","A",0
2282,1,2363,0,94.425257," ","integrate((e*x+d)**(5/2)*(c*x**2+b*x+a)**3,x)","a^{3} d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 a^{3} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 a^{3} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{6 a^{2} b d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{12 a^{2} b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{6 a^{2} b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{6 a^{2} c d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{12 a^{2} c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{6 a^{2} c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{6 a b^{2} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{12 a b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{6 a b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{12 a b c d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{24 a b c d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{12 a b c \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{6 a c^{2} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{12 a c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{6 a c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{2 b^{3} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{4 b^{3} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 b^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{6 b^{2} c d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{12 b^{2} c d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{6 b^{2} c \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{6 b c^{2} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{12 b c^{2} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{6 b c^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{2 c^{3} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{4 c^{3} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{2 c^{3} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}}"," ",0,"a**3*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a**3*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*a**3*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 6*a**2*b*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 12*a**2*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 6*a**2*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 6*a**2*c*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 12*a**2*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 6*a**2*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 6*a*b**2*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 12*a*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 6*a*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 12*a*b*c*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 24*a*b*c*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 12*a*b*c*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 6*a*c**2*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 12*a*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 6*a*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 2*b**3*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 4*b**3*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*b**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 6*b**2*c*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 12*b**2*c*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 6*b**2*c*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 6*b*c**2*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 12*b*c**2*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 6*b*c**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 2*c**3*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 4*c**3*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 2*c**3*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7","A",0
2283,1,1411,0,54.120769," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x+a)**3,x)","a^{3} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{3} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{6 a^{2} b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{6 a^{2} b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{6 a^{2} c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{6 a^{2} c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{6 a b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{6 a b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{12 a b c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{12 a b c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{6 a c^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{6 a c^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{2 b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{6 b^{2} c d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{6 b^{2} c \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{6 b c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{6 b c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{2 c^{3} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{2 c^{3} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}}"," ",0,"a**3*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**3*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 6*a**2*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 6*a**2*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 6*a**2*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 6*a**2*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 6*a*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 6*a*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 12*a*b*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 12*a*b*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 6*a*c**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 6*a*c**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 2*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 6*b**2*c*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 6*b**2*c*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 6*b*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 6*b*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 2*c**3*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 2*c**3*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7","A",0
2284,1,539,0,8.928564," ","integrate((c*x**2+b*x+a)**3*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{c^{3} \left(d + e x\right)^{\frac{15}{2}}}{15 e^{6}} + \frac{\left(d + e x\right)^{\frac{13}{2}} \left(3 b c^{2} e - 6 c^{3} d\right)}{13 e^{6}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(3 a c^{2} e^{2} + 3 b^{2} c e^{2} - 15 b c^{2} d e + 15 c^{3} d^{2}\right)}{11 e^{6}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(6 a b c e^{3} - 12 a c^{2} d e^{2} + b^{3} e^{3} - 12 b^{2} c d e^{2} + 30 b c^{2} d^{2} e - 20 c^{3} d^{3}\right)}{9 e^{6}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(3 a^{2} c e^{4} + 3 a b^{2} e^{4} - 18 a b c d e^{3} + 18 a c^{2} d^{2} e^{2} - 3 b^{3} d e^{3} + 18 b^{2} c d^{2} e^{2} - 30 b c^{2} d^{3} e + 15 c^{3} d^{4}\right)}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(3 a^{2} b e^{5} - 6 a^{2} c d e^{4} - 6 a b^{2} d e^{4} + 18 a b c d^{2} e^{3} - 12 a c^{2} d^{3} e^{2} + 3 b^{3} d^{2} e^{3} - 12 b^{2} c d^{3} e^{2} + 15 b c^{2} d^{4} e - 6 c^{3} d^{5}\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{3} e^{6} - 3 a^{2} b d e^{5} + 3 a^{2} c d^{2} e^{4} + 3 a b^{2} d^{2} e^{4} - 6 a b c d^{3} e^{3} + 3 a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} + 3 b^{2} c d^{4} e^{2} - 3 b c^{2} d^{5} e + c^{3} d^{6}\right)}{3 e^{6}}\right)}{e}"," ",0,"2*(c**3*(d + e*x)**(15/2)/(15*e**6) + (d + e*x)**(13/2)*(3*b*c**2*e - 6*c**3*d)/(13*e**6) + (d + e*x)**(11/2)*(3*a*c**2*e**2 + 3*b**2*c*e**2 - 15*b*c**2*d*e + 15*c**3*d**2)/(11*e**6) + (d + e*x)**(9/2)*(6*a*b*c*e**3 - 12*a*c**2*d*e**2 + b**3*e**3 - 12*b**2*c*d*e**2 + 30*b*c**2*d**2*e - 20*c**3*d**3)/(9*e**6) + (d + e*x)**(7/2)*(3*a**2*c*e**4 + 3*a*b**2*e**4 - 18*a*b*c*d*e**3 + 18*a*c**2*d**2*e**2 - 3*b**3*d*e**3 + 18*b**2*c*d**2*e**2 - 30*b*c**2*d**3*e + 15*c**3*d**4)/(7*e**6) + (d + e*x)**(5/2)*(3*a**2*b*e**5 - 6*a**2*c*d*e**4 - 6*a*b**2*d*e**4 + 18*a*b*c*d**2*e**3 - 12*a*c**2*d**3*e**2 + 3*b**3*d**2*e**3 - 12*b**2*c*d**3*e**2 + 15*b*c**2*d**4*e - 6*c**3*d**5)/(5*e**6) + (d + e*x)**(3/2)*(a**3*e**6 - 3*a**2*b*d*e**5 + 3*a**2*c*d**2*e**4 + 3*a*b**2*d**2*e**4 - 6*a*b*c*d**3*e**3 + 3*a*c**2*d**4*e**2 - b**3*d**3*e**3 + 3*b**2*c*d**4*e**2 - 3*b*c**2*d**5*e + c**3*d**6)/(3*e**6))/e","A",0
2285,1,1406,0,158.272079," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{3} d}{\sqrt{d + e x}} - 2 a^{3} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{6 a^{2} b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{6 a^{2} b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{6 a^{2} c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{6 a^{2} c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{6 a b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{6 a b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{12 a b c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{12 a b c \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{6 a c^{2} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{6 a c^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{2 b^{3} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{2 b^{3} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{6 b^{2} c d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{6 b^{2} c \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{6 b c^{2} d \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{5}} - \frac{6 b c^{2} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} - \frac{2 c^{3} d \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{6}} - \frac{2 c^{3} \left(- \frac{d^{7}}{\sqrt{d + e x}} - 7 d^{6} \sqrt{d + e x} + 7 d^{5} \left(d + e x\right)^{\frac{3}{2}} - 7 d^{4} \left(d + e x\right)^{\frac{5}{2}} + 5 d^{3} \left(d + e x\right)^{\frac{7}{2}} - \frac{7 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{3} + \frac{7 d \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}}}{e} & \text{for}\: e \neq 0 \\\frac{a^{3} x + \frac{3 a^{2} b x^{2}}{2} + \frac{b c^{2} x^{6}}{2} + \frac{c^{3} x^{7}}{7} + \frac{x^{5} \left(3 a c^{2} + 3 b^{2} c\right)}{5} + \frac{x^{4} \left(6 a b c + b^{3}\right)}{4} + \frac{x^{3} \left(3 a^{2} c + 3 a b^{2}\right)}{3}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**3*d/sqrt(d + e*x) - 2*a**3*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 6*a**2*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 6*a**2*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 6*a**2*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 6*a**2*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 6*a*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 6*a*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 12*a*b*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 12*a*b*c*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 6*a*c**2*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 6*a*c**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 2*b**3*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 2*b**3*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 6*b**2*c*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 6*b**2*c*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 6*b*c**2*d*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**5 - 6*b*c**2*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**5 - 2*c**3*d*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**6 - 2*c**3*(-d**7/sqrt(d + e*x) - 7*d**6*sqrt(d + e*x) + 7*d**5*(d + e*x)**(3/2) - 7*d**4*(d + e*x)**(5/2) + 5*d**3*(d + e*x)**(7/2) - 7*d**2*(d + e*x)**(9/2)/3 + 7*d*(d + e*x)**(11/2)/11 - (d + e*x)**(13/2)/13)/e**6)/e, Ne(e, 0)), ((a**3*x + 3*a**2*b*x**2/2 + b*c**2*x**6/2 + c**3*x**7/7 + x**5*(3*a*c**2 + 3*b**2*c)/5 + x**4*(6*a*b*c + b**3)/4 + x**3*(3*a**2*c + 3*a*b**2)/3)/sqrt(d), True))","A",0
2286,1,428,0,138.864171," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**(3/2),x)","\frac{2 c^{3} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{7}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(6 b c^{2} e - 12 c^{3} d\right)}{9 e^{7}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(6 a c^{2} e^{2} + 6 b^{2} c e^{2} - 30 b c^{2} d e + 30 c^{3} d^{2}\right)}{7 e^{7}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(12 a b c e^{3} - 24 a c^{2} d e^{2} + 2 b^{3} e^{3} - 24 b^{2} c d e^{2} + 60 b c^{2} d^{2} e - 40 c^{3} d^{3}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(6 a^{2} c e^{4} + 6 a b^{2} e^{4} - 36 a b c d e^{3} + 36 a c^{2} d^{2} e^{2} - 6 b^{3} d e^{3} + 36 b^{2} c d^{2} e^{2} - 60 b c^{2} d^{3} e + 30 c^{3} d^{4}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(6 a^{2} b e^{5} - 12 a^{2} c d e^{4} - 12 a b^{2} d e^{4} + 36 a b c d^{2} e^{3} - 24 a c^{2} d^{3} e^{2} + 6 b^{3} d^{2} e^{3} - 24 b^{2} c d^{3} e^{2} + 30 b c^{2} d^{4} e - 12 c^{3} d^{5}\right)}{e^{7}} - \frac{2 \left(a e^{2} - b d e + c d^{2}\right)^{3}}{e^{7} \sqrt{d + e x}}"," ",0,"2*c**3*(d + e*x)**(11/2)/(11*e**7) + (d + e*x)**(9/2)*(6*b*c**2*e - 12*c**3*d)/(9*e**7) + (d + e*x)**(7/2)*(6*a*c**2*e**2 + 6*b**2*c*e**2 - 30*b*c**2*d*e + 30*c**3*d**2)/(7*e**7) + (d + e*x)**(5/2)*(12*a*b*c*e**3 - 24*a*c**2*d*e**2 + 2*b**3*e**3 - 24*b**2*c*d*e**2 + 60*b*c**2*d**2*e - 40*c**3*d**3)/(5*e**7) + (d + e*x)**(3/2)*(6*a**2*c*e**4 + 6*a*b**2*e**4 - 36*a*b*c*d*e**3 + 36*a*c**2*d**2*e**2 - 6*b**3*d*e**3 + 36*b**2*c*d**2*e**2 - 60*b*c**2*d**3*e + 30*c**3*d**4)/(3*e**7) + sqrt(d + e*x)*(6*a**2*b*e**5 - 12*a**2*c*d*e**4 - 12*a*b**2*d*e**4 + 36*a*b*c*d**2*e**3 - 24*a*c**2*d**3*e**2 + 6*b**3*d**2*e**3 - 24*b**2*c*d**3*e**2 + 30*b*c**2*d**4*e - 12*c**3*d**5)/e**7 - 2*(a*e**2 - b*d*e + c*d**2)**3/(e**7*sqrt(d + e*x))","A",0
2287,1,348,0,162.138285," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**(5/2),x)","\frac{2 c^{3} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{7}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(6 b c^{2} e - 12 c^{3} d\right)}{7 e^{7}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(6 a c^{2} e^{2} + 6 b^{2} c e^{2} - 30 b c^{2} d e + 30 c^{3} d^{2}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(12 a b c e^{3} - 24 a c^{2} d e^{2} + 2 b^{3} e^{3} - 24 b^{2} c d e^{2} + 60 b c^{2} d^{2} e - 40 c^{3} d^{3}\right)}{3 e^{7}} + \frac{\sqrt{d + e x} \left(6 a^{2} c e^{4} + 6 a b^{2} e^{4} - 36 a b c d e^{3} + 36 a c^{2} d^{2} e^{2} - 6 b^{3} d e^{3} + 36 b^{2} c d^{2} e^{2} - 60 b c^{2} d^{3} e + 30 c^{3} d^{4}\right)}{e^{7}} - \frac{6 \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right)^{2}}{e^{7} \sqrt{d + e x}} - \frac{2 \left(a e^{2} - b d e + c d^{2}\right)^{3}}{3 e^{7} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"2*c**3*(d + e*x)**(9/2)/(9*e**7) + (d + e*x)**(7/2)*(6*b*c**2*e - 12*c**3*d)/(7*e**7) + (d + e*x)**(5/2)*(6*a*c**2*e**2 + 6*b**2*c*e**2 - 30*b*c**2*d*e + 30*c**3*d**2)/(5*e**7) + (d + e*x)**(3/2)*(12*a*b*c*e**3 - 24*a*c**2*d*e**2 + 2*b**3*e**3 - 24*b**2*c*d*e**2 + 60*b*c**2*d**2*e - 40*c**3*d**3)/(3*e**7) + sqrt(d + e*x)*(6*a**2*c*e**4 + 6*a*b**2*e**4 - 36*a*b*c*d*e**3 + 36*a*c**2*d**2*e**2 - 6*b**3*d*e**3 + 36*b**2*c*d**2*e**2 - 60*b*c**2*d**3*e + 30*c**3*d**4)/e**7 - 6*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)**2/(e**7*sqrt(d + e*x)) - 2*(a*e**2 - b*d*e + c*d**2)**3/(3*e**7*(d + e*x)**(3/2))","A",0
2288,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2289,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2290,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2291,1,155,0,49.076117," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x+a),x)","2 e \operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{3} e^{4} - 128 a b^{2} c^{2} e^{4} + 16 b^{4} c e^{4}\right) + t^{2} \left(- 16 a b c e^{3} + 32 a c^{2} d e^{2} + 4 b^{3} e^{3} - 8 b^{2} c d e^{2}\right) + a e^{2} - b d e + c d^{2}, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} e^{2} - 16 t^{3} b^{2} c e^{2} - 2 t b e + 4 t c d + \sqrt{d + e x} \right)} \right)\right)}"," ",0,"2*e*RootSum(_t**4*(256*a**2*c**3*e**4 - 128*a*b**2*c**2*e**4 + 16*b**4*c*e**4) + _t**2*(-16*a*b*c*e**3 + 32*a*c**2*d*e**2 + 4*b**3*e**3 - 8*b**2*c*d*e**2) + a*e**2 - b*d*e + c*d**2, Lambda(_t, _t*log(64*_t**3*a*c**2*e**2 - 16*_t**3*b**2*c*e**2 - 2*_t*b*e + 4*_t*c*d + sqrt(d + e*x))))","A",0
2292,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x+a),x)","\int \frac{1}{\sqrt{d + e x} \left(a + b x + c x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(d + e*x)*(a + b*x + c*x**2)), x)","F",0
2293,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x+a),x)","\int \frac{1}{\left(d + e x\right)^{\frac{3}{2}} \left(a + b x + c x^{2}\right)}\, dx"," ",0,"Integral(1/((d + e*x)**(3/2)*(a + b*x + c*x**2)), x)","F",0
2294,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2295,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2296,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2297,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2298,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2299,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2300,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2301,-1,0,0,0.000000," ","integrate(1/x**(5/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2302,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2303,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2304,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2305,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2306,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2307,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(a+I*b*x+c*x**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2308,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(a+I*b*x+c*x**2),x)","\int \frac{1}{\sqrt{d + e x} \left(a + i b x + c x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(d + e*x)*(a + I*b*x + c*x**2)), x)","F",0
2309,1,292,0,87.704528," ","integrate((1+2*x)**(7/2)/(5*x**2+3*x+2),x)","\frac{4 \left(2 x + 1\right)^{\frac{5}{2}}}{25} + \frac{16 \left(2 x + 1\right)^{\frac{3}{2}}}{75} - \frac{76 \sqrt{2 x + 1}}{125} + 4 \operatorname{RootSum} {\left(1230080 t^{4} + 1984 t^{2} + 7, \left( t \mapsto t \log{\left(9920 t^{3} + 8 t + \sqrt{2 x + 1} \right)} \right)\right)} - \frac{408 \operatorname{RootSum} {\left(1230080 t^{4} + 1984 t^{2} + 7, \left( t \mapsto t \log{\left(9920 t^{3} + 8 t + \sqrt{2 x + 1} \right)} \right)\right)}}{25} - \frac{84 \operatorname{RootSum} {\left(1722112 t^{4} + 1984 t^{2} + 5, \left( t \mapsto t \log{\left(- \frac{27776 t^{3}}{5} + \frac{108 t}{5} + \sqrt{2 x + 1} \right)} \right)\right)}}{5} - \frac{12 \operatorname{RootSum} {\left(1230080 t^{4} + 1984 t^{2} + 7, \left( t \mapsto t \log{\left(9920 t^{3} + 8 t + \sqrt{2 x + 1} \right)} \right)\right)}}{5} + \frac{112 \operatorname{RootSum} {\left(1722112 t^{4} + 1984 t^{2} + 5, \left( t \mapsto t \log{\left(- \frac{27776 t^{3}}{5} + \frac{108 t}{5} + \sqrt{2 x + 1} \right)} \right)\right)}}{125} + \frac{504 \operatorname{RootSum} {\left(1722112 t^{4} + 1984 t^{2} + 5, \left( t \mapsto t \log{\left(- \frac{27776 t^{3}}{5} + \frac{108 t}{5} + \sqrt{2 x + 1} \right)} \right)\right)}}{25} + \frac{976 \operatorname{RootSum} {\left(1230080 t^{4} + 1984 t^{2} + 7, \left( t \mapsto t \log{\left(9920 t^{3} + 8 t + \sqrt{2 x + 1} \right)} \right)\right)}}{125}"," ",0,"4*(2*x + 1)**(5/2)/25 + 16*(2*x + 1)**(3/2)/75 - 76*sqrt(2*x + 1)/125 + 4*RootSum(1230080*_t**4 + 1984*_t**2 + 7, Lambda(_t, _t*log(9920*_t**3 + 8*_t + sqrt(2*x + 1)))) - 408*RootSum(1230080*_t**4 + 1984*_t**2 + 7, Lambda(_t, _t*log(9920*_t**3 + 8*_t + sqrt(2*x + 1))))/25 - 84*RootSum(1722112*_t**4 + 1984*_t**2 + 5, Lambda(_t, _t*log(-27776*_t**3/5 + 108*_t/5 + sqrt(2*x + 1))))/5 - 12*RootSum(1230080*_t**4 + 1984*_t**2 + 7, Lambda(_t, _t*log(9920*_t**3 + 8*_t + sqrt(2*x + 1))))/5 + 112*RootSum(1722112*_t**4 + 1984*_t**2 + 5, Lambda(_t, _t*log(-27776*_t**3/5 + 108*_t/5 + sqrt(2*x + 1))))/125 + 504*RootSum(1722112*_t**4 + 1984*_t**2 + 5, Lambda(_t, _t*log(-27776*_t**3/5 + 108*_t/5 + sqrt(2*x + 1))))/25 + 976*RootSum(1230080*_t**4 + 1984*_t**2 + 7, Lambda(_t, _t*log(9920*_t**3 + 8*_t + sqrt(2*x + 1))))/125","A",0
2310,1,206,0,56.211478," ","integrate((1+2*x)**(5/2)/(5*x**2+3*x+2),x)","\frac{4 \left(2 x + 1\right)^{\frac{3}{2}}}{15} + \frac{16 \sqrt{2 x + 1}}{25} + 4 \operatorname{RootSum} {\left(1230080 t^{4} + 1984 t^{2} + 7, \left( t \mapsto t \log{\left(9920 t^{3} + 8 t + \sqrt{2 x + 1} \right)} \right)\right)} - \frac{136 \operatorname{RootSum} {\left(1230080 t^{4} + 1984 t^{2} + 7, \left( t \mapsto t \log{\left(9920 t^{3} + 8 t + \sqrt{2 x + 1} \right)} \right)\right)}}{25} - \frac{56 \operatorname{RootSum} {\left(1722112 t^{4} + 1984 t^{2} + 5, \left( t \mapsto t \log{\left(- \frac{27776 t^{3}}{5} + \frac{108 t}{5} + \sqrt{2 x + 1} \right)} \right)\right)}}{5} - \frac{8 \operatorname{RootSum} {\left(1230080 t^{4} + 1984 t^{2} + 7, \left( t \mapsto t \log{\left(9920 t^{3} + 8 t + \sqrt{2 x + 1} \right)} \right)\right)}}{5} + \frac{168 \operatorname{RootSum} {\left(1722112 t^{4} + 1984 t^{2} + 5, \left( t \mapsto t \log{\left(- \frac{27776 t^{3}}{5} + \frac{108 t}{5} + \sqrt{2 x + 1} \right)} \right)\right)}}{25}"," ",0,"4*(2*x + 1)**(3/2)/15 + 16*sqrt(2*x + 1)/25 + 4*RootSum(1230080*_t**4 + 1984*_t**2 + 7, Lambda(_t, _t*log(9920*_t**3 + 8*_t + sqrt(2*x + 1)))) - 136*RootSum(1230080*_t**4 + 1984*_t**2 + 7, Lambda(_t, _t*log(9920*_t**3 + 8*_t + sqrt(2*x + 1))))/25 - 56*RootSum(1722112*_t**4 + 1984*_t**2 + 5, Lambda(_t, _t*log(-27776*_t**3/5 + 108*_t/5 + sqrt(2*x + 1))))/5 - 8*RootSum(1230080*_t**4 + 1984*_t**2 + 7, Lambda(_t, _t*log(9920*_t**3 + 8*_t + sqrt(2*x + 1))))/5 + 168*RootSum(1722112*_t**4 + 1984*_t**2 + 5, Lambda(_t, _t*log(-27776*_t**3/5 + 108*_t/5 + sqrt(2*x + 1))))/25","A",0
2311,1,119,0,31.695572," ","integrate((1+2*x)**(3/2)/(5*x**2+3*x+2),x)","\frac{4 \sqrt{2 x + 1}}{5} + 4 \operatorname{RootSum} {\left(1230080 t^{4} + 1984 t^{2} + 7, \left( t \mapsto t \log{\left(9920 t^{3} + 8 t + \sqrt{2 x + 1} \right)} \right)\right)} - \frac{28 \operatorname{RootSum} {\left(1722112 t^{4} + 1984 t^{2} + 5, \left( t \mapsto t \log{\left(- \frac{27776 t^{3}}{5} + \frac{108 t}{5} + \sqrt{2 x + 1} \right)} \right)\right)}}{5} - \frac{4 \operatorname{RootSum} {\left(1230080 t^{4} + 1984 t^{2} + 7, \left( t \mapsto t \log{\left(9920 t^{3} + 8 t + \sqrt{2 x + 1} \right)} \right)\right)}}{5}"," ",0,"4*sqrt(2*x + 1)/5 + 4*RootSum(1230080*_t**4 + 1984*_t**2 + 7, Lambda(_t, _t*log(9920*_t**3 + 8*_t + sqrt(2*x + 1)))) - 28*RootSum(1722112*_t**4 + 1984*_t**2 + 5, Lambda(_t, _t*log(-27776*_t**3/5 + 108*_t/5 + sqrt(2*x + 1))))/5 - 4*RootSum(1230080*_t**4 + 1984*_t**2 + 7, Lambda(_t, _t*log(9920*_t**3 + 8*_t + sqrt(2*x + 1))))/5","A",0
2312,1,32,0,4.567373," ","integrate((1+2*x)**(1/2)/(5*x**2+3*x+2),x)","4 \operatorname{RootSum} {\left(1230080 t^{4} + 1984 t^{2} + 7, \left( t \mapsto t \log{\left(9920 t^{3} + 8 t + \sqrt{2 x + 1} \right)} \right)\right)}"," ",0,"4*RootSum(1230080*_t**4 + 1984*_t**2 + 7, Lambda(_t, _t*log(9920*_t**3 + 8*_t + sqrt(2*x + 1))))","A",0
2313,0,0,0,0.000000," ","integrate(1/(1+2*x)**(1/2)/(5*x**2+3*x+2),x)","\int \frac{1}{\sqrt{2 x + 1} \left(5 x^{2} + 3 x + 2\right)}\, dx"," ",0,"Integral(1/(sqrt(2*x + 1)*(5*x**2 + 3*x + 2)), x)","F",0
2314,0,0,0,0.000000," ","integrate(1/(1+2*x)**(3/2)/(5*x**2+3*x+2),x)","\int \frac{1}{\left(2 x + 1\right)^{\frac{3}{2}} \left(5 x^{2} + 3 x + 2\right)}\, dx"," ",0,"Integral(1/((2*x + 1)**(3/2)*(5*x**2 + 3*x + 2)), x)","F",0
2315,0,0,0,0.000000," ","integrate(1/(1+2*x)**(5/2)/(5*x**2+3*x+2),x)","\int \frac{1}{\left(2 x + 1\right)^{\frac{5}{2}} \left(5 x^{2} + 3 x + 2\right)}\, dx"," ",0,"Integral(1/((2*x + 1)**(5/2)*(5*x**2 + 3*x + 2)), x)","F",0
2316,-1,0,0,0.000000," ","integrate((1+2*x)**(7/2)/(5*x**2+3*x+2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2317,-1,0,0,0.000000," ","integrate((1+2*x)**(5/2)/(5*x**2+3*x+2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2318,1,248,0,111.048121," ","integrate((1+2*x)**(3/2)/(5*x**2+3*x+2)**2,x)","\frac{320 \left(2 x + 1\right)^{\frac{3}{2}}}{- 4960 x + 3100 \left(2 x + 1\right)^{2} + 1860} - \frac{1120 \left(2 x + 1\right)^{\frac{3}{2}}}{- 34720 x + 21700 \left(2 x + 1\right)^{2} + 13020} - \frac{128 \sqrt{2 x + 1}}{- 4960 x + 3100 \left(2 x + 1\right)^{2} + 1860} - \frac{3024 \sqrt{2 x + 1}}{- 34720 x + 21700 \left(2 x + 1\right)^{2} + 13020} + 16 \operatorname{RootSum} {\left(407144088666112 t^{4} + 3325152256 t^{2} + 11045, \left( t \mapsto t \log{\left(\frac{33312534528 t^{3}}{235} + \frac{166784 t}{235} + \sqrt{2 x + 1} \right)} \right)\right)} - \frac{112 \operatorname{RootSum} {\left(19950060344639488 t^{4} + 498437272576 t^{2} + 10878125, \left( t \mapsto t \log{\left(- \frac{11049511452672 t^{3}}{2205125} + \frac{307918256 t}{2205125} + \sqrt{2 x + 1} \right)} \right)\right)}}{5} - \frac{16 \operatorname{RootSum} {\left(407144088666112 t^{4} + 3325152256 t^{2} + 11045, \left( t \mapsto t \log{\left(\frac{33312534528 t^{3}}{235} + \frac{166784 t}{235} + \sqrt{2 x + 1} \right)} \right)\right)}}{5} + \frac{16 \operatorname{RootSum} {\left(1722112 t^{4} + 1984 t^{2} + 5, \left( t \mapsto t \log{\left(- \frac{27776 t^{3}}{5} + \frac{108 t}{5} + \sqrt{2 x + 1} \right)} \right)\right)}}{5}"," ",0,"320*(2*x + 1)**(3/2)/(-4960*x + 3100*(2*x + 1)**2 + 1860) - 1120*(2*x + 1)**(3/2)/(-34720*x + 21700*(2*x + 1)**2 + 13020) - 128*sqrt(2*x + 1)/(-4960*x + 3100*(2*x + 1)**2 + 1860) - 3024*sqrt(2*x + 1)/(-34720*x + 21700*(2*x + 1)**2 + 13020) + 16*RootSum(407144088666112*_t**4 + 3325152256*_t**2 + 11045, Lambda(_t, _t*log(33312534528*_t**3/235 + 166784*_t/235 + sqrt(2*x + 1)))) - 112*RootSum(19950060344639488*_t**4 + 498437272576*_t**2 + 10878125, Lambda(_t, _t*log(-11049511452672*_t**3/2205125 + 307918256*_t/2205125 + sqrt(2*x + 1))))/5 - 16*RootSum(407144088666112*_t**4 + 3325152256*_t**2 + 11045, Lambda(_t, _t*log(33312534528*_t**3/235 + 166784*_t/235 + sqrt(2*x + 1))))/5 + 16*RootSum(1722112*_t**4 + 1984*_t**2 + 5, Lambda(_t, _t*log(-27776*_t**3/5 + 108*_t/5 + sqrt(2*x + 1))))/5","A",0
2319,1,83,0,7.849341," ","integrate((1+2*x)**(1/2)/(5*x**2+3*x+2)**2,x)","\frac{80 \left(2 x + 1\right)^{\frac{3}{2}}}{- 992 x + 620 \left(2 x + 1\right)^{2} + 372} - \frac{32 \sqrt{2 x + 1}}{- 992 x + 620 \left(2 x + 1\right)^{2} + 372} + 16 \operatorname{RootSum} {\left(407144088666112 t^{4} + 3325152256 t^{2} + 11045, \left( t \mapsto t \log{\left(\frac{33312534528 t^{3}}{235} + \frac{166784 t}{235} + \sqrt{2 x + 1} \right)} \right)\right)}"," ",0,"80*(2*x + 1)**(3/2)/(-992*x + 620*(2*x + 1)**2 + 372) - 32*sqrt(2*x + 1)/(-992*x + 620*(2*x + 1)**2 + 372) + 16*RootSum(407144088666112*_t**4 + 3325152256*_t**2 + 11045, Lambda(_t, _t*log(33312534528*_t**3/235 + 166784*_t/235 + sqrt(2*x + 1))))","A",0
2320,0,0,0,0.000000," ","integrate(1/(1+2*x)**(1/2)/(5*x**2+3*x+2)**2,x)","\int \frac{1}{\sqrt{2 x + 1} \left(5 x^{2} + 3 x + 2\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(2*x + 1)*(5*x**2 + 3*x + 2)**2), x)","F",0
2321,0,0,0,0.000000," ","integrate(1/(1+2*x)**(3/2)/(5*x**2+3*x+2)**2,x)","\int \frac{1}{\left(2 x + 1\right)^{\frac{3}{2}} \left(5 x^{2} + 3 x + 2\right)^{2}}\, dx"," ",0,"Integral(1/((2*x + 1)**(3/2)*(5*x**2 + 3*x + 2)**2), x)","F",0
2322,0,0,0,0.000000," ","integrate(1/(1+2*x)**(5/2)/(5*x**2+3*x+2)**2,x)","\int \frac{1}{\left(2 x + 1\right)^{\frac{5}{2}} \left(5 x^{2} + 3 x + 2\right)^{2}}\, dx"," ",0,"Integral(1/((2*x + 1)**(5/2)*(5*x**2 + 3*x + 2)**2), x)","F",0
2323,-1,0,0,0.000000," ","integrate((1+2*x)**(9/2)/(5*x**2+3*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2324,-1,0,0,0.000000," ","integrate((1+2*x)**(7/2)/(5*x**2+3*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2325,-1,0,0,0.000000," ","integrate((1+2*x)**(5/2)/(5*x**2+3*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2326,1,527,0,167.231718," ","integrate((1+2*x)**(3/2)/(5*x**2+3*x+2)**3,x)","\frac{1145600 \left(2 x + 1\right)^{\frac{7}{2}}}{- 120547840 x + 26908000 \left(2 x + 1\right)^{4} - 43052800 \left(2 x + 1\right)^{3} + 92563520 \left(2 x + 1\right)^{2} - 7534240} - \frac{8870400 \left(2 x + 1\right)^{\frac{7}{2}}}{- 843834880 x + 188356000 \left(2 x + 1\right)^{4} - 301369600 \left(2 x + 1\right)^{3} + 647944640 \left(2 x + 1\right)^{2} - 52739680} - \frac{1295360 \left(2 x + 1\right)^{\frac{5}{2}}}{- 120547840 x + 26908000 \left(2 x + 1\right)^{4} - 43052800 \left(2 x + 1\right)^{3} + 92563520 \left(2 x + 1\right)^{2} - 7534240} - \frac{4701760 \left(2 x + 1\right)^{\frac{5}{2}}}{- 843834880 x + 188356000 \left(2 x + 1\right)^{4} - 301369600 \left(2 x + 1\right)^{3} + 647944640 \left(2 x + 1\right)^{2} - 52739680} + \frac{3017984 \left(2 x + 1\right)^{\frac{3}{2}}}{- 120547840 x + 26908000 \left(2 x + 1\right)^{4} - 43052800 \left(2 x + 1\right)^{3} + 92563520 \left(2 x + 1\right)^{2} - 7534240} - \frac{6868736 \left(2 x + 1\right)^{\frac{3}{2}}}{- 843834880 x + 188356000 \left(2 x + 1\right)^{4} - 301369600 \left(2 x + 1\right)^{3} + 647944640 \left(2 x + 1\right)^{2} - 52739680} + \frac{640 \left(2 x + 1\right)^{\frac{3}{2}}}{- 34720 x + 21700 \left(2 x + 1\right)^{2} + 13020} - \frac{974848 \sqrt{2 x + 1}}{- 120547840 x + 26908000 \left(2 x + 1\right)^{4} - 43052800 \left(2 x + 1\right)^{3} + 92563520 \left(2 x + 1\right)^{2} - 7534240} - \frac{27016640 \sqrt{2 x + 1}}{- 843834880 x + 188356000 \left(2 x + 1\right)^{4} - 301369600 \left(2 x + 1\right)^{3} + 647944640 \left(2 x + 1\right)^{2} - 52739680} + \frac{1728 \sqrt{2 x + 1}}{- 34720 x + 21700 \left(2 x + 1\right)^{2} + 13020} + 64 \operatorname{RootSum} {\left(75465931487403231630327808 t^{4} + 9053854476152406016 t^{2} + 333142578125, \left( t \mapsto t \log{\left(\frac{21632117045402271744 t^{3}}{158378125} + \frac{10865340674816 t}{1108646875} + \sqrt{2 x + 1} \right)} \right)\right)} - \frac{448 \operatorname{RootSum} {\left(3697830642882758349886062592 t^{4} + 2111968303753265086464 t^{2} + 705698730253125, \left( t \mapsto t \log{\left(- \frac{3459438283411209322496 t^{3}}{1377792122625} + \frac{251494140770688 t}{357205365125} + \sqrt{2 x + 1} \right)} \right)\right)}}{5} - \frac{64 \operatorname{RootSum} {\left(75465931487403231630327808 t^{4} + 9053854476152406016 t^{2} + 333142578125, \left( t \mapsto t \log{\left(\frac{21632117045402271744 t^{3}}{158378125} + \frac{10865340674816 t}{1108646875} + \sqrt{2 x + 1} \right)} \right)\right)}}{5} + \frac{64 \operatorname{RootSum} {\left(19950060344639488 t^{4} + 498437272576 t^{2} + 10878125, \left( t \mapsto t \log{\left(- \frac{11049511452672 t^{3}}{2205125} + \frac{307918256 t}{2205125} + \sqrt{2 x + 1} \right)} \right)\right)}}{5}"," ",0,"1145600*(2*x + 1)**(7/2)/(-120547840*x + 26908000*(2*x + 1)**4 - 43052800*(2*x + 1)**3 + 92563520*(2*x + 1)**2 - 7534240) - 8870400*(2*x + 1)**(7/2)/(-843834880*x + 188356000*(2*x + 1)**4 - 301369600*(2*x + 1)**3 + 647944640*(2*x + 1)**2 - 52739680) - 1295360*(2*x + 1)**(5/2)/(-120547840*x + 26908000*(2*x + 1)**4 - 43052800*(2*x + 1)**3 + 92563520*(2*x + 1)**2 - 7534240) - 4701760*(2*x + 1)**(5/2)/(-843834880*x + 188356000*(2*x + 1)**4 - 301369600*(2*x + 1)**3 + 647944640*(2*x + 1)**2 - 52739680) + 3017984*(2*x + 1)**(3/2)/(-120547840*x + 26908000*(2*x + 1)**4 - 43052800*(2*x + 1)**3 + 92563520*(2*x + 1)**2 - 7534240) - 6868736*(2*x + 1)**(3/2)/(-843834880*x + 188356000*(2*x + 1)**4 - 301369600*(2*x + 1)**3 + 647944640*(2*x + 1)**2 - 52739680) + 640*(2*x + 1)**(3/2)/(-34720*x + 21700*(2*x + 1)**2 + 13020) - 974848*sqrt(2*x + 1)/(-120547840*x + 26908000*(2*x + 1)**4 - 43052800*(2*x + 1)**3 + 92563520*(2*x + 1)**2 - 7534240) - 27016640*sqrt(2*x + 1)/(-843834880*x + 188356000*(2*x + 1)**4 - 301369600*(2*x + 1)**3 + 647944640*(2*x + 1)**2 - 52739680) + 1728*sqrt(2*x + 1)/(-34720*x + 21700*(2*x + 1)**2 + 13020) + 64*RootSum(75465931487403231630327808*_t**4 + 9053854476152406016*_t**2 + 333142578125, Lambda(_t, _t*log(21632117045402271744*_t**3/158378125 + 10865340674816*_t/1108646875 + sqrt(2*x + 1)))) - 448*RootSum(3697830642882758349886062592*_t**4 + 2111968303753265086464*_t**2 + 705698730253125, Lambda(_t, _t*log(-3459438283411209322496*_t**3/1377792122625 + 251494140770688*_t/357205365125 + sqrt(2*x + 1))))/5 - 64*RootSum(75465931487403231630327808*_t**4 + 9053854476152406016*_t**2 + 333142578125, Lambda(_t, _t*log(21632117045402271744*_t**3/158378125 + 10865340674816*_t/1108646875 + sqrt(2*x + 1))))/5 + 64*RootSum(19950060344639488*_t**4 + 498437272576*_t**2 + 10878125, Lambda(_t, _t*log(-11049511452672*_t**3/2205125 + 307918256*_t/2205125 + sqrt(2*x + 1))))/5","B",0
2327,1,199,0,11.723537," ","integrate((1+2*x)**(1/2)/(5*x**2+3*x+2)**3,x)","\frac{286400 \left(2 x + 1\right)^{\frac{7}{2}}}{- 24109568 x + 5381600 \left(2 x + 1\right)^{4} - 8610560 \left(2 x + 1\right)^{3} + 18512704 \left(2 x + 1\right)^{2} - 1506848} - \frac{323840 \left(2 x + 1\right)^{\frac{5}{2}}}{- 24109568 x + 5381600 \left(2 x + 1\right)^{4} - 8610560 \left(2 x + 1\right)^{3} + 18512704 \left(2 x + 1\right)^{2} - 1506848} + \frac{754496 \left(2 x + 1\right)^{\frac{3}{2}}}{- 24109568 x + 5381600 \left(2 x + 1\right)^{4} - 8610560 \left(2 x + 1\right)^{3} + 18512704 \left(2 x + 1\right)^{2} - 1506848} - \frac{243712 \sqrt{2 x + 1}}{- 24109568 x + 5381600 \left(2 x + 1\right)^{4} - 8610560 \left(2 x + 1\right)^{3} + 18512704 \left(2 x + 1\right)^{2} - 1506848} + 64 \operatorname{RootSum} {\left(75465931487403231630327808 t^{4} + 9053854476152406016 t^{2} + 333142578125, \left( t \mapsto t \log{\left(\frac{21632117045402271744 t^{3}}{158378125} + \frac{10865340674816 t}{1108646875} + \sqrt{2 x + 1} \right)} \right)\right)}"," ",0,"286400*(2*x + 1)**(7/2)/(-24109568*x + 5381600*(2*x + 1)**4 - 8610560*(2*x + 1)**3 + 18512704*(2*x + 1)**2 - 1506848) - 323840*(2*x + 1)**(5/2)/(-24109568*x + 5381600*(2*x + 1)**4 - 8610560*(2*x + 1)**3 + 18512704*(2*x + 1)**2 - 1506848) + 754496*(2*x + 1)**(3/2)/(-24109568*x + 5381600*(2*x + 1)**4 - 8610560*(2*x + 1)**3 + 18512704*(2*x + 1)**2 - 1506848) - 243712*sqrt(2*x + 1)/(-24109568*x + 5381600*(2*x + 1)**4 - 8610560*(2*x + 1)**3 + 18512704*(2*x + 1)**2 - 1506848) + 64*RootSum(75465931487403231630327808*_t**4 + 9053854476152406016*_t**2 + 333142578125, Lambda(_t, _t*log(21632117045402271744*_t**3/158378125 + 10865340674816*_t/1108646875 + sqrt(2*x + 1))))","A",0
2328,0,0,0,0.000000," ","integrate(1/(1+2*x)**(1/2)/(5*x**2+3*x+2)**3,x)","\int \frac{1}{\sqrt{2 x + 1} \left(5 x^{2} + 3 x + 2\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(2*x + 1)*(5*x**2 + 3*x + 2)**3), x)","F",0
2329,0,0,0,0.000000," ","integrate(1/(1+2*x)**(3/2)/(5*x**2+3*x+2)**3,x)","\int \frac{1}{\left(2 x + 1\right)^{\frac{3}{2}} \left(5 x^{2} + 3 x + 2\right)^{3}}\, dx"," ",0,"Integral(1/((2*x + 1)**(3/2)*(5*x**2 + 3*x + 2)**3), x)","F",0
2330,-1,0,0,0.000000," ","integrate(x**(9/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2331,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2332,1,24,0,2.461544," ","integrate((x**2-x+3)/x**(1/3),x)","\frac{3 x^{\frac{8}{3}}}{8} - \frac{3 x^{\frac{5}{3}}}{5} + \frac{9 x^{\frac{2}{3}}}{2}"," ",0,"3*x**(8/3)/8 - 3*x**(5/3)/5 + 9*x**(2/3)/2","A",0
2333,0,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right)^{3} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**3*sqrt(a + b*x + c*x**2), x)","F",0
2334,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right)^{2} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**2*sqrt(a + b*x + c*x**2), x)","F",0
2335,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)*sqrt(a + b*x + c*x**2), x)","F",0
2336,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2),x)","\int \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2), x)","F",0
2337,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{d + e x}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d + e*x), x)","F",0
2338,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d + e*x)**2, x)","F",0
2339,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**3,x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d + e*x)**3, x)","F",0
2340,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**4,x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d + e*x)**4, x)","F",0
2341,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**5,x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d + e*x)**5, x)","F",0
2342,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**6,x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d + e*x)**6, x)","F",0
2343,0,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**(3/2),x)","\int \left(d + e x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)**3*(a + b*x + c*x**2)**(3/2), x)","F",0
2344,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**(3/2),x)","\int \left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)**2*(a + b*x + c*x**2)**(3/2), x)","F",0
2345,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x+a)**(3/2),x)","\int \left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)*(a + b*x + c*x**2)**(3/2), x)","F",0
2346,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2),x)","\int \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2), x)","F",0
2347,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x), x)","F",0
2348,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**2, x)","F",0
2349,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**3,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**3, x)","F",0
2350,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**4,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**4, x)","F",0
2351,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**5,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**5, x)","F",0
2352,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**6,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**6, x)","F",0
2353,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**7,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**7, x)","F",0
2354,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**8,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{8}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**8, x)","F",0
2355,0,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**(5/2),x)","\int \left(d + e x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x)**3*(a + b*x + c*x**2)**(5/2), x)","F",0
2356,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**(5/2),x)","\int \left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x)**2*(a + b*x + c*x**2)**(5/2), x)","F",0
2357,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x+a)**(5/2),x)","\int \left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x)*(a + b*x + c*x**2)**(5/2), x)","F",0
2358,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2),x)","\int \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2), x)","F",0
2359,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{d + e x}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2)/(d + e*x), x)","F",0
2360,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)**2,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2)/(d + e*x)**2, x)","F",0
2361,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2)/(d + e*x)**3, x)","F",0
2362,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2)/(d + e*x)**4, x)","F",0
2363,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)**5,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/2)/(d + e*x)**5, x)","F",0
2364,0,0,0,0.000000," ","integrate((5*x**2-3*x-2)**(1/2)/x,x)","\int \frac{\sqrt{\left(x - 1\right) \left(5 x + 2\right)}}{x}\, dx"," ",0,"Integral(sqrt((x - 1)*(5*x + 2))/x, x)","F",0
2365,0,0,0,0.000000," ","integrate((-x**2-x+2)**(1/2)/x**2,x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 2\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 2))/x**2, x)","F",0
2366,1,85,0,0.280462," ","integrate((1+x)**3*(x**2+2*x+2)**(1/2),x)","\frac{x^{4} \sqrt{x^{2} + 2 x + 2}}{5} + \frac{4 x^{3} \sqrt{x^{2} + 2 x + 2}}{5} + \frac{19 x^{2} \sqrt{x^{2} + 2 x + 2}}{15} + \frac{14 x \sqrt{x^{2} + 2 x + 2}}{15} + \frac{2 \sqrt{x^{2} + 2 x + 2}}{15}"," ",0,"x**4*sqrt(x**2 + 2*x + 2)/5 + 4*x**3*sqrt(x**2 + 2*x + 2)/5 + 19*x**2*sqrt(x**2 + 2*x + 2)/15 + 14*x*sqrt(x**2 + 2*x + 2)/15 + 2*sqrt(x**2 + 2*x + 2)/15","B",0
2367,0,0,0,0.000000," ","integrate((-2+3*x)*(9*x**2+12*x+8)**(1/2),x)","\int \left(3 x - 2\right) \sqrt{9 x^{2} + 12 x + 8}\, dx"," ",0,"Integral((3*x - 2)*sqrt(9*x**2 + 12*x + 8), x)","F",0
2368,0,0,0,0.000000," ","integrate((7-2*x)*(-4*x**2+16*x+9)**(1/2),x)","- \int 2 x \sqrt{- 4 x^{2} + 16 x + 9}\, dx - \int \left(- 7 \sqrt{- 4 x^{2} + 16 x + 9}\right)\, dx"," ",0,"-Integral(2*x*sqrt(-4*x**2 + 16*x + 9), x) - Integral(-7*sqrt(-4*x**2 + 16*x + 9), x)","F",0
2369,0,0,0,0.000000," ","integrate((x**2-x-1)**(1/2)/(1+x),x)","\int \frac{\sqrt{x^{2} - x - 1}}{x + 1}\, dx"," ",0,"Integral(sqrt(x**2 - x - 1)/(x + 1), x)","F",0
2370,0,0,0,0.000000," ","integrate((x**2-x-1)**(1/2)/(1-x),x)","- \int \frac{\sqrt{x^{2} - x - 1}}{x - 1}\, dx"," ",0,"-Integral(sqrt(x**2 - x - 1)/(x - 1), x)","F",0
2371,0,0,0,0.000000," ","integrate(x**6/(c*x**2+b*x+a)**(1/2),x)","\int \frac{x^{6}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(x**6/sqrt(a + b*x + c*x**2), x)","F",0
2372,0,0,0,0.000000," ","integrate(x**5/(c*x**2+b*x+a)**(1/2),x)","\int \frac{x^{5}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(x**5/sqrt(a + b*x + c*x**2), x)","F",0
2373,0,0,0,0.000000," ","integrate((e*x+d)**4/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{4}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**4/sqrt(a + b*x + c*x**2), x)","F",0
2374,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{3}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**3/sqrt(a + b*x + c*x**2), x)","F",0
2375,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{2}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**2/sqrt(a + b*x + c*x**2), x)","F",0
2376,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)/sqrt(a + b*x + c*x**2), x)","F",0
2377,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/sqrt(a + b*x + c*x**2), x)","F",0
2378,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
2379,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{2} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**2*sqrt(a + b*x + c*x**2)), x)","F",0
2380,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{3} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**3*sqrt(a + b*x + c*x**2)), x)","F",0
2381,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{4} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**4*sqrt(a + b*x + c*x**2)), x)","F",0
2382,0,0,0,0.000000," ","integrate((e*x+d)**4/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{4}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**4/(a + b*x + c*x**2)**(3/2), x)","F",0
2383,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(a + b*x + c*x**2)**(3/2), x)","F",0
2384,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(a + b*x + c*x**2)**(3/2), x)","F",0
2385,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{d + e x}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
2386,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(-3/2), x)","F",0
2387,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
2388,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**2*(a + b*x + c*x**2)**(3/2)), x)","F",0
2389,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d + e x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**3*(a + b*x + c*x**2)**(3/2)), x)","F",0
2390,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d + e x\right)^{4} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**4*(a + b*x + c*x**2)**(3/2)), x)","F",0
2391,-1,0,0,0.000000," ","integrate((e*x+d)**5/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2392,-1,0,0,0.000000," ","integrate((e*x+d)**4/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2393,-1,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2394,-1,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2395,-1,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2396,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x+a)**(5/2),x)","\int \frac{1}{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(-5/2), x)","F",0
2397,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**(5/2),x)","\int \frac{1}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(a + b*x + c*x**2)**(5/2)), x)","F",0
2398,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x+a)**(5/2),x)","\int \frac{1}{\left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**2*(a + b*x + c*x**2)**(5/2)), x)","F",0
2399,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x+a)**(5/2),x)","\int \frac{1}{\left(d + e x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**3*(a + b*x + c*x**2)**(5/2)), x)","F",0
2400,0,0,0,0.000000," ","integrate((3+x)/(-x**2-4*x+5)**(1/2),x)","\int \frac{x + 3}{\sqrt{- \left(x - 1\right) \left(x + 5\right)}}\, dx"," ",0,"Integral((x + 3)/sqrt(-(x - 1)*(x + 5)), x)","F",0
2401,0,0,0,0.000000," ","integrate(1/2*(5-4*x)/(-x**2+3*x-2)**(1/2),x)","- \frac{\int \frac{4 x}{\sqrt{- x^{2} + 3 x - 2}}\, dx + \int \left(- \frac{5}{\sqrt{- x^{2} + 3 x - 2}}\right)\, dx}{2}"," ",0,"-(Integral(4*x/sqrt(-x**2 + 3*x - 2), x) + Integral(-5/sqrt(-x**2 + 3*x - 2), x))/2","F",0
2402,0,0,0,0.000000," ","integrate((3+2*x)/(x**2+2*x+5)**(1/2),x)","\int \frac{2 x + 3}{\sqrt{x^{2} + 2 x + 5}}\, dx"," ",0,"Integral((2*x + 3)/sqrt(x**2 + 2*x + 5), x)","F",0
2403,0,0,0,0.000000," ","integrate((-1+x)/(x**2-4*x+3)**(1/2),x)","\int \frac{x - 1}{\sqrt{\left(x - 3\right) \left(x - 1\right)}}\, dx"," ",0,"Integral((x - 1)/sqrt((x - 3)*(x - 1)), x)","F",0
2404,0,0,0,0.000000," ","integrate(1/(1-x)/(x**2+2*x-4)**(1/2),x)","- \int \frac{1}{x \sqrt{x^{2} + 2 x - 4} - \sqrt{x^{2} + 2 x - 4}}\, dx"," ",0,"-Integral(1/(x*sqrt(x**2 + 2*x - 4) - sqrt(x**2 + 2*x - 4)), x)","F",0
2405,0,0,0,0.000000," ","integrate(1/(-2+x)/(x**2-4*x+3)**(1/2),x)","\int \frac{1}{\sqrt{\left(x - 3\right) \left(x - 1\right)} \left(x - 2\right)}\, dx"," ",0,"Integral(1/(sqrt((x - 3)*(x - 1))*(x - 2)), x)","F",0
2406,0,0,0,0.000000," ","integrate((1+x)/(x**2+3*x+2)**(3/2),x)","\int \frac{x + 1}{\left(\left(x + 1\right) \left(x + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x + 1)/((x + 1)*(x + 2))**(3/2), x)","F",0
2407,0,0,0,0.000000," ","integrate(2/(e*x+d)/(1/c*b**2+4*b*x+4*c*x**2)**(1/2),x)","2 \int \frac{1}{d \sqrt{\frac{b^{2}}{c} + 4 b x + 4 c x^{2}} + e x \sqrt{\frac{b^{2}}{c} + 4 b x + 4 c x^{2}}}\, dx"," ",0,"2*Integral(1/(d*sqrt(b**2/c + 4*b*x + 4*c*x**2) + e*x*sqrt(b**2/c + 4*b*x + 4*c*x**2)), x)","F",0
2408,0,0,0,0.000000," ","integrate(1/(1/2*b*e/c+e*x)/(c*x**2+b*x+a)**(1/2),x)","\frac{2 c \int \frac{1}{b \sqrt{a + b x + c x^{2}} + 2 c x \sqrt{a + b x + c x^{2}}}\, dx}{e}"," ",0,"2*c*Integral(1/(b*sqrt(a + b*x + c*x**2) + 2*c*x*sqrt(a + b*x + c*x**2)), x)/e","F",0
2409,0,0,0,0.000000," ","integrate(1/(e*x+d)/((b*d*e-c*d**2)/e**2+b*x+c*x**2)**(1/2),x)","\int \frac{1}{\sqrt{\left(\frac{d}{e} + x\right) \left(b - \frac{c d}{e} + c x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(sqrt((d/e + x)*(b - c*d/e + c*x))*(d + e*x)), x)","F",0
2410,0,0,0,0.000000," ","integrate(2/(1/2*b*e/c+e*x)/(1/c*b**2+4*b*x+4*c*x**2)**(1/2),x)","\frac{4 c \int \frac{1}{b \sqrt{\frac{b^{2}}{c} + 4 b x + 4 c x^{2}} + 2 c x \sqrt{\frac{b^{2}}{c} + 4 b x + 4 c x^{2}}}\, dx}{e}"," ",0,"4*c*Integral(1/(b*sqrt(b**2/c + 4*b*x + 4*c*x**2) + 2*c*x*sqrt(b**2/c + 4*b*x + 4*c*x**2)), x)/e","F",0
2411,0,0,0,0.000000," ","integrate(x/(3*x**2+4*x+2)**(1/2),x)","\int \frac{x}{\sqrt{3 x^{2} + 4 x + 2}}\, dx"," ",0,"Integral(x/sqrt(3*x**2 + 4*x + 2), x)","F",0
2412,0,0,0,0.000000," ","integrate(x/(-3*x**2+4*x+2)**(1/2),x)","\int \frac{x}{\sqrt{- 3 x^{2} + 4 x + 2}}\, dx"," ",0,"Integral(x/sqrt(-3*x**2 + 4*x + 2), x)","F",0
2413,0,0,0,0.000000," ","integrate(x/(3*x**2+5*x+2)**(1/2),x)","\int \frac{x}{\sqrt{\left(x + 1\right) \left(3 x + 2\right)}}\, dx"," ",0,"Integral(x/sqrt((x + 1)*(3*x + 2)), x)","F",0
2414,0,0,0,0.000000," ","integrate(x/(-3*x**2+5*x+2)**(1/2),x)","\int \frac{x}{\sqrt{- \left(x - 2\right) \left(3 x + 1\right)}}\, dx"," ",0,"Integral(x/sqrt(-(x - 2)*(3*x + 1)), x)","F",0
2415,0,0,0,0.000000," ","integrate(x/(3*x**2+4*x-2)**(1/2),x)","\int \frac{x}{\sqrt{3 x^{2} + 4 x - 2}}\, dx"," ",0,"Integral(x/sqrt(3*x**2 + 4*x - 2), x)","F",0
2416,0,0,0,0.000000," ","integrate(x/(-3*x**2+4*x-2)**(1/2),x)","\int \frac{x}{\sqrt{- 3 x^{2} + 4 x - 2}}\, dx"," ",0,"Integral(x/sqrt(-3*x**2 + 4*x - 2), x)","F",0
2417,0,0,0,0.000000," ","integrate(x/(3*x**2+5*x-2)**(1/2),x)","\int \frac{x}{\sqrt{\left(x + 2\right) \left(3 x - 1\right)}}\, dx"," ",0,"Integral(x/sqrt((x + 2)*(3*x - 1)), x)","F",0
2418,0,0,0,0.000000," ","integrate(x/(-3*x**2+5*x-2)**(1/2),x)","\int \frac{x}{\sqrt{- \left(x - 1\right) \left(3 x - 2\right)}}\, dx"," ",0,"Integral(x/sqrt(-(x - 1)*(3*x - 2)), x)","F",0
2419,1,12,0,0.120847," ","integrate(1/x/((2+3*x)**2)**(1/2),x)","\frac{\log{\left(x \right)}}{2} - \frac{\log{\left(x + \frac{2}{3} \right)}}{2}"," ",0,"log(x)/2 - log(x + 2/3)/2","A",0
2420,1,12,0,0.121441," ","integrate(1/x/((-2+3*x)**2)**(1/2),x)","- \frac{\log{\left(x \right)}}{2} + \frac{\log{\left(x - \frac{2}{3} \right)}}{2}"," ",0,"-log(x)/2 + log(x - 2/3)/2","A",0
2421,0,0,0,0.000000," ","integrate(1/x/(-(-2+3*x)**2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(3 x - 2\right)^{2}}}\, dx"," ",0,"Integral(1/(x*sqrt(-(3*x - 2)**2)), x)","F",0
2422,0,0,0,0.000000," ","integrate(1/x/(-(2+3*x)**2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(3 x + 2\right)^{2}}}\, dx"," ",0,"Integral(1/(x*sqrt(-(3*x + 2)**2)), x)","F",0
2423,1,10,0,0.165955," ","integrate(1/x/((b*x+a)**2)**(1/2),x)","\frac{\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}}{a}"," ",0,"(log(x) - log(a/b + x))/a","A",0
2424,1,10,0,0.170843," ","integrate(1/x/((b*x-a)**2)**(1/2),x)","\frac{- \log{\left(x \right)} + \log{\left(- \frac{a}{b} + x \right)}}{a}"," ",0,"(-log(x) + log(-a/b + x))/a","A",0
2425,0,0,0,0.000000," ","integrate(1/x/(-(b*x-a)**2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(- a + b x\right)^{2}}}\, dx"," ",0,"Integral(1/(x*sqrt(-(-a + b*x)**2)), x)","F",0
2426,0,0,0,0.000000," ","integrate(1/x/(-(b*x+a)**2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(a + b x\right)^{2}}}\, dx"," ",0,"Integral(1/(x*sqrt(-(a + b*x)**2)), x)","F",0
2427,0,0,0,0.000000," ","integrate(x*(-x**2-2*x+3)**(1/2),x)","\int x \sqrt{- \left(x - 1\right) \left(x + 3\right)}\, dx"," ",0,"Integral(x*sqrt(-(x - 1)*(x + 3)), x)","F",0
2428,0,0,0,0.000000," ","integrate(x*(-x**2+2*x+8)**(1/2),x)","\int x \sqrt{- \left(x - 4\right) \left(x + 2\right)}\, dx"," ",0,"Integral(x*sqrt(-(x - 4)*(x + 2)), x)","F",0
2429,0,0,0,0.000000," ","integrate(x*(x**2+2*x+4)**(1/2),x)","\int x \sqrt{x^{2} + 2 x + 4}\, dx"," ",0,"Integral(x*sqrt(x**2 + 2*x + 4), x)","F",0
2430,0,0,0,0.000000," ","integrate(1/x/(3*x**2+4*x+2)**(1/2),x)","\int \frac{1}{x \sqrt{3 x^{2} + 4 x + 2}}\, dx"," ",0,"Integral(1/(x*sqrt(3*x**2 + 4*x + 2)), x)","F",0
2431,0,0,0,0.000000," ","integrate(1/x/(-3*x**2+4*x+2)**(1/2),x)","\int \frac{1}{x \sqrt{- 3 x^{2} + 4 x + 2}}\, dx"," ",0,"Integral(1/(x*sqrt(-3*x**2 + 4*x + 2)), x)","F",0
2432,0,0,0,0.000000," ","integrate(1/x/(3*x**2+5*x+2)**(1/2),x)","\int \frac{1}{x \sqrt{\left(x + 1\right) \left(3 x + 2\right)}}\, dx"," ",0,"Integral(1/(x*sqrt((x + 1)*(3*x + 2))), x)","F",0
2433,0,0,0,0.000000," ","integrate(1/x/(-3*x**2+5*x+2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(x - 2\right) \left(3 x + 1\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(-(x - 2)*(3*x + 1))), x)","F",0
2434,0,0,0,0.000000," ","integrate(1/x/(3*x**2+4*x-2)**(1/2),x)","\int \frac{1}{x \sqrt{3 x^{2} + 4 x - 2}}\, dx"," ",0,"Integral(1/(x*sqrt(3*x**2 + 4*x - 2)), x)","F",0
2435,0,0,0,0.000000," ","integrate(1/x/(-3*x**2+4*x-2)**(1/2),x)","\int \frac{1}{x \sqrt{- 3 x^{2} + 4 x - 2}}\, dx"," ",0,"Integral(1/(x*sqrt(-3*x**2 + 4*x - 2)), x)","F",0
2436,0,0,0,0.000000," ","integrate(1/x/(3*x**2+5*x-2)**(1/2),x)","\int \frac{1}{x \sqrt{\left(x + 2\right) \left(3 x - 1\right)}}\, dx"," ",0,"Integral(1/(x*sqrt((x + 2)*(3*x - 1))), x)","F",0
2437,0,0,0,0.000000," ","integrate(1/x/(-3*x**2+5*x-2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(x - 1\right) \left(3 x - 2\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(-(x - 1)*(3*x - 2))), x)","F",0
2438,0,0,0,0.000000," ","integrate(1/x**3/(x**2+x+1)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{x^{2} + x + 1}}\, dx"," ",0,"Integral(1/(x**3*sqrt(x**2 + x + 1)), x)","F",0
2439,0,0,0,0.000000," ","integrate(1/x-1/x/(c*x**2+b*x+1)**(1/2),x)","\int \frac{\sqrt{b x + c x^{2} + 1} - 1}{x \sqrt{b x + c x^{2} + 1}}\, dx"," ",0,"Integral((sqrt(b*x + c*x**2 + 1) - 1)/(x*sqrt(b*x + c*x**2 + 1)), x)","F",0
2440,0,0,0,0.000000," ","integrate((d*x)**(5/2)*(c*x**2+b*x+a)**(1/2),x)","\int \left(d x\right)^{\frac{5}{2}} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d*x)**(5/2)*sqrt(a + b*x + c*x**2), x)","F",0
2441,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right)^{\frac{3}{2}} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*sqrt(a + b*x + c*x**2), x)","F",0
2442,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(c*x**2+b*x+a)**(1/2),x)","\int \sqrt{d + e x} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral(sqrt(d + e*x)*sqrt(a + b*x + c*x**2), x)","F",0
2443,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/sqrt(d + e*x), x)","F",0
2444,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d + e*x)**(3/2), x)","F",0
2445,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d + e*x)**(5/2), x)","F",0
2446,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**(7/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d + e*x)**(7/2), x)","F",0
2447,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x+a)**(3/2),x)","\int \left(d + e x\right)^{\frac{3}{2}} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*(a + b*x + c*x**2)**(3/2), x)","F",0
2448,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(c*x**2+b*x+a)**(3/2),x)","\int \sqrt{d + e x} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(a + b*x + c*x**2)**(3/2), x)","F",0
2449,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2450,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**(3/2), x)","F",0
2451,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**(5/2), x)","F",0
2452,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**(7/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**(7/2), x)","F",0
2453,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**(9/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**(9/2), x)","F",0
2454,0,0,0,0.000000," ","integrate((d*x)**(1/2)*(c*x**2+b*x+a)**(5/2),x)","\int \sqrt{d x} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(sqrt(d*x)*(a + b*x + c*x**2)**(5/2), x)","F",0
2455,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2456,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2457,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2458,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2459,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2460,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2461,0,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{7}{2}}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**(7/2)/sqrt(a + b*x + c*x**2), x)","F",0
2462,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{5}{2}}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**(5/2)/sqrt(a + b*x + c*x**2), x)","F",0
2463,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/sqrt(a + b*x + c*x**2), x)","F",0
2464,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/sqrt(a + b*x + c*x**2), x)","F",0
2465,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\sqrt{d + e x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
2466,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{3}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(3/2)*sqrt(a + b*x + c*x**2)), x)","F",0
2467,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{5}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(5/2)*sqrt(a + b*x + c*x**2)), x)","F",0
2468,0,0,0,0.000000," ","integrate(1/(e*x+d)**(7/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{7}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(7/2)*sqrt(a + b*x + c*x**2)), x)","F",0
2469,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2470,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2471,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2472,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\sqrt{d + e x}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
2473,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\sqrt{d + e x} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(d + e*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
2474,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{3}{2}} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(3/2)*(a + b*x + c*x**2)**(3/2)), x)","F",0
2475,0,0,0,0.000000," ","integrate(1/(e*x+d)**(5/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{5}{2}} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(5/2)*(a + b*x + c*x**2)**(3/2)), x)","F",0
2476,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2477,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2478,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2479,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2480,-1,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2481,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x+a)**(5/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{3}{2}} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(3/2)*(a + b*x + c*x**2)**(5/2)), x)","F",0
2482,0,0,0,0.000000," ","integrate((3+5*x)**(1/2)/(-12*x**2+5*x+2)**(1/2),x)","\int \frac{\sqrt{5 x + 3}}{\sqrt{- \left(3 x - 2\right) \left(4 x + 1\right)}}\, dx"," ",0,"Integral(sqrt(5*x + 3)/sqrt(-(3*x - 2)*(4*x + 1)), x)","F",0
2483,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**(4/3),x)","\int \left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((d + e*x)**2*(a + b*x + c*x**2)**(4/3), x)","F",0
2484,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x+a)**(4/3),x)","\int \left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((d + e*x)*(a + b*x + c*x**2)**(4/3), x)","F",0
2485,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3),x)","\int \left(a + b x + c x^{2}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(4/3), x)","F",0
2486,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(e*x+d),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{4}{3}}}{d + e x}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(4/3)/(d + e*x), x)","F",0
2487,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(e*x+d)**2,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{4}{3}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(4/3)/(d + e*x)**2, x)","F",0
2488,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(4/3)/(e*x+d)**3,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{4}{3}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(4/3)/(d + e*x)**3, x)","F",0
2489,-1,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**(7/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2490,-1,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**(7/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2491,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x+a)**(7/3),x)","\int \frac{d + e x}{\left(a + b x + c x^{2}\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral((d + e*x)/(a + b*x + c*x**2)**(7/3), x)","F",0
2492,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x+a)**(7/3),x)","\int \frac{1}{\left(a + b x + c x^{2}\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(-7/3), x)","F",0
2493,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**(7/3),x)","\int \frac{1}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral(1/((d + e*x)*(a + b*x + c*x**2)**(7/3)), x)","F",0
2494,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x+a)**(7/3),x)","\int \frac{1}{\left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral(1/((d + e*x)**2*(a + b*x + c*x**2)**(7/3)), x)","F",0
2495,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x+a)**(7/3),x)","\int \frac{1}{\left(d + e x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral(1/((d + e*x)**3*(a + b*x + c*x**2)**(7/3)), x)","F",0
2496,0,0,0,0.000000," ","integrate(1/(e*x+d)/(3*c**2*e**2*x**2+3*b*c*e**2*x+b**2*e**2-b*c*d*e+c**2*d**2)**(1/3),x)","\int \frac{1}{\left(d + e x\right) \sqrt[3]{b^{2} e^{2} - b c d e + 3 b c e^{2} x + c^{2} d^{2} + 3 c^{2} e^{2} x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(b**2*e**2 - b*c*d*e + 3*b*c*e**2*x + c**2*d**2 + 3*c**2*e**2*x**2)**(1/3)), x)","F",0
2497,0,0,0,0.000000," ","integrate((2+3*x)**3/(27*x**2-54*x+52)**(1/3),x)","\int \frac{\left(3 x + 2\right)^{3}}{\sqrt[3]{27 x^{2} - 54 x + 52}}\, dx"," ",0,"Integral((3*x + 2)**3/(27*x**2 - 54*x + 52)**(1/3), x)","F",0
2498,0,0,0,0.000000," ","integrate((2+3*x)**2/(27*x**2-54*x+52)**(1/3),x)","\int \frac{\left(3 x + 2\right)^{2}}{\sqrt[3]{27 x^{2} - 54 x + 52}}\, dx"," ",0,"Integral((3*x + 2)**2/(27*x**2 - 54*x + 52)**(1/3), x)","F",0
2499,0,0,0,0.000000," ","integrate((2+3*x)/(27*x**2-54*x+52)**(1/3),x)","\int \frac{3 x + 2}{\sqrt[3]{27 x^{2} - 54 x + 52}}\, dx"," ",0,"Integral((3*x + 2)/(27*x**2 - 54*x + 52)**(1/3), x)","F",0
2500,0,0,0,0.000000," ","integrate(1/(2+3*x)/(27*x**2-54*x+52)**(1/3),x)","\int \frac{1}{\left(3 x + 2\right) \sqrt[3]{27 x^{2} - 54 x + 52}}\, dx"," ",0,"Integral(1/((3*x + 2)*(27*x**2 - 54*x + 52)**(1/3)), x)","F",0
2501,0,0,0,0.000000," ","integrate(1/(2+3*x)**2/(27*x**2-54*x+52)**(1/3),x)","\int \frac{1}{\left(3 x + 2\right)^{2} \sqrt[3]{27 x^{2} - 54 x + 52}}\, dx"," ",0,"Integral(1/((3*x + 2)**2*(27*x**2 - 54*x + 52)**(1/3)), x)","F",0
2502,0,0,0,0.000000," ","integrate(1/(2+3*x)**3/(27*x**2-54*x+52)**(1/3),x)","\int \frac{1}{\left(3 x + 2\right)^{3} \sqrt[3]{27 x^{2} - 54 x + 52}}\, dx"," ",0,"Integral(1/((3*x + 2)**3*(27*x**2 - 54*x + 52)**(1/3)), x)","F",0
2503,0,0,0,0.000000," ","integrate((2+3*x)**3/(27*x**2+54*x+28)**(1/3),x)","\int \frac{\left(3 x + 2\right)^{3}}{\sqrt[3]{27 x^{2} + 54 x + 28}}\, dx"," ",0,"Integral((3*x + 2)**3/(27*x**2 + 54*x + 28)**(1/3), x)","F",0
2504,0,0,0,0.000000," ","integrate((2+3*x)**2/(27*x**2+54*x+28)**(1/3),x)","\int \frac{\left(3 x + 2\right)^{2}}{\sqrt[3]{27 x^{2} + 54 x + 28}}\, dx"," ",0,"Integral((3*x + 2)**2/(27*x**2 + 54*x + 28)**(1/3), x)","F",0
2505,0,0,0,0.000000," ","integrate((2+3*x)/(27*x**2+54*x+28)**(1/3),x)","\int \frac{3 x + 2}{\sqrt[3]{27 x^{2} + 54 x + 28}}\, dx"," ",0,"Integral((3*x + 2)/(27*x**2 + 54*x + 28)**(1/3), x)","F",0
2506,0,0,0,0.000000," ","integrate(1/(2+3*x)/(27*x**2+54*x+28)**(1/3),x)","\int \frac{1}{\left(3 x + 2\right) \sqrt[3]{27 x^{2} + 54 x + 28}}\, dx"," ",0,"Integral(1/((3*x + 2)*(27*x**2 + 54*x + 28)**(1/3)), x)","F",0
2507,0,0,0,0.000000," ","integrate(1/(2+3*x)**2/(27*x**2+54*x+28)**(1/3),x)","\int \frac{1}{\left(3 x + 2\right)^{2} \sqrt[3]{27 x^{2} + 54 x + 28}}\, dx"," ",0,"Integral(1/((3*x + 2)**2*(27*x**2 + 54*x + 28)**(1/3)), x)","F",0
2508,0,0,0,0.000000," ","integrate(1/(2+3*x)**3/(27*x**2+54*x+28)**(1/3),x)","\int \frac{1}{\left(3 x + 2\right)^{3} \sqrt[3]{27 x^{2} + 54 x + 28}}\, dx"," ",0,"Integral(1/((3*x + 2)**3*(27*x**2 + 54*x + 28)**(1/3)), x)","F",0
2509,0,0,0,0.000000," ","integrate(1/(e*x+d)/(9*c**2*e**2*x**2+9*b*c*e**2*x+2*b**2*e**2+b*c*d*e-c**2*d**2)**(1/3),x)","\int \frac{1}{\sqrt[3]{\left(b e + c d + 3 c e x\right) \left(2 b e - c d + 3 c e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(((b*e + c*d + 3*c*e*x)*(2*b*e - c*d + 3*c*e*x))**(1/3)*(d + e*x)), x)","F",0
2510,0,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**(1/4),x)","\int \left(d + e x\right)^{3} \sqrt[4]{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**3*(a + b*x + c*x**2)**(1/4), x)","F",0
2511,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**(1/4),x)","\int \left(d + e x\right)^{2} \sqrt[4]{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**2*(a + b*x + c*x**2)**(1/4), x)","F",0
2512,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x+a)**(1/4),x)","\int \left(d + e x\right) \sqrt[4]{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)*(a + b*x + c*x**2)**(1/4), x)","F",0
2513,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/4),x)","\int \sqrt[4]{a + b x + c x^{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(1/4), x)","F",0
2514,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/4)/(e*x+d),x)","\int \frac{\sqrt[4]{a + b x + c x^{2}}}{d + e x}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(1/4)/(d + e*x), x)","F",0
2515,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/4)/(e*x+d)**2,x)","\int \frac{\sqrt[4]{a + b x + c x^{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(1/4)/(d + e*x)**2, x)","F",0
2516,0,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**(3/4),x)","\int \left(d + e x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{3}{4}}\, dx"," ",0,"Integral((d + e*x)**3*(a + b*x + c*x**2)**(3/4), x)","F",0
2517,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**(3/4),x)","\int \left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{3}{4}}\, dx"," ",0,"Integral((d + e*x)**2*(a + b*x + c*x**2)**(3/4), x)","F",0
2518,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x+a)**(3/4),x)","\int \left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{4}}\, dx"," ",0,"Integral((d + e*x)*(a + b*x + c*x**2)**(3/4), x)","F",0
2519,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/4),x)","\int \left(a + b x + c x^{2}\right)^{\frac{3}{4}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/4), x)","F",0
2520,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/4)/(e*x+d),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{4}}}{d + e x}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/4)/(d + e*x), x)","F",0
2521,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/4)/(e*x+d)**2,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{4}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/4)/(d + e*x)**2, x)","F",0
2522,0,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**(5/4),x)","\int \left(d + e x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{5}{4}}\, dx"," ",0,"Integral((d + e*x)**3*(a + b*x + c*x**2)**(5/4), x)","F",0
2523,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**(5/4),x)","\int \left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{5}{4}}\, dx"," ",0,"Integral((d + e*x)**2*(a + b*x + c*x**2)**(5/4), x)","F",0
2524,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x+a)**(5/4),x)","\int \left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{4}}\, dx"," ",0,"Integral((d + e*x)*(a + b*x + c*x**2)**(5/4), x)","F",0
2525,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/4),x)","\int \left(a + b x + c x^{2}\right)^{\frac{5}{4}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/4), x)","F",0
2526,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/4)/(e*x+d),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{4}}}{d + e x}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/4)/(d + e*x), x)","F",0
2527,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/4)/(e*x+d)**2,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{5}{4}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(5/4)/(d + e*x)**2, x)","F",0
2528,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**(1/4),x)","\int \frac{\left(d + e x\right)^{3}}{\sqrt[4]{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(a + b*x + c*x**2)**(1/4), x)","F",0
2529,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**(1/4),x)","\int \frac{\left(d + e x\right)^{2}}{\sqrt[4]{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(a + b*x + c*x**2)**(1/4), x)","F",0
2530,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x+a)**(1/4),x)","\int \frac{d + e x}{\sqrt[4]{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)/(a + b*x + c*x**2)**(1/4), x)","F",0
2531,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x+a)**(1/4),x)","\int \frac{1}{\sqrt[4]{a + b x + c x^{2}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(-1/4), x)","F",0
2532,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**(1/4),x)","\int \frac{1}{\left(d + e x\right) \sqrt[4]{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(a + b*x + c*x**2)**(1/4)), x)","F",0
2533,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x+a)**(1/4),x)","\int \frac{1}{\left(d + e x\right)^{2} \sqrt[4]{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**2*(a + b*x + c*x**2)**(1/4)), x)","F",0
2534,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x+a)**(1/4),x)","\int \frac{1}{\left(d + e x\right)^{3} \sqrt[4]{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**3*(a + b*x + c*x**2)**(1/4)), x)","F",0
2535,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**(3/4),x)","\int \frac{\left(d + e x\right)^{3}}{\left(a + b x + c x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((d + e*x)**3/(a + b*x + c*x**2)**(3/4), x)","F",0
2536,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**(3/4),x)","\int \frac{\left(d + e x\right)^{2}}{\left(a + b x + c x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((d + e*x)**2/(a + b*x + c*x**2)**(3/4), x)","F",0
2537,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x+a)**(3/4),x)","\int \frac{d + e x}{\left(a + b x + c x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((d + e*x)/(a + b*x + c*x**2)**(3/4), x)","F",0
2538,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x+a)**(3/4),x)","\int \frac{1}{\left(a + b x + c x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(-3/4), x)","F",0
2539,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**(3/4),x)","\int \frac{1}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((d + e*x)*(a + b*x + c*x**2)**(3/4)), x)","F",0
2540,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x+a)**(3/4),x)","\int \frac{1}{\left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((d + e*x)**2*(a + b*x + c*x**2)**(3/4)), x)","F",0
2541,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**2+b*x+a)**(3/4),x)","\int \frac{1}{\left(d + e x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((d + e*x)**3*(a + b*x + c*x**2)**(3/4)), x)","F",0
2542,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**2+b*x+a)**(5/4),x)","\int \frac{\left(d + e x\right)^{3}}{\left(a + b x + c x^{2}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((d + e*x)**3/(a + b*x + c*x**2)**(5/4), x)","F",0
2543,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**2+b*x+a)**(5/4),x)","\int \frac{\left(d + e x\right)^{2}}{\left(a + b x + c x^{2}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((d + e*x)**2/(a + b*x + c*x**2)**(5/4), x)","F",0
2544,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x+a)**(5/4),x)","\int \frac{d + e x}{\left(a + b x + c x^{2}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((d + e*x)/(a + b*x + c*x**2)**(5/4), x)","F",0
2545,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x+a)**(5/4),x)","\int \frac{1}{\left(a + b x + c x^{2}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(-5/4), x)","F",0
2546,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**(5/4),x)","\int \frac{1}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((d + e*x)*(a + b*x + c*x**2)**(5/4)), x)","F",0
2547,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+b*x+a)**(5/4),x)","\int \frac{1}{\left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((d + e*x)**2*(a + b*x + c*x**2)**(5/4)), x)","F",0
2548,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x+a)**(1/4),x)","\int \frac{1}{\left(d + e x\right)^{\frac{3}{2}} \sqrt[4]{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**(3/2)*(a + b*x + c*x**2)**(1/4)), x)","F",0
2549,-1,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2550,-1,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2551,1,10171,0,10.310154," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**2,x)","\begin{cases} d^{m} \left(a^{2} x + a b x^{2} + \frac{2 a c x^{3}}{3} + \frac{b^{2} x^{3}}{3} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{5}}{5}\right) & \text{for}\: e = 0 \\- \frac{3 a^{2} e^{4}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{2 a b d e^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{8 a b e^{4} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{2 a c d^{2} e^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{8 a c d e^{3} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{12 a c e^{4} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{b^{2} d^{2} e^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{4 b^{2} d e^{3} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{6 b^{2} e^{4} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{6 b c d^{3} e}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{24 b c d^{2} e^{2} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{36 b c d e^{3} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{24 b c e^{4} x^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{25 c^{2} d^{4}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{88 c^{2} d^{3} e x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{72 c^{2} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{108 c^{2} d^{2} e^{2} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c^{2} d e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c^{2} d e^{3} x^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{12 c^{2} e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} & \text{for}\: m = -5 \\- \frac{a^{2} e^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{a b d e^{3}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{3 a b e^{4} x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{2 a c d^{2} e^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{6 a c d e^{3} x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{6 a c e^{4} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{b^{2} d^{2} e^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{3 b^{2} d e^{3} x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{3 b^{2} e^{4} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{6 b c d^{3} e \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{11 b c d^{3} e}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{18 b c d^{2} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{27 b c d^{2} e^{2} x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{18 b c d e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{18 b c d e^{3} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{6 b c e^{4} x^{3} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{22 c^{2} d^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{54 c^{2} d^{3} e x}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 c^{2} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{36 c^{2} d^{2} e^{2} x^{2}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} - \frac{12 c^{2} d e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} + \frac{3 c^{2} e^{4} x^{4}}{3 d^{3} e^{5} + 9 d^{2} e^{6} x + 9 d e^{7} x^{2} + 3 e^{8} x^{3}} & \text{for}\: m = -4 \\- \frac{a^{2} e^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{2 a b d e^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{4 a b e^{4} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 a c d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{6 a c d^{2} e^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{8 a c d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{8 a c d e^{3} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 a c e^{4} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 b^{2} d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{3 b^{2} d^{2} e^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 b^{2} d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 b^{2} d e^{3} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 b^{2} e^{4} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{12 b c d^{3} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{18 b c d^{3} e}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{24 b c d^{2} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{24 b c d^{2} e^{2} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{12 b c d e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 b c e^{4} x^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{18 c^{2} d^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 c^{2} d^{3} e x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 c^{2} d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{4 c^{2} d e^{3} x^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{c^{2} e^{4} x^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} & \text{for}\: m = -3 \\- \frac{3 a^{2} e^{4}}{3 d e^{5} + 3 e^{6} x} + \frac{6 a b d e^{3} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{6 a b d e^{3}}{3 d e^{5} + 3 e^{6} x} + \frac{6 a b e^{4} x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{12 a c d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{12 a c d^{2} e^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{12 a c d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{6 a c e^{4} x^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{6 b^{2} d^{2} e^{2} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{6 b^{2} d^{2} e^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{6 b^{2} d e^{3} x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{3 b^{2} e^{4} x^{2}}{3 d e^{5} + 3 e^{6} x} + \frac{18 b c d^{3} e \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{18 b c d^{3} e}{3 d e^{5} + 3 e^{6} x} + \frac{18 b c d^{2} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{9 b c d e^{3} x^{2}}{3 d e^{5} + 3 e^{6} x} + \frac{3 b c e^{4} x^{3}}{3 d e^{5} + 3 e^{6} x} - \frac{12 c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} - \frac{12 c^{2} d^{4}}{3 d e^{5} + 3 e^{6} x} - \frac{12 c^{2} d^{3} e x \log{\left(\frac{d}{e} + x \right)}}{3 d e^{5} + 3 e^{6} x} + \frac{6 c^{2} d^{2} e^{2} x^{2}}{3 d e^{5} + 3 e^{6} x} - \frac{2 c^{2} d e^{3} x^{3}}{3 d e^{5} + 3 e^{6} x} + \frac{c^{2} e^{4} x^{4}}{3 d e^{5} + 3 e^{6} x} & \text{for}\: m = -2 \\\frac{a^{2} \log{\left(\frac{d}{e} + x \right)}}{e} - \frac{2 a b d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{2 a b x}{e} + \frac{2 a c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{2 a c d x}{e^{2}} + \frac{a c x^{2}}{e} + \frac{b^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{b^{2} d x}{e^{2}} + \frac{b^{2} x^{2}}{2 e} - \frac{2 b c d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{2 b c d^{2} x}{e^{3}} - \frac{b c d x^{2}}{e^{2}} + \frac{2 b c x^{3}}{3 e} + \frac{c^{2} d^{4} \log{\left(\frac{d}{e} + x \right)}}{e^{5}} - \frac{c^{2} d^{3} x}{e^{4}} + \frac{c^{2} d^{2} x^{2}}{2 e^{3}} - \frac{c^{2} d x^{3}}{3 e^{2}} + \frac{c^{2} x^{4}}{4 e} & \text{for}\: m = -1 \\\frac{a^{2} d e^{4} m^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{14 a^{2} d e^{4} m^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{71 a^{2} d e^{4} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{154 a^{2} d e^{4} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a^{2} d e^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{a^{2} e^{5} m^{4} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{14 a^{2} e^{5} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{71 a^{2} e^{5} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{154 a^{2} e^{5} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a^{2} e^{5} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{2 a b d^{2} e^{3} m^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{24 a b d^{2} e^{3} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{94 a b d^{2} e^{3} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{120 a b d^{2} e^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 a b d e^{4} m^{4} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 a b d e^{4} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{94 a b d e^{4} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a b d e^{4} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 a b e^{5} m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{26 a b e^{5} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{118 a b e^{5} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{214 a b e^{5} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a b e^{5} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{4 a c d^{3} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{36 a c d^{3} e^{2} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{80 a c d^{3} e^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{4 a c d^{2} e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{36 a c d^{2} e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{80 a c d^{2} e^{3} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 a c d e^{4} m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{20 a c d e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{58 a c d e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 a c d e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 a c e^{5} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 a c e^{5} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{98 a c e^{5} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{156 a c e^{5} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{80 a c e^{5} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 b^{2} d^{3} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{18 b^{2} d^{3} e^{2} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 b^{2} d^{3} e^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{2 b^{2} d^{2} e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{18 b^{2} d^{2} e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{40 b^{2} d^{2} e^{3} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{b^{2} d e^{4} m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{10 b^{2} d e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{29 b^{2} d e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{20 b^{2} d e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{b^{2} e^{5} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 b^{2} e^{5} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{49 b^{2} e^{5} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{78 b^{2} e^{5} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 b^{2} e^{5} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 b c d^{4} e m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{60 b c d^{4} e \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 b c d^{3} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{60 b c d^{3} e^{2} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{6 b c d^{2} e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{36 b c d^{2} e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{30 b c d^{2} e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 b c d e^{4} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{16 b c d e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{34 b c d e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{20 b c d e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 b c e^{5} m^{4} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{22 b c e^{5} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{82 b c e^{5} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{122 b c e^{5} m x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{60 b c e^{5} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 c^{2} d^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{24 c^{2} d^{4} e m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 c^{2} d^{3} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 c^{2} d^{3} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{4 c^{2} d^{2} e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 c^{2} d^{2} e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{8 c^{2} d^{2} e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{c^{2} d e^{4} m^{4} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 c^{2} d e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{11 c^{2} d e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 c^{2} d e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{c^{2} e^{5} m^{4} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{10 c^{2} e^{5} m^{3} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{35 c^{2} e^{5} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{50 c^{2} e^{5} m x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 c^{2} e^{5} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a**2*x + a*b*x**2 + 2*a*c*x**3/3 + b**2*x**3/3 + b*c*x**4/2 + c**2*x**5/5), Eq(e, 0)), (-3*a**2*e**4/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 2*a*b*d*e**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 8*a*b*e**4*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 2*a*c*d**2*e**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 8*a*c*d*e**3*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 12*a*c*e**4*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - b**2*d**2*e**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 4*b**2*d*e**3*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 6*b**2*e**4*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 6*b*c*d**3*e/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 24*b*c*d**2*e**2*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 36*b*c*d*e**3*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 24*b*c*e**4*x**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 12*c**2*d**4*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 25*c**2*d**4/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c**2*d**3*e*x*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 88*c**2*d**3*e*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 72*c**2*d**2*e**2*x**2*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 108*c**2*d**2*e**2*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c**2*d*e**3*x**3*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c**2*d*e**3*x**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 12*c**2*e**4*x**4*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4), Eq(m, -5)), (-a**2*e**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - a*b*d*e**3/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 3*a*b*e**4*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 2*a*c*d**2*e**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 6*a*c*d*e**3*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 6*a*c*e**4*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - b**2*d**2*e**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 3*b**2*d*e**3*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 3*b**2*e**4*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 6*b*c*d**3*e*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 11*b*c*d**3*e/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 18*b*c*d**2*e**2*x*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 27*b*c*d**2*e**2*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 18*b*c*d*e**3*x**2*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 18*b*c*d*e**3*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 6*b*c*e**4*x**3*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 12*c**2*d**4*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 22*c**2*d**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*c**2*d**3*e*x*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 54*c**2*d**3*e*x/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*c**2*d**2*e**2*x**2*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 36*c**2*d**2*e**2*x**2/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) - 12*c**2*d*e**3*x**3*log(d/e + x)/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3) + 3*c**2*e**4*x**4/(3*d**3*e**5 + 9*d**2*e**6*x + 9*d*e**7*x**2 + 3*e**8*x**3), Eq(m, -4)), (-a**2*e**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 2*a*b*d*e**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 4*a*b*e**4*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*a*c*d**2*e**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 6*a*c*d**2*e**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 8*a*c*d*e**3*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 8*a*c*d*e**3*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*a*c*e**4*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*b**2*d**2*e**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 3*b**2*d**2*e**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*b**2*d*e**3*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*b**2*d*e**3*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*b**2*e**4*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 12*b*c*d**3*e*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 18*b*c*d**3*e/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 24*b*c*d**2*e**2*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 24*b*c*d**2*e**2*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 12*b*c*d*e**3*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*b*c*e**4*x**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*c**2*d**4*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 18*c**2*d**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*c**2*d**3*e*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*c**2*d**3*e*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*c**2*d**2*e**2*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 4*c**2*d*e**3*x**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + c**2*e**4*x**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2), Eq(m, -3)), (-3*a**2*e**4/(3*d*e**5 + 3*e**6*x) + 6*a*b*d*e**3*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 6*a*b*d*e**3/(3*d*e**5 + 3*e**6*x) + 6*a*b*e**4*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 12*a*c*d**2*e**2*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 12*a*c*d**2*e**2/(3*d*e**5 + 3*e**6*x) - 12*a*c*d*e**3*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 6*a*c*e**4*x**2/(3*d*e**5 + 3*e**6*x) - 6*b**2*d**2*e**2*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 6*b**2*d**2*e**2/(3*d*e**5 + 3*e**6*x) - 6*b**2*d*e**3*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 3*b**2*e**4*x**2/(3*d*e**5 + 3*e**6*x) + 18*b*c*d**3*e*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 18*b*c*d**3*e/(3*d*e**5 + 3*e**6*x) + 18*b*c*d**2*e**2*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 9*b*c*d*e**3*x**2/(3*d*e**5 + 3*e**6*x) + 3*b*c*e**4*x**3/(3*d*e**5 + 3*e**6*x) - 12*c**2*d**4*log(d/e + x)/(3*d*e**5 + 3*e**6*x) - 12*c**2*d**4/(3*d*e**5 + 3*e**6*x) - 12*c**2*d**3*e*x*log(d/e + x)/(3*d*e**5 + 3*e**6*x) + 6*c**2*d**2*e**2*x**2/(3*d*e**5 + 3*e**6*x) - 2*c**2*d*e**3*x**3/(3*d*e**5 + 3*e**6*x) + c**2*e**4*x**4/(3*d*e**5 + 3*e**6*x), Eq(m, -2)), (a**2*log(d/e + x)/e - 2*a*b*d*log(d/e + x)/e**2 + 2*a*b*x/e + 2*a*c*d**2*log(d/e + x)/e**3 - 2*a*c*d*x/e**2 + a*c*x**2/e + b**2*d**2*log(d/e + x)/e**3 - b**2*d*x/e**2 + b**2*x**2/(2*e) - 2*b*c*d**3*log(d/e + x)/e**4 + 2*b*c*d**2*x/e**3 - b*c*d*x**2/e**2 + 2*b*c*x**3/(3*e) + c**2*d**4*log(d/e + x)/e**5 - c**2*d**3*x/e**4 + c**2*d**2*x**2/(2*e**3) - c**2*d*x**3/(3*e**2) + c**2*x**4/(4*e), Eq(m, -1)), (a**2*d*e**4*m**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 14*a**2*d*e**4*m**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 71*a**2*d*e**4*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 154*a**2*d*e**4*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a**2*d*e**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + a**2*e**5*m**4*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 14*a**2*e**5*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 71*a**2*e**5*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 154*a**2*e**5*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a**2*e**5*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 2*a*b*d**2*e**3*m**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 24*a*b*d**2*e**3*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 94*a*b*d**2*e**3*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 120*a*b*d**2*e**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*a*b*d*e**4*m**4*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*a*b*d*e**4*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 94*a*b*d*e**4*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a*b*d*e**4*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*a*b*e**5*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 26*a*b*e**5*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 118*a*b*e**5*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 214*a*b*e**5*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a*b*e**5*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 4*a*c*d**3*e**2*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 36*a*c*d**3*e**2*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 80*a*c*d**3*e**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 4*a*c*d**2*e**3*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 36*a*c*d**2*e**3*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 80*a*c*d**2*e**3*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*a*c*d*e**4*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 20*a*c*d*e**4*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 58*a*c*d*e**4*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*a*c*d*e**4*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*a*c*e**5*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*a*c*e**5*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 98*a*c*e**5*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 156*a*c*e**5*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 80*a*c*e**5*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*b**2*d**3*e**2*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 18*b**2*d**3*e**2*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*b**2*d**3*e**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 2*b**2*d**2*e**3*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 18*b**2*d**2*e**3*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 40*b**2*d**2*e**3*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + b**2*d*e**4*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 10*b**2*d*e**4*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 29*b**2*d*e**4*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 20*b**2*d*e**4*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + b**2*e**5*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*b**2*e**5*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 49*b**2*e**5*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 78*b**2*e**5*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*b**2*e**5*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*b*c*d**4*e*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 60*b*c*d**4*e*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*b*c*d**3*e**2*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 60*b*c*d**3*e**2*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 6*b*c*d**2*e**3*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 36*b*c*d**2*e**3*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 30*b*c*d**2*e**3*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*b*c*d*e**4*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 16*b*c*d*e**4*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 34*b*c*d*e**4*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 20*b*c*d*e**4*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*b*c*e**5*m**4*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 22*b*c*e**5*m**3*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 82*b*c*e**5*m**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 122*b*c*e**5*m*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 60*b*c*e**5*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*c**2*d**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 24*c**2*d**4*e*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*c**2*d**3*e**2*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*c**2*d**3*e**2*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 4*c**2*d**2*e**3*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*c**2*d**2*e**3*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 8*c**2*d**2*e**3*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + c**2*d*e**4*m**4*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*c**2*d*e**4*m**3*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 11*c**2*d*e**4*m**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*c**2*d*e**4*m*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + c**2*e**5*m**4*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 10*c**2*e**5*m**3*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 35*c**2*e**5*m**2*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 50*c**2*e**5*m*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*c**2*e**5*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5), True))","A",0
2552,1,1416,0,2.138376," ","integrate((e*x+d)**m*(c*x**2+b*x+a),x)","\begin{cases} d^{m} \left(a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3}\right) & \text{for}\: e = 0 \\- \frac{a e^{2}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} - \frac{b d e}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} - \frac{2 b e^{2} x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 c d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{3 c d^{2}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 c d e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{4 c d e x}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} + \frac{2 c e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}} & \text{for}\: m = -3 \\- \frac{a e^{2}}{d e^{3} + e^{4} x} + \frac{b d e \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} + \frac{b d e}{d e^{3} + e^{4} x} + \frac{b e^{2} x \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{2 c d^{2} \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} - \frac{2 c d^{2}}{d e^{3} + e^{4} x} - \frac{2 c d e x \log{\left(\frac{d}{e} + x \right)}}{d e^{3} + e^{4} x} + \frac{c e^{2} x^{2}}{d e^{3} + e^{4} x} & \text{for}\: m = -2 \\\frac{a \log{\left(\frac{d}{e} + x \right)}}{e} - \frac{b d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{b x}{e} + \frac{c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{c d x}{e^{2}} + \frac{c x^{2}}{2 e} & \text{for}\: m = -1 \\\frac{a d e^{2} m^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{5 a d e^{2} m \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{6 a d e^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{a e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{5 a e^{3} m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{6 a e^{3} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} - \frac{b d^{2} e m \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} - \frac{3 b d^{2} e \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{b d e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{3 b d e^{2} m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{b e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{4 b e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{3 b e^{3} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{2 c d^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} - \frac{2 c d^{2} e m x \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{c d e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{c d e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{c e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{3 c e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} + \frac{2 c e^{3} x^{3} \left(d + e x\right)^{m}}{e^{3} m^{3} + 6 e^{3} m^{2} + 11 e^{3} m + 6 e^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a*x + b*x**2/2 + c*x**3/3), Eq(e, 0)), (-a*e**2/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) - b*d*e/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) - 2*b*e**2*x/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*c*d**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 3*c*d**2/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*c*d*e*x*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 4*c*d*e*x/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2) + 2*c*e**2*x**2*log(d/e + x)/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2), Eq(m, -3)), (-a*e**2/(d*e**3 + e**4*x) + b*d*e*log(d/e + x)/(d*e**3 + e**4*x) + b*d*e/(d*e**3 + e**4*x) + b*e**2*x*log(d/e + x)/(d*e**3 + e**4*x) - 2*c*d**2*log(d/e + x)/(d*e**3 + e**4*x) - 2*c*d**2/(d*e**3 + e**4*x) - 2*c*d*e*x*log(d/e + x)/(d*e**3 + e**4*x) + c*e**2*x**2/(d*e**3 + e**4*x), Eq(m, -2)), (a*log(d/e + x)/e - b*d*log(d/e + x)/e**2 + b*x/e + c*d**2*log(d/e + x)/e**3 - c*d*x/e**2 + c*x**2/(2*e), Eq(m, -1)), (a*d*e**2*m**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 5*a*d*e**2*m*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 6*a*d*e**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + a*e**3*m**2*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 5*a*e**3*m*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 6*a*e**3*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) - b*d**2*e*m*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) - 3*b*d**2*e*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + b*d*e**2*m**2*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 3*b*d*e**2*m*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + b*e**3*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 4*b*e**3*m*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 3*b*e**3*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 2*c*d**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) - 2*c*d**2*e*m*x*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + c*d*e**2*m**2*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + c*d*e**2*m*x**2*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + c*e**3*m**2*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 3*c*e**3*m*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3) + 2*c*e**3*x**3*(d + e*x)**m/(e**3*m**3 + 6*e**3*m**2 + 11*e**3*m + 6*e**3), True))","A",0
2553,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x+a),x)","\int \frac{\left(d + e x\right)^{m}}{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*x + c*x**2), x)","F",0
2554,-1,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2555,-2,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**(5/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2556,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**(3/2),x)","\int \left(d + e x\right)^{m} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x)**m*(a + b*x + c*x**2)**(3/2), x)","F",0
2557,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right)^{m} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**m*sqrt(a + b*x + c*x**2), x)","F",0
2558,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{m}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**m/sqrt(a + b*x + c*x**2), x)","F",0
2559,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*x + c*x**2)**(3/2), x)","F",0
2560,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x+a)**(5/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(a + b x + c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*x + c*x**2)**(5/2), x)","F",0
2561,-1,0,0,0.000000," ","integrate((d*x)**m*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2562,-1,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2563,-1,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2564,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**p,x)","\int \left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{p}\, dx"," ",0,"Integral((d + e*x)**2*(a + b*x + c*x**2)**p, x)","F",0
2565,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x+a)**p,x)","\int \left(d + e x\right) \left(a + b x + c x^{2}\right)^{p}\, dx"," ",0,"Integral((d + e*x)*(a + b*x + c*x**2)**p, x)","F",0
2566,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p,x)","\int \left(a + b x + c x^{2}\right)^{p}\, dx"," ",0,"Integral((a + b*x + c*x**2)**p, x)","F",0
2567,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(e*x+d),x)","\int \frac{\left(a + b x + c x^{2}\right)^{p}}{d + e x}\, dx"," ",0,"Integral((a + b*x + c*x**2)**p/(d + e*x), x)","F",0
2568,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2569,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2570,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2571,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2572,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(e*x+d)**(1/2),x)","\int \frac{\left(a + b x + c x^{2}\right)^{p}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**p/sqrt(d + e*x), x)","F",0
2573,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2574,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**p/((e*x+d)**(2*p)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2575,-1,0,0,0.000000," ","integrate((e*x+d)**(-1-2*p)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2576,-2,0,0,0.000000," ","integrate((e*x+d)**(-2-2*p)*(c*x**2+b*x+a)**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2577,-1,0,0,0.000000," ","integrate((e*x+d)**(-3-2*p)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2578,-1,0,0,0.000000," ","integrate((e*x+d)**(-4-2*p)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2579,-1,0,0,0.000000," ","integrate((e*x+d)**(-5-2*p)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2580,-1,0,0,0.000000," ","integrate((e*x+d)**(-6-2*p)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2581,-1,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**(-2-1/2*m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2582,0,0,0,0.000000," ","integrate(1/(1+x)**(1/3)/(x**2-x+1)**(1/3),x)","\int \frac{1}{\sqrt[3]{x + 1} \sqrt[3]{x^{2} - x + 1}}\, dx"," ",0,"Integral(1/((x + 1)**(1/3)*(x**2 - x + 1)**(1/3)), x)","F",0
2583,0,0,0,0.000000," ","integrate(1/(1+x)**(2/3)/(x**2-x+1)**(2/3),x)","\int \frac{1}{\left(x + 1\right)^{\frac{2}{3}} \left(x^{2} - x + 1\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((x + 1)**(2/3)*(x**2 - x + 1)**(2/3)), x)","F",0
2584,0,0,0,0.000000," ","integrate((1+x)**p*(x**2-x+1)**p,x)","\int \left(x + 1\right)^{p} \left(x^{2} - x + 1\right)^{p}\, dx"," ",0,"Integral((x + 1)**p*(x**2 - x + 1)**p, x)","F",0
2585,0,0,0,0.000000," ","integrate(1/(1-x)**(1/3)/(x**2+x+1)**(1/3),x)","\int \frac{1}{\sqrt[3]{1 - x} \sqrt[3]{x^{2} + x + 1}}\, dx"," ",0,"Integral(1/((1 - x)**(1/3)*(x**2 + x + 1)**(1/3)), x)","F",0
2586,0,0,0,0.000000," ","integrate(1/(1-x)**(2/3)/(x**2+x+1)**(2/3),x)","\int \frac{1}{\left(1 - x\right)^{\frac{2}{3}} \left(x^{2} + x + 1\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((1 - x)**(2/3)*(x**2 + x + 1)**(2/3)), x)","F",0
2587,0,0,0,0.000000," ","integrate((1-x)**p*(x**2+x+1)**p,x)","\int \left(1 - x\right)^{p} \left(x^{2} + x + 1\right)^{p}\, dx"," ",0,"Integral((1 - x)**p*(x**2 + x + 1)**p, x)","F",0
2588,0,0,0,0.000000," ","integrate(1/(-c*e*x+b*e)**(1/3)/(c**2*x**2+b*c*x+b**2)**(1/3),x)","\int \frac{1}{\sqrt[3]{- e \left(- b + c x\right)} \sqrt[3]{b^{2} + b c x + c^{2} x^{2}}}\, dx"," ",0,"Integral(1/((-e*(-b + c*x))**(1/3)*(b**2 + b*c*x + c**2*x**2)**(1/3)), x)","F",0
2589,0,0,0,0.000000," ","integrate(1/(-c*e*x+b*e)**(2/3)/(c**2*x**2+b*c*x+b**2)**(2/3),x)","\int \frac{1}{\left(- e \left(- b + c x\right)\right)^{\frac{2}{3}} \left(b^{2} + b c x + c^{2} x^{2}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((-e*(-b + c*x))**(2/3)*(b**2 + b*c*x + c**2*x**2)**(2/3)), x)","F",0
2590,0,0,0,0.000000," ","integrate((-c*e*x+b*e)**p*(c**2*x**2+b*c*x+b**2)**p,x)","\int \left(- e \left(- b + c x\right)\right)^{p} \left(b^{2} + b c x + c^{2} x^{2}\right)^{p}\, dx"," ",0,"Integral((-e*(-b + c*x))**p*(b**2 + b*c*x + c**2*x**2)**p, x)","F",0
